Maximum likelihood estimation (MLE) is a popular method for parameter estimation in both applied probability and statistics but MLE cannot solve the problem of incomplete data or hidden data because it is impossible to maximize likelihood function from hidden data. Expectation maximum (EM) algorithm is a powerful mathematical tool for solving this problem if there is a relationship between hidden data and observed data. Such hinting relationship is specified by a mapping from hidden data to observed data or by a joint probability between hidden data and observed data. In other words, the relationship helps us know hidden data by surveying observed data. The essential ideology of EM is to maximize the expectation of likelihood function over observed data based on the hinting relationship instead of maximizing directly the likelihood function of hidden data. Pioneers in EM algorithm proved its convergence. As a result, EM algorithm produces parameter estimators as well as MLE does. This tutorial aims to provide explanations of EM algorithm in order to help researchers comprehend it. Moreover some improvements of EM algorithm are also proposed in the tutorial such as combination of EM and third-order convergence Newton-Raphson process, combination of EM and gradient descent method, and combination of EM and particle swarm optimization (PSO) algorithm.

Fungal infections caused by Candida spp. are responsible for high hospital morbidity and mortality rates. Therefore, there is a continuous search for new antifungal medicines, particularly ones with anti-Candida activity. This review analyzed articles published between 2002 and 2023 considering the anti-Candida activity of chemical compounds identified or isolated in plants of the Anacardiaceae family. In addition, the in-silico prediction of the isolated compounds described was performed. The analysis of 35 studies showed that extracts, essential oils, and compounds from the anti-Candida activity were frequently determined in vitro using the minimum inhibitory concentration (MIC). The most commonly tested species were Candida albicans, C. tropicalis, C. parapsilosis, C. glabrata, C. krusei, and C. guilliermondii, respectively. Essential oils were the most used form (37% of the studies). The isolated compounds with antifungal effects include cardanol, estragole, trans-anethole, β-caryophyllene, myrcene, catechin-3-o-rhamnoside, β-sitosterol-3-O-glucoside, 24Z-isomasticadienolic acid, oleanolic acid, and oleanolic aldehyde. The in-silico evaluation of those isolated compounds revealed the compounds' drug-likeness and possible antifungal activity. However, some of them showed high toxicity. In conclusion, compounds from the Anacardiaceae family show promise for developing new therapeutic antifungal drugs, especially in combination with conventional antifungals.

The current letter complements my info-geometric discoveries, especially those provided from two papers of mine. Fundamentally, the statistical relativization of the Generalized Brownian Motion Manifold. Following this innovative and unprecedented track of research will open a plethora of numerous info-geometric investigations to many unexplored related phenomena in the hope to uncover more new interpretations for the Generalized Brownian Motion Manifold from an info-geometric perspective.

A difficult open problem that has never been fully resolved in the literature to date is the behaviour of the (TDCDP) third approximation. As a giant step towards modern control theory, this cutting-edge paper will advance control theory and other relevant inter-disciplinary subjects. Because control theory is important in industry and engineering, this study will be especially beneficial to anyone working in these disciplines who wish to understand more about recent advances in control theory settings. In contrast, the wealth of applications of Fokker Planck Kolmogorov (FPK) equations numerous disciplines As a result, the study instantly gains more taste and credibility. At the end of the paper, there are several challenging open problems, some concluding remarks, and recommendations for further investigation.

Conobea scoparioides (Plantaginaceae) is an herbaceous plant known as "pataqueira" that grows wild in seasonally wet areas of the Amazon region. It is used for aromatic baths and anti-protozoan remedies by the Brazilian Amazon native people. The main volatile compounds identified in the essential oil of "Pataqueira" were the phenolic monoterpenes thymol and thymol methyl ether and their precursors, the monoterpene hydrocarbons α-phellandrene and p-cymene. A hydrotalcite synthesized from blast-furnace slag exhibited a 3:2 (Mg/Al) molar ratio, and this layered double hydroxide (LDH) was evaluated as a catalyst in converting the main monoterpenes of the "Pataqueira" oil. This action significantly increased thymol content, from 41% to 95%, associated with the percentual reduction of other main components, such as thymol methyl ether, α-phellandrene, and p-cymene. The LDH reaction showed a strong tendency towards producing hydroxylated derivatives, and its behavior was similar to the hypothetical plant biosynthetic pathway, which leads to the production of the monoterpenes of "Pataqueira" oil. Thymol and its derivatives are potent antiseptics applied in pharmaceutical and hygienic products as antibacterial, antifungal, and antioxidant properties, among others. The present work reports a natural source with a high thymol content in aromatic plants from the Amazon, with evident economic value.

Kininogens are multidomain glycoproteins found in the blood of most vertebrates. They are important in the blood coagulation cascade pathways - in intrinsic pathway activation leading to thrombin generation partially independently from tissue factor dependent extrinsic pathway, connecting blood coagulation with the kallikrein-kinin system. Nothing is known about the shape on atomic level therefore the endeavor to obtain the good-quality spatial structure of kininogens is important for a better understanding of their role in disease and treatment. Application of cryo-EM is important for solving the spatial structure of kininogens, drawing new frontiers in understanding the function and opening new pathways for drug development.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

Nowadays, animal breeders look for effective innovations to care animal health. Use of probiotics, postbiotics, parabiotics and the other beneficial natural substances are dominated. Mundticin-like substance EM 41/3 is thermo-stable bacteriocin (postbiotic) with a broad antimicrobial spectrum. In this study its effect in broiler rabbits was assessed. Rabbits represent food-derived animal and they are also suitable animal model. The parameters tested were analyzed by validated methods. Administration of MLS EM 41/3 produced by non-autochthonous strain Enterococcus mundtii EM 41/3 lead to significant increase of parameter immunity-phagocytic activity, while it did not influence microbiota composition. It also did not influence blood biochemistry and no oxidative stress was noted. Moreover, higher growth parameters were noted and also stimulated hydrolytic activity. Finally, no negative influence on rabbit meat quality was noted. Postbiotic MLS EM 41/3 administration in feeding strategy seems to be contributing fact for rabbit health status maintaining.

Information geometry (IG) is a fascinating combination of differential geometry and statistics where a Riemannian manifold's structure is applied to a statistical model. It may find numerous fascinating uses in the domains of theoretical neurology, machine learning, complexity, and (quantum) information theory, among others. (IG) aims to provide a differential-geometric perspective on statistical geodesic models' structure. In this case, IG, KD, and J-divergence (JD) are used to define the manifold of the Generalised Brownian Motion (GBM). Consequently, the geodesic equations (GEs) are devised, and GB information matrix exponential (IME) is presented. Moreover, for first time ever, the necessary and sufficient mathematical requirement that characterizes the developability of Generalized Brownian Motion(GBM) manifold is devised. Also, a novel sufficient and necessary conditions which characterizes the regions where the surface describing GBM is minimal is determined. Also, it is shown that GBM has a non-zero 0-Gaussian and Ricci curvatures. Consequently, this advances the establishment of a unified GBM- Relativistic Info-Geometric based analysis.

Plant cells' ability to withstand abiotic stress is strongly linked to modifications in their mechanical characteristics. Nevertheless, the lack of a workable method for consistently tracking plant cell mechanical properties severely restricts our comprehension of the mechanical alterations in plant cells under stress. With Polyethylene Glycol (PEG6000), we created a drought-like environment, and we used the Double Resonator Piezoelectric Cytometry (DRPC) method to dynamically and non-invasively track changes in the stress (ΔS) created and viscoelasticity (storage modulus G' and loss modulus G") of protoplasts and suspension cells of rice during drought stress. The findings demonstrate that, rice suspension cells and protoplasts react mechanically differently to 5%–15% PEG6000 stress, implying distinct resistance mechanisms. However, neither of them can withstand 25% PEG6000 stress, they respond mechanically similarly to 25% PEG6000 stress. The results of DRPC are further corroborated by the morphological alterations of rice cells and protoplasts observed under an optical microscope. To sum up, the DRPC technique functions as a precise cellular mechanical sensor and offers novel research tools for the evaluation of plant cell adversity and differentiating between the mechanical reactions of cells and protoplasts under abiotic stress.

Fumaric acid is a chemical building block with many applications, namely in the polymer industry. The fermentative production of fumaric acid from renewable feedstock is a promising and sustainable alternative to petroleum-based chemical synthesis. The use of existing industrial side-streams as raw-material within biorefineries potentially enable production costs competitive against current chemical processes, while preventing the use of refined sugars competing with food and feed uses and avoiding purposely grow crops requiring large areas of arable land. However, most industrial side streams contain a diversity of molecules that will add complexity to the purification of fumaric acid from the fermentation broth. A process for the recovery and purification of fumaric acid from complex fermentation medium containing spent sulfite liquor (SSL) as carbon source was developed and is herein described. A simple two-stage precipitation procedure involving separation unit operations, pH and temperature manipulation and polishing through the removal of contaminants with activated carbon allowed the recovery of fumaric acid with 68.3% recovery yield with specifications meeting the requirements of the polymer industry. Further, process integration opportunities were implemented that allowed minimizing the generation of waste streams containing fumaric acid which enabled increasing the yield to 81.4% while keeping the product specifications.

6G is already being planned and will employ much higher frequencies, leading to a revolutionary era in communication between people as well as things. It is well known that weather, especially rain, can cause increased attenuation of signal transmission for higher frequencies. The standard methods for evaluating the effect of rain on symbol error rate are based on long-term averaging. These methods are an inaccurate, which results with an inefficient system design. This is critical regarding bandwidth scarcity and energy consumption and requires a more significant margin of effort to cope with the imprecision. Recently we have developed a new and more precise method for calculating communication system performance in case of rain, using the probability density function of rain rate. For high rain rate (above 10mm/hr), for a typical set of parameters, our method shows the symbol error rate in this range to be higher by orders of magnitude than that found by ITU standard methods. Our model also indicates that sensing and measuring the rain rate probability is important in order to provide the required bit error rate to the users. To the best knowledge of the authors, this novel analysis is unique. It can constitute a more effi-cient performance metric for the new era of 6G communication and prevent disruption due to incorrect system design. Keywords: atmospheric propagation, communication system performance, attenuation, com-munication

In this paper, we propose a methodology for analyzing the near-field coupling between two surface mount device (SMD) inductors using a 3-dimensional electromagnetic (3D-EM) model. To develop the 3D-EM model, we first extract the effective permeability of core magnetic material in the SMD using the loss tangent in the equivalent circuit model. Then the effective permeability is used in the magnetic material for the 3D-EM modeling of SMD inductor. The validity of the proposed 3D-EM model is confirmed by comparing the impedance and S-parameters obtained from both measured and EM-simulated values for the two near-field coupled SMDs. Finally, the near-field coupling effects between the two adjacent SMD inductors are visualized in terms of magnetic coupling path visualization (CPV) using the proposed 3D-EM model, which demonstrates its usefulness for near-field coupling analysis.

Soil moisture can be an important indicator of climate change in humid and semi-arid areas. This indicator can more efficiently propose different public policies related to climate change than just using precipitation and temperature data. Given the above, the objective of this study is to evaluate changes in soil moisture in the state of Pernambuco during the period 1961-2021, using the System of Hydrological Response Units for Pernambuco. In this study, two river basins in the state of Pernambuco that represent the different climatic conditions of the state will be chosen. The results show that in the coastal region, there is a tendency towards more saturated soils, and in the semi-arid region, there is a tendency towards drier soils. With these results, it is possible to conclude that public policy decisions for the economy, environment, and society must consider this vital water balance variable.

Modelling diameter distribution is an integral part of forest management. It requires the use of a suitable probability density function or cumulative distribution function with the appropriate fitting method. In this study, we compared the suitability of eight probability density functions fitted by derivative and optimization methods used for diameter distribution estimation of forest stands. The derivation and optimization were used on A Charlier, beta, generalized beta, gamma, Gumbel, Johnson’s SB, and Weibull (2 and 3-parameter). We used data from 167 permanent sample plots from Atlantic forest (Quercus robur) and 59 temporary sample plots from tropical forests (Tectona grandis). The quality of the fits was evaluated with different indices such as Kolmogorov–Smirnov, Cramer-von Mises, mean absolute error, bias and mean squared error. The results showed Johnson’s SB function was more suitable for describing the diameter distribution of the stands. Johnson’s SB, 3-parameter Weibull and generalized beta had consistent performance regardless of the fitting methods. The quality of fits produced by gamma, Gumbel and 2-parameter Weibull was poor.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

In this paper, we study the semilinear pseudo-parabolic equations $\displaystyle u_{t} - \triangle_{\mathbb{B}}u - \triangle_{\mathbb{B}}u_{t} = \left|u\right|^{p-1}u$ on a manifold with conical singularity, where $\triangle _{\mathbb{B}}$ is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary $x_{1} = 0$. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence and nonexistence of global weak solution: for the low initial energy $J(u_{0})<d$, the solution is global in time with $I(u_{0}) >0$ or $\displaystyle\Vert \nabla_{\mathbb{B}}u_{0}\Vert_{L_{2}^{\frac{n}{2}}(\mathbb{B})} = 0$ and blows up in finite time with $I(u_{0}) < 0$; for the critical initial energy $J(u_{0}) = d$, the solution is global in time with $I(u_{0}) \geq0$ and blows up in finite time with $I(u_{0}) < 0$. The decay estimate of the energy functional for the global solution and the estimates of the lifespan of local solution are also given.

In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The paper is motivated by the settlement delay in the real-time gross settlement (RTGS) system. Both the central bank and the participating banks in the system are concerned about the liquidity risk, and are interested in the first time that the duration of settlement delay exceeds a predefined limit, we reduce this problem to the calculation of the Parisian time. The Parisian time is also crucial in the pricing of Parisian type options; to this end, we will compare our results with the existing literature.

Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing, and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented as well.

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

Condition-specific competition, when environmental conditions alter the outcome of competition, can foster the persistence of resident species after the invasion of a competitively superior invader. We test whether condition-specific competition can facilitate the areawide persistence of the resident and principal West Nile virus vector mosquito Culex pipiens with the competitively superior invasive, Aedes albopictus, in water from different urban container habitats. (2) Methods: We tested the effects of manipulated numbers of A. albopictus on C. pipiens survival and development in water collected from common functional and discarded containers in Baltimore, Maryland, USA. The experiment was conducted with typical numbers of larvae found in field surveys of C. pipiens and A. albopictus and container water quality. (3) Results: We found increased densities of A. albopictus negatively affected the survivorship and development of C. pipiens in water from discarded containers but had little effect in water from functional containers. This finding was driven by water from trash cans, which allowed consistently higher C. pipiens survival and development and had greater mean ammonia and nitrate concentrations that can promote microbial food than other container types. (4) Conclusions: These results suggest that the contents of different urban containers alter the effects of invasive A. albopictus competition on resident C. pipiens, that trash cans, in particular, facilitate the persistence of C. pipiens, and that there could be implications for West Nile virus risk as a result.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

The paper is considering of the basic differential equations of hydrodynamics: the equation of continuity and motion. On the simplest example, it is shown that the equation of continuity in a system with the equation of motion leads to contradictions and erroneous results of modeling. A more correct form of the continuity equation is described. It is shown that the equations of motion can be written in the form of complete differentials. Three possible integral forms of the equations of motion are presented. As a conclusion, the existence and smoothness of the solution of the Navier-Stokes equations are considered.

The information entropy for Smoluchowski coagulation equation is proposed based on statistical mechanics. And the normalized particle size distribution is a lognormal function at equilibrium from the principle of maximum entropy and moment constraint. The geometric mean volume and standard deviation in the distribution function are determined as simple constant. The results reveal that the assumption that algebraic mean volume be unit in self-preserving hypothesis is reasonable in some sense. Based on the present definition of information entropy, the Cercignani’s conjecture holds naturally for Smoluchowski coagulation equation. Together with the proof that the conjecture is also true for Boltzmann equation, Cercignani’s conjecture will holds for any two-body collision systems, which will benefit the understanding of Brownian motion and molecule kinematic theory, such as the stability of the dissipative system, and the mathematical theory of convergence to thermodynamic equilibrium.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

This paper discusses about the quantum energy levels of muonic hydrogen considering only Coulomb interaction. The computational analysis in this paper will help the reader get a good understanding of how different a muonic hydrogen is from its electronic counterparts. Energy eigenvalues are calculated by numerical method and the probability density distribution of muon around the nucleus is plotted for different quantum states using special functions. The code is written in python. A comparative study of emission spectra between the muonic hydrogen and hydrogen has also been discussed.

Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modelling, a flexible family of two-parameter distribution functions associated with the exponential distribution is proposed here. Mathematical and statistical properties of the novel distribution are examined, including quantiles, mode, moments, hazard rate function, and its characterization. The parameter estimation procedure using the maximum likelihood method was carried out, and applications to environmental and engineering data were also considered. To this end, various statistical tests are used, along with some other information criterion indicators to determine how well the model fits the data. The proposed model is found to be the most efficient plan in most cases for the datasets considered.

Capsule endoscopy (CE) has been a widely used medical imaging tool for the diagnosis of gastrointestinal tract abnormalities like bleeding. But the CE captures a huge number of image frames that are time-consuming and tedious tasks for medical experts to diagnose manually. To address this issue, researchers focused on the computer-aided bleeding detection system to identify bleeding automatically in real-time. This paper presents a systematic review of the available state-of-the-art computer-aided bleeding detection algorithms for capsule endoscopy. The review was carried out by searching five different repositories: Scopus, PubMed, IEEE Xplore, ACM Digital Library, and ScienceDirect for all original publications on computer-aided bleeding detection published between 2001 and 2021. The PRISMA methodology was used to perform the review, and 112 full-texts of scientific papers were reviewed. The contributions of this paper are I) a taxonomy for computer-aided bleeding detection algorithms for capsule endoscopy is identified, II) the available state-of-the-art computer-aided bleeding detection algorithms including various color spaces (RGB, HSV, etc.), feature extraction techniques, and classifiers are discussed, and III) identify the most effective algorithm for practical use cases. Finally, the paper is concluded by providing future direction for computer-aided bleeding detection research.

This work is the first in literature to tackle the difficult open problem of determining the upper bound and threshold theorem for the TDCDP (time-dependent controller parameter) of the (Fokker Planck Kolmogorov) probability density function. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to information theory, graph theory, data science, finance, economics, and beyond. So, this by default adds more taste and credibility to this study. This leads by nature to introducing a different flavor to this ground-breaking research by highlighting the impact of Fokker Planck Kolmogorov(FPK) to revolutionize crypocurrency,which have received its name because it uses encryption to verify transactions, a new debatable digital payment system that doesn't rely on banks to verify transactions. It’s a peer-to-peer system that can enable anyone anywhere to send and receive payments. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.

We work with reference to a well-known semiclassical model, in which quantum degrees of freedom interact with classical ones. We show that, in the classical limit, it is possible to represent classical results (e.g., classical chaos) by means a pure-state density matrix.

Single-molecule fluorescence detection (SMFD) experiments are useful in distinguishing sub-populations of molecular species when measuring heterogeneous samples. One experimental platform for SMFD is based on a confocal microscope, where molecules randomly traverse an effective detection volume. The non-uniformity of the excitation profile and the random nature of Brownian motion, produce fluctuating fluorescence signals. For these signals to be distinguished from the background, burst analysis is frequently used. Yet, the relation between the results of burst analyses and the underlying information of the diffusing molecules is still obscure and requires systematic assessment. In this work we performed three-dimensional Brownian motion simulations of SMFD, and tested the positions at which molecules emitted photons that passed the burst analysis criteria for different values of burst analysis parameters. The results of this work verify which of the burst analysis parameters and experimental conditions influence both the position of molecules in space when fluorescence is detected and taken into account, and whether these bursts of photons arise purely from single molecules, or not entirely. Finally, we show, as an example, the effect of bursts that are not purely from a single molecule on the accuracy in single-molecule Förster resonance energy transfer measurements.

Organic wastes and by-products from several activities, including food industries, farming, and animal husbandry, are a hygiene threat when aerobically decomposed. Therefore, their manage-ment is crucial for public health. In this direction, anaerobic digestion (AD) systems may be the solution by transforming waste into energy, which may decrease the environmental impact. However, their efficacy should be carefully examined. In this innovative study, we evaluated the physicochemical and microbial characteristics of liquid digestate (LD) retrieved from organic animal wastes in northern Greece using nanofiltration. Using treatment technologies including physical (solid-liquid separation, microfiltration and nanofiltration) and biological (anaerobic digestion), heavy metals and microbial (i.e., Salmonella spp., Escherichia coli, Enterococcus faecalis) concentrations reduced and nutrients were recovered. This work sets the basis for the efficient management of liquid digestate. Our method may enable the use of treated liquid digestate for unlimited irrigation water and other industrial applications of water. Apart from the sanitation process, the recovery of nutrients for soil fertilization seems to be a more sustainable way for fu-ture agricultural practices.

We studies the initial value problem for the fractional Navier-Stokes-Coriolis equations, which obtained by replacing the Laplacian operator in the Navier-Stokes-Coriolis equation by the more general operator $(-\Delta)^\alpha$ with $\alpha>0$. We introduce function spaces of the Besove type characterized by the time evolution semigroup associated with the general linear Stokes-Coriolis operator. Next, we establish the unique existence of global in time mild solutions for small initial data belonging to our function spaces characterized by semigroups in both the scaling subcritical and critical settings.

The diffusion coefficient--a measure of dissipation, and the entropy--a measure of fluctuation are found to be intimately correlated in many physical systems. Unlike the fluctuation dissipation theorem in linear response theory, the correlation is often strongly non-linear. To understand this complex dependence, we consider the classical Brownian diffusion in this work. Under certain rational assumption, i.e. in the bi-component fluid mixture, the mass of the Brownian particle $M$ is far greater than that of the bath molecule $m$, we can adopt the weakly couple limit. Only considering the first-order approximation of the mass ratio $m/M$, we obtain a linear motion equation in the reference frame of the observer as a Brownian particle. Based on this equivalent equation, we get the Hamiltonian at equilibrium. Finally, using canonical ensemble method, we define a new entropy that is similar to the Kolmogorov-Sinai entropy. Further, we present an analytic expression of the relationship between the diffusion coefficient $D$ and the entropy $S$ in the thermal equilibrium, that is to say, $D =\frac{\hbar}{eM} \exp{[S/(k_Bd)]}$, where $d$ is the dimension of the space, $k_B$ the Boltzmann constant, $\hbar $ the reduced Planck constant and $e$ the Euler number. This kind of scaling relation has been well-known and well-tested since the similar one for single component is firstly derived by Rosenfeld with the expansion of volume ratio.

Centrifugal pumps are widely employed in the oil refinery industry due to their efficiency and effectiveness in fluid transfer applications. The reliability of pumps plays a pivotal role in ensuring uninterrupted plant productivity and safe operations. Analysis of failure history data shows that bearings have been identified as critical components in oil refinery pump groups. However, traditional reliability estimation theories may not apply when data is limited or subject to right censoring. This paper addresses the complexity of estimating the Weibull distribution parameters using the maximum-likelihood method under the abovementioned conditions. The likelihood equation lacks an explicit analytical solution, necessitating the use of numerical methods for resolution. The proposed approach presented in this article leverages the Expectation-Maximization (EM) algorithm for estimating the Weibull distribution parameters. This method provides more accurate estimates of failure rates and probabilities by accounting for limited and censored data. The findings are demonstrated through a case study, showcasing the practical application of the proposed approach.

The hard open problem of finding the lower bound for the Fokker Planck Kolmogorov’s time-dependent controller parameter probability density function is addressed for the first time in literature in this work. This revolutionary exposition will put control theory and other related inter-disciplinary fields to a higher level towards contemporary control theory. Notably, based on the influential role of control theory in both engineering and industry, this paper will be of great value to all engineering and industry professionals who seek to know more about advanced trends within control theory settings. On the other remit of the spectrum, Fokker Planck Kolmogorov(FPK) equations are of high importance to physicists as well as mathematicians, based on their multiple applicability to multi-interdisciplinary fields of human knowledge, and beyond. So, this by default adds more taste and credibility to this study. Concluding thoughts are included at the end of the work along with a difficult outstanding problem and the direction of future work.

The optical response of bulk germanium sulfide (GeS) is investigated systematically using different polarization-resolved experimental techniques, such as photoluminescence (PL), reflectance contrast (RC), and Raman scattering (RS). It is shown that while the low-temperature (T=5 K) optical band-gap absorption is governed by a single resonance related to the neutral exciton, the corresponding emission is dominated by the disorder/impurity- and/or phonon-assisted recombination processes. Both the RC and PL spectra are found to be linearly polarized along the armchair direction. The low and room (T=300 K) temperature RS spectra consist of six Raman peaks identified with the help of Density Fuctional Theory (DFT) calculations: Ag1, Ag2, Ag3, Ag4, B1g1, and B1g2, which polarization properties are studied under four different excitation energies. We found that the polarization orientations of the Ag2 and Ag4 modes under specific excitation energy can be useful tools to determine the GeS crystallographic directions: armchair and zigzag.

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters which fit the shape of peakedness in bimodality on real line. The special values of peakedness parameters of the distribution are combination of half Laplace and half normal distributions on real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data.

The multivariate Gaussian random fields with matrix-based scaling laws are widely used for inference in statistics and many applied areas. In such contexts interests are often in symmetry and in the rates of change of spatial surfaces in any given direction. This article analyzes the almost sure sample function behavior for operator fractional Brownian motion, including multivariate fractional Brownian motion. We obtain the estimations of small ball probability and the strongly locally nondeterministic for operator fractional Brownian motion in any given direction. Applying these estimates we obtain Chung's laws of the iterated logarithm for spatial surfaces of operator fractional Brownian motion. Our results show that the precise rates of change of spatial surfaces are completely determined by the self-similarity exponent.

Proposed fundamental laws of biology and a model of health and disease underscore the importance of the lymphatic system. The lymphatics are responsible for two of the laws of biology and the fulcrum of health and disease balancing proliferation with regeneration through the immune system. It is responsible for protection from the environment and repair of senile and damaged tissue. Life is constantly bombarded by forces that increase entropy. Lymphatics provide negative entropy to maintain health. Lymphatics help maintain cellular homeostasis removing products of metabolism. Using these principles, the role of lymphatics is investigated in salt sensitivity hypertension, cardiorenal system, the new pillar of heart failure and kidney disease - Sodium-Glucose Transport Protein 2 (SGLT2) Inhibitors, and brain diseases. The realization of organ lymphatics in maintenance of health and disease opens the avenue to new therapeutics. This is the unrealized potential of lymphatic study.

This paper attempts to extend the Riemann Zeta function of a complex number to a function of a matrix and/or a tensor $A$, namely $$\zeta (A)=\sum _{n=1}^{\infty} \frac{1}{n^{A}}= \sum _{n=1}^{\infty} \sum_{k=1}^n\lambda_k A^k$$ and inverse $$A=\sum _{n=1}^{\infty} \sum_{k=1}^n \mu(n)\lambda_k \zeta(A^k)$$ where $\mu(n)$ is the M\"obius function, $A$ is a complex matrix or tensor with any order, and $\lambda_k$ is eigenvalue of the matri/tensor $A$. This kind of calculations on the Riemann Zeta function has never been seen in the literature. Some examples are provided.

Control of autonomous robot motion in radial mass density field is presented. In that sense the robot motion is described as the function of the radial mass density parameters. The radial mass density field is between the maximal radial mass density and the minimal radial mass density. Between these two limited values one can use n points (n = 1, 2, . . . nmax) and calculate the related radial mass density for each point. The radial mass density is maximal at the minimal gravitational radius and minimal at the maximal gravitational radius. This conclusion is valid for Planck scale, but also for the scales that are less or higher of that one. Using the ratio of the Planck mass and Planck radius it is generated energy conservation constant with value κ = 0.99993392118. Further, in this theory it is possible to connect Planck’s and gravitational parameters as functions of the maximal (or minimal) radial mass density. In that sense the autonomous robot motion in radial mass density field is important for the control of the robot motion at micro and nano scales.

Intelligent ship technology is currently an international research hotspot, and model predictive control is widely used in the path-tracking control of intelligent vehicles. To construct an intelligent ship anti-disturbance path-tracking control method, firstly, an environmental disturbance model was constructed with the actual meteorological data of the target sea area. Secondly, the Fossen ship equation of motion is linearized and discretized as the ship motion model. Thirdly, the expression of the prediction equation is derived from the ship motion model. Fourthly, the cost function is constructed by using the polar diameter and polar angle values of the ship. Fifth, the power function in the cost function is replaced with an exponential function to obtain an improved cost function. Sixthly, according to the Lyapunov theory and the MPC terminal constraint theory, the stability of the improved cost function is verified. Seventh, different test paths are set up, the environmental disturbance model is taken as the external disturbance, the ship motion model, the prediction equation, and the improved cost function are used to design the anti-disturbance path-tracking control algorithm according to the model prediction control idea for simulation experiments. Finally, different MATLAB simulation results show that the improved cost function can resist disturbance of the external wave, current, and wind, and effectively track the target path. Therefore, this study provides a reference for improving the navigation safety of ship path-tracking.

Sarcopenia is associated with clinical complications, which increase mortality. Effective sarcopenia risk screening in the elderly should be grounded in a comprehensive assessment, encompassing both nutritional status and medication use. Current screening tools, while emphasizing muscular per-formance, exhibit limited sensitivity in identifying elderly individuals at risk of sarcopenia. This cross-sectional study aimed to develop a sarcopenia risk screening tool, named Sarc-Global, with enhanced sensitivity, incorporating factors pertinent to the overall health of the elderly. Utilizing the criteria established by EWGSOP2 for diagnosing sarcopenia, we evaluated 395 communi-ty-dwelling elderly individuals. This evaluation served as a reference for assessing the efficacy of two validated questionnaires, Sarc-F and Sarc-CalF, and our newly developed Sarc-Global. Con-structed through multiple logistic regression, Sarc-Global integrates variables such as sex, age, medication use, body mass index, arm circumference, and handgrip strength – all significantly associated with sarcopenia (p

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

Macromolecular assemblies, such as protein complexes, undergo continuous structural dynamics, including global reconfigurations critical for their function. Two fast analytical methods are widely used to study these global dynamics, namely elastic network model normal mode analysis and principal component analysis of ensembles of structures. These approaches have found wide use in various computational studies, driving the development of complex pipelines in several software packages. One common one has been conformational sampling through hybrid simulations incorporating all-atom molecular dynamics and global modes of motion. However, wide functionality is only available for experienced programmers with limited capabilities for other users. We have, therefore, integrated one popular and extensively developed software for such analyses, the ProDy Python application programming interface, into the Scipion workflow engine. This enables a wider range of users to access a complete range of macromolecular dynamics pipelines beyond the core functionalities available in its command-line applications and the normal mode wizard in VMD. The new protocols and pipelines can be further expanded and integrated into larger workflows together with other software packages for cryo-electron microscopy image analysis and molecular simulations. We present the resulting plugin, Scipion-EM-ProDy, in detail, highlighting the rich functionality made available by its development.

The Serra da Estrela Natural Park (NPSEs) in Portugal stands out as a well-preserved region abundant in medicinal plants, particularly known for their pharmaceutical applications in diabetes prevention and treatment. This comprehensive review explores these plants' botanical diversity, traditional uses, pharmacological applications, and chemical composition. The NPSEs boast a rich diversity with 138 medicinal plants across 55 families identified as traditionally and pharmacologically used against diabetes globally. Notably, the Asteraceae and Lamiaceae families are prevalent in anti-diabetic applications. In vitro studies reveal their significant inhibition of carbohydrate-metabolizing enzymes, and certain plant co-products regulate genes involved in carbohydrate metabolism and insulin secretion. In vivo trials demonstrate anti-diabetic effects, including glycaemia regulation, insulin secretion, antioxidant activity, and lipid profile modulation. Medicinal plants in NPSE exhibit various activities beyond anti-diabetic, such as antioxidant, anti-inflammatory, antibacterial, anticancer, and more. Chemical analysis identifies over fifty compounds like phenolic acids, flavonoids, terpenoids, and polysaccharides responsible for their efficacy against diabetes. The findings underscore the potential of NPSE medicinal plants as anti-diabetic candidates, urging further research to develop effective plant-based anti-diabetic drugs, beverages, and supplements.

Dermal penetration is considered to mainly occur via passive diffusion. Therefore, a high concentration gradient of dissolved active ingredient between formulation and skin is needed to achieve an effective dermal penetration. The concentration gradient between formulation and skin can be changed by changing the amount of dissolved active ingredient in the formulation. In case of poorly soluble active ingredients this can be achieved by using nanosized drug material instead of larger sized material. The smaller size and the resulting larger surface increase the kinetic solubility and thus increase the concentration gradient of dissolved active ingredient between formulation and skin, which then results in an increased dermal penetration. In this study we demonstrated that the concentration gradient between formulation and skin can also be influenced by the number of particles being present in the formulation and by the dose (volume of formulation) applied to the skin. Particles of undissolved active ingredient are known to act as a reservoir by releasing dissolved molecules in the liquid phase of the formulation. It could now be demonstrated that the particles - once the liquid in which they are dispersed evaporates - can connect to the skin via an aqueous meniscus. The aqueous meniscus contains dissolved active ingredient and therefore creates a small local spot with a locally high concentration gradient and improved dermal penetration. Therefore, the dermal penetration can be increased with formulations that contain high amounts of particles. This can be achieved by applying formulations with high numbers of particles and/or by applying larger volumes of particle containing formulations to the skin.

Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

We prove general stability theorems for $n$-dimensional quartic-cubic-quadratic-additive type functional equations of the form \begin{eqnarray*} \sum_{i=1}^\ell c_i f \big( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big) = 0 \end{eqnarray*} by applying the direct method. These stability theorems can save us much trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

The aim of this study was to investigate the physicochemical characterization and biological activities of chitosan (CH) based composite films with the incorporation of chestnut flower essential oil (CFEO). The composite films were prepared by casting method and characterized in terms of structural, morphological and mechanical properties via FT-IR, XRD, UV, SEM and TGA. The results proved the significantly increased water vapor permeability (WVP), heat resistance, antibacterial and antioxidant capabilities of CH-CFEO films. The incorporation of CH and CFEO enhanced the UV blocking, which made the film shield almost all UV light. Films with the tensile strength of 6.37 ± 0.41 MPa and elongation at break of 22.57 ± 0.35% were got with 6 mg mL-1 CFEO. Subsequently, the fruit preservation experiments also confirmed that the composite films could effectively extend the shelf life of bananas through their excellent water vapor and oxygen barrier. These desirable performances enable our newly developed composite films to be a remarkable packaging material to solve the fresh fruit preservation dilemma.

Due to its aggressive and invasive nature glioblastoma (GBM), the most common and aggressive primary brain tumour in adults, remains almost invariably lethal. Significant advances in the last several years have elucidated much of the molecular and genetic complexities of GBM. However, GBM exhibits a vast genetic variation and a wide diversity of phenotypes that has complicated the development of effective therapeutic strategies. This complex pathogenesis makes it necessary the development of experimental models that could be used to further understand the disease, and also to provide a more realistic testing ground for potential therapies. In this report, we describe the process of transformation of primary mouse embryo astrocytes into immortalized cultures with neural stem cell characteristics, that are able to generate of GBM when injected in the brain of C57BL/6 mice, or heterotopic tumours when injected iv. Overall, our results show that oncogenic transformation is a fate for NSC if cultured for long periods in vitro. In addition, since no additional hit is necessary to induce the oncogenic transformation, our model may be used to investigate the pathogenesis of gliomagenesis and to test the effectiveness of different drugs throughout the natural history of GBM.

Assessing dietary inadequacies can contribute to understanding the nutritional vulnerabilities of a country. This study aimed to investigate nutrient intakes and micronutrient inadequacies in the Brazilian adult population, with an interest in different age subgroups. Cross-sectional study with 1812 individuals aged 19 to 65 years from a population-based study with a representative sample of Brazilian adults. Dietary intake was assessed by two 24-hour food recalls, and the probabilities of inadequate intake were estimated using the Dietary Reference Intake targets. Adequate macronutrient intake was over 99% for proteins, 84.7% for carbohydrates, and 80.7% for total fats. There was a high probability of inadequacy (above 90%) for vitamins D and E, but vitamin D inadequacy was very similar between sexes. In contrast, vitamin E was more likely to be inadequately consumed among women. A high probability of inadequacy (above 85%) of calcium and magnesium was found in the population, regardless of age group. Except for iron, the probability of inadequacy of other minerals increased with age. The results showed a relevant proportion of nutrient inadequacies, with those most at risk being women and older individuals, helping with better targeting and monitoring of public health policies that address nutritional problems in the population.

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p - k Gamma Function and Generalized p - k Pochhammer symbol and denoted as $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ respectively. We prove the several identities for $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ those satisfied by the classical Gamma function. Also we provide the integral representation for the $ _{p}^{a}\Gamma_{k}(x) $

In this paper, we study the global existence and exponential decay for a dynamic contact problem between a Timoshenko beam with second sound and two rigid obstacles, of which the heat flux is given by Cattaneo's law instead of the usual Fourier's law. The main difficulties arise from the irregular boundary terms, from the low regularity of the weak solution and from the weaker dissipative effects of heat conduction induced by Cattaneo's law. By considering related penalized problems, proving some a priori estimates and passing to the limit, we prove the global existence of the solutions. By considering the approximate framework, constructing some new functionals and applying the perturbed energy method, we obtain the exponential decay result for the approximate solution, and then prove the exponential decay rate to the original problem by utilizing the weak lower semicontinuity arguments.

The physiological characteristics of liquid digestate retrieved from various biogas plants based in northern Greece are presented. Preliminary photocatalysis experiments on inoculated liquid di-gestate sampled showed that disinfection is possible when pre-treated digestate with a combination of centrifuge-flocculation-μFiltration after 5.5 hours of 0.7g/L suspended TiO2 under UVA illumination for the experimental conditions is used. A novel design photocatalytic nanofiltration reactor was implemented for disinfection experiments on pre-treated liquid digestate, giving promising results. This work sets the basis for the efficient operation and engineering application of technology collaboration with photocatalysis as the final step for liquid digestate sanitation and reusable water recovery.

In this paper, we study the fractional pseudo-parabolic equations u_t + (−△)^s u + (−△)^s u_t = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−△)^s and the fractional Sobolev space H^s and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global weak solution: for the low initial energy J(u₀) < d, the solution is global in time with I(u₀) > 0 or ∥u₀∥X_0(Ω) = 0 and blows up +∞ with I(u₀) < 0; for the critical initial energy J(u₀) = d, the solution is global in time with I(u₀) ≥ 0 and blows up at +∞ with I(u₀) < 0. The decay estimate of the energy functional for the global solution is also given.

Background: In this investigation, we explored the effects of pharmacological cholinergic stimulation on cardiac function and renal inflammation following acute myocardial infarction (AMI) in spontaneously hypertensive rats (SHRs). Methods: Adult male SHRs were randomized into three experimental groups: sham-operated; AMI+Veh (infarcted, treated with vehicle); and AMI+PY (infarcted, treated with the cholinesterase inhibitor pyridostigmine bromide (PY) - 40 mg/kg, once daily for seven days). Rats were euthanized 7 or 30 days post-surgery. Clinical parameters were assessed on the day before euthanasia. Subsequent to euthanasia, blood samples were collected and renal tissues were harvested for histological and gene expression analyses aimed to evaluate inflammation and injury. Results: Seven days post-surgery, the AMI+PY group demonstrated improvements in left ventricular diastolic function and autonomic regulation, and a reduction in renal macrophage infiltration compared to the AMI+Veh group. Furthermore, there was a notable downregulation of pro-inflammatory gene expression and an upregulation of anti-inflammatory gene expression. Analysis 30 days post-surgery showed that PY treatment had a sustained positive effect on renal gene expression, correlated with a decrease in biomarkers indicative of subclinical kidney injury. Conclusion: Short-term cholinergic stimulation with PY provides both cardiac and renal protection by mitigating the inflammatory response after AMI.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

The ceramic sherds from approximately 20 samples of lead-glazed tableware, recovered from diverse archaeological sites, including three repurposed storage pits transformed into dumpsters within the medieval city of Santarém (13th-14th century), underwent a meticulous examination. This investigation utilized techniques such as micro-Raman, ground state diffuse reflectance absorption, and X-ray fluorescence spectroscopies, in addition to X-ray diffraction and stereomicroscopy. A parallel study was conducted on contemporaneous European ceramics (glazed sherds) sourced from archaeological sites dating back to the 13th-15th centuries in Saintonge (France), Ardenne, Zomergem, and Bruges (Belgium), as well as Surrey-Hampshire, Kingston, and Cheam (England). The colour of the ceramic bodies is predominantly white or whitish, with a few exhibiting a vivid red hue. Ceramic sherds with a light paste composition were likely crafted using kaolin clays as raw materials. Analyses of fabric, mineralogical, and elemental composition of the sherds suggest that the majority of Santarém's glazed ceramics were locally or regionally produced, potentially derived from a Pliocene kaolin-rich sand formation. However, this conclusion is not supported by the absence of discovered lead glaze kilns or workshops in Santarém for the late Middle Ages. A distinctive feature from the European workshop ceramics lies in the quartz temper content and fabric.

Background: We assessed the pertinence of yearly updating the International Working Group on the Diabetic Foot (IWGDF) risk classification in people with diabetes by quantifying the changes in the risk group and its accuracy in identifying those developing an ulcer (DFU) in a primary care setting. Methods: In our retrospective cohort study, we included all people with diabetes with a foot as-sessment registry between January 2016 and December 2018 in the Baixo Alentejo Local Health Unit. Foot-related data was collected at baseline after one and two years. DFU and/or death until December 2019 were registered. The proportion of people changing their risk status each year was calculated. Accuracy measures of the IWGDF classification to predict DFU occurrence at one, two, and three years were calculated. Results: A total of 2097 people were followed for three years, during which 0.1% died, and 12.4% developed a DFU. After two years, 3.6% of the participants had progressed to a higher-risk group. The IWGDF classification presented specificity values superior to 90% and negative predictive values superior to 99%. Conclusion: Foot risk status can be safely updated every two years instead of yearly. The IWGDF classification can accurately identify those not at risk of DFU.

Cells actively sense differences in topology, matrix elasticity and protein composition of the extracellular microenvironment and adapt their function and morphology. In this study, we focus on the cross-talk between matrix stiffness and protein coating density that regulate morphology and proliferation dynamics of single myocytes. For this, C2C12 myocytes were monitored on L-DOPA functionalized hydrogels of 22 different elasticity and fibronectin density compositions. Static images were recorded and statistically analyzed to determine morphological differences and to identify the optimized extracellular matrix (ECM). Using that information, selected ECMs were used to study the dynamics before and after cell proliferation by statistical comparison of distinct cell states. We observed a fibronectin density independent increase of the projected cell area until 12 kPa. Additionally, changes in the fibronectin density led to an area optimum at about 2.6 μg/cm, which was confirmed by an independent F-actin analysis, revealing a maximum actin filament to cell area ratio of 7.5 %. The proliferation evaluation showed an opposite correlation between cell spreading duration and speed to the matrix elasticity and protein density, which did not affect the cell cycle duration. In summary, we identified an optimized ECM composition, while independent matrix properties regulate distinct cell characteristics.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

This article is about a framework for determining the degree of realism of any given 1 passenger ride motion discomfort measurement formula. After providing some context and reviewing 2 evidence of deficiency in currently popular ride motion discomfort measurement formulas, the article 3 outlines the research program that needs to be carried out in order to establish such a framework. 4 The research begins with gathering recordings of uncomfortable ride motion episodes encountered in 5 a chosen type of passenger transport service. It then has test subjects compare the episodes via a ride 6 motion simulator and adjust their amplitudes pair wise until they cause equal discomfort. It explains 7 how to take the pair wise amplitude adjustments and determine amplitude adjustments that bring all 8 of the motion episode recordings to a common level of discomfort so that they form a normalized set. 9 Then, the lower the scatter of the scores assigned by any given discomfort measurement formula to 10 the members of that set, the more realistic that formula will be for the chosen service.

The development of forecasting models for the evaluation of potential slope instability after rainfall event represents an important issue for the scientific community. This topic has received considerable impetus due to climate change effect on the territory [1, 2] as several studies demonstrate that the increase in global warming can significantly influence the landslide activity and stability conditions of natural and artificial slopes [3]. A consolidated approach in evaluating rainfall induced landslide hazard is based on the integration of rainfall forecasts and physically based (PB) predictive models through deterministic laws. However, considering the complex nature of the processes and the high variability of the random quantities involved, probabilistic approaches are recommended in order to obtain reliable predictions. A crucial aspect of the stochastic approach is represented by the definition of appropriate probability density functions (pdfs) to model the uncertainty of the input variables as this may have an important effect on the evaluation of the probability of failure (PoF). The role of the pdf definition on reliability analysis is discussed through a comparison of PoF maps generated using Monte Carlo (MC) simulations performed over a study area located in the Umbria Region of central Italy.

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

In this paper, we investigate the Green measure for a class of non-Gaussian processes in $\mathbb{R}^{d}$. These measures are associated with the family of generalized grey Brownian motions $B_{\beta,\alpha}$, $0

Crash prediction of the sharp horizontal curve segment (SHCS) of a freeway is an important tool in analyzing safety of SHCSs and in building a crash prediction model (CPM). The design and crash report data of 88 SHCSs from different institutions were surveyed and three negative binomial (NB) regression models and three generalized negative binomial (GNB) regression models were built to prove that the interactive influence of explanatory variables plays an important role in fitting goodness. The study demonstrates the effective use of the GNB model in analyzing the interactive influence of explanatory variables and in predicting freeway basic segments. Traffic volume, highway horizontal radius, and curve length have been formulated as explanatory variables. Subsequently, we performed statistical analysis to determine the model parameters and conducted sensitivity analysis. Among the six models, the result of model 6, which considered interactive influence, is much better than those of the other models by fitting rules. We also compared the actual results from crashes of 88 SHCSs with those predicted by models 1, 3, and 6. Results demonstrate that model 6 is much more reasonable than models 1 and 3.

Portable Document Format (PDF) is one of the most widely used files types worldwide in data exchange, this has encourage hackers to utilize such files to spread any malicious content through PDF, utilizing different methods and techniques to accomplish that, on the other hand, security researches kept trying to improve detection methods to cope up to the rapidly increasing number of malwares daily, one of the commonly used detection technique nowadays is by utilizing artificial intelligence and Machine learning classificat; thision to help detecting PDF Malwares, in this paper, we utilize machine learning classifier Random Forest on a newly released PDF Malware dataset CIC-Evasive-PDFMal2022 to achieve the main goal of detecting malicious PDF documents, results showing a detection accuracy of around 99.5%

The goal of this work is to develop a sustainable value chain of carbonaceous adsorbents that can be produced from the solid fibrous digestate (SFD) of biogas plants and further applied in integrated desulphurisation-upgrading (CO2/CH4 separation) processes of biogas to yield high purity biomethane. On this purpose, physical and chemical activation of the SFD derived biochar was optimised to afford micro-mesoporous activated carbons (ACs) of high BET surface area (590-2300 m2g−1) and enhanced pore volume (0.57-1.0 cm3g−1). Gas breakthrough experiments from fixed bed columns of the obtained ACs, using real biogas mixture as feedstock, unveiled that the physical and chemical activation conclude to different types of ACs which are sufficient for biogas upgrade and biogas desulphurisation respectively. Performing breakthrough experiments at three temperatures close to ambient it was possible to define the optimum conditions for enhanced H2S/CO2 separation. It was also concluded that the H2S adsorption capacity is significantly affected by restriction to gas diffusion. Hence, the best performance was obtained at 50 oC and the maximum observed in the H2S adsorption capacity vs the temperature is attributed to the counterbalance between adsorption and diffusion processes.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

In this review, we outline our current understanding of the mechanisms involved in the absorption, storage, and transport of dietary vitamin A to the eye, the trafficking of rod opsin protein to the photoreceptor outer segments, which encompasses the logistical backbone required for visual function. Two key mechanisms of this process are emphasized in this manuscript: Ocular and systemic vitamin A membrane transporters, and rhodopsin transporters. Understanding the complementary mechanisms responsible for the generation and proper transport of the retinylidene opsin to the photoreceptor outer segment will eventually shed light on the importance of genes encoded by these proteins, and their relationship on normal visual function and in the pathophysiology of retinal degenerative diseases.

With the global warming and the frequent occurrences of harsh environments, mooring line failures are frequent. Response analysis of the platform structure and its residual mooring system under multiple mooring line failures is needed. Therefore, it is necessary to investigate the change law of platform motion response after mooring line failure to find out the reasons for the change. Studies for different failure combinations of mooring lines show that the variation of the steady-state equilibrium position of the platform is closely related to the stiffness, with a clear functional. The duration and amplitude of the transient response are mainly influenced by the Morison drag force. And it was found that the suspended mooring line reduced the motion responses. It is also found that the mooring line failure increased the effective tension and suspension length of the riser. Based on the improved Dezert-Smarandache theory (DSmT), it is calculated that mooring line failure has little effect on the failure probability in different zones of the riser.

For many years marine algae has been subject of numerous researches and as a source of natural products with antiviral activity, such as terpenes, alkaloids and sulphated polysaccharides. However, the anti-Zika virus (ZIKV) potential of algae has not been studied. In this study we evaluated extracts seven species of the three major classes of seaweeds (Phaeophyceae, Chlorophyceae and Rhodophyceae) against ZIKV. All seaweeds tested are native of the Brazilian coast, except for Kappaphycus alvarezii that can be cultivated. ZIKV a mosquito-borne flavivirus, has become a public health problem. In recent years there has been an increase in the number of cases and a strong association between ZIKV outbreak and the spread of cases of Guillain-Barré Syndrome and microcephaly. All seaweed extracts tested in this work inhibits ZIKV replication in a dose-dependent manner. Caulerpa racemosa, Kappaphycus alvarezii and Osmundaria obtusiloba extracts were able to inhibit viral replication at low concentrations with EC₅₀ values ranging from 1.38 to 1.98 µg/mL. We observed that O. obtusiloba presented a significant virucidal effect. Our results suggest that extracts of C. racemosa, K. alvarezii and O. obtusiloba presented very promising results, being excellent candidates for further studies, demonstrating that marine algae are an interesting source for the development of novel anti-ZIKV agents.

In the paper we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of differential equations of Cauchy-type in covariant derivatives. We have found the number of essential parameters which the solution of the system depends on. Similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

The main goal of this article is to demonstrate the impact of environmental data on the spreading of Covid-19. In this research, data has been collected from 70 cities/provinces that are affected by Covid-19. Here, environmental data refers to temperatures, humidity and population density in each of these cities/provinces. This data has been analyzed using statistical models such as Poisson, Quasi-Poisson and negative Binomial. It is found that a negative Binomial regression model is the best fit for our data. Our results reveal that average high temperature is the vital factor to slow down the spread of Covid-19. In addition, higher population density found to be an important factor for the quick spreading of Covid-19 where it is quite impossible to maintain the social distance and the virus can spread easily.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

The extracellular matrix (ECM) is a ubiquitous member of the body and is key to the maintenance of tissues and organs integrity. Initially thought to be a by-stander in many cellular processes, the extracellular matrix has been shown to have diverse components that regulate and activate many cellular processes and ultimately influence cell phenotype. Importantly, the ECM composition, architecture, and stiffness/elasticity influence cellular phenotypes. Under normal conditions and during development, the synthesized ECM is constantly undergoing degradation and remodeling processes via the action of matrix proteases that maintain tissue homeostasis. In many pathological conditions including fibrosis and cancer, the ECM synthesis, remodeling, and degradation is dysregulated causing its integrity to be altered. Both physical and chemical cues from the ECM are sensed via receptors including integrins and play key roles in driving cellular proliferation and differentiation and in various disease progression such as cancers. Advances in ‘omics’ technologies have seen an increase in studies focussing on bi-directional cell-matrix interactions and here we highlight emerging knowledge on the role played by the ECM during normal development and in pathological conditions. This review summarizes current ECM-targeted-therapies that can modify tumor ECM to overcome drug resistance and better cancer treatment.

Native and exotic fruits from the Amazon have varied characteristics, with aroma being a decisive factor in attracting and accepting them and their medicinal use as a nutraceutical supplement. This work aimed to analyze the chemical constituents of the volatile concentrates of some Myrtaceous fruit species sampled in the Brazilian Amazon. The fruit's pulps were subjected to simultaneous distillation-extraction, and gas chromatography-mass spectrometry was used to analyze their volatile chemical composition. In the volatile concentrate of Eugenia stipitata (Araçá-boi) were identified α-pinene (17.5%), citronellyl butanoate (15.6%), and pogostol (13.5%) as primary constituents; in Eugenia uniflora (Ginja) were curzerene (30.5%), germacrone (15.4%), atractylone (13.1%), and (E)-β-ocimene (11.1%); in Myrciaria dubia (Camu-Camu) were α-pinene (55.8%), (E)-β-ocimene (13.1%), and α-terpineol (10.0%); in Psidium guajava (Goiaba) were (2E)-hexenal (21.7%), hexanal (15.4%), caryophylla-4(12),8(13)-dien-5-β-ol (10.5%), caryophyllene oxide (9.2%), and pogostol (8.3%); and in Psidium guineense (Araçá) were limonene (25.2%), ethyl butanoate (12.1%), epi-β-bisabolol (9.8%), and α-pinene (9.2%). The analyzed fruit species' volatile concentrates presented a significant diversity of constituents with a predominance of functional groups, such as monoterpenes, sesquiterpenes, and fatty acid derivatives, originating from the plant's secondary metabolism and representing significant importance regarding their nutritional and medicinal uses.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.

The developments of confirmed daily Sars-CoV-2 infections can be modeled a posteriori in a comparatively simple and satisfactory way by means of a special exponential function: its exponential coefficient varies exponentially with time itself. This property enables the function to directly simulate the „daily case“ curve fragments observed for the first waves of the current epidemics in a number of counties and countries. Linear combinations of two or more of the functions allow for the modeling of the complete curves observed in the vast majority of all regions for which case number developments have been tabulated.

More than 20 years after the discovery of the first anelloviruses (AVs), they still remain a mysterious group of viruses. To date, there is no clear understanding of their impact on the host organism, although information is emerging about their participation in various pathologies. However, it is well known that AVs are an important component of the human virome. In the current study we assessed the abundance of AVs in viromes from four nasal and pharyngeal samples from children with respiratory symptoms using a metagenomic approach. It is worth noting that three patients had known respiratory viruses and one did not have any. Regarding AVs, they were detected in all samples, namely Torque teno mini virus (TTMV). The greatest abundance and diversity of AVs (Torque teno virus (TTV), TTMV and Torque teno midi virus (TTMDV)) were shown in a diseased patient with an absence of respiratory viruses, which may indicate the potential involvement of AVs in the maintenance of respiratory symptoms. An activated immune system to combat the main pathogens, against the background of which the number of AVs decreases, is discussed as a possible reason for the reduced diversity of anellome in other patients. We also compared the results of the metagenomic approach and qPCR for major respiratory viruses, which were in agreement. In addition, metagenomic sequencing made it possible to obtain additional data on viral genomes in order to establish their taxonomic identification and characterize individual viral profiles in patients from the Siberian part of Russia.

Electrospun ultrathin fibers based on binary compositions of polylactide (PLA) and poly(ε-caprolactone) (PCL) with different ratios of polymer components from 0/100 to 100/0 wt. % were studied. Using a combination of thermal (DSC) and relaxation (EPR) measurements, the effect of biopolymers content on the characteristics of the crystal structure of PLA and PCL and the diffusive rotational mobility of the stable TEMPO radical in the amorphous regions of PLA/PCL compositions was shown. It was revealed that after PLA and PCL blending, significant changes in the degree of crystallinity of PLA, PCL segmental mobility, sorption capacity of the radical as well as activation energy of rotational diffusion in the amorphous regions of PLA/PCL composition are observed. The characteristic region of biopolymers’ composition from 50/50 to 30/70 % PLA/PCL blends ratio was found, where the inversion transition of PLA from dispersive medium to dispersive phase where an inversion transition is assumed when the continuous medium of the PLA transforms into a discrete phase. The performed studies made it possible for the first time to carry out a comprehensive analysis of the effect of the system component ratio on the structural and dynamic characteristics of the PLA/PCL film material at the molecular level.

Atomic structure of N-electron atoms is often determined using the Hartree-Fock method, which is an integro-differential equation. The exchange term of the Hartree-Fock equations is usually treated as an inhomogeneous term of a differential equation, or with a local density approximation. This work uses matrix methods to solve for the Hartree-Fock equations, rather than the more commonly-used shooting method to integrate an inhomogeneous differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using computer linear-algebra packages. We extend the same technique to integro-differential equations, where a discretized integral can be written as a sum in matrix form. This method is compared against experiment and standard atomic structure calculations. We also can use this method for free-electron wavefunctions. This technique is important for spectral line broadening in two ways: improving the atomic structure calculations, and improving the motion of the plasma electrons that collide with the atom.

The paper explores the Kullback-Leibler divergence formalism (KLDF) applied to the stable MG1 queue manifold. It explores the analytic forms of state probabilities and their maximization based on entropy functionals, subject to normalization and mean value constraints. The credibility of KLDF is justified through consistency axioms, and the application of Rényi's and Tsallis's formalisms on a stable M/G/1 queue is examined, resulting in novel state probabilities and insights into information theory of Queue Learning.

Studies performed at single-cell resolution have demonstrated the physiological significance of cell-to-cell variability. Various types of mathematical models and systems analyses of biological networks have further been used to gain a better understanding of the sources and regulatory mechanisms of such variability. In this work, we present a novel sensitivity analysis method, called molecular density function perturbation (MDFP), for the dynamical analysis of cellular heterogeneity. The proposed analysis is based on introducing perturbations to the density or distribution function of the cellular state variables at specific time points, and quantifying how such perturbations affect the state distribution at later time points. We applied the MDFP analysis to a model of signal transduction pathway involved in TRAIL (tumor necrosis factor-related apoptosis-inducing ligand)-induced apoptosis in HeLa cells. The MDFP analysis showed that caspase-8 activation regulates the timing of the switch-like increase of cPARP (cleaved poly(ADP-ribose) polymerase), an indicator of apoptosis. Meanwhile, the cell-to-cell variability in the commitment to apoptosis depended on mitochondrial outer membrane permeabilization (MOMP) and events following MOMP, including the release of Smac (second mitochondria-derived activator of caspases) and cytochrome-C from mitochondria, the inhibition of XIAP (X-linked inhibitor of apoptosis) by Smac and the formation of apoptosome.

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E. T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to $SL(2,R)$. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.

The aim of this paper is to investigate whether multifractal analysis can be applied to study choroidal blood vessels and help ophthalmologists for the early diagnosis of retinitis pigmentosa (RP). In a case study, we use Spectral Domain Optical Coherence Tomography (SDOCT), which is a non-invasive and highly sensitive imaging technique of the retina and choroid. The image of a choroidal branching pattern can be regarded as a multifractal. Therefore, we calculate generalized Renyi point-centered dimensions, which is considered a measure of inhomogeneity of data, to prove that it increases in the patients with RP with respect to the control group.

Revealing the spatial distribution mechanism of the coupling effect between soil water and salt is essential for managing saline-alkali farmland. This study utilized the multifractal method to analyze soil water and salt under varying water content levels in arid saline-alkali farmland. Soil samples were collected on the second (S1), fifth (S2), eighth (S3), eleventh (S4), and fourteenth (S5) days after a rainfall event. The findings showed that a significant decrease in soil water content, contrasting with an increase in soil salt content throughout the soil layers post-rainfall. As water content decreased, the spatial variability of soil water initially increased from S1-3 and then decreased, while the spatial variability of soil salt decreased. The spatial distribution between soil water and salt exhibited a high correlation at S3-4 (with relative water content of soil ranging from 0.52 to 0.75) due to their coupling effect. However, soil salt was unevenly leached by rainfall at high water content levels (S1-2) and precipitated at low water content levels (S5), resulting in low spatial variability correlations between soil water and salt. This study elucidated the coupling process of soil water and salt, identifying their spatiotemporal distribution mechanism in dryland agricultural areas.

Generalized Bayes is a Bayesian approach based on the learning rate parameter η. In this study, we examine the effect of parameter η on the estimation results considering joint type-I and type-II hybrid censored samples from k exponential populations. In addition to the learning rate parameter, we consider two loss functions, the Linex and general entropy loss functions in the Bayesian approach. Monte Carlo simulations are performed to compare the performances of the estimation results under losses and different values of η. An illustrative example is performed to study the effect of the learning rate parameter and the different losses with different parameters.

The aims of this study are to measure the technical efficiency (TE) of Cambodian household’s rice production and trying to determine its main influencing factors using the stochastic frontier production function. The study utilized primary data collected from 301 rice farmers in three selected districts of Battambang by structured questionnaires. The empirical results indicated the level of household rice output varied according to differences in the efficiency of production processes. The mean TE is 0.34 which means that famers produce 34% of rice at best practice at the current level of production inputs and technology, indicates that rice output has the potential of being increased further by 66% at the same level of inputs if farmers had been technically efficient. Furthermore, between 2013-2015 TE of household’s rice production recorded -14.3% decline rate due to highly affected of drought during dry season of 2015. Moreover, evidence reveals that land, fertilizer, and pesticide are the major influencing input factors of household’s rice production, while disaster, education of household head, family size and other crops’ cultivated area are core influencing factors decreasing TE. Conversely, the main influencing factors increasing TE are irrigated area, number of plot area and sex of household head.

The aims of this study are to measure the technical efficiency (TE) of Cambodian household’s rice production and trying to determine its main influencing factors using the stochastic frontier production function. The study utilized primary data collected from 301 rice farmers in three selected districts of Battambang by structured questionnaires. The empirical results indicated the level of household rice output varied according to differences in the efficiency of the production processes. The mean TE is 0.34 which means that famers produce 34% of rice at best practice at the current level of production inputs and technology, indicates that rice output has the potential of being increased further by 66% at the same level of inputs if farmers had been technically efficient. Furthermore, between 2013-2015, TE of household’s rice production recorded -14.3% decline rate due to highly affected of drought during dry season of 2015. Moreover, evidence reveals that land, fertilizer, and pesticide are the major influencing input factors of household’s rice production, while disaster, education of household head, family size and other crops’ cultivated area are core influencing factors decreasing TE. Conversely, the main influencing factors increasing TE are irrigated area, number of plot area and sex of household head.

The present study aims to measure the technical efficiency and establish core factors effecting rice production in Cambodia. Four-years dataset generated from the central government document “Profile on Economics and Social” of entire 25 provinces between 2012-2015 and the stochastic production frontier model (SFA) was applied. The results indicated that the level of output (quantity) of Cambodian rice production varied according to the different level of capital investment in agricultural machineries, total rice actual harvested area, and technically fertilizers application within provinces. Furthermore, evidence revealed the overall mean efficiency of rice production is 78.4% implies that there is still room to further improve technical efficiency by given the same level of inputs and technology. More importantly, the findings revealed that irrigation, production technique and amount of agricultural supporting staffs are being as the most important influencing factors of rice production’s technical efficiency in Cambodia. In conclusion, present study strongly recommends the development of irrigation systems and good water management practices to be considered and bring into more effective actions by the central government as well as related agencies for improving rice production in Cambodia in addition to capital investment and improving technical skills of supporting staffs and rural farmers.