For a positive integer k, a radio k-coloring of a simple connected graph G = (V (G), E(G)) is a mapping | f(u) - f(v)| ≥ k +1-d (u , v ) such that f :V (G)→{0,1, 2,...} for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f, rck(f), is the maximum integer it assigns to some vertex of G. The radio k-chromatic number, rck(G) of G is min{rck(f)}, where the minimum is taken over all radio k-colorings f of G. If k is the diameter of G, then rck(G) is known as the radio number of G. In this work, we propose four algorithms (two serial algorithms and their parallel versions) which related to the radio k-coloring problem. One of them is an approximate algorithm that determines an upper bound of the radio number of a given graph. The other is an exact algorithm which finds the radio number of a graph G. The approximate algorithm is a polynomial time algorithm while the exact algorithm is an exponential time algorithm. The parallel algorithms are parallelized using the Message Passing Interface (MPI) standard. The experimental results prove the ability of the proposed algorithms to achieve a speedup 7 for 8 processors.

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.

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

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.

The Goldbach Conjecture, which is frequently termed as “1 + 1”, has been a fascinating goal for many mathematicians over centuries. A Chinese mathematician, Dr. Jingrun Chen, proved 1 + 2, which is a great success and the best result so far achieved. Although there were several attempts proving the conjecture, these attempts are either tediously long, complicated, or logically imperfect, thus not widely accepted. Taking advantage of the periodicity of primes, here the author provides a straight forward rigorous proof for the Conjecture.

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

this paper we present approaches for generating random numbers along with potential applications. Rather than trying to provide extensive coverage of several techniques or algorithms that have appeared in the scientific literature, we focus on some representative approaches presenting their workings and properties in detail. Our goal is to delineate their strengths and weaknesses as well as their potential application domains so as the reader can judge what would be the best approach for the application in hand, possibly a combination of the available approaches. For instance, a physical source of randomness can be used for the initial seed, then suitable preprocessing can enhance its randomness and then the output of the preprocessing can feed different types of generators, e.g. a linear congruential generator, a cryptographically secure one and one based on the combination of one way hash functions and shared key cryptoalgorithms in various modes of operation. Then, if desired, the outputs of the different generators can be combined giving the final random sequence. Moreover, we present a set of practical randomness tests which can be applied on the outputs of random number generators in order to assess their randomness characteristics. In order to demonstrate the importance of unpredictable random sequences, we present an application of cryptographically secure generators in domains where unpredictability is one of the major requirements, i.e. eLotteries and cryptographic key generation.

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.

It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

We evaluate some binomial cubic Fibonacci sums.

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 $R_0$.

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.

Reliability assessment in traditional power distribution systems has played a key role in power system planning, design, and operation. Recently, new information and communication technologies have been introduced in power systems automation and asset management, making the distribution network even more complex. In order to achieve efficient energy management, the distribution grid has to adopt a new configuration and operational conditions that are changing the paradigm of the actual electrical system. Therefore, the emergence of the cyber-physical systems concept to face future energetic needs requires alternative approaches for evaluating the reliability of modern distribution systems, especially in the smart grids environment. In this paper, a reliability approach that makes use of failure modes of power and cyber network main components is proposed to evaluate risk analysis in smart electrical distribution systems. We introduce the application of Failure Modes and Effects Analysis (FMEA) method in future smart grid systems in order to establish the impact of different failure modes on their performance. A smart grid test system is defined and failure modes and their effects for both power and the cyber components are presented. Preventive maintenance tasks are proposed and systematized to minimize the impact of high-risk failures and increase reliability.

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.

A multiscale mathematical model is proposed seeking to study the propagation dynamics of the Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through sexual contact without protection, considering the use of antiretroviral therapy (ART) and therapeutic failure. The model consists in a scale-free complex network that follows a power law, coupled with the immunological dynamics of each individual, that is, it considers the infection by the virus in the immune system of each HIV carrier, through a system of non-linear differential equations that govern the infection’s behavior in the immune system. Propagation of the virus in the network is modelled by taking into account information from the immunological status of each person. The study found that for a population to have high HIV prevalence, it is not necessary at the beginning of the simulation time for the virus to propagate rapidly. In addition, the study proves that with a higher number of sexual partners, there will be greater prevalence of HIV in the population and that the use of ART helps to control the propagation of the infection in the population. As an interesting result, it was also found that there is a higher number of HIV carriers who abandon ART than those who have access to it.

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion formula for the Bell polynomials in terms of the Stirling numbers of the first and second kinds, with the aid of the above explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials; (3) constructs some determinantal and product inequalities and deduces the logarithmic convexity of the Bell polynomials, with the assistance of the complete monotonicity of generating functions of the Bell polynomials. These inequalities are main results of the paper.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

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.

Mechanisms for somatic chromosomal mosaicism (SCM) and chromosomal instability (CIN) are incompletely understood. During SNP-array molecular karyotyping and bioinformatic analyses of children with neurodevelopmental disorders and congenital malformations (n=612), we observed colocalizaion of regular chromosomal imbalances or copy number variations (CNV) with mosaic ones (n=47 or 7.7%). Analyzing molecular karyotyping data and pathways affected by CNV burdens, we proposed a mechanism for SCM/CIN, which had been designated as “chromohelkosis” (from the Greek chromosome ulceration/open wound). Briefly, structural chromosomal imbalances are likely to cause local instability (“wreckage”) at the breakpoints, which results either to partial/whole chromosome loss (e.g. aneuploidy) or elongation of duplicated regions. Accordingly, a function for classical/alpha satellite DNA (protection from the wreckage towards the centromere) has been hypothesized. Since SCM and CIN are ubiquitously involved in development, homeostasis and disease (e.g. prenatal development, cancer, brain diseases, aging), we have metaphorically (ironically) designate the system explaining chromohelkosis contribution to SCM/CIN as the cytogenomic “theory of everything” like the homonymous theory in physics inasmuch as it might explain numerous phenomena in chromosome biology. Recognizing possible empirical and theoretical weaknesses of this “theory”, we nevertheless believe that studies of chromohelkosis-like processes are required to understand structural variability and flexibility of the genome.

While examination malpractice has been a recognized social problem among students, the control of the phenomenon remains a challenge. In this study, we formulate a mathematical model describing the population dynamics of examination malpractice among students. Initial insight into the dynamics of the model is gained by analyzing some important mathematical features of the model such as the basic malpractice number. The malpractice-free equilibrium and endemic equilibrium points of the model are shown to be locally asymptotically stable when the basic malpractice number is less than unity. This result implies that examination malpractice can be totally eradicated among students when the basic malpractice number is less than unity. To understand the impact of controlling this social problem, we extend the model to incorporate awareness campaign and disciplinary measure as control strategies in curtailing the act. Our analysis reveals that incorporating control strategies have some influence in reducing examination malpractice among students. Further analysis indicates that considering both control strategies simultaneously yields a better result in reducing examination malpractice and examination malpractice will grow faster when control strategies are not introduced.

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.

Next Generation Sequencing (NGS), now widely used in the clinical setting, offers an efficient and comprehensive molecular approach for patients with Familial hypercholesterolemia (FH). Although the dominant form of disease is mostly due to low-density lipoprotein receptor (LDLR) small-scale pathogenic variants, approximately 10% of molecularly defined FH cases are due to Copy Number Variations (CNVs). Here, we report a novel large deletion of the LDLR gene involving exons 4–18, identified by bioinformatic analysis of NGS data in an Italian family. A long PCR strategy was employed for breakpoint region analysis where an insertion of 6 nucleotides (TTCACT) was found. Two Alu sequences, identified within intron 3 and exon 18, could underlie the identified rearrangement by a Nonallelic Homologous Recombination (NAHR) mechanism. NGS proves to be a powerful tool used to precisely identify CNVs, in addition to small-scale variants in FH-related genes. At this purpose, the use and implementation of this cost-effective, efficient molecular approach meets the clinical need for personalized diagnosis in FH cases.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

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)).

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

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.

The common dandelion uses a bundle of drag-enhancing bristles (the pappus) that enables seed dispersal over formidable distances; however, the scaling laws of aerodynamic drag underpinning pappus-mediated flight remains unresolved. In this paper, we study the aerodynamic shape of dandelion, derive the scaling law of resistance, determine the Vogel exponent. In particular, we find that the total drag coefficient is proportional to the -2/3 power of the dandelion pappus Reynolds number, and obtain the terminal velocity of the dandelion seed under gravitation field.

The cyclic load applied to civil and mining structures can lead to a reduction of the materials’ strength, different from that which would occur with a monotonous load. Numerous cases can be found where the decay of the rock parameters subjected to this type of stress leads to progressive or sudden collapse: among them, tunnel walls, pillars and slabs in mining operations, roads with a heavy vehicle transit, abutments of bridges and dams can be quoted. The topic can therefore be fundamental for a correct structural design, to avoid problems during the life of the structure. However, given the heterogeneity of the rock materials and the difficulty of their characterization under this aspect, an unequivocal analysis is hardly achievable. Then, the discussion initially develops through a general historical review of the concept of fatigue, with a synthetic collection of case histories. The laboratory tests on rock samples are then examined and the most important results obtained are discussed. Finally, a comparison between different types of tests is proposed. The experimental data are expressed through the Wӧhler diagram. The goal is to fill the lack of design codes or standards in the field of cyclic stresses applied to rock materials, the understanding of its effect being of great interest in order to apply suitable parameters in the design phase.

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.

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.

Coronavirus disease 2019 (COVID-19), the emissary behind the worst global pandemic of the 21st century, is primarily a respiratory disease-causing virus called SARS-CoV-2 which is responsible for millions of new cases (incidence) and deaths (mortalities), worldwide. Many factors have played a role in the differential morbidity and mortality experienced by nations and ethnicities against SARS-CoV-2, such as the quality of primary medical health facilities or enabling economies. Nevertheless, the most important variable, i.e., the subsequent ability of individuals to be immunologically sensitive or resistant to the infection, was not properly discussed before. Therefore, an astounding issue arose when some developed countries experienced higher morbidity and mortality, compared with their relatively underdeveloped counterparts, despite having excellent medical health facilities. Hence this investigative review attempts to analyze the issue from an angle of previously undiscussed genetic, epigenetic, and molecular immune resistance mechanisms in correlation with the pathophysiology of SARS-CoV-2 and varied ethnicity-based immunological responses against it. The biological factors discussed here include the overall landscape of human microbiota, endogenous retroviral genes spliced into the human genome, copy number variation, and how they could modulate the innate and adaptive immune systems, which put a particular ethnic genetic architecture at a higher risk of SARS-CoV-2 infection than others. Considering an array of these factors in their entirety may help explain the geographic disparity of disease incidence, severity, and subsequent mortality associated with the disease while at the same time encouraging scientists to design new experimental approaches to investigation.

A ~3-kb deletion-type DNA copy-number variation (CNV, esv3587290) located at intron 7 of the VANGL1 gene (1p13.1, MIM*610132) has been proposed as a genetic factor for developing lupus nephritis (LN) in adult systemic lupus erythematosus (SLE) patients across European-descent populations, but its replication in other ethnicities has been inconsistent and its association with LN in childhood-onset SLE (cSLE) remains unknown. Here, we performed an exploratory association study in a sample of 66 unrelated cSLE Mexican patients (11 males, 55 females; ages 7.8 to 18.6 years). Two stratified groups were compared: cSLE patients with (N=37) or without (N=29) LN, as diagnosed by renal biopsy (N=15), proteinuria (N=33), urinary protein:creatinine ratio >0.2 (N=34), and erythrocyturia and/or granular casts in urinary sediment (N=16). For esv3587290 CNV genotyping, we performed an end-point PCR assay with breakpoint confirmation by Sanger sequencing. We also determined the allelic frequencies of the esv3587290 CNV in 181 deidentified ethnically-matched individuals (reference group). The obtained genotypes were tested for Hardy-Weinberg equilibrium (HWE) by 2 test. Associations between LN and esv3587290 CNV were tested by calculating the Odds Ratio (OR) and using Pearson's 2 tests with a 95% confidence interval and p≤0.05. Contrary to the results described in European-descent populations, the esv3587290 CNV showed a significant protective effect against LN development (OR 0.14, 95% CI 0.066-0.31, p≤0.05), whereas the wild-type homozygous VANGL1 genotype showed a risk trend for LN development (OR 2.15, 95% CI 0.7711-6.18, p≤0.05). Finally, we characterized the precise breakpoint of the esv3587290 CNV as NG_016548.1(NM_138959.3):c.1314+1339_1315-897del (https://databases.lovd.nl/shared/variants/0000918418#00025811) in our population. This report supports the notion that a broad genetic heterogeneity underlies the susceptibility for developing LN.

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.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

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.

In this article, some kinds of triple belongs to metric dimensions are defined. Some classes of graphs in the matter of these kinds, are studied and the relation amid these kinds are considered. The kind of having equivalency amid these notions and some classes of graphs, is obtained. The kind of locating some vertices by some vertices when the number of locating vertices is increased, has the key role to analyze the classes of graphs, general graphs, and graph's parameters.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

A framework of similarity laws, termed oriented-density-length-velocity (ODLV) framework, is suggested for the geometric distorted structures subjected to impact loading. The distinct feature of this framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for physical quantity are explicitly expressed by the characteristic lengths of three spatial directions, which overcome the inherent defects that traditional scalar dimensional analysis could not express the effects of structural geometric characteristics and spatial directions for similarity. The non-scalabilities of geometrical distortion as well as other distortions such as different materials and gravity could be compensated by the reasonable correction for the impact velocity, the geometrical thickness and the density, when the proposed dimensionless number of equivalent stress is used between scaled model and prototype. Three analytical models of beam, plate and shell subjected to impact mass or impulsive velocity are verified by equation analysis. And a numerical model of circular plate subjected to dynamic pressure pulse is verified in more detail, form the view of point of space deformation, deformation history and the components of displacement, strain and stress. The results show that the proposed dimensionless numbers have attractively perfect ability to express the dimensionless response equations of displacement, angle, time, strain and strain rate. When the proposed dimensionless numbers are used to regularize impact models, the structural responses of the geometrically distorted scaled models can behave the completely identical behaviors with those of the prototype on space and time —not only for the direction-independent equivalent stress, strain and strain rate but also for the direction-dependent displacement, stress and strain components.

Here, we describe the bicomplex (p,q)- Fibonacci numbers and the bicomplex (p,q)- Fibonacci quaternions that are based on these numbers and give some of their equations, including the Binet formula, generating function, Catalan, Cassini, d’Ocagne’s identities, and some summation formulas for both of them. Finally, we create a matrix for bicomplex (p,q)- Fibonacci quaternions, and we obtain a determinant of a special matrix that gives the terms of that quaternion.

Aspergillus fumigatus is a ubiquitous, critical priority human fungal pathogen. Despite its clinical importance, there is limited knowledge regarding the variations of the genome within mitochondria, the powerhouse organelle within eukaryotic cells. In this study, we leveraged publicly available raw, whole genome sequence data from 1939 isolates to investigate the variations in the mitochondrial genomes of A. fumigatus. These isolates were isolated from 22 countries on six continents, as well as from outer space and from within the International Space Station. In total, our analysis revealed 39 mitochondrial single nucleotide polymorphisms (mtSNPs) within this global sample and together, these 39 mtSNPs grouped the 1939 isolates into 79 mitochondrial multilocus genotypes (MLGs). Among the 79 MLGs, 39 were each distributed in at least two countries and 30 were each shared by at least two continents. The two most frequent MLGs were also broadly distributed: MLG11 represented 420 isolates from 11 countries and four continents and while MLG79 represented 418 isolates from 18 countries and five continents, consistent with long-distance dispersals of mitogenomes. Our population genetic analyses of the mtSNPs revealed limited differentiation among continental populations but highly variable genetic differences among national populations, largely due to localized clonal expansions of different MLGs. Phylogenetic analysis and Discriminant Analysis of Principal Components of mtSNPs suggested the presence of at least three mitogenome clusters. Linkage disequilibrium, Index of Association, and phylogenetic incompatibility analyses collectively suggested evidence for mitogenome recombination in natural populations of A. fumigatus. In addition, sequence read depth analyses revealed an average ratio of ~20 mitogenomes per nuclear genome in this global population but the ratios varied among strains within and between certain geographic populations. Together, our results suggest evidence for organelle dynamics, genetic differentiation, recombination, and both widespread and localized clonal expansion of the mitogenomes in the global A. fumigatus population.

Mathematical modeling is crucial in investigating the pandemic of the ongoing coronavirus disease (COVID-19). The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower repertory track. During this viral infection, infected cells can initiate innate and adaptive immune responses to viral infection. Immune response in COVID -19 infection can lead to longer recovery time and more severe secondary complications. We formulate a target cell limited mathematical model by incorporating a saturation term for SARS-CoV-2 infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points has been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for $R_0<1$, and endemic equilibrium exists and is globally stable for $R_0>1$. Impulsive application of drug dosing has been applied for the treatment of covid-19 patients. Also, the dynamics of the impulsive system are discussed when a patient takes drug holidays. The numerical simulations are performed in support of our analytical findings and for the qualitative analysis of the system's dynamics with and without impulse drug dosing.

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.

We present a mixing length based algebraic turbulence model calibrated to pipe flow; the main purpose of the model is to capture the increasing turbulence production-to-dissipation ratio observed in connection with the high Reynolds number transition region. The model includes the mixing length description by Gersten and Herwig which takes the observed variation of the von Kármán number with Reynolds number into account. Pipe wall roughness effects are included in the model. Results are presented for area-averaged (integral) quantities which can be used both as a self-contained model and as initial inlet boundary conditions for computational fluid dynamics simulations.

In the paper, using two inversion theorems for the Stirling numbers and binomial coecients, employing properties of the Bell polynomials of the second kind, and utilizing a higher order derivative formula for the ratio of two dierentiable functions, the authors present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.

Successive-addition-of-digits-of-a-number(SADN) refers to the process of adding up the digits of an integer number until a single digit is obtained. Concept of SADN has been occasionally identified but seldom employed in extensive mathematical applications. This paper discusses SADN and its properties in terms of addition, subtraction and multiplication. Further, the paper applies the multiplication-property of SADN to understand the distribution of prime numbers. For this purpose the paper introduces three series of numbers -S1, S3 and S5 series- into which all odd numbers can be placed, depending on their SADN and the rationale of such classification. Extending the analysis the paper explains how composite numbers of the S1 and S5 series can be derived. Based on this discussion it concludes that even as the concept of SADN is rather simple in its formulation and appears as an obvious truism but a profound analysis of the properties of SADN in terms of fundamental mathematical functions reveals that SADN holds a noteworthy position in number theory and may have significant implications for unfolding complex mathematical questions like understanding the distribution of prime numbers and Goldbach-problem.

{\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.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

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.

This paper provides a new discovery that adds to the contemporary theory of modelling of non-stationary queues, by capturing analytically the behavior of the root parameter, for the G1/M/1 PSFFA model of non-stationary Ek/M/1 queue. Additionally, it has been also revealed that the resulting root parameter reduces to the PSFFA model of non-stationary queue. Potential applications of PSFFA to Computer engineering are provided. Some challenging open problems are addressed combined with closing remarks and future research directions.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

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.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

Based on three assumptions of our 4G model of final unification, we have developed simple logics for estimating the unified atomic mass unit, atomic electrochemical equivalents, Faraday constant and Avogadro number. We appeal the science community to review the following points. 1) Unified atomic mass or energy unit can be considered as ‘average rest energy of nucleons minus average binding energy per nucleon of all atomic nuclides plus electron rest energy’. 2) Electrochemical equivalent of any atomic ion is nothing but the ratio of its mass to its charge. 3) Faraday charge is nothing but the ratio of elementary charge to unified atomic mass unit. 4) Faraday mass can be considered as the inverse of Faraday charge. 5) Avogadro number is nothing but the inverse of unified atomic mass unit. 6) Number of atoms per kg can be called as Kg-mole and number of atoms per gram can be called as gram-mole. Following our 4G model, starting form A=5 to 340, for isobars, ‘average binding energy per nucleon’ having maximum binding energy can be estimated with a simple relation of the form, BE/A=A^-1[1-(0.5+0.000935A²)-A^1/3]10.1MeV. It needs a review and fine tuning.

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.

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 the literature, the question of the amount of data necessary and sufficient to validate different models of the occurrence of risk of adverse events for patients or the classification of the presence or absence of pathological features has been repeatedly raised. In the presented study, we propose a new approach to determine the necessary and enough studies for validation of medical software based on artificial intelligence technology, whose main task is to classify medical X-rays according to the presence of normality and pathology. It is shown that for several studies in a dataset, when AUC ROC has maximum heterogeneity, it varies depending on the balance of "norm"/"pathology" classes. Thus, for a balance of "normal"/"abnormality", where 90% is "normal" and 10% is "abnormality", maximum heterogeneity is achieved for 190 studies, for a balance of 80% ("normal")/20% ("abnormality") for 80 studies, for a balance of 70% ("norm")/30% ("abnormality") - 120 trials, for a balance of 60% ("norm")/40% ("abnormality") the maximum heterogeneity is reached at 110 trials, and for a balance of 50% ("norm")/50% ("abnormality") - at 70 trials. The obtained data are in good agreement with the previous results. They allow us to determine a sufficient (necessary) number of studies in the dataset to perform an unbiased assessment of AUC ROC.

We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The strength of our method is that no additional information is required about the given original identity. The method readily extends to a generalized Fibonacci sequence.

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained a large number of results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry.

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.

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.

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.

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: $u^+=\frac{1}{\kappa}\ln(2\kappa {y^+} +\sqrt{1+4\kappa^2{y^+} ^2})-\frac{2{y^+} }{1+\sqrt{1+4\kappa^2{y^+} ^2}}$.

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.

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 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.

In my paper, a divisibility rule named the Queen function is de- scribed, which has been generalized for every integer and encompasses all pre- viously established divisibility rules. Subsequently, the paper discusses other areas where this function is instrumental. These include simplifying ratios, generating prime numbers, and more. Towards the end of the paper, a set of hypotheses is also presented. Among these, the most significant is the novel approach involving the application of the Queen function for prime number generation.

Cardiomyopathies are major causes of heart failure. Chagas disease (CD) is caused by the parasite Trypanosoma cruzi, and it is endemic in Central, South America. Thirty percent of the cases evolve into chronic cardiomyopathy (CCC) with worse prognosis as compared with other cardiomyopathies. In vivo bioenergetic analysis and ex vivo proteomic analysis of myocardial tissues highlighted worse mitochondrial dysfunction in CCC, and previous studies identified nuclear-encoded mitochondrial gene variants segregating with CCC. Here, we assessed the role of the mitochondrial genome through mtDNA copy number variations and mtDNA haplotyping and sequencing from heart or blood tissues of severe, moderate CCC and asymptomatic/indeterminate Chagas disease as well as healthy controls as an attempt to help decipher mitochondrial-intrinsic genetic involvement in Chagas disease development. We have found that mtDNA copy number was significantly lower in CCC than in heart tissue from healthy individuals, while blood mtDNA content was similar among asymptomatic Chagas disease, moderate and severe CCC patients. MtDNA haplogrouping study has indicated that African haplogroups were over represented in the Chagas subject groups in comparison with Brazilian healthy individuals. The European lineage is associated to protection against cardiomyopathy and the macro haplogroup H is associated with increased risk towards CCC. By mitochondria DNA sequencing, 84 mtDNA-encoded protein sequence pathogenic variants were associated with CCC. Among them, two variants were associated to left ventricular non-compaction and two to hypertrophic cardiomyopathy. The finding that mitochondrial protein-coding SNPs and mitochondrial haplogroups associate with risk of evolving to CCC is consistent with a key role of mitochondrial DNA in the development of Chronic Chagas disease Cardiomyopathy.

In the paper it is demonstrated that a valid path to a contradiction in complex number theory exists. In the path use is made of Euler’s identity and simple trigonometry. Each step can be easily verified.

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

Low-Level Virtual Machine (LLVM) compiler infrastructure is a useful tool for building Just-in-time (JIT) compilers, besides its reliable front-end represented by clang compiler and its elaborated middle-end containing different optimizations that improve the runtime performance. This paper addresses specifically the part of building a JIT compiler using LLVM with the scope of getting the hardware architecture details of the underlying machine such as the number of cores and the number of logical cores per processing unit and providing them to NUMA-BTLP static thread classification algorithm and to NUMA-BTDM static thread mapping algorithm. Afterwards, the hardware-aware algorithms are run by the JIT compiler within an optimization pass. JIT compiler in this paper is designed to run on a parallel C/C++ application (which creates threads using Pthreads), before the first time the application is executed on a machine. To do that, the JIT compiler takes the native code of the application, gets the corresponding LLVM IR (Intermediate Representation) for the native code and executes the hardware-aware thread classification and the thread mapping algorithms on the IR. The NUMA-Balanced Task and Loop Parallelism (NUMA-BTLP) and NUMA-Balanced Thread and Data Mapping (NUMA-BTDM) are expected to optimize the energy consumption up to 15%, on NUMA systems.

This work presents a design and model of the thermo-hydrodynamic behavior applying CFD for pin-fin heat sink with square shape (rectangular fin profile), through a novel pin arrangement that improves heat removal in the system. The novelty consist in the insertion of a deflector row that will help to direct the flow, so it hits the rectangular cross-sectional fins the presents in the system. The heat sink model is placed in channel designed in which air flows as suitable medium, and its overall performance is investigated. In addition, a constant heat flux is applied to the bottom wall of the heat sink model, equal values and amounts that​ correspond to the heat fluxes generated by current electronic equipment and devices. The numerical results of the global thermal resistance, the pressure drop and the Nusselt number are reported. The results allow determining best arrangement or geometry configuration, location and functionality of the fin-deflectors were collocated for evaluate thermal-hydraulic efficiency of system.

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.

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.

Physics-informed neural networks are a promising method to yield surrogate models of flow fields. We present a metamodeling technique for variable geometries based on physics-informed neural networks. The method was applied to the DU99W350 airfoil at a Reynolds number of 1×10⁵. The model predicted the Reynolds-averaged velocity and pressure field around the airfoil for arbitrary angles of attack between 10.0° and 17.5°. The model was trained with data from CFD simulations for a limited set of angles of attack. Additionally, satisfaction of the a priori known boundary conditions as well as the Reynolds-averaged Navier-Stokes equations were trained. A sensitivity analysis concerning the Reynolds number, the amount and distribution of training data, and the turbulence model was conducted showing the superiority of the pseudo-Reynolds stress method and the demand of labeled training data in the domain. The trained network was capable of predicting the developing flow separation on the suction surface and exhibited excellent agreement with CFD results even in the proximity to the wall for interpolations as well as extrapolations from the labeled data set.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

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.

This study aims to examine the non-volatile Particle Number (PN) emissions of a retrofitted Heavy-Duty Spark-Ignition (HD-SI) engine powered by liquefied petroleum gas (LPG) under both steady-state and transient conditions. The engine was tested under seven steady-state operating points to investigate the PN behavior and Particle Size Distribution (PSD) upstream and down-stream of the Three-Way Catalyst (TWC). This analysis intends to assess the impact of including particles with diameters ranging from 10 nm to 23 nm in the total particle count, a consideration for future regulations. The study employed the World Harmonized Transient Cycle (WHTC) for transient conditions to encompass the same engine working region used in the steady-state analysis. A Dekati FPS-4000 diluted the exhaust sample to measure the PSD and PN for particle diameters between 5.6 nm and 560 nm using the TSI-Engine Exhaust Particle Sizer (EEPS) 3090. Findings indicate that PN levels tend to increase downstream of the TWC under steady-state conditions in operating points with low exhaust gas temperatures and flows (equal to or less than 500 °C and 120 kg/h). Furthermore, the inclusion of particles with diameters between 10 nm and 23 nm leads to an increase in PN emissions by 17.70% to 40.84% under steady conditions and by an average of 40.06% under transient conditions, compared to measurements that only consider particles larger than 23 nm. Notably, in transient conditions, most PN emissions occur during the final 600 seconds of the cycle, linked to the most intense phase of the WHTC.

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.

A novel plasma source of pulsed electrolyte cathode atmospheric pressure discharge (pulsed-ECAD) driven by an alternating current (AC) power supply coupled with a high voltage diode was generated, and the discharge was generated in the open-to-air atmosphere between a metal electrode and a small-sized flowing liquid cathode. The spatial distribution of plasma temperatures (excitation, vibrational and rotational) of the pulsed-ECAD were investigated. The electron excitation temperature of H T_exc(H), vibrational temperature of N₂ T_vib(N₂), and rotational temperature of OH T_rot(OH) were measured as 4900±36-6800±108 K, 4600±86-5800±100 K and 1050±20-1140±10 K, respectively. Meanwhile, the temperature characteristics of dc solution cathode glow discharge (dc-SCGD) were also studied for comparison with pulsed-ECAD. The effects of operating parameters, including discharge voltage and discharge frequency, on the plasma temperatures were investigated. The electron number density determined in the discharge system and dc-SCGD were within the range (3.8–18.9) ×10¹⁴ cm^-3 and 2.6×10¹⁴-17.2×10¹⁴ cm^-3, respectively.

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.

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) .

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.

We review and assess the classic SIR and SEIR epidemiological models regarding possible applications to the COVID-19 pandemic. In spite of numerous more complicated models, we show how the qualitative features of the solution to the SIR and SEIR models continue to provide valuable public health insights in some scenarios. Using estimated COVID-19 data as of this date, the SEIR model shows that if it were possible to reduce R₀ from 2.5 to 1.25 through social distancing and other measures, the maximum fraction of the population that would become infected at any particular time would drop from 17% to 4%, provided that all of the model assumptions are satisfied. Finally, we compare the classic SIR model with a recent stochastic model with favorable results. Since this comparison underscores the importance of underlying connectivity assumptions, we conclude with Monte-Carlo simulations with specific connectivity that reproduce the classical SIR model with standard incidence.

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 Harmonic Graphs Conjecture states that there exists an asymptotic relation involving the Harmonic Index and the natural logarithm as the order of the graph increases. This conjecture, grounded in the novel context of Prime Graphs, draws upon the Prime Number Theorem and the sum of divisors function to unveil a compelling asymptotic connection. By carefully expanding the definitions of the harmonic index and the sum of divisors function, and leveraging the prime number theorem's approximations, we establish a formula that captures this intricate relationship. This work is an effort to contribute to the advancement of graph theory, introducing a fresh lens through which graph connectivity can be explored. The synthesis of prime numbers and graph properties not only deepens our understanding of structural complexity but also paves the way for innovative research directions.

The efficient generation of high-quality random numbers is essential in the operation of cryptographic modules. The quality of a random number generator is evaluated by the min-entropy of its entropy source. Typical method used to achieve high min-entropy of the output sequence is an entropy accumulation based on a hash function. This is grounded in the famous Leftover Hash Lemma which guarantees a lower bound on the min-entropy of the output sequence. However, the hash function based entropy accumulation has slow speed in general. For a practical perspective we need a new efficient entropy accumulation with the theoretical background for the min-entropy of the output sequence. In this work, we obtain the theoretical bound for the min-entropy of the output random sequence through the very efficient entropy accumulation using only bitwise XOR operations, where the input sequences from the entropy source are independent. Moreover we examine our theoretical results by applying to the quantum random number generator that uses dark noise arising from image sensor pixels as its entropy source.

Nowadays the practice of developing algorithms to maintain the confidentiality of data shows that there is a lack of some features, such as velocity, predictability, etc. Generating pseudorandom numbers is one such problem that lies in the basement of many algorithms, even in hardware microprograms. An unreliable generator can cause cyberattacks on it, despite the security in the upper layers. At the same time, the algorithm should be fast enough to provide uninterrupted circuit work for the entire system. The paper presents a new algorithm generating pseudorandom numbers on cellular automata, which is not only fast and easy-repeating, but unpredictable enough and can be used in cryptographic systems. Using the NIST statistical test suite for random and pseudorandom number generators (PRNG), it is shown that the presented algorithm is more than three times superior to the state-of-the-art methods and algorithms in terms of ? − ?????. A high level of the presented algorithm’s parallelization allows for implementation it effectively on calculators with parallel structure. CPU-based architecture, FPGA-based architecture, CUDA- based architecture of PRNG and different PRNG implementations are presented to confirm high performance of the proposed solution.

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

We derive the thermal noise spectrum of the Fourier transform of the electric field operator of a given wave vector starting from the quantum-statistical definitions and relate it to the complex frequency and wave vector dependent complex conductivity in a homogeneous, isotropic system of electromagnetic interacting electrons. We analyze separately the longitudinal and transverse case with their peculiarities. The Nyquist formula for vanishing frequency and wave vector, as well as its modification for non-vanishing frequencies and wave vectors follow immediately. Furthermore we discuss also the noise of the photon occupation numbers. It is important to stress that no additional assumptions at all were used in this straightforward proof.

Micro-technology has played a substantial role in bioscience, biomedical and biotechnological research due to its core advantages in modern science and engineering. It has created unique development in various sectors of bio-research and upsurges the efficacy of research at the molecular level in recent years. Microfluidic technology makes it possible to manipulate sample volumes at the micro- and nano-level (called nanofluidics) with terrific control outside in vivo cellular microenvironment, enabling the reduction of discrepancies between in vivo and in vitro environments as well as reducing reaction time and cost. In this review, we discuss various effective integrations of microfluidic technologies into biotechnology and its paradigmatic significance in bio-research, supporting mechanical and chemical in vitro cellular micro-environment. Specific innovations relating to the application of microfluidics to advance microbial life, solitary and co-cultures along with a multiple-type cell culturing, cellular communications, cellular interactions and population dynamics are discussed.

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.

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.

This study describes the seasonal course of denitrifying and nitrate reducing bacteria in a dimictic mesotrophic lake (Lake Scharmützelsee, Brandenburg, Germany) within a three-year period from 2011 to 2013. The bacterial cell numbers were quantified by fluorescence microscopy, most probable number (MPN) and PCR dependent quantification of the chromosomal 16S rDNA and of the nirS and nirK gene copy number. The highest seasonal differences (up to three orders of magnitudes) has been measured by MPN in the epilimnion. This variation was not reflected by PCR dependent approaches or direct microscopical enumeration. At adverse conditions (low temperature and/or low nitrate concentrations), the differences between MPN and gene copy numbers increased up to five orders of magnitudes and decreased to one magnitude at favorable environmental conditions. These results can be explained best by an increasing ratio of viable but not cultivable (VBNC) cells or dead cells at impairing conditions. In the hypolimnion, the courses of MPN and nir gene copy numbers were similar. This can be explained by higher feeding pressure and therefore smaller amounts of dormant cells. In the pelagial in general, the total cell numbers enumerated by either microscopical or molecular approaches were similar. In the sediment, more than 99 % of the DNA was obviously not related to viable bacteria but was rather “dead DNA” in dead cells or adsorbed to particle surfaces.

Unsupervised physics-informed deep learning can be used to solve computational physics problems by training neural networks to satisfy the underlying equations and boundary conditions without labeled data. Parameters such as network architecture and training method determine the training success. However, the best choice is unknown a priori as it is case specific. Here, we investigated network shapes, sizes, and types for unsupervised physics-informed deep learning of the two-dimensional Reynolds-averaged flow around cylinders. We trained mixed-variable networks and compared them to traditional models. Several network architectures with different shape factors and sizes were evaluated. The models were trained to solve the Reynolds-averaged Navier-Stokes equations incorporating Prandtl's mixing length turbulence model. No training data were deployed to train the models. The superiority of the mixed-variable approach was confirmed for the investigated high Reynolds number flow. The mixed-variable models were sensitive to the network shape. For the two cylinders, differently deep networks showed superior performance. The best fitting models were able to capture important flow phenomena such as stagnation regions, boundary layers, flow separation, and recirculation. We also encountered difficulties when predicting high Reynolds number flows without training data