We developed some questions regarding twin prime conjecture by examining the bounded gaps between composite numbers and explained the relations between the formulas regarding composite numbers. Then we proved the twin prime conjecture to answer the new questions raised by proving the expression: \[ \liminf_{n\to\infty} (c_n_+_1 - c_n) \ge 10. \] In addition, we prove many different approaches have been and it has been proved that there must be a twin prime in the range $(p_k_2\cdot p_k_1, p^2_k_1)$, where $p \neq 2$.

We propose a method that enables precise determination of the number of atoms in a Dick-noise-free optical lattice clock, by effectively addressing quantum projection noise. Our approach relies on conducting stability measurements at three distinct parameter sets, allowing us to differentiate between quantum projection noise, photon shot noise, and technical noise. Importantly, our method enables accurate extraction of the atom number, even in the presence of photon shot noise and technical noise. To validate the effectiveness of our approach, we employ numerical simulations and optimize the modulation parameters to achieve the smallest uncertainty possible. The numerical simulations show the validity of our method and demonstrate a measurement uncertainty in the atom number that is below 4% across a wide range of atom numbers, provided that the standard deviation of atom number fluctuation is kept below 0.23 times the average atom number.

Gastric mixing relies both on enzymatic reactions and mechanical solicitations through antral contraction waves (ACWs). This work aims at discussing the influence of ACWs frequency and digesta viscosity on human gastric mixing efficiency by comparison with that of a soft elastic reactor (SER), that induces mixing by vibration of its wall in a similar way as ACWs promote stomach motility. The SER mixing curve was considered in order to determine the flow regime reached during gastric mixing. The number of contractions required to achieve homogenization was found to depend on the viscosity of the stomach content and the ACWs amplitude. Moreover, it was deduced from the same range of SER and ACWs operating points that the mechanical solicitation provided by human peristalsis was low and that gastric mixing was confined in laminar regime. Further efforts are needed to investigate the role of other physiological processes such as gastric secretions and emptying in overall gastric mixing performance.

Prime numbers are the atoms of mathematics and mathematics is needed to make sense of the real world. Finding the Prime number structure and eventually being able to crack their code is the ultimate goal in what is called Number Theory. From the evolution of species to cryptography, Nature finds help in Prime numbers. One of the most important advances in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In that paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function defined by: Where ζ(z) is a function of a complex variable z that analytically continues the Dirichlet series. Riemann also formulated a conjecture about the location of the zeros of RZF, which fall into two classes: the "trivial zeros" -2, -4, -6, etc., and those whose real part lies between 0 and 1. Riemann's conjecture Riemann hypothesis [RH] was formulated as this: [RH] The real part of every nontrivial zero z* of the RZF is 1/2. Proving the RH is, as of today, one of the most important problems in mathematics. In this paper we will provide a proof of the RH. The proof of the RH will be built following these five parts: PART 1: Description of the RZF PART 2: The C-transformation PART 3: Application of the C-transformation to in Re(z) 0 to obtain ζ(z)=X(z)-Y(z) PART 4: Analysis of the values of z such that X(z)=Y(z), and |X(z)|=|Y(z)|, that equates to ζ(z)=0 Proof that |X(z)|=|Y(z)| only if Re(z)=1/2 Conclude that ζ(z)=0 only if Re(z)=1/2 for Re(z) 0 PART 5: We will also prove that all non-trivial zeros of ζ(z) in the critical line of the form are not distributed randomly. There is a relationship between the values of those zeros and the Harmonic function that leads to an algebraic relationship between any two zeros.

Cognitive linguistics is founded on the assumption that language is a reflection of universal cognitive principles, implying that all cognitive processes share a common origin. This assumption is known as the 'Cognitive Commitment.' The present article examines the sensory schema hypothesis, which traces all forms of expression back to sensations. This theoretical framework integrates the physicality of the body with sensations that underlie human experiences and their linguistic and non-linguistic expressions. By challenging the traditional dichotomy between mind and body, it provides a more integrated understanding.

Here we analyze three well-known conjectures: (i) the existence of infinitely-many twin primes, (ii) Goldbach’s strong conjecture, and (iii) Polignac’s conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of the Goldbach’s strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac’s conjecture. Our first step is an analysis of the existence of infinitely-many twin primes numbers. For this, using the formula 4((n−1)!+1) ≡ −n (mod n(n + 2)) – satisfied if and only if (n, n + 2) are twin primes –, together with Wilson’s theorem, we obtain conditions that must be met for two numbers to be twin primes. Our results, obtained from an analytic and functional study, lead us to conclude that there may exist infinitely-many twin primes. Next, we consider the validity of the Goldbach’s strong conjecture. After showing that the conjecture is true for the first even numbers, we notice a pattern that we analyze for any even number, reducing it to three cases: (i) when the even number 2n is two times a prime number n; (ii) when the even number 2n is such that n = 2m, with 2m − 1 and 2m + 1 twin primes; (iii) all other cases, i.e., for any 2n even number ∀n ∈ N with n > 1, n prime or not, with independence of n = 2m being 2m−1 and 2m+1 twin primes or not. In this last case we show that one can always find a certain r ∈ N such that 1 < r < n satisfying that n−r and n+r are primes, so that their sum is 2n. In this case we use the reduction to absurd method, and our results lead us to conclude that Goldbach’s strong conjecture is true to the best of our calculations, as well as the Polignac’s conjecture.

Hepatitis B is a potentially life-threatening infectious disease caused by the hepatitis B virus (HBV), which affects the liver. Every year, about 390,000 people die from HBV-related diseases in China, about 86 million people are carriers of HBV, accounting for about 6% of the total population, and 30 million people are chronically infected. From 2002 to 2007, though China government launched “The Global Alliance for Vaccines and Immunization (GAVI)” program to reduce HBV infection in children, but the number of hepatitis B cases in China remains high. Reasonable estimation of potential HBV carriers is crucial to prevention and control the spread hepatitis B virus. This study is based on the case data from the National Bureau of Statistics of China from 2003 to 2021. We build a dynamic model that includes potential hepatitis B virus carriers, use nonlinear least squares and genetic algorithms to fit the parameters in the model, and calculate the reproduction number of hepatitis B virus transmission in the population and obtain R_c=1.741. The number of potential hepatitis B virus carriers is estimated to be 449,535 (95%CI [415651 to 483420]) based on our model, which is 30.49% of the total number of hepatitis B cases, and the simulation results show the number of chronic hepatitis B incidence decreases as the vaccination rate α increases, increasing α by 20%, the number of chronic hepatitis B incidence decreases by 169,469 on average.

Commercial banks usually classify customers according to their credit reports when making loans. In this study, we put our focus on classifying customers based on their credit reports from the People's Bank of China (PBC). Since there are no target labels of users in the credit report of the People's Bank of China, we put forward the fuzzy clustering method for the initial label, and then Construct ant colony search to optimize intelligent recognition. Finally, this study uses SVM, BP neural network, and random forest to classify users and compare their results. The research re-sults indicate that using ant colony clustering algorithm and random forest for classification is the most effective method with the PBC credit reports.

The UNUSUAL FLORAL ORGANS (UFO) gene is an essential regulatory factor of class B genes and plays a vital role in the process of inflorescence primordial and flower primordial development. We investigated the role of UFO genes in soybean to better understand the development of floral organs through gene cloning, expression analysis, and gene knockout. In situ hybridization demonstrated predominant expression of the GmUFO1 gene in the flower primordium. Phenotypic observation of GmUFO1 knockout mutant lines (Gmufo1) showed obvious alteration in floral organ number and shape, and mosaic organ formation. In contrast, GmUFO2 knockout mutant lines (Gmufo2) showed no obvious difference in floral organs. However, the GmUFO1 and GmUFO2 double knockout lines (Gmufo1ufo2) showed a more severe mutant phenotype than the Gmufo1 lines. Gene expression analysis also showed differences in the expression of major ABC function genes in the knockout lines. Based on the phenotypic and expression analysis, our results suggest the major role of GmUFO1 in the regulation of flower organ formation in soybean and that GmUFO2 does not have any direct effect, but it might have an interaction role with GmUFO1 in the regulation of flower development. In conclusion, the present study identified UFO genes in soybean and improved our understanding of floral development that could be useful for flower design in hybrid soybean breeding.

The effect of biotic (e.g., growth characteristics) and a-biotic (e.g., crown closure) factors on cone production, fertility variation and gene diversity was evaluated in two consecutive years in 130 year old natural populations of Taurus cedar also called cedar of Lebanon (Cedrus libani A. Rich.). The a-biotic factors viz., altitude, temperature, aspect and rainfall varied; while some of them can be managed by cultural operations like management of crown and stand density. Impact of crown closure on cone production, fertility variation and related parameters were observed in Taurus cedar’s natural populations sampled from southern Turkey. Maximum cone production of 29 and 40/tree was recorded with full crown closure in two consecutive years by large differences among individuals within crown closure class. For instance, cone productions were between 10 and 67 in full crown closure of first year. The sibling coefficient, which is a measure of the fertility variation in a stand, was the highest (1.16) for full crown closure in the first (meaning 86% fertile trees) and the second year (1.55, 65%), while it was the lowest for medium crown closure (1.09, 92%) in both years. Gene diversity decreased from a degraded patch (0.987) to that with full crown closure (0.984). Results of variance analysis showed significant (p≤0.05) difference between crown closure classes for cone production within second year, and between years. Significant positive (p0.05) correlations were noted between years for cone production (r=0.22), and between cone production and crown closure in first and second years (r=0.29). However, growth characteristics had no effective on cone productions in individual crown closure classes, while there were significant (p0.05) correlations between diameter at breast height and cone production for both years (r= 0.15 and 0.17) in pooled populations.

A century-old scientific conundrum is solved in this paper. The Prandtl mixing length modelled plane boundary turbulent flow is described by: $\frac{du^+}{d{y^+} }+\kappa^2{y^+} ^2\left( \frac{du^+}{d{y^+} }\right)^2=1$, together with boundary condition $ {y^+} =0:\, u^+=0$. Only an approximate solution to this nonlinear ordinary differential equation (ODE) has been sought so far, however, the exact solution to this ODE has not been obtained. By introducing a transformation, $2\kappa y^+=\sinh \xi$, I successfully find the exact solution of the ODE as follows: $u^+=\frac{1}{\kappa}\ln(2\kappa {y^+} +\sqrt{1+4\kappa^2{y^+} ^2})-\frac{2{y^+} }{1+\sqrt{1+4\kappa^2{y^+} ^2}}$.

Mechanical properties such as shape, volume and size affect the dynamics of biological systems. Most of the current methodological approaches are inclined to remove the existence of holes and impurities from systems’ description, regarding them as routes toward mechanical failure. On the contrary, we suggest that the occurrence of holes might be of utmost functional importance, allowing reversible transformations of cellular structures. The focus here is on the widespread occurrence of intracytoplasmic holes, that deeply modifies the topology of living cells and provides researchers with novel operational tools to investigate intracellular dynamics. We take as example the prokaryotic gas vesicles, i.e., intracellular cavities filled with gases spreading from the nearby medium. The mechanical and topological cellular properties dictated by intracytoplasmic holes are investigated, focusing on the physical constraints imposed by their very existence. For instance, the presence of gas vesicles breaks the cytoplasmic homogeneity, leading to inhomogeneity in functional activities and modifications in intracellular flows. Also, a topological approach to cytoplasmic holes suggests novel physiological roles for gas vesicles. For example, the gas vesicles’ ability to increase/decrease cellular volumes provides a mechanism that counteracts the detrimental effects of the surface/volume ratio. In conclusion, a structural/methodological approach based on the occurrence of holes testifies once again how the simple biophysical structure alone can dictate the function.

New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

We generalize the dynamical analog of the Berry geometric phase setup to the quaternionic model of Avron et al. In our dynamical quaternionic system, the fast half-integer spin subsystem interacts with a slow two-degrees-of-freedom subsystem. The model is invariant under the 1:1:2 weighted SO(2) symmetry and spin inversion. There is one formal control parameter in addition to four dynamical variables of the slow subsystem. We demonstrate that the most elementary qualitative phenomenon associated with the rearrangement of the energy super-bands of our model consists of the rearrangement of one energy level between two energy superbands which takes place when the formal control parameter takes the special isolated value associated with the conical degeneracy of the semi-quantum eigenvalues. This qualitative phenomenon is of the topological origin, and is characterized by the second Chern class of the associated semi-quantum system. The correspondence between the number of redistributed energy levels and the second Chern number is confirmed through a series of examples.

Proteomic technology has improved at a staggering pace in recent years, with even practitioners challenged to keep up with new methods and hardware. The most common metric used for method performance is the number of peptides and proteins identified. While this metric may be helpful for proteomics researchers shopping for new hardware, this is often not the most biologically relevant metric. Biologists often utilize proteomics in the search for protein regulators that are of lower relative copy number in the cell. In this review, I re-evaluate untargeted proteomics data using a simple graphical representation of the absolute copy number of proteins present in a single cancer cell as a metric. By comparing single shot proteomics data to the coverage of the most in-depth proteomic analysis of that cell line acquired to-date we can obtain a rapid metric of method performance. Using a simple copy number metric allows visualization of how proteomics has developed in both sensitivity and overall dynamic range when using both relatively long and short acquisition times. To enable reanalysis beyond what is presented here, two available web applications have been developed for single and multi-experiment comparisons with reference protein copy number data for multiple cell lines and organisms.

The widely used logistic model for epidemic case reporting data may be either restrictive or unrealistic in presence of containment measures when implemented after an epidemic outbreak. For flexibility in epidemic case reporting data modelling, we combined an exponential growth curve for the early epidemic phase with a flexible growth curve to account for the potential change in growth pattern after implementation of containment measures. We also fitted logistic regression models to recoveries and deaths from the confirmed positive cases. In addition, the growth curves were integrated into a SIQR (Susceptible, Infective, Quarantined, Recovered) model framework to provide an overview on the modelled epidemic wave. We focused on the estimation of: (1) the delay between the appearance of the first infectious case in the population and the outbreak (“epidemic latency period"); (2) the duration of the exponential growth phase; (3) the basic and the time-varying reproduction numbers; and (4) the peaks (time and size) in confirmed positive cases, active cases and new infections. The application of this approach to COVID-19 data from West Africa allowed to discuss the effectiveness of some containment measures implemented across the region.

To quantify the time-varying reproduction number (Rt) for Malaysia using the COVID-19 incidence data., we used data the from the Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE) Coronavirus repository. Day 1 was taken from the first assumed local transmission of COVID-19. Data was split into four intervals: a) Interval 1: from Day 1 to Day 10 MCO 1, b) Interval 2: from Day 1 to Day 10 MCO 2, c) Interval 3: from Day 1 to Day 10 MCO 3 and d) Interval 4: from Day 1 to Day 10 MCO 4. We estimated the Rt using the EpiEstim package. The means for Rt at Day 1, Day 5 and Day 10 for all MCOs ranged between 0.665 to 1.147. The average Rt gradually decreased in MCO 1 and MCO 2. However, Rt increased in MCO 3 before stabilized around 0.8 in MCO 4. MCO 1 and MCO 2 which were stricter coincide with the gradual reduction of Rt. However, the more relaxed MCO 3 and MCO 4 correspond to a slight increase in the Rt before it stabilized.

In this paper the problem of sampling from uniform probability distributions is approached by means of space-filling curves (SFCs), a topological concept that has found a number of important applications in recent years. Departing from the theoretical fact that they are surjective but not necessarilly injective, the investigation focused upon the structure of the distributions obtained when their domain is swept in a uniform and discrete manner, and the corresponding values used to build histograms, that are approximations of their true PDFs. This work concentrates on the real interval [0,1], and the Sierpinski space-filling curve was chosen because of its favorable computational properties. In order to validate the results, the Kullback-Leibler distance is used when comparing the obtained distributions in several levels of granularity with other already established sampling methods. In truth, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. In this fashion, sequences resulting from this sort of process are not truly random.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

A new – syntropic – criterion obtained using the synergetic theory of information has been proposed for determining the start date for the cancellation of restrictive measures in the COVID-19 pandemic. Under this criterion, the restrictions should be lifted when the average number of new cases per day during a week becomes disproportionately smaller than at the peak of the pandemic. The article gives the derivation of this criterion, and its practical use is shown by the example of a number of EU countries. In this case, a comparison is made of the dates set by the syntropic criterion with the actual dates of the beginning of the lifting of restrictions.

In this study, a monoethanolamine aerosol growth model was developed to investigate the aerosol growth factor. Interactions among the internal conditions in an absorber were considered in this aerosol model. Additionally, an experiment was conducted to measure aerosol particle size, for collecting in-house validation data. Sucrose was used as the aerosol nuclei instead of sulfuric acid to prevent the corrosion of equipment used in the experiment. Experimental results showed that the outlet aerosol sizes increased to the same size regardless of the sucrose concentrations. The aerosol growth model was validated using the in-house experimental data. The aerosol growth model efficiently predicted the aerosol size. For investigating aerosol growth effects, particle number concentration was determined to be the primary factor affecting aerosol growth and amine emissions. When the particle number concentration increased, the aerosol size decreased, whereas the MEA emission increased.

The open source CFD code OpenFOAM has emerged as one of the most popular alternative to commercial CFD solvers. The recent version of OpenFOAM supports overlapping grids, so called Overset mesh. In this type of mesh, one or more sub-collection of control volumes (or cells) are allowed to overlap with other set of cells. This allows for great flexibility in modelling Fluid Structure Interaction (FSI) problems. Fluid mesh can be standard structured mesh of a rectangular/cuboidal/or cylindrical domain. The structure mesh can be generated separately by creating multiple layers around a given body. The overset mesh functionality allows for overlapping or immersing this structured mesh inside the fluid mesh and a relevant FSI or moving dynamics problems can be solved. The idea of overset mesh has been around since eighties but its support in OpenFOAM is very recent. Most CFD codes which support overset mesh have either been in-house or commercial CFD codes. OpenFOAM's support for overset is the first major open source code resource available for CFD problems. The aim of this research is to solve a classical benchmark airfoil problem using OpenFOAM overset mesh and compare the numerical results with experimental result. We report here flow simulations results around NACA 0018. The result obtained from overset mesh compares convincingly well with experimental results. Computations have been carried out for Reynolds numbers in the range of 10⁵ with angle of attack ranging from α= 5 degree to α= 30 degree with an interval of 5 degree. Turbulence is incorporated using k - ε turbulence model. This study helps developing confidence in using OpenFOAM overset support for more complicated flows and moving dynamics. This report is complemented with a brief description of finite volume discretization using overset mesh.

Monogenity is a classical area of algebraic number theory that is very actively researched even today. This paper is a collection of the results obtained during the last few years in this area. Several of these results were presented at the series of online conferences "Monogenity and power integral bases".

In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the authors establish meaningfully and significantly two identities which simplify coefficients in a family of ordinary differential equations associated with higher order Bernoulli numbers of the second kind.

Industrial hemp (Cannabis sativa L.) is primarily a dioecious plant, and monoecious varieties developed for high yield. Production practices vary by varieties prompting the need for the present study aimed to describe the floral characteristics and evaluate pollen quantity and viability of a monoecious (Henola) and three dioecious (CFX-2, Canda, and Joey) varieties. All varieties have five lanceolate anthers, basifixed to a threadlike filament. Anther length was significantly different but not anther width among varieties. The longest length (0.38 ± 0.046 cm) was recorded in Henola, and shortest (0.34 ± 0.043 cm) in CFX-2. Anther width ranged from 0.088 ± 0.0024 to 0.095 ± 0.0021cm. Pollen grains were triporate and spheroidal in shape and size differed significantly with the largest in Joey (27.83 ± 0.78 μm) and Henola (27.489 ± 0.99 μm), and smallest in Canda (22.04 ± 0.56 μm). The number of pollen grains differed significantly among varieties ranging from 29,183 in Henola to 104,548 in Joey. Even though Henola recorded the lowest pollen number it had the highest percentage (69.3%) of viable pollen and Canda recorded the lowest. There was a moderate, positive and significant relationship (r = 0.496) between anther length and the number of pollen grains in Joey. The relationship in Henola was moderate and non-significant (r = 0.356), weak and non-significant in Canda (r = 0.188), and in CFX-2 (r = 0.037). The findings from our study provide information for growers and researchers on hemp breeding and cultivation practices that may contribute to prevent cross pollination.

Prime numbers are the building blocks of number theory, and their properties have intrigued mathematicians for centuries. In this paper, we explore a specific categorization of primes, which we refer to as "twin primes", “cousin primes” and "sexy primes". We begin by examining the form of prime numbers greater than 7 and analyze their potential to be expressed in terms of $6n + 5$ or $6n + 7$. This investigation leads to the identification of conditions under which prime numbers can form twin, cousin and sexy pairs. We further develop a general framework to characterize the product of all twin (except 15), cousin (except 21) and sexy primes, providing insights into their algebraic structure.

In vertical coordinates, (x,y,z), the gradient Richardson number Ri=N^2⁄S^2 is the square of the ratio between buoyancy frequency N and vertical-shear amplitude S, where N^2=-(g⁄ρ) ∂ρ⁄∂z and S^2=(∂u⁄∂z)^2+ (∂v⁄∂z)^2, with ρ potential density, (u,v) the horizontal velocity components and g gravity acceleration, so that a decrease in stratification brings a decrease in dynamic stability and vice versa. In the isopycnic coordinate system, (x,y,ρ), however, Ri=M^2⁄〖S_ρ〗^2 , is the ratio between 〖M^2≡N〗^(-2) and the squared diapycnal shear 〖S_ρ〗^2=(ρ⁄g)^2 [(∂u⁄∂ρ)^2+ (∂v⁄∂ρ)^2 ], so a decrease in stratification leads to an increase in dynamic stability and vice versa. The apparently different role of stratification arises because S and S_ρ are related through the stratification itself, S_ρ=S⁄N^2 or, equivalently, τ=〖t_o〗^2⁄t_d , which is interpreted as a natural oscillation time τ≡S_ρ that equals the buoyancy or oscillation time t_o=N^(-1) normalized by the ratio t_o⁄t_d , where the deformation time is t_d=S^(-1). Here we follow simple arguments and use field data from three different situations (island shelf-break, Gulf Stream and Mediterranean outflow) to endorse the usefulness of the isopycnal approach. In particular, we define the reduced squared vertical σ^2= S^2-N^2 and reduced squared diapycnal shear 〖σ_ρ〗^2= 〖S_ρ〗^2-M^2, which are positive for unstable conditions and negative for stable conditions. It turns out that Ri and σ^2 remain highly variable for all stratification conditions; in contrast, the mean 〖σ_ρ〗^2 values display a univocal tendency, its magnitude decreasing with stratification. We propose 〖σ_ρ〗^2 and 〖S_ρ〗^2 to be good indexes for the occurrence of effective mixing under high stratification conditions.

We explored an extension of the Cauchy-Riemann equations to the algebra of treons, recently described by Alejandro Bermejo, whose elements are ordered 3-tuples. We leveraged the isomorphism between the algebra of treons and algebra B, and deduced the Cauchy-Riemann equations for the algebra of treons, establishing the necessary conditions for analyticity in this algebraic structure. This work significantly broadened our horizons in complex analysis and introduced new possibilities for applications across various fields of advanced mathematics.

This study investigated the efficiency of scale-propellers, typically used on small drones. A scale-propeller is accepted as having a diameter of 7 to 21 inches. The Ukraine War has demonstrated the utility of relatively small, low-cost first-person view (FPV) drones, which are attritable. This investigation outlines the development of a MATLAB optimisation code, based on minimum induced loss propeller theory, which calculates the optimal chord and twist distribution for a chosen propeller operating in known flight conditions. The MATLAB code includes a minimum Reynolds number functionality, which provides the option to alter the chord distribution to ensure the entire propeller is operating above a set threshold value of Reynolds (&gt;100,000), as this has been found to be a transition point between low and high section lift-to-drag ratios. Additional functions allow plotting of torque and thrust distributions along the blade. The results have been validated on experimental data taken from an APC ‘Thin Electric’ 10” x 7” propeller, where it was found that both the chord and twist distributions were accurately modelled. The MATLAB code resulted in a 16% increase in the maximum propulsive efficiency. Further work will investigate a direct interface to SolidWorks to aid rapid propeller manufacturing capability.

This study presents head losses (hL) and loss coefficients (K) obtained experimentally for schedule 40 PVC pipe elbows, with 90o and 45o in small commercial diameters of ½ to 1½ inches that are commonly used in small networks. The investigation was conducted on a system constructed with short pipes and fittings necessary to measure, direct, and control flow, as well as to evaluate pressure head losses at elbows. Simple water flow was used with rates of 0.342 to 0.980 lps (Q), which generated moderate Reynolds numbers (Re) of 13337 to 80221. It was found that hL showed dependence on the velocity head in all elbows, as well as that hL are greater as the diameter increases for same velocity head. The K values in the elbows tended to be constant when Q &gt; 0.75 lps, but for Q &lt; 0.75 lps the K coefficient increased inversely proportional to Q, becoming larger as the diameter increased. Likewise, the K coefficient tended to increase as Re decreased, while K tended to be constant as Re increased. The results of the experimental coefficient were compared against K values reported in the literature, where significant similarities and discrepancies were found.

This paper presents a comprehensive analysis of the SEIRS COVID-19 pandemic model with saturated incidence rate. By modifying the existing model and proposing a new simplified version, we investigate the dynamics of disease transmission, including the impact of saturation terms on disease spread. Through stability analysis at disease-free and endemic equilibria, we aim to enhance understanding of the spread of COVID-19 and inform effective control strategies. Drawing on mathematical models and epidemiological insights, this study contributes to the ongoing efforts to combat the global pandemic.

The paper deals with exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination of multiples of primes. These elementary number theory activities, appropriate for technology-enhanced secondary mathematics education courses, are supported by a spreadsheet, Wolfram Alpha, Maple, and the Online Encyclopedia of Integer Sequences. General formulas for subsequences of polygonal numbers referred to in the paper as polygonal number sieves of order k that include base-two exponential functions of k have been developed. Different problem-solving approaches to the derivation of such and other sieves based on the technology-immune/technology-enabled framework have been used. The accuracy of computations and mathematical reasoning is confirmed through the technique of computational triangulation enabled by using more than one digital tool. A few relevant excerpts from the history of mathematics are briefly featured.

Study of differential equation theory has come a long way with applications in the various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives on metric Lr which proved to be better in applications than approximate derivatives. But most of the studies involved are on fuzzy set theory, so it seems likely that intuitionistic fuzzy Lr - norm - based derivatives deserve study. In the study, the fuzzy derivative is extended to intuitionistic fuzzy derivatives with respect.to Lr - norm - based derivatives using intuitionistic fuzzy number valued functions. The efficacy of the proposed method is established by proving the associated theorems along with numerical examples. Further, the Cauchy problem is also studied with respect to intuitionistic fuzzy setting.

The success rate of extracorporeal shock wave lithotripsy (ESWL) is influenced by various factors, including stone density, which is determined through computed tomography scans in Hounsfield Units (HU). Materials and method: This retrospective single-center study was conducted in King Fahad hospital. Sixty-seven adult patients with renal and ureteric stones were selected randomly and enrolled in the study. Their age ranged from 20 to 69 years. The patients were examined with non-contrast enhancement (NCCT) to assess the HU of stones, consequently, treated with ESWL. Results: of the 67 patients, 37.3% of the stones were completely fragmented, while 62.7% were partially fragmented. HU, location of the stone, a multiplicity of the stone, and patient age were significant factors contributing to stone fragility (p-values&lt; 0.05). The HU has a positive significant linear correlation with serum calcium (r= .28, p-value=.036), while serum acid has a negative correlation (r=-.55, p-value= &lt; .001). Thus, the probability of calcium-containing stones formation increased with increased HU. In contrast, uric acid stone formation is likely to develop with decreasing HU with serum uric acid. Renal stones in patients with diabetes mellitus and hypertension were not completely fragmented compared to those without clinical history. Conclusion: Mean HU, location of the stone, laterality, status of stone, and the number of ESWL sessions were the most significant factors affecting stone fragility. CT attenuation values can predict the composition of stones from serum calcium and uric acid examinations. Hypertension and Diabetes mellitus are risk factors for renal stone fragmentation.

Mouse wild-derived strains (WDS) combine the advantages of classical laboratory stocks and wild animals, and thus appear as promising tools for diverse biomedical and evolutionary studies. We employed 18 WDS representing three non-synanthropic species (Mus spretus, M. spicilegus, and M. macedonicus) and three house mouse subspecies (M. musculus musculus, M. m. domesticus, M. m. castaneus) which are all important human commensals to explore whether the number of major urinary protein (MUP) genes and their final protein levels in the urine are correlated with the level of commensalism. Contrary to expectations, MUP copy number (CN) and protein excretion in the strains derived from M. m. castaneus, which is supposed to be the strongest commensal, were not significantly different from the non-commensal species. Regardless of an overall tendency for higher MUP amounts in taxa with higher CN, there is no significant correlation at the strain level. Our study thus suggests that the expansion of the Mup cluster, which appeared before the house mouse diversification, is unlikely to facilitate commensalism with humans in the three house mouse subspecies. Finally, we found considerable variation among con(sub)specific WDS, warning against generalisations of results based on a few strains.

Typhoid fever is an infectious disease that affects humanity worldwide particularly in the lower socio-economic communities where many individuals are exposed to a dirty environment and unclean food. A mathematical model is formulated to analyze the impact of control measures such as vaccination of susceptible humans, treatment of infected humans and sanitation in the different socio-economic communities. The model assumed that the population comprises of two socio-economic classes. The essential dynamical system analysis of our model was appropriately carried out. The impact of the control measures was analyzed, and the optimal control theory was applied on the control model to explore the impact of the different control measures. Numerical simulation of the models and the optimal controls were carried out and results obtained indicates that the overall combination of the control measures eradicates Typhoid fever in the population but the controls are more optimal in the higher socio-economic communities.

The amount of heat transfer in gas turbine blades depends on cooling techniques and various flow phenomena. The effect of eddies, passing shock waves and free flow turbulence has been noticed by many researchers since the beginning. The focus of the upcoming work is on the numerical investigation of the effects of turbulence intensity and Reynolds number on the amount of heat transfer from the blade surface with internal cooling. The SST model has been used to solve this problem, which has been compared with the experimental work to ensure the correctness of the numerical simulation. In this regard, by changing the free flow turbulence intensity with values of 1, 5, 7, and 10% and at three Reynolds numbers of 150,000, 350,000, and 750,000, the changes in heat transfer coefficients have been investigated. The results show that with the increase of the turbulence intensity at different Reynolds numbers, due to the positive effect of the flow turbulence on the suppression of separation and promotion of the boundary layer transition, the blade surface heat transferincreases and this increase is more evident at higher Reynolds numbers.

A (2,6)-fullerene F is a 2-connected cubic planar graph whose faces are only 2-length and 6-length. Furthermore, it consists of exactly three 2-length faces by Euler's formula. The (2,6)-fullerene comes from Do\v{s}li\'{c}'s (k,6)-fullerene, a 2-connected 3-regular plane graph with only k-length faces and hexagons. Do\v{s}li\'{c} showed that the (k,6)-fullerenes only exist for k = 2, 3, 4 or 5, and some of the structural properties of (k,6)-fullerene for k = 3, 4 or 5 are studied. In this paper, we study the properties of (2,6)-fullerene. We obtain that the edge-connectivity of (2,6)-fullerenes is 2. Every (2,6)-fullerene is 1-extendable, but not 2-extendable. F is said to be k- resonant (k>0) if the deleting of any i (0=< i<= k) disjoint even faces of F results in a graph with at least one perfect matching. We have that every (2,6)-fullerene is 1-resonant. An edge set S of F is called an anti-Kekule set if F-S is connected and has no perfect matchings, where F-S denotes the subgraph obtained by deleting all edges in S from F. The anti-Kekule number of F, denoted by ak(F), is the cardinality of a smallest anti-Kekule set of F. We have that every (2,6)-fullerene F with |V(F)|>6 has anti-Kekule number 4. Further we mainly prove that there exists a (2,6)-fullerene F having f_{F} hexagonal faces, where f_{F} is related to the two parameters n, m.

To assess the impact of tourism on the incidence of HIV and AIDS using Malaysian epidemiological data over the period of 1986-2011 with additional consideration for newborns infected with HIV. A population-level mathematical model was used to investigate: i) the role of tourism in the spread of HIV and measures used to reduce HIV spread in Malaysia; ii) whether the stability of infectious disease transmission is dependent on the flow of visiting tourists. We first derived an equation for the reproduction number (R0) threshold to quantify the contagiousness of HIV in Malaysia. Sensitivity analyses were used to determine the effect of various parameters on HIV transmission with respect to the increase in tourism. Our findings suggest that a stable disease-free state is sustainable based on the low value of R0 was 0.0017. This result is encouraging from a public health perspective. Approximately 14% of outbound tourists who leave the country return infected with HIV and the difference between the rate at which tourists move to the susceptible category and the rate at which tourists leave the susceptible is category is 12%. Estimated parameters for the influx of tourist rates, δ=1.1540x10-3[1.1477x10-3 - 1.15954x10-3], δ1=7.7901x10-4[7.7867x10-4 - 7.79418x10-4], and δ2=1.4030x10-8[-7.2287x10-7-7.5096x10-7], significantly impacted the spread of HIV in Malaysia. Some significant adjustments were made to the expected parameters. The methods used are helpful to public health analyses and provide a framework for epidemiological modeling of HIV spread among tourists. The trend and magnitude of tourist inflows may be determinants in the incidence of HIV and AIDS in Malaysia.

Windthrows in the forestry fund, which have become more frequent due to the increase in extreme weather events, have had and continue to have negative economic and ecological effects, making them a pressing issue in forestry research. Their urgency has been amplified in light of the need to develop sustainable forest management systems. The main objectives of this study are to evaluate the effects of windthrows on some microbiological properties of forest soils and to monitor the evolution of the degraded tree regeneration, 4 years after the event, for three tree species: Norway spruce (Picea abies L.), sessile oak (Quercus petraea), and European beech (Fagus sylvatica L.). The experimental plot used is arranged in dispersed blocks and subdivided plots, with three repetitions, bifactorial, factor A representing the tree species, and factor B the windthrows: in two situations: affected (AW) and not affected by felling (WW). Three representative soil profiles were studied for each tree species, including dehydrogenase activity (DA) and the number of fungi (NF) in the organic horizon at the soil surface. Dehydrogenase activity was determined by the extraction of triphenylformazan, and NF was evaluated using the Plate Count Method (Petri plates) and the Sabouraud Agar culture medium. The values of Current Dehydrogenase Activity (CDA) and Potential Dehydrogenase Activity (PDA) did not show significant statistical differences in relation to the windthrow factor, but were distinctly significant (p &lt; 0.01) for the tree species factor. On the other hand, NF showed statistical significance for both tree species and windthrows factors, at a level of p &lt; 0.01. Correlations were highlighted between the differences in AW and WW of CDA, PDA, and NF with the number of naturally regenerated seedlings (NRS), and the type of soil. The regressions established between NRS and the differences in CDA and PDA, the dependence of the differences in PDA on the differences in NF, and the regression between the differences in NF and the type of soil demonstrate the importance of soil characteristics in the natural regeneration process of the main tree species - Norway spruce, sessile oak, and European beech. Stimulating NRS in AW forests and increasing the volume of terrestrial organic carbon (TOC) biomass is directly dependent on soil fertility, primarily determined by soil organic carbon (SOC), which accumulates in the soil as a result of organic matter, deposited on the surface. Sustainable forest management of AW plots should stimulate the accumulation of SOC, including the partial or total preservation of dead trees, provided that the attack of specific diseases and pests is avoided.

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

The first attempt to control and mitigate an epidemic outbreak caused by a previously unknown virus occurs primarily via non-pharmaceutical interventions (NPIs). In case of the SARS-CoV-2 virus, which since the early days of 2020 caused the COVID-19 pandemic, NPIs aimed at reducing transmission enabling contacts between individuals. The effectiveness of contact reduction measures directly correlates with the number of individuals adhering to such measures. Here, we illustrate by means of a very simple compartmental model how partial noncompliance with NPIs can prevent these from stopping the spread of an epidemic.

The complex interplay among pathogens, host factors, and the integrity and composition of the endogenous microbiome determine the course and outcome of gastrointestinal infections. The model organism Yersinia entercolitica (Ye) is one of the five top frequent causes of bacterial gastroenteritis based on the Epidemiological Bulletin of the Robert Koch Institute (RKI) published on September 10, 2020. A fundamental challenge in predicting the course of an infection is to understand whether co-infection with two Yersinia strains differing only in their capacity to resist killing by the host immune system may decrease the overall virulence by competitive exclusion or increase it by acting cooperatively. Herein, we study the primary interactions among Ye, the host immune system and the microbiota, and their influence on Yersinia population dynamics. The employed model considers two host compartments, the intestinal mucosa and lumen, commensal bacteria, the co-existence of wild-type and mutant Yersinia strains, as well the host immune responses. We determine four possible equilibria: the disease-free, wild-type-free, mutant-free, and co-existence of wild-type and mutant equilibrium. We also calculate the reproduction number for each strain as a threshold parameter to determine if the population may either be eradicated or persist within the host. We conclude that the infection should disappear if the reproduction numbers for each strain fall below one, and the commensal bacteria’s growth rate exceeds the pathogens’ growth rates. These findings will help inform public health control strategies. The supplement includes MATLAB source script, Maple workbook, and figures.

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

Therapeutic proteins are used to successfully treat hemophilia, Crohn’s Disease, diabetes, and cancer. Recent product recalls have occurred because of sub-visible particle formation resulting from the inherent instability of proteins. It has been suggested that particle formation is associated with late stage processing steps of filling, shipping, and delivery. Previous works demonstrated that cavitation might occur in therapeutic vials subjected to agitation or accidentally dropped, but that mitigation can be achieved with fluid property manipulation. The goal of this research was to (1) assess the risk of cavitation under common pharmaceutical manufacturing conditions (i.e., pipe contraction and pumps), (2) establish a simple threshold criterion for when particulate will form, and (3) suggest a series of mitigation techniques based on these thresholds. To accomplish these tasks, computational fluid dynamic simulations for a variety of pipe contraction and fluid properties were performed. The results of this research show that reducing the turbulence in a fluid system will reduce the likelihood of cavitation. Additionally, threshold bounds were created that establish a definitive transition at which cavitation will occur.

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations x_{n+1} = (1/(x_{n}(x_{n-1}±1)±1)), x_{n+1} = ((-1)/(x_{n}(x_{n-1}±1)∓1)), such that their solutions are associated with Tribonacci numbers.

In this paper is discussed sediment transport as a mechanical process that characterises a natural stream or channel flow regime. The objective of experimental work presented in this paper is to recall and to give another prospect of well-known Meyer-Peter and Müller approach for estimation of Shield’s number (θ_c,θ) in laboratory conditions, and calibration of dimensionless MPM number (A). For this purpose two different experiments are conducted, during the first experiment water amount flushed on the flume and bed slope was changed simultaneously until equilibrium state is achieved, meanwhile is estimated the critical Shield’s number (θ_c). While, during the second experiment, water amount was kept constant, only bed slope of flume was continuously tilted, meanwhile sediment, discharge and Shield’s number (θ) was determined for given hydraulic conditions. In addition calibration of dimensionless MPM number (A) was performed, where several iteration were considered until for (A=3.42), sediment discharge measured become almost equal with sediment discharge computed by using MPM formula. After these experiments, is concluded that MPM formula can be used also for other certain initial condition and similar procedure may be adopted to calibrate the dimensionless MPM number (A) .

An SIRS (Susceptible–Infected–Removed-Susceptible) mathematical model for the transmission dynamics of the Transfusion–Transmitted Malaria (TTM) model with optimal control pair u₁(t) and u₂(t) was developed and studied in this research work. The model Transfusion–Transmitted Malaria disease–free equilibrium and endemic equilibriums points were determined. The model exhibited two equilibriums; disease-free and endemic equilibrium. It is shown that the disease–free equilibrium was locally asymptotically stable if the associated basic reproduction numbers R₀ is less than unity while the disease persists if R₀ is greater than unity. The global stability of the Transfusion–Transmitted Malaria model at the disease-free equilibrium was established using the comparison method. The optimality system was derived and an optimal control model of blood screening and drug treatment for the Transfusion–Transmitted Malaria model was investigated. Conditions for the optimal control were considered using Pontryagin’s Maximum Principle and solved numerically using the Forward and Backward Finite Difference Method (FBDM). Numerical results obtained are in perfect agreement with our analytical results.

We propose a new Mamdani fuzzy rule-based system in which the fuzzy sets in the antecedents and consequents are assigned in a discrete set of points and approximated by using the extended inverse fuzzy transforms, whose components are calculated by verifying that the dataset is sufficiently dense with respect to the uniform fuzzy partition. We test our system in the problem of spatial analysis consisting in the evaluation of the liveability of residential housings in all the municipalities of the district of Naples (Italy). Comparisons are done with the results obtained by using trapezoidal fuzzy numbers in the fuzzy rules.

In the paper, the authors nd a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

In the paper, by a very simple approach, the author establishes an expression in terms of a lower Hessenberg determinant for the Euler polynomials. By the determinantal expression, the author finds a recurrence relation for the Euler polynomials. By the way, the author derives the corresponding expression and recurrence relation for the Euler numbers.

In the article, we define a sequence F: F(0) = 2, F(1) = 10, F(2) = 16, F(3) = 22, F(4) = 26, F(4) = 28, · · · , F(i) = F(i − 1) + l, where the number l ≤ 8 is defined by using prime numbers and matrix algebra. The sequence includes only even numbers and can be used to define a series of numbers F(i) + 1, the non-Goldbach sequence, that contains all numbers that cannot be written as the sum of two primes. The result is related to Goldbach’s conjecture. The famous Goldbach conjecture states that every even integer greater than 2 can be expressed as the sum of two primes.

One of the most important agrotechnical factors that influence the growth conditions of crops is plant density. Alterations in habitat conditions result in the emergence of phytophagous organisms, whose development is closely associated with host plants. The objective of this study was to assess the abundance and species composition of thrips (Thysanoptera) collected in soybean plants of different varieties cultivated under different plant arrangements (row spacing, number of seeds sown differed). The research was conducted at two locations in southwestern Poland between 2015 and 2018. The herbivores that inhabit plants were caught using an entomological net. The experiments were carried out using the complete randomised block design, with four replications. Regardless of location and treatment, thrips were the most numerous group of pests. Thrips tabaci and T. fuscipes were the dominant species within the collected material. A total of 24 species of thrips were identified and their dietary specialisation was determined. The assemblages of studied insects were also analysed due to the density of the plants and the stage of development. The increase in the sowing density of soybean (90 seeds per m2) resulted in a greater total number of thrips compared to a lower sowing density (50 seeds per m2). The number of thrips significantly increased during the flowering period and shortly after the flowering time, which made them a significant threat to the plants. Therefore, it is crucial to develop innovative pest management strategies tailored to effectively grow soybean to mitigate potential pest-related challenges.

The generation of arithmetic sequences involves arithmetic operations. However, is it possible to generate such sequences without being subject to any arithmetic or related operations, all by just hand? The answer may be negative, as the very rule defining these sequences itself relies on arithmetic operations. Nonetheless, this paper presents a few results demonstrating that the exact sequences of $an$, where, $a \in \{ 2,3,\cdots,9,10\}$ and $n \in \mathbb N \cup \{0\}$, can indeed be generated up to any desired number of terms without relying on any arithmetic operations and others derived from such. This is done by the formation of a specialized table that leverages numerical patterns and the notion of concatenation.

Over the last decade, a lot of research has been conducted on memristors. Most of this research focusses on using memristors for Artificial Intelligence (AI) applications and to fabricate non-volatile memory, but also the security aspects of memristors have been examined. The current study summarises and compares five reviews on the security aspects of memristors. These reviews cover two different perspectives: (1) security applications of memristors such as Physical Unclonable Functions (PUFs) or True Random Number Generators (TRNGs), and (2) potential threats when using memristors to train and store neural networks. The comparison of the reviews reveals that different sets of studies are included in the reviews and different characterisations of the studies are provided. This shows that different perspectives are necessary to get a comprehensive overview of the security aspects of memristors. By synthesising the perspectives of different reviews, this study helps to get such an overview.

Molecular analysis of growing teratoma syndrome has not been extensively studied. Here, we report a 14-year-old boy with a growing mass during treatment for a mixed germ cell tumor of the pineal region. Tumor markers were negative; thus, growing teratoma syndrome was suspected. A radical resection via the occipital transtentorial approach was performed, and histopathological examination revealed a teratoma with malignant features. Methylation classifier analysis confirmed the diagnosis of teratoma, and DMRT1 loss and 12p gain were identified by copy number variation analysis, potentially elucidating the cause of growth and malignant transformation of the teratoma. The patient remains in remission after intense chemoradiation treatment as a high-risk germ cell tumor.

I had previously developed an approach called Gocgen approach, which claimed to prove twin prime conjecture. In this paper, I processed the previously developed Gocgen approach with the zeta function and explained the relationship between the zeta function with some formulas to offer another perspective on the zeta function, and also created a new function that explains the Gocgen approach using the zeta function. Understanding the new function created will provide insight into the frequency of prime numbers.

We study electrohydrodynamic (EHD) linear (in)stability of microfluidic channel flows, i.e. the stability of interface between two-shearing viscous (perfect) dielectrics exposed to an electric field in large aspect ratio microchannels. We then apply our results to particular microfluidic systems known as electroosmotic (EO) pumps. Our results are detailed analytical expressions for the growth rate of two-dimensional EHD modes in Couette-Poiseuille flows in the limit of small Reynolds number ($R$); the expansions to both zeroth- and first-order-$R$ are considered. The growth rates are complicated functions of viscosity-, height-, density- and dielectric-constant ratio, as well as of wavenumbers and voltages, and to our knowledge have not been presented before in literature. To make the results more useful, e.g., for voltage-control EO pump operations, we also derive equations for the impending voltages of the neutral stability curves that divide stable from unstable regions in voltage-wavenumber stability diagrams. The voltage equations and the stability diagrams are given for all wavenumbers. We finally outline the flow regimes in which our first-order-$R$ voltage corrections could potentially be experimentally measured. Our work gives the insight into the coupling mechanism between electric field and shear flow in parallel-planes channel flows, correcting an erroneous attempt from literature. Our general analysis enables us also to refine the renowned instability mechanism due to viscosity stratification, i.e., the case of pure shear instability, when the first-order-$R$ voltage correction equals zero.

This research proposes an algorithm to sign messages using the ElGamal asymmetric cryptosystem, called: Digital signature algorithm based on ElGamal, Diffie-Hellman protocol and the number π (DSAπ). This proposal has a high level of security like the DSA standard, in addition, execution times are reduced in relation to it. The Diffie-Hellman protocol and the number π were used in the construction of the digital signature algorithm in conjunction with the Hash-Sha-512 function. Some experiments are presented to provide evidence that the bits on the right side of the decimal point of π appear randomly, such as: a color image was constructed of a string of consecutive bits chosen at random, of the number π. Subsequently, parameters such as: entropy, correlation, discrete Fourier transform, goodness-of-fit test χ2 were evaluated. It is mentioned that an S-box 8×8 is involved in the signature. The sensitivity of the signature was measured, that is, when small changes are made to the sender’s private key, or small changes to the message. Finally, an image was constructed using the signatures of random texts, and subsequently the randomness of its pixels was obtained, to verify that there is no relationship between the different signatures.

Broadly speaking, binominal and biverbal lexical constructions have been studied independently in different research traditions and frameworks. It is true that the two do not necessarily have overlapping areal distributions, but the fundamental question remains whether Indo-European NN compounds and Transeurasian VV compounds have nothing in common. From a purely theoretical perspective also, the cross-categorial parallelism is worthy of serious investigation because a theory of the process of compounding that inherits the spirit of X-bar theory strives to capture commonalities among various compounding patterns and category-specific constraints observed within and across languages. Against this background, a cross-categorial comparison, not within but across languages, is made of coordinative binominal and biverbal constructions. NN and VV coordinate compounds from English and Japanese are examined in detail using the methodology of contrastive morphology and decompositional lexical semantics. It is shown that dvandva is possible not only in NN but also in VV coordinate compounds and furthermore that the dvandva-appositive distinction in NN coordinate compounds recurs in VV coordinate compounds.

A symbolic analysis of Archimedes’ periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented,, by remarking the cruciality of this topic in number theory. Periods of ordinal numbers, and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship among numbers and information, which shed new light on a red line passing through the whole history of mathematics

The idea of strong and weak adjacencies between vertices has been generalized into fuzzy graphs and intuitionistic fuzzy graphs (IFGs) and it is an important part of making decisions. However, one or two membership degrees are not always sufficient for making decisions on real-world problems that need an answer of types “yes, neutral, and no". Consequently, in previous work, we generalized the concept into picture fuzzy graphs (PFGs) where each element in the PFG has membership, neutral, and non-membership degrees. Moreover, we constructed the notion of the coloring of PFGs based on strong and weak adjacencies between vertices. In this paper, we investigate some properties of the chromatic number of PFGs based on the concept of strong and weak adjacencies between vertices. According to the properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is usefull when we work with large PFGs. Further, we improve the method to implement the PFG’s coloring for determining traffic signal phasing at an intersection. A case study has also been done to evaluate the method.

Measles is a highly contagious airborne disease that is endemic in many developing countries with low levels of vaccination coverage. In this paper, we propose a deterministic compartmental mathematical model for measles disease dynamics. We establish the global stability conditions for the disease-free and endemic equilibria using the Lyapunov function stability method. \textcolor{red}{Using arbitrary parameters it is obtained that the proposed model exhibits forward bifurcation}. Numerical integration using MATLAB software was used to simulate the model solution of the forward problem. We calibrate the proposed model to estimate the parameters with a 95\% confidence interval (CI) using real data from Ethiopia by formulating an inverse problem. We notice that the model fits well with the real data of Ethiopia. The estimated basic reproduction number ($R_0$) is found to be $R_0=1.3973$ which proves that the disease is endemic. It is also obtained from the local sensitivity analysis that reducing the transmission rate and increasing the vaccination rate could effectively minimize the $R_0$.

Due to its high specific surface area and rich porous structure, acacia-derived porous activated carbon is the most potentially effective material for wastewater treatment. This research study aimed to prepare activated carbon using Acacia erioloba seedpods as carbonaceous materials and phosphoric acid as an activating agent. The specific surface area of the prepared activated carbon sample was characterised by Brunauer–Emmett–Teller instrument. The specific surface area value was 387 m²/g. The activated carbon prepared was then sieved into three different particle sizes of 50, 100 and 200 micrometres and characterised using various analytical procedures, including proximate analysis to study moisture content, ash content, volatile matter content and fixed carbon content. The bulk density, SEM, power of hydrogen, iodine number and methylene blue number index were also investigated to determine the adsorption properties of the prepared activated carbon. Batch adsorption dynamics for the removal of organic compounds such as methylene blue and unsaturated character of fatty acid from aqueous solution were also carried out at room temperature to evaluate the prepared activated carbon's applicability in water treatment. The iodine number was 528, 638, and 554 mg/g for the 50, 100, and 200 μm activated carbon particles, respectively. From the results, the adsorption of methylene blue favoured the Freundlich adsorption model, showing higher correlation (R²) values than the Langmuir model. The results indicate that methylene blue particles were adsorbed on heterogeneous surfaces.

This research investigates a model for the COVID-19 outbreak in Indonesia by analyzing comorbid diseases, self-quarantine, government-provided quarantine, and immunization regimens. Some model parameters are derived from academic journals, others are extrapolated from data collected by the Indonesian Ministry of Health in 2020, and others are assumed. Evaluation of the model reveals non-endemic equilibrium points, endemic equilibrium points, and the basic reproduction number (BRN). The contact rate and infected probability factors impact the increase in the number of COVID-19-infected individuals with comorbid disease within a group. According to the sensitivity analysis of the BRN, the key parameters impacting the spread of COVID-19 are the rate of susceptible recruitment, the rate of contact, the COVID-19 infection death rate, and the likelihood of infection. In addition, sensitivity analyses are provided to examine the effect of parameter changes on subpopulations. We discovered that the natural death rate is the most sensitive parameter based on the sensitivity index after reaching equilibrium. Symmetry aspects appear in some of the visualization of the model’s solution and the BRN and parameters’ sensitivity.

It is well established the complex exponential and logarithm are multivalued functions, both failing to maintain most identities originally valid over the positive integers domain. Moreover the general case of complex logarithm, with a complex base, is hardly mentionned in mathematic litterature. We study the exponentiation and logarithm as binary operations where all operands are complex. In a redefined complex number system using an extension of the C field, hereafter named E, we prove both operations always produce single value results and maintain the validity of identities such as log_u (w v) = log_u (w) + log_u (v) where u, v, w in E. There is a cost as some algebraic properties of the addition and subtraction will be diminished, though remaining valid to a certain extent. In order to handle formulas in a C and E dual number system, we introduce the notion of set precision and set truncation. We show complex numbers as defined in C are insufficiently precise to grasp all subtleties of some complex operations, as a result multivaluation, identity failures and, in specific cases, wrong results are obtained when computing exclusively in C. A geometric representation of the new complex number system is proposed, in which the complex plane appears as an orthogonal projection, and where the complex logarithm and exponentiation can be simply represented. Finally we attempt an algebraic formalization of E.

Turbulence is a fluid dynamic problem refractory to mathematical treatment. Examining a theoretical model of liquid water flowing in a cylinder at different Raleigh numbers, we propose a novel approach to elucidate the first stages of turbulent flows. The weakly bonded molecular assemblies of liquid water form a fluctuating branched polymer in which every micro-cluster displays different density. Against the common view of liquid water as an incompressible and continuous fluid, we suggest that the occurrence of transient local aggregates could be able to generate the vortices and eddies that are the hallmarks of turbulence. We quantify the local changes in velocity, diameter and density required to engender “obstacles” to the average flow. Then, we show how these microstructures, equipped with different Raleigh numbers and characterized by high percolation index, could generate boundary layers that contribute to micro-vortices production. We conclude that the genesis of turbulence cannot be assessed in terms of collective phenomena, rather is sustained, among many other factors, by the underrated microscopic inhomogeneities of fluids like liquid water.

Trachsummaroma is an eye infectious disease caused by Chlamydia Trachomatis bacterium, which may lead to irreversible blindness. The disease is spread directly or indirectly by contacting a contaminated material. It can also be transmitted through the disease vector known as “Musca sorbens” or “Bazaar fly”. To curtail the spread of the disease in a population, a meaningful information on the spread and possible control of the disease is required. Mathematical modeling provides efficient tools that can be used to understand and analyze the dynamics of the disease and its control. Several compartmental epidemic models have been proposed in the literature to study the dynamics of trachoma; including SI, SIR and SEIR. However, majority of the existing trachoma models consider only person to person transmission. Thus, the information provided by such models is insufficient since they did not capture the disease vector transmission. The current study proposed a novel SEIR-SEI model that consider both person-person and vector transmission dynamics. The threshold quantity, basic reproduction number R0 is obtained using the next generation matrix, and it was proved that the disease-free equilibrium is asymptotically stable when R0 < 1, and the endemic equilibrium is globally asymptotically stable when R0 > 1. Some simulation results with the aid of mesh plots for the reproductive number as a function of two different biological parameters were obtained. Furthermore, a comprehensive sensitivity analysis is conducted to identify the influence of the individual parameters on the R0. Numerical results show that the vector contact rate has the highest sensitivity with respect to R0, and the value of R0 increases with increase in, hence, the disease can be controlled by decreasing the vector contact rate. Similarly, improving the rate of environmental hygiene and facial cleanliness will decrease the size of R0 and result in the declination of the disease transmission. Moreover, a detailed parameter estimation of the model parameters and model fitting was presented with the use of field data cases from Northern Nigeria using least-square fitting method. The study provides alternative tools that can be used for planning trachoma control program to achieve global eradication of trachoma as a public heath challenge as targeted by WHO in 2030.

Spatial evaluation of flood-prone areas at the drainage basins is one of the basic strategies in the field of flood risk management. The present study aims to investigate the efficiency of the CN logistic and hydrological regression model for predicting and zoning floods. In the first stage, 13 runoff parameters, hydrologic soil groups (HSGs), slope, lithology, drainage density (DD), land curvature, elevation, distance to waterways/rivers, topographic wetness index (TWI), stream power index (SPI), rainfall, land use, and NDVI were employed. In the SCS-CN model of the drainage basin, the infiltration rate (S) and runoff amount (Q) were determined. The weights of the used layers were weighted by the AHP. Also, a flood zoning map of the drainage basin with different 5, 15, 25, and 50 year return periods was drawn by applying the weights of the layers. To ensure the accuracy of the zoning map with the logistic regression model, the ROC curve, and the area below the curve were used. The results showed that for the prediction rate, the AUC is 0.81%, indicating that the model has acceptable accuracy. The most important factors affecting flood are geological index; distance to waterways/rivers; and NDVI in the logistic regression model, and slope, DD, rainfall, and land use in the SCS-CN model respectively. 30 to 46% of the drainage basin area during 5 to 50 year periods has moderate flood potential, and 28 to 34% has high potential.

When different strain hardening and strain rate sensitive materials are used for scaled model and prototype, the traditional pure geometrical similarity laws of solid mechanics will fail. Although correcting the basic scaling factors of velocity, density and geometry have been developed to compensate for the material distortion in recent non-geometric scaling works, it is difficult to be widely used because of its inherent indirect (depending on the structural strain and strain rate responses) and inexact (having significant prediction errors for prototype) defects. In this paper, a framework of material similarity, based on the new suggested material dimensionless numbers and the ‘Material number vs. strain/strain-rate’ function curves, are further developed, which represents the objective requirement of similarity theory for the basic mechanical properties of materials. It is demonstrated what is similitude materials of solid mechanics and how to use the best similitude materials to overcome the non-scalabilities of materials for identical or different materials. The direct and exact solution of the basic correction factors is further obtained and therefore overcomes the previous inherent indirect and inexact defects radically. Based on the similarity evaluation of different materials of the classical constitutive models, the impacted structures of circular plate and crooked plate with strain hardening and strain rate sensitive materials are verified numerically. The results show the completely different materials can be exact similitude for various structural behaviors (strain, strain rate, stress and displacement) of time and space fields after using the best similitude materials; and the basic correction factors do not depend on the structural strain and strain rate responses. As a contrast, when the non-similitude materials are used, the similarity results are very sensitive to the selection of strain/strain-rate and often leads to failed predictions. In addition, for the material elastic and temperature effects, the proposed method is also discussed to be valid.

The optimization problem of two or more special-purpose functions of the energy system is subjected to an analysis. Based on experience of our research and general knowledge of partial solutions of energy system optimization at the level of control of production and power energy supply by energy companies in the Czech Republic, a special-purpose (cost) function has been defined. By analysing the special-purpose function, penalty and limitations have been defined. Using the fuzzy logic, a set of suitable solutions for the special-purpose function is accepted. An optimum of the special-purpose function is looked for using the simulated annealing method. The history of electricity consumption is sorted by day and by hour, representing the multidimensional data. When using the cluster analysis, type daytime diagrams of consumption are defined. Type daytime diagrams form prototypes of identified clusters. The so-called self-organizing neural network with Kohonen map attached is used to perform the cluster analysis. The result of our research is presented by an experiment.

To investigate the influence of supplemental lighting intensity on the production of cut gerbera during Canada’s supplemental lighting season (November to March), trials were carried out at a research greenhouse. Five supplemental LED light intensity (LI) treatments provided canopy-level photosynthetic photon flux densities (PPFD) ranging from 41 to 180 µmol·m-2·s-1. With a 12-h photoperiod, the treatments provided 1.76 to 7.72 mol·m-2·d-1 of supplemental light. Two cultivars of cut gerbera (Gerbera jamesonii H. Bolus ex Hook.f) were used to evaluate vegetative growth and flower production. Plugs of ‘Ultima’ were assessed for vegetative growth and rate of flower development. There were minor LI treatment effects on number of leaves and chlorophyll content index and flowers from plants under the highest vs. lowest LI matured 10% faster. Reproductively mature ‘Panama’ plants were assessed for flower yield and quality. ‘Panama’ flowers from the highest LI treatment had shorter stems than the three lowest LI treatments, flowers from the middle LI treatment had larger diameter than the other treatments. Flowers from the lowest LI treatment had lower fresh mass than the three highest LI treatments. There were linear relationships between LI and numbers of flowers harvested, with the highest LI treatment producing 10.3 and 7.0 more total and marketable flowers per plant than the lowest LI treatment. In general, increasing levels of supplemental light had only minor effects on vegetative growth (young plants) and size and quality of harvested flowers (mature plants) but flowers from plants grown under higher LIs were more numerous and matured faster.

Real-time estimation of the parameters characterising infectious disease transmission is important for optimization quarantine interventions during outbreaks. One of the most significant parameters is the effective reproduction number - number of secondary cases produced by a single infection. The current study presents an approach for estimating the effective reproduction number and its application to COVID-19 outbreak. The method is based on fitting SIR epidemic model to observation data in a sliding time window and allows to show real-time dynamics of reproduction number at any phase of epidemic for countries globally. Online data on COVID-19 daily cases of infections, recoveries, deaths are used.Finally, time-dependent reproduction number is explored in connection with dynamics of peoples mobility. The method allows to assess the disease transmission potential and understand the effect of interventions on epidemics spread. It also can be easily adapted to future outbreaks of different pathogens. The tool is available online as Python code from the Github repository.

The COVID-19 epidemic is an emerging infectious disease of the viral zoonosis type caused by the corona-virus strain SARS-CoV-2, is classified as a human-to-human communicable disease and is currently a pandemic worldwide. In this paper, we propose conceptual mathematical models the epidemic dynamics of four compartments. We have collected data from the Djibouti health ministry. We define the positivity, boundedness of solutions and basic reproduction number. Then, we study local and global stability and bifurcation analysis of equilibrium to examine its epidemiological relevance. Finally, we analyze the fit of the data in comparison with the result of our mathematical results, to validate the model and estimating the important model parameters and prediction about the disease, we consider the real cases of Djibouti from 23th March to 10th June, 2020.

In this research, a novel method to investigation the transient heat transfer coefficient in a channel is suggested experimentally, in which the water flow, itself, is considered both just liquid phase and liquid-vapor phase. The experiments were designed to predict the temporal and spatial resolution of Nusselt number. The inverse technique method is non-intrusive, in which time history of temperature is measured, using some thermocouples within the wall to provide input data for the inverse algorithm. The conjugate gradient method is used mostly as an inverse method. The temporal and spatial changes of heat flux, Nusselt number, vapor quality, convection number, and boiling number have all been estimated, showing that the estimated local Nusselt numbers of flow for without and with phase change are close to those predicted from the correlations of Churchill and Ozoe (1973) and Kandlikar (1990), respectively. This study suggests that the extended inverse technique can be successfully utilized to calculate the local time-dependent heat transfer coefficient of boiling flow.

Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator (RNG). At the same time, it directly determines the extraction ratio of true randomness from the raw data, in other words, it obviously affects quantum random bits generating rate. In this work, we commit to enhancing quantum entropy content in the vacuum noise based quantum RNG. We have taken into account main factors in this proposal to establish the theoretical model of quantum entropy content, including the effects of classical noise, the optimum dynamical analog-digital convertor (ADC) range, the local gain and the electronic gain of the homodyne system. We demonstrate that by amplifying the vacuum quantum noise, abundant quantum entropy is extractable in the step of post-processing even classical noise excursion, which may be deliberately induced by an eavesdropper, is large. Based on the discussion and the fact that the bandwidth of quantum vacuum noise is infinite, we propose large dynamical range and moderate TIA gain to pursue higher local oscillator (LO) amplification of vacuum quadrature and broader detection bandwidth in homodyne system. High true randomness extraction ratio together with high sampling rate is attainable. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the laser power of the LO when classical noise excursions of the raw data is obvious.

Many cryptographic systems require random numbers, and weak random numbers lead to insecure systems. In the modern world, there are several techniques for generating random numbers, of which the most fundamental and important methods are deterministic extractors proposed by von Neumann, Elias, and Peres. Elias’s extractor achieves the optimal rate (i.e., information theoretic upper bound) h(p) if the block size tends to infinity, where h(·) is the binary entropy function and p is probability that each bit of input sequences occurs. Peres’s extractor achieves the optimal rate h(p) if the length of input and the number of iterations tend to infinity. The previous researches related to both extractors did not mention practical aspects including running time and memory-size with finite input sequences. In this paper, based on some heuristics, we derive a lower bound on the maximum redundancy of Peres’s extractor, and we show that Elias’s extractor is better than Peres’s one in terms of the maximum redundancy (or the rates) if we do not pay attention to time complexity or space complexity. In addition, we perform numerical and non-asymptotic analysis of both extractors with a finite input sequence with any biased probability under the same environments. For doing it, we implemented both extractors on a general PC and simple environments. Our empirical results show that Peres’s extractor is much better than Elias’s one for given finite input sequences under the almost same running time. As a consequence, Peres’s extractor would be more suitable to generate uniformly random sequences in practice in applications such as cryptographic systems.

Graph coloring is a manifestation of graph partitioning, wherein, a graph is partitioned based on the adjacency of its elements. Partitioning serves potentially as a compartmentalization for any structural problem. Vertex coloring is the heart of the problem which is to find the chromatic number of a graph. The fact that there is no general efficient solution to this problem that may work unequivocally for all graphs opens up the realistic scope for combinatorial optimization algorithms to be invoked. The algorithmic complexity of graph coloring is non-deterministic in polynomial time (NP) and hard. To the best of our knowledge, there is no algorithm as yet that procures an exact solution of the chromatic number comprehensively for any and all graphs within the polynomial (P) time domain. However, several heuristics as well as some approximation algorithms have been attempted to obtain an approximate solution for the same. Here, we present a novel heuristic, namely, the 'trailing path', which returns an approximate solution of the chromatic number within polynomial time, and, with a better accuracy than most existing algorithms. The ‘trailing path’ algorithm is effectively a subtle combination of the search patterns of two existing heuristics (DSATUR and Largest First), and, operates along a trailing path of consecutively connected nodes (and thereby effectively maps to the problem of finding spanning tree(s) of the graph) during the entire course of coloring, where essentially lies both the novelty and the apt of the current approach. The study also suggests that the judicious implementation of randomness is one of the keys towards rendering an improved accuracy in such combinatorial optimization algorithms. Apart from the algorithmic attributes, essential properties of graph partitioning in random and different structured networks have also been surveyed, followed by a comparative study. The study reveals the remarkable stability and absorptive property of chromatic number across a wide array of graphs. Finally, a case study is presented to demonstrate the potential use of graph coloring in protein design – yet another hard problem in structural and evolutionary biology.

In this study, a matched-mode autoregressive source depth estimation method (MMAR) based on autoregressive (AR) wavenumber estimation is proposed for a moving source in shallow water waveguides. The signal original frequency and the environmental parameters, namely, the sound speed profile and bottom properties are known as a prior knowledge. The mode wavenumbers are estimated by the AR modal wavenumber spectrum. On the basis of the mode wavenumber estimation, the mode amplitudes can be estimated by the wavenumber spectrum that is obtained by generalized Hankel transform. The source depth estimation is determined by the peak of source depth function wherein the data mode best matches the replica mode that is calculated using a propagation model. Compared with other methods of moving source depth estimation, the proposed method exhibits a better performance in source depth estimation under low signal-to-noise ratio or the small range span. The selection of horizontal line array depth is illustrated by simulation and normal mode theory in details.

In the paper, by virtue of some properties for the Riemann zeta function, the author finds a double inequality for the ratio of two consecutive Bernoulli numbers with even indexes and analyzes the approximating accuracy of the double inequality.

Abstract: This paper outlines the methodology and results for a two species finite volume scalar computational drug transport model developed for simulating the mass transport of Poly(lactic-co-glycolic acid (PLGA) ) from a half-embedded single strut implanted in a coronary arterial vessel wall. The mathematical drug transport model incorporates the convection-diffusion equation in scalar form (dimensionless) with a two species (free-drug and bound-drug) mass transport setup including reversible equilibrium reaction source terms for the free and bound-drug states to account for the pharmaco-kinetic reactions in the arterial wall. The relative reaction rates of the added source terms control the interconversion of drug between the free and bound-drug states. The model is solved by a 2-D finite-volume method for discretizing and solving the free and bound drug transport equations with anisotropic vascular drug diffusivities. This model is an improvement over our previously developed model using the finite-difference method. A dimensionless characteristic scaling pre-analysis was conducted a priori to evaluate the significance of implementing the reaction source terms in the transport equations. This paper reports the findings of an investigation of the interstitial flow profile into the arterial wall and the free and bound drug diffusion profiles with a parametric study of varying polymer drug concentration (low and high), tortuosity, porosity, and Peclet and DamKöhler numbers over the course of 400 hours (16.67 days). The results also reveal how a single species drug delivery model that neglects both a reversible binding reaction source term and the porosity and tortuosity of the arterial wall cannot accurately predict the distribution of both the free and bound drug.

In our recent publications, based on strong and electroweak interactions, we have developed a completely new formula for estimating nuclear binding energy. With reference to currently believed Semi Empirical Mass Formula (SEMF), we call our formula as ‘Strong and Electroweak Mass Formula’ (SEWMF). Our formula constitutes 4 simple terms and only one energy coefficient of magnitude 10.1 MeV. First term is a volume term, second term seems to be a representation of free nucleons associated with electroweak interaction, third term is a radial term and fourth one is an asymmetry term about the mean stable mass number. In this paper, we make an attempt to understand and estimate the maximum binding energy associated with any mass number. It can be expressed as, for A > 4, $\left(BE\right)_A\cong \left[A-0.000935A^2-A^{1/3}-A^{-1/2}\right]$ MeV. We are working on refining the 4^th term with even-odd corrections, shell corrections and other microscopic corrections. Proceeding further, stable mass numbers and super heavy mass numbers can be understood with a relation of the form, $\left[\textrm{RoundOff}\left(\left(Z+2.9464\right)^{1.2}-1.7165\right)\right]\pm\left[0,1\right]\pm\left(2n\right)$ where $n \cong 0,1,2$. It needs a review with respect to even-odd proton numbers and other microscopic corrections.Very interesting point to be noted is that based on the concept of “binding energy per nucleon”, the most complicated Avogadro number and Unified atomic mass unit can be estimated in a unified approach.

In this paper, we give closed-form expressions of the $p$-Frobenius number for the triple of the generalized star numbers $a n(n-1)+1$ for an integer $a\ge 4$. When $a=6$, it is reduced to the famous star number. For the set of given positive integers $\{a_1,a_2,\dots,a_k\}$, the $p$-Frobenius number is the largest integer $N$ whose number of nonnegative integer representations $N=a_1 x_1+a_2 x_2+\dots+a_k x_k$ is at most $p$. When $p=0$, the $0$-Frobenius number is the classical Frobenius number, which is the central topic of the famous linear Diophantine problem of Frobenius.

The heat transfer and fluid mechanics analysis in agitated vessels is usually performed using the Dittus-Boelter correlation. In this study, we propose the analysis of an agitated vessel with a draft tube through the analysis of dimensionless numbers correlations. The heat transfer and fluid mechanics simulation was conducted using ANSYS Fluent software. The simulation used the Sliding Mesh approach and the SST k-ω turbulent model to capture the vessel's fluid flow and heat transfer phenomena. A grid independence study was conducted by varying the number of time steps to obtain an appropriate time step size for the simulation. The convective heat transfer coefficient, as indicated by the mean values of the Nusselt number, was calculated. The local values along the radial coordinate of the heat transfer surface were also determined. These results provide insights into the distribution of heat transfer rates within the vessel, which can help optimize process efficiency and equipment design. The simulation results were analyzed by varying the c and m coefficients in the Nusselt correlation presented as Nu= c Rem Pr1/3. Furthermore, correlations describing the mean Nusselt number at the bottom and wall of the vessel are presented and compared with existing literature, contributing to advancing knowledge in this field.

This research is concentrated on the physical technique of carbon activation from carbon-based material such as bamboo. In addition, we impregnated the activated carbon by use of experimental methods. In the first case, the results from various parameters on the carbon activation process, such as kiln rotation speed, steaming time, calcination temperature and heating rate at the different levels has been investigated on iodine number of activated carbon. Using the Taguchi method and ANOVA analysis, the optimal test results were obtained which are as follows: steaming time and calcination temperature were the most influential factors and heating rate and kiln rotation speed were the less influential factors in the process. In the second case, palladium-impregnated activated carbon (Pa/AC) was prepared at different conditions of the experiment and effects of optimum ratios on the responses have been studied.

Mitochondrial DNA copy number (mtDNAcn) is associated with mitochondrial function contributing various diseases. Understanding of the association between mtDNAcn and infant neurodevelopment, as well as the role of racial disparities, remains unknown. A cohort study was conducted with 55 preterm infants and a single blood sample was collected from each infant during their NICU stay to measure mtDNAcn. NICU Network Neurobehavioral Scale (NNNS) and Bayley Scale of Infant Developmental testing Edition III was assessed during NICU until 2 years of corrected age (CA). Linear regression models were performed to investigate the relationship between the clinical characteristics, neurobehavioral outcomes and mtDNAcn. Majority of our subjects were male, White, non-Hispanic, had C-section, and without preterm premature rupture of membrane (PPROM). Increased mtDNAcn was found associated with younger birth gestational age (GA), nonoptimal neurodevelopment. However, the opposite associations between mtDNAcn and neurodevelopmental outcomes were observed between Black and White infants up to 1 year of CA. Adverse early life experience, together with increased mtDNAcn in White infants, and decreased mtDNAcn in Black infants may be considered as significant positive predictors of poor early life neurodevelopmental outcomes in infants.

Let a,b,c be positive integers such that a²+b²=c², 2|b,gcd(a,b)=1. In 1956, Jesmanowicz conjectured that for any positive integer w, the only solution of (aw)^x+(bw)^y=(cw)^z in positive integers is (x, y, z) = (2, 2, 2). In this paper, based on Gaussian integer ring, we show that Je$\acute{s}$manowicz' conjecture is true for any positive integer

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

The present work provides continuity with studies where currently the industrial market is characterized by a highly variable demand in terms of quantities and flexibility of manufacturing or mass customization, which translates into a more demanding production context in terms of the continuous changes required to the production systems, the effect of which results in an increase in the fatigue subjected to the machines that make up the production systems. On the other hand, current production systems tend to use highly communicative and sensorized cyber-physical systems; these characteristics can be used to integrate them into decision-assisted systems in order to improve the availability of the industrial plant. The assisted system developed focuses on collecting and taking advantage of historical knowledge of industrial plant failures and breakdowns. By ideally integrating the Reliability Centered Maintenance (RCM) methodology and Case-Based Reasoning (CBR) algorithms implemented in a Java application, it is possible to design maintenance plans adjusted to a real and changing operational context of any industrial plant. As a result, faster and more accurate decisions are made, as they are based on data. This article focuses on improving certain aspects of the developed assisted system by adding more value to it by incorporating Fuzzy Logic (FL) techniques. The aim is to improve the way of entering information about risk factors and their relative importance, by incorporating natural language, instead of a numerical score, resulting in increased precision in the calculation of the Risk Priority Number (RPN) of the new cases incorporated into the assisted system.

A new approach for predicting the geometrical characteristics of the mixing behavior of an inclined dense jet for angles ranging from 15° to 85° is proposed in this study. This approach is called group method of data handling (GMDH) which is based on the artificial neural network (ANN) technique. The proposed model was trained and tested using existing experimental data reported in literature. The model was then evaluated using statistical indices as well as compared with analytical models from previous studies. The results of the coefficient of determination (R2) indicate a high accuracy of the proposed model with values of 0.9719 and 0.9513 for training and testing for the dimensionless of the distance from the nozzle to the return point xr/D, and 0.9454 and 0.9565 for training and testing for the dimensionless of the terminal rise height yt/D . Moreover, four previous analytical models were used to evaluate the GMDH model. The results showed the superiority of the proposed model in predicting the geometrical characteristics of the inclined dense jet for all tested angles. Finally, the standard error of estimate (SEE) was applied to demonstrate which model performed the best in terms of getting closer to the actual data. The results illustrate that all fitting lines of the GMDH model performed very well for all geometrical parameter predictions and was the best model with approximately 10% error, which was the lowest value of error among the models. Therefore, this study confirms that the GMDH model can be used to predict the geometrical properties of the inclined negatively buoyant jet with high performance and accuracy.

This study revisits the Reynolds-averaged Navier--Stokes equations (RANS) and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds' averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of on the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

Searching for neutrinoless double beta decay is a top priority in particle and astroparticle physics, being the most sensitive test of lepton number violation and the only suitable process to probe the Majorana nature of neutrinos. In order to increase the experimental sensitivity for this particular search, ton-scale detectors operated at nearly zero-background conditions with a few keV energy resolution are required. In this scenario, cryogenic detectors have proven effective in addressing many of these issues simultaneously. After long technical developments, the CUORE experiment established the possibility to operate large scale detectors based on this technology. Parallel studies pointed out that scintillating cryogenic detectors represent a suitable upgrade for the CUORE design, directed towards higher sensitivities. In this work, we review the recent development of cryogenic detectors, starting from the status of the art and outlying the path toward next-generation experiments.

{\bf Abstract.} \\ {\bf Background:} Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 burden among the Rohingya refugees of Bangladesh to keep up with the disease outbreak's pace, health needs, and disaster preparedness. \noindent{\bf Methodology and Findings:} To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a modified Susceptible-Exposed-Infectious Recovered (SEIR) transmission model. All the values of different parameters used in this model were from the Bangladesh Government’s database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and good fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be good control over the transmission of the COVID-19 disease. At the end of December 2020, there will be only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number ($ \mathcal{R}_{0} $) has been estimated to be 0.7563. \noindent{\bf Conclusion:} Our analysis suggests that, due to the extensive precautions from the Bangladesh government as well as other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. Although detailed and pragmatic preparedness should be adopted for the worst scenario.

The rapid growth of the smart Internet of Things (IoT) and massive propagation of wireless technologies revealed the recent opportunities for development in various domains of real life such as smart cities and E-Health applications. A slight defense against different forms of attacks is offered for the current secure and lightweight Routing Protocol for Low Power and Lossy Networks (RPL) of IoT resource-constrained devices. Data packets are highly likely to be exposed while transmitting them during data packets routing. The RPL rank and version number attacks, which are two forms of RPL attacks, can have critical consequences for RPL networks. The studies conducted on these attacks have several security defects and performance shortcomings. The research proposes a Secure RPL Routing Protocol (SRPL-RP) for rank and version number attacks. It mainly detects, mitigates and isolates attacks in the RPL networks. The detection is based on a comparison of ranks strategy. The mitigation uses threshold and attacks status tables, and the isolation adds them to a blacklist table and alerts relevant nodes to skip them. SRPL-RP supports diverse types of network topologies and is comprehensively analyzed with multiple studies such as Standard RPL with Attacks, SBIDS and RPL+ Shield. The analysis results showed that the SRPL-RP achieves great improvements with Packet Delivery Ratio (PDR) of 98.48%, control message value of 991 packets/second, and average energy consumption of 1231.75 joules. It provides a better accuracy rate with 98.17% under the attacks.

The present novel corona virus (2019-nCoV) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. The infection induced death rate is also very high. There is no vaccine or anti-viral medicine for such infection. So at this moment a major worldwide problem is that how we can control this pandemic. On the other hand, India is a high population density country, where the corona virus disease (COVID-19) has started to spread from $1^{st}$ week of March, 2020 in a significant number of COVID-19 positive cases. Due to this high population density human to human social contact rate is very high in India. So control of the pandemic COVID-19 in early stage is very urgent and challenging problem. Mathematical models are employed in this paper to study the COVID-19 dynamics, to identify the influential parameters and to find the proper prevention strategies to reduce the outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the key model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impacts on the disease dynamics have also been studied. Future trends of the disease transmission has been Predicted from our model with some control measures. Finally, the positive measures to control the disease have been summarized.

In this paper, by using the q-integer, we introduce a new generalization of Fibonacci and Lucas sedenions called q-Fibonacci and q-Lucas sedenions. We present some fundamental properties of these type of sedenions such as Binet formulas, exponential generating fuctions, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity.

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

We explore the class of positive integers n that admit idempotent factorizations n=pq such that lambda(n) divides (p-1)(q-1), where lambda(n) is the Carmichael lambda function. Idempotent factorizations with p and q prime have received the most attention due to their cryptographic advantages, but there are an infinite number of n with idempotent factorizations containing composite p and/or q. Idempotent factorizations are exactly those p and q that generate correctly functioning keys in the RSA 2-prime protocol with n as the modulus. While the resulting p and q have no cryptographic utility and therefore should never be employed in that capacity, idempotent factorizations warrant study in their own right as they live at the intersection of multiple hard problems in computer science and number theory. We present some analytical results here. We also demonstrate the existence of maximally idempotent integers, those n for which all bipartite factorizations are idempotent. We show how to construct them, and present preliminary results on their distribution.

The aim of this study is to introduce a novel method which can separate sand or gravel dominated bed load transport in rivers with mixed-size bed material. In engineering practice, the Shields-Parker diagram could be used for such purposes, however, the method has certain applicability limits, due to the fact that it is based on uniform bed material and provides information rather on river-scale, instead of reach or local scale. When dealing with large rivers with complex hydrodynamics and morphodynamics the bed load transport modes can also indicate strong variation even locally, which requires a more suitable approach to estimate the locally unique behavior of the sediment transport. Here, we suggest that the decision criteria utilizes the shear Reynolds number (Re*). The method was verified against field and laboratory measurement data, both performed at non-uniform bed material compositions. The comparative assessment of the results show that the shear Reynolds number based method operates more reliably than the Shields-Parker diagram and it is expected to predict the sand or gravel transport domination with a < 5% uncertainty. The introduced results can greatly contribute to the improvement of numerical sediment transport modeling as well as to the field implementation of bed load transport measurements.