ALBERT

Description: Let G k , n ℂ for 2 ≤ k

Description: Motivated by applications in evacuation planning, we consider a problem of optimizing flow with arc reversals in which the transit time depends on the orientation of the arc. In the considered problems, the transit time on an arc may change when it is reversed, contrary to the problems considered in the existing literature. Extending the existing idea of auxiliary network construction to allow asymmetric transit time on arcs, we present strongly polynomial time algorithms for solving single-source-single-sink maximum dynamic contraflow problem and quickest contraflow problem. The results are substantiated by a computational experiment in a Kathmandu road network. An algorithm to solve the corresponding earliest arrival contraflow problem with a pseudo-polynomial-time complexity is also presented. The partial contraflow approach for the corresponding problems has also been discussed.

Description: Mixed estimators in nonparametric regression have been developed in models with one response. The biresponse cases with different patterns among predictor variables that tend to be mixed estimators are often encountered. Therefore, in this article, we propose a biresponse nonparametric regression model with mixed spline smoothing and kernel estimators. This mixed estimator is suitable for modeling biresponse data with several patterns (response vs. predictors) that tend to change at certain subintervals such as the spline smoothing pattern, and other patterns that tend to be random are commonly modeled using kernel regression. The mixed estimator is obtained through two-stage estimation, i.e., penalized weighted least square (PWLS) and weighted least square (WLS). Furthermore, the proposed biresponse modeling with mixed estimators is validated using simulation data. This estimator is also applied to the percentage of the poor population and human development index data. The results show that the proposed model can be appropriately implemented and gives satisfactory results.

Description: In the present paper, we summarize the results of the research devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls. The walls of the vessel are subject to traveling waves. Experimental data show that the energy of the flowing fluid can be transferred and consumed by the structure (the walls), inducing “traveling wave flutter.” The problem of stability of fluid-structure interaction splits into two parts: (a) stability of fluid flow in the channel with harmonically moving walls and (b) stability of solid structure participating in the energy exchange with the flow. Stability of fluid flow, the main focus of the research, is obtained by solving the initial boundary value problem for the stream function. The main findings of the paper are the following: (i) rigorous formulation of the initial boundary problem for the stream function, ψ x , y , t , induced by the fluid-structure interaction model, which takes into account the axisymmetric pattern of the flow and “no-slip” condition near the channel walls; (ii) application of a double integral transformation (the Fourier transformation and Laplace transformation) to both the equation and boundary and initial conditions, which reduces the original partial differential equation to a parameter-dependent ordinary differential equation; (iii) derivation of the explicit formula for the Fourier transform of the stream function, ψ ˜ k , y , t ; (iv) evaluation of the inverse Fourier transform of ψ ˜ k , y , t and proving that reconstruction of ψ x , y , t can be obtained through a limiting process in the complex k -plane, which allows us to use the Residue theorem and represent the solution in the form of an infinite series of residues. The result of this research is an analytical solution describing blood flowing through a channel with flexible walls that are being perturbed in the form of a traveling wave.

Description: Analytical solutions for the transient single-phase and two-phase inward solid-state diffusion and solidification applied to the radial cylindrical and spherical geometries are proposed. Both solutions are developed from the differential equation that treats these phenomena in Cartesian coordinates, which are modified by geometric correlations and suitable changes of variables to achieve closed-form solutions. The modified differential equations are solved by using two well-known closed-form solutions based on the error function, and then equations are obtained to analyze the diffusion interface position as a function of time and position in cylinders and spheres. These exact correlations are inserted into the closed-form solutions for the slab and are used to update the roots for each radial position of the moving boundary interface. The predictions provided by the proposed analytical solutions are validated against the results of a numerical approach. Finally, a comparative study of diffusion in slabs, cylinders, and spheres is also presented for single-phase and two-phase solid-state diffusion and solidification, which shows the importance of the effects imposed by the radial cylindrical and spherical curvatures with respect to the Cartesian coordinate system in the process kinetics. The analytical model is proved to be general, as far as, a semi-infinite solution for diffusion problems with phase change exists in the form of the error function, which enables exact closed-form analytical solutions to be derived, by updating the root at each radial position the moving boundary interface.

Description: The contraflow approach has been extensively considered in the literature for modeling evacuations and has been claimed, due to its lane-direction-reversal capability, as an efficient idea to speed up the evacuation process. This paper considers the contraflow evacuation model on network with prioritized capacitated vertices that allows evacuees to be held at intermediate spots too, respecting their capacities and priority order. In particular, it studies the maximum flow evacuation planning problem and proposes polynomial and pseudo-polynomial time solution algorithms for static network and dynamic multinetwork, respectively. A real dataset of Kathmandu road network with evacuation spaces is considered to implement the algorithm designed for dynamic multinetwork and to observe its computational performance.

Description: This paper presents a mathematical model of glucose-insulin dynamics which is specific for type 2 diabetic patients. The general modelling is obtained by simplification of a global compartmental model by John Thomas Sorensen. The model parameters are estimated using nonlinear optimization and data collected in Rwanda for type 2 diabetic patients. In order to identify and evaluate possible abnormalities of type 2 diabetic patients, the Sampling Importance Resampling (SIR) particle filtering algorithm is used and implemented through discretization of the developed mathematical model. This process is done by clamping insulin and glucose concentrations at around clinical trial values as proposed by Defronzo. Furthermore, for detecting potential abnormalities in type 2 diabetic patients, we compare our results with results obtained from a simulation of the mathematical model for healthy subjects. The proposed mathematical model allows further investigation of the dynamic behavior of glucose, insulin, glucagon, stored insulin, and labile insulin in different organs for type 2 diabetic patients.

Description: Research has shown that current health expenditure in most countries, especially in sub-Saharan Africa, is inadequate and unsustainable. Yet, fraud, abuse, and waste in health insurance claims by service providers and subscribers threaten the delivery of quality healthcare. It is therefore imperative to analyze health insurance claim data to identify potentially suspicious claims. Typically, anomaly detection can be posited as a classification problem that requires the use of statistical methods such as mixture models and machine learning approaches to classify data points as either normal or anomalous. Additionally, health insurance claim data are mostly associated with problems of sparsity, heteroscedasticity, multicollinearity, and the presence of missing values. The analyses of such data are best addressed by adopting more robust statistical techniques. In this paper, we utilized the Bayesian quantile regression model to establish the relations between claim outcome of interest and subject-level features and further classify claims as either normal or anomalous. An estimated model component is assumed to inherently capture the behaviors of the response variable. A Bayesian mixture model, assuming a normal mixture of two components, is used to label claims as either normal or anomalous. The model was applied to health insurance data captured on 115 people suffering from various cardiovascular diseases across different states in the USA. Results show that 25 out of 115 claims (21.7%) were potentially suspicious. The overall accuracy of the fitted model was assessed to be 92%. Through the methodological approach and empirical application, we demonstrated that the Bayesian quantile regression is a viable model for anomaly detection.

Description: In this paper, we study a decomposition D -module structure of the polynomial ring. Then, we illustrate a geometric interpretation of the Specht polynomials. Using Brauer’s characterization, we give a partial generalization of the fact that factors of the discriminant of a finite map π : spec B ⟶ spec A generate the irreducible factors of the direct image of B under the map π .

Description: We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.

Description: We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.

Description: The concept of frames in Hilbert spaces continues to play a very interesting role in many kinds of applications. In this paper, we study the notion of dual continuous K -g-frames in Hilbert spaces. Also, we establish some new properties.

Description: Any continuous function with values in a Hausdorff topological space has a closed graph and satisfies the property of intermediate value. However, the reverse implications are false, in general. In this article, we treat additional conditions on the function, and its graph for the reverse to be true.

Description: For a Gaussian prime π and a nonzero Gaussian integer β = a + b i ∈ ℤ i with a ≥ 1 and β ≥ 2 + 2 , it was proved that if π = α n β n + α n − 1 β n − 1 + ⋯ + α 1 β + α 0 ≕ f β where n ≥ 1 , α n ∈ ℤ i 0 , α 0 , … , α n − 1 belong to a complete residue system modulo β , and the digits α n − 1 and α n satisfy certain restrictions, then the polynomial f x is irreducible in ℤ i x . For any quadratic field K ≔ ℚ m , it is well known that there are explicit representations for a complete residue system in K , but those of the case m ≡ 1   mod 4 are inapplicable to this work. In this article, we establish a new complete residue system for such a case and then generalize the result mentioned above for the ring of integers of any imaginary quadratic field.

Description: For parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems inverse in time. It linearly combines the meaning of the solution at the initial and some intermediate points in time. The conditions for the correct solvability of this problem are clarified and the formula for its solution is found. Using the results obtained, the corresponding problems with impulse action were solved.

Description: Combinatorial sums and binomial identities have appeared in many branches of mathematics, physics, and engineering. They can be established by many techniques, from generating functions to special series. Here, using a simple mathematical induction principle, we obtain a new combinatorial sum that involves ordinary powers, falling powers, and binomial coefficient at once. This way, and without the use of any complicated analytic technique, we obtain a result that already exists and a generalization of an identity derived from Sterling numbers of the second kind. Our formula is new, genuine, and several identities can be derived from it. The findings of this study can help for better understanding of the relation between ordinary and falling powers, which both play a very important role in discrete mathematics.

Description: A graph G is called cycle books B 4 , m , 2 if G consists of m cycles C 4 with a common path P 2 . Figueroa-Centeno, Ichishima, and Muntaner-Batle conjecture that the graph B 4 , m , 2 is super edge-magic total if and only if m is even or m ≡ 5   mod 8 . In this article, we prove this conjecture for m  ≥ 36 and m  = 0 mod (2).

Description: A mapping   ℸ :   V G ⟶ N ∪ 0 for a connected graph G = V , E is called a radial radio labelling if it satisfies the inequality     ℸ x −   ℸ   y + d x , y ≥ rad G + 1 ∀ x , y ∈ V G , where rad G is the radius of the graph G . The radial radio number of ℸ denoted by r r ℸ   is the maximum number mapped under ℸ . The radial radio number of G denoted by r r G is equal to min { r r ℸ   / ℸ   is a radial radio labelling of G }.

Description: For a polynomial p z of degree n , it follows from the maximum modulus theorem that max z = R ≥ 1 p z ≤ R n max z = 1 p z . It was shown by Ankeny and Rivlin that if p z ≠ 0 for z

Description: In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds M , g , f , λ , ξ by a real tensor field f of type 1,1 , a real function λ such that f 3 = λ 2 f where ξ is its characteristic vector field. We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. In 1976, Blair proved that the vector field ξ of a normal contact manifold is Killing. Contrary to this, we have shown in Theorem 2 that, in general, ξ of a normal CPF-manifold is non-Killing. We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations symmetries, and almost Ricci soliton manifolds, supported by three applications. Contrary to the odd-dimensional contact manifolds, we construct several examples of even- and odd-dimensional semi-Riemannian and lightlike CPF-manifolds and propose two problems for further consideration.

Description: In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

Description: This paper presents a new approach to determine the number of solutions of three-variable Frobenius-related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius-related problem means the number of variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three-variable Frobenius-related problems. The first method is used to reduce the equation of order three from a three-variable Frobenius-related problem to be a system of equations with two fixed variables. The second method reduces the equation of order three into three equations of order two, for which an algorithm is designed with an interesting open problem on solutions left as a conjecture.

Description: In this paper, we present and establish a new result on the stability analysis of solutions for fuzzy nonlinear fractional differential equations by extending Lyapunov’s direct method from the fuzzy ordinary case to the fuzzy fractional case. As an application, several examples are presented to illustrate the proposed stability result.

Description: Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.

Description: This article deals with the study of mathematical models and the assessment of the stability of the motion of ships, investigating properties of the system such as kinetics and stability. This is essential for the selection of suitable control methods according to the requirements set out for the problem. Some control methods require the author to specify control parameters before the operation of the system can be started. Therefore, the survey of the article is useful for the above problem. Control methods through simulation results (PID controller, lag compensator, and lead compensator) give me results that reflect properties of the system (the stability of the operation cycle of the ship model). In addition, control methods for this model, which serve for research and education, are also presented below. Simulation is done by Matlab.

Description: The study recognized the worth of understanding the how’s of handling censoring and censored data in survival analysis and the potential biases it might cause if researchers fail to identify and handle the concepts with utmost care. We systematically reviewed the concepts of censoring and how researchers have handled censored data and brought all the ideas under one umbrella. The review was done on articles written in the English language spanning from the late fifties to the present time. We googled through NCBI, PubMed, Google scholar and other websites and identified theories and publications on the research topic. Revelation was that censoring has the potential of biasing results and reducing the statistical power of analyses if not handled with the appropriate techniques it requires. We also found that, besides the four main approaches (complete-data analysis method; imputation approach; dichotomizing the data; the likelihood-based approach) to handling censored data, there were several other innovative approaches to handling censored data. These methods include censored network estimation; conditional mean imputation method; inverse probability of censoring weighting; maximum likelihood estimation; Buckley-Janes least squares algorithm; simple multiple imputation strategy; filter algorithm; Bayesian framework; β -substitution method; search-and-score-hill-climbing algorithm and constraint-based conditional independence algorithm; frequentist; Markov chain Monte Carlo for imputed data; quantile regression; random effects hierarchical Cox proportional hazards; Lin’s Concordance Correlation Coefficient; classical maximum likelihood estimate. We infer that the presence of incomplete information about subjects does not necessarily mean that such information must be discarded, rather they must be incorporated into the study for they might carry certain relevant information that holds the key to the understanding of the research. We anticipate that through this review, researchers will develop a deeper understanding of this concept in survival analysis and select the appropriate statistical procedures for such studies devoid of biases.

Description: We extend the well-known characterizations of convergence in the spaces l p ( 1 ≤ p

Description: In this paper, we are interested in the inverse problem of the determination of the unknown part ∂ Ω , Γ 0 of the boundary of a uniformly Lipschitzian domain Ω included in ℝ N from the measurement of the normal derivative ∂ n v on suitable part Γ 0 of its boundary, where v is the solution of the wave equation ∂ t t v x , t − Δ v x , t + p x v x = 0 in Ω × 0 , T and given Dirichlet boundary data. We use shape optimization tools to retrieve the boundary part Γ of ∂ Ω . From necessary conditions, we estimate a Lagrange multiplier k Ω which appears by derivation with respect to the domain. By maximum principle theory for hyperbolic equations and under geometrical assumptions, we prove a uniqueness result of our inverse problem. The Lipschitz stability is established by increasing of the energy of the system. Some numerical simulations are made to illustrate the optimal shape.

Description: For any two distinct vertices and in a connected graph , let be the length of path and the D–distance between and of is defined as: , where the minimum is taken over all paths and the sum is taken over all vertices of path . The D-index of G is defined as . In this paper, we found a general formula that links the Wiener index with D-index of a regular graph G. Moreover, we obtained different formulas of many special irregular graphs.

Description: Using an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoids, and normal subgroupoids. We also present the isomorphism theorems for groupoids and their applications and obtain the corresponding version of the Zassenhaus Lemma and the Jordan-Hölder theorem for groupoids. Finally, inspired by the Ehresmann-Schein-Nambooripad theorem we improve a result of R. Exel concerning a one-to-one correspondence between partial actions of groups and actions of inverse semigroups.

Description: In this paper, we give an explicit lower bound for the class number of real quadratic field , where is a square-free integer, using which is the number of odd prime divisors of .

Description: Autism spectrum disorder (ASD) is an early developmental disorder characterized by mutation of enculturation associated with attention deficit disorder in the visual perception of emotional expressions. An estimated one in more than 100 people has autism. Autism affects almost four times as many boys than girls. Data analysis and classification of ASD is still challenging due to unsolved issues arising from many severity levels and range of signs and symptoms. To understanding the functions which involved in autism, neuroscience technology analyzed responses to stimuli of autistic audio and video. The study focuses on analyzing the data set of adults and children with ASD using practical component analysis method. To satisfy this aim, the proposed method consists of three main stages including: (1) data set preparation, (2) Data analysis, and (3) Unsupervised Classification. The experimental results were performed to classify adults and children with ASD. The classification results in adults give a sensitivity of 78.6% and specificity of 82.47%, while the classification results in children give a sensitivity of 87.5% and specificity of 95.7%.

Description: Frameproof codes were first introduced by Boneh and Shaw in 1998 in the context of digital fingerprinting to protect copyrighted materials. These digital fingerprints are generally denoted as codewords in , where Q is an alphabet of size q and n is a positive integer. A 2-frameproof code is a code C such that any 2 codewords in C cannot form a new codeword under a particular rule. Thus, no pair of users can frame a user who is not a member of the coalition. This paper concentrates on the upper bound for the size of a q-ary 2-frameproof code of length 4. Our new upper bound shows that when q is odd and .

Description: We consider the complex Grassmannian of k-dimensional subspaces of . There is a natural inclusion . Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in the space of mappings from to for and in particular to show that the cohomology of contains a truncated algebra , where , for and .

Description: The aim of this paper is to provide an approximation of the value-at-risk of the multivariate copula associated with financial loss and profit function. A higher dimensional extension of the Taylor–Young formula is used for this estimation in a Euclidean space. Moreover, a time-varying and conditional copula is used for the modeling of the VaR.

Description: Autism spectrum disorder (ASD) is an early developmental disorder characterized by mutation of enculturation associated with attention deficit disorder in the visual perception of emotional expressions. An estimated one in more than 100 people has autism. Autism affects almost four times as many boys than girls. Data analysis and classification of ASD is still challenging due to unsolved issues arising from many severity levels and range of signs and symptoms. To understanding the functions which involved in autism, neuroscience technology analyzed responses to stimuli of autistic audio and video. The study focuses on analyzing the data set of adults and children with ASD using practical component analysis method. To satisfy this aim, the proposed method consists of three main stages including: (1) data set preparation, (2) Data analysis, and (3) Unsupervised Classification. The experimental results were performed to classify adults and children with ASD. The classification results in adults give a sensitivity of 78.6% and specificity of 82.47%, while the classification results in children give a sensitivity of 87.5% and specificity of 95.7%.

Description: A method of finding exact solutions of the modified Veselov–Novikov (mVN) equation is constructed by Moutard transformations, and a geometric interpretation of these transformations is obtained. An exact solution of the mVN equation is found on the example of a higher order Enneper surface, and given transformations are applied in the game theory via Kazakh proverbs in terms of trees.

Description: In this paper, we present a continuous mathematical model of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number . We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number . The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium when . When , drinking present equilibrium exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium .

Description: The relationship between JW-algebras (resp. JC-algebras) and their universal enveloping von Neumann algebras (resp. C ∗ -algebras) can be described as significant and influential. Examples of numerous relationships have been established. In this article, we established a relationship between the set of split faces of the state space (resp. normal states) of a JC-algebra (resp. a JW-algebra) and the set of split faces of the state space (resp. normal states) of its universal enveloping C ∗ -algebra (resp. von Neumann algebra), and we tied up this relationship with the correspondence between the classes of invariant faces, closed ideals, and central projections of these Jordan algebras and of their universal enveloping algebras.

Description: In this paper, we derive a fixed-point theorem for self-mappings. That is, it is shown that every isometric self-mapping on a weakly compact convex subset of a strictly convex Banach space has a fixed point.

Description: In this paper, we present a sufficient condition for the output reachability of discrete-time positive switched systems. Besides, necessary and sufficient conditions for output monomial reachability and zero output controllability are provided. Further, some examples are shown.

Description: In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of θ -contraction and θ − ϕ -contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.

Description: In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy sparse noises, the new proposed approach incorporates novel ideas affine transformations and Tikhonov regularization into high-dimensional images. The highly corrupted, distorted, or misaligned images can be adjusted through the use of affine transformations and Tikhonov regularization term to ensure a trustful image decomposition. These novel ideas are very essential, especially in pruning out the potential impacts of annoying effects in high-dimensional images. Then, finding optimal variables through a set of affine transformations and Tikhonov regularization term is first casted as mathematical and statistical convex optimization programming techniques. Afterward, a fast alternating direction method for multipliers (ADMM) algorithm is applied, and the new equations are established to update the parameters involved and the affine transformations iteratively in the form of the round-robin manner. Moreover, the convergence of these new updating equations is scrutinized as well, and the proposed method has less time computation as compared to the state-of-the-art works. Conducted simulations have shown that the new robust method surpasses to the baselines for image alignment and recovery relying on some public datasets.

Description: In this paper, we establish a set of convenient conditions of controllability for semilinear fractional finite dimensional control systems involving conformable fractional derivative. Indeed, sufficient conditions of controllability for a semilinear conformable fractional system are presented, assuming that the corresponding linear systems are controllable. The present method is based on conformable fractional exponential matrix, Gramian matrix, and the iterative technique. Two illustrated examples are carried out to establish the facility and efficiency of this technique.

Description: Autism spectrum disorder (ASD) is an early developmental disorder characterized by mutation of enculturation associated with attention deficit disorder in the visual perception of emotional expressions. An estimated one in more than 100 people has autism. Autism affects almost four times as many boys than girls. Data analysis and classification of ASD is still challenging due to unsolved issues arising from many severity levels and range of signs and symptoms. To understanding the functions which involved in autism, neuroscience technology analyzed responses to stimuli of autistic audio and video. The study focuses on analyzing the data set of adults and children with ASD using practical component analysis method. To satisfy this aim, the proposed method consists of three main stages including: (1) data set preparation, (2) Data analysis, and (3) Unsupervised Classification. The experimental results were performed to classify adults and children with ASD. The classification results in adults give a sensitivity of 78.6% and specificity of 82.47%, while the classification results in children give a sensitivity of 87.5% and specificity of 95.7%.

Description: In this paper, we examine the relation between graph folding of a given graph and foldings of new graphs obtained from this graph by some techniques like dual, gear, subdivision, web, crown, simplex, crossed prism, and clique-sum graphs. In each case, we obtained the necessary and sufficient conditions, if exist, for these new graphs to be folded.

Description: Using an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and study subgroupoids, wide subgroupoids, and normal subgroupoids. We also present the isomorphism theorems for groupoids and their applications and obtain the corresponding version of the Zassenhaus Lemma and the Jordan-Hölder theorem for groupoids. Finally, inspired by the Ehresmann-Schein-Nambooripad theorem we improve a result of R. Exel concerning a one-to-one correspondence between partial actions of groups and actions of inverse semigroups.

Description: For any two distinct vertices u and  v in a connected graph G, let lPu,v=lP be the length of u−v path P and the D–distance between u and v of G is defined as: dDu,v=minplP+∑∀y∈VPdeg y, where the minimum is taken over all u−v paths P and the sum is taken over all vertices of u−v path P. The D-index of G is defined as WDG=1/2∑∀v,u∈VGdDu,v. In this paper, we found a general formula that links the Wiener index with D-index of a regular graph G. Moreover, we obtained different formulas of many special irregular graphs.

Description: A method of finding exact solutions of the modified Veselov–Novikov (mVN) equation is constructed by Moutard transformations, and a geometric interpretation of these transformations is obtained. An exact solution of the mVN equation is found on the example of a higher order Enneper surface, and given transformations are applied in the game theory via Kazakh proverbs in terms of trees.

Description: In this paper, we give an explicit lower bound for the class number of real quadratic field ℚd, where d=n2+4 is a square-free integer, using  ωn which is the number of odd prime divisors of n.

Description: We consider the complex Grassmannian Grk,n of k-dimensional subspaces of ℂn. There is a natural inclusion in,r:Grk,n↪Grk,n+r. Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in,r in the space of mappings from Grk,n to Grk,n+r for r≥1 and in particular to show that the cohomology of mapGrn,k,Grn,k+r;in,r contains a truncated algebra ℚx/xr+n+k2−nk, where x=2, for k≥2 and n≥4.

Description: In the present study, an attempt is made to explore the flow field inside the differentially heated lid-driven square cavity. The governing equations along with boundary conditions are solved numerically. The simulated results (100 ≤ Re ≤ 1000 and 0.001 ≤ Ri ≤ 10) are validated with previous results in the literature. The convection differencing schemes, namely, UPWIND, QUICK, SUPERBEE, and SFCD, are discussed and are used to simulate the flow using the MPI code. It is observed that the computational cost for all the differencing schemes get reduced tremendously when the MPI code is implemented. Plots demonstrate the influences of Re and Ri in terms of the contours of the fluid streamlines, isotherms, energy streamlines, and field synergy principle.

Description: In this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium E0 when R0≤1. When R0〉1, drinking present equilibrium E∗ exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium E∗.

Description: The aim of this paper is to provide an approximation of the value-at-risk of the multivariate copula associated with financial loss and profit function. A higher dimensional extension of the Taylor–Young formula is used for this estimation in a Euclidean space. Moreover, a time-varying and conditional copula is used for the modeling of the VaR.

Description: This paper considers a deterministic model for the dynamics of measles transmission in a population divided into six classes with respect to the disease states: susceptible, vaccinated, exposed, infected, treated, and recovered. First, we investigate the dynamical properties of the SVEITR model such as its equilibrium points, their stability, and parameter sensitivity by applying constant controls. Criteria for determining the stability of disease-free and endemic equilibrium points are provided in terms of basic reproduction number. The model is then extended by incorporating vaccination, therapy, and treatment rates as time-dependent control variables representing the level of coverages. Application of Pontryagin’s maximum principle provides the necessary conditions that must be satisfied for the existence of optimal controls aiming at minimization of the number of exposed and infected individuals simultaneously with the control effort. Numerical simulations that were carried out using the backward sweep method and Runge–Kutta scheme suggest that optimal controls under moderate and high scenarios can effectively reduce the cases of measles. In particular, the moderate scenario that utilizes the existing coverage level of 86% for MCV1 and 69% for MCV2 can degrade the cost functional by 47% of the low scenario. Meanwhile, high scenario that takes the 2020 target of 96% as coverage only makes a slight difference in reducing the number of exposed and infected individuals.

Description: Cross contamination that results in food-borne disease outbreaks remains a major problem in processed foods globally. In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. A contamination threshold ℛwf is determined. Analysis of the model shows that the disease-free equilibrium point is locally stable for ℛwf1. The time-dependent sensitivity analysis is performed using Latin hypercube sampling to determine model input parameters that significantly affect the severity of the listeriosis. Numerical simulations are carried out, and the results are discussed. The results show that a reduction in the number of contaminated workers and removal of contaminated food products are essential in eliminating the disease in the human population and vice versa. The results have significant public health implications in the management and containment of any listeriosis disease outbreak.

Description: A real form G0 of a complex semisimple Lie group G has only finitely many orbits in any given compact G-homogeneous projective algebraic manifold Z=G/Q. A maximal compact subgroup K0 of G0 has special orbits C which are complex submanifolds in the open orbits of G0. These special orbits C are characterized as the closed orbits in Z of the complexification K of K0. These are referred to as cycles. The cycles intersect Schubert varieties S transversely at finitely many points. Describing these points and their multiplicities was carried out for all real forms of SLn,ℂ by Brecan (Brecan, 2014) and (Brecan, 2017) and for the other real forms by Abu-Shoga (Abu-Shoga, 2017) and Huckleberry (Abu-Shoga and Huckleberry). In the present paper, we deal with the real form SOp,q acting on the SO (2n, C)-manifold of maximal isotropic full flags. We give a precise description of the relevant Schubert varieties in terms of certain subsets of the Weyl group and compute their total number. Furthermore, we give an explicit description of the points of intersection in terms of flags and their number. The results in the case of G/Q for all real forms will be given by Abu-Shoga and Huckleberry.

Description: Frameproof codes were first introduced by Boneh and Shaw in 1998 in the context of digital fingerprinting to protect copyrighted materials. These digital fingerprints are generally denoted as codewords in Qn, where Q is an alphabet of size q and n is a positive integer. A 2-frameproof code is a code C such that any 2 codewords in C cannot form a new codeword under a particular rule. Thus, no pair of users can frame a user who is not a member of the coalition. This paper concentrates on the upper bound for the size of a q-ary 2-frameproof code of length 4. Our new upper bound shows that C≤2q2−2q+1 when q is odd and q〉10.

Description: African trypanosomiasis is a vector-borne disease that is mainly transmitted by infected tsetse flies. A deterministic model of tsetse fly vector, human, and cattle hosts is formulated and analyzed to gain insights into the disease dynamics. The roles of public health education, treatment, and tsetse fly traps are studied. The effective reproduction number, a threshold used to determine whether the disease persists or dies out in the population, is determined. The sensitivity analysis of the model parameters is performed to determine their relationship with the effective reproduction number. The results show that the tsetse fly biting rate is the most sensitive parameter to the effective reproduction number. Furthermore, the model’s numerical simulation shows that a combination of all three interventions has the most significant impact on the control of African trypanosomiasis. Thus, we recommend that these control measures be put concurrently in endemic areas for effective control of the disease transmission.

Description: For polynomials x + y i and x + y − i satisfying the noncommutative multiplication y x = − x y , let C − 1 and N − 1 be the arithmetic tables, respectively. We investigate sequential properties of various diagonal sums over the tables C − 1 and N − 1 and prove that they are types of interlocked Fibonacci sequence and Padovan sequence.

Description: In this paper, we make use of the notion of the character of a transformation on a fixed set X , provided by Purisang and Rakbud in 2016, and the notion of a Δ -structure on X , provided by Magill Jr. and Subbiah in 1974, to define a sub-semigroup of the full-transformation semigroup T X . We also define a sub-semigroup of that semigroup. The regularity of those two semigroups is also studied.

Description: Count outcomes are commonly encountered in health sector data. The occurrence of count outcomes that exhibit many zeros has necessitated the extension of the ubiquitous Poisson regression model to accommodate the zero inflation and overdispersion as a result of the extra dispersion. We explored different extensions of the Poisson model including mixed models within the generalized linear mixed model framework to account for the repeated measurement of outcomes. These models are applied to maternal mortality data from fifty-six health facilities in four regions of Ghana. The objective is to identify factors associated with maternal mortality. The best-fitting model, the zero-inflated Poisson generalized linear mixed model, revealed that maternal mortality in hospital facilities is influenced by the number of referrals (into and out) of the hospital facility, number of antenatal visits exceeding four, number of midwives, and number of medical doctors at the facility. To be able to achieve targeted results in reducing maternal mortality and achieve the Sustainable Development Goal 3, the government, together with the ministry of health, should provide adequate maternal health services, especially at the district and community level. Additionally, there is a need for increased investment in Community Health Planning Services and related healthcare infrastructure and systems within the context of the Ouagadougou Declaration, that is, improve the training of skilled birth workers (midwives and doctors) and employ them at clinics to deal with labour complications without referring them to major hospitals. Furthermore, a well-structured awareness campaign is needed with importance given to avoiding adolescent pregnancy and improving antenatal care attendance to, at least, four, the gold standard, before delivery. Also, we recommend quality assessment form an essential part of all services that are directed towards improving maternal health and that more emphasis is needed to be given on research with multiple allied partners.

Description: In this paper, we present a new reduction algorithm for solving system of linear differential-algebraic equations with power series coefficients. In the proposed algorithm, we transform the given system of differential-algebraic equations into another simple equivalent system using the elementary algebraic techniques. This algorithm would help to implement the manual calculations in commercial packages such as Mathematica, Maple, MATLAB, Singular, and Scilab. Maple implementation of the proposed algorithm is discussed, and sample computations are presented to illustrate the proposed algorithm.

Description: The multicommodity flow problem arises when several different commodities are transshipped from specific supply nodes to the corresponding demand nodes through the arcs of an underlying capacity network. The maximum flow over time problem concerns to maximize the sum of commodity flows in a given time horizon. It becomes the earliest arrival flow problem if it maximizes the flow at each time step. The earliest arrival transshipment problem is the one that satisfies specified supplies and demands. These flow over time problems are computationally hard. By reverting the orientation of lanes towards the demand nodes, the outbound lane capacities can be increased. We introduce a partial lane reversal approach in the class of multicommodity flow problems. Moreover, a polynomial-time algorithm for the maximum static flow problem and pseudopolynomial algorithms for the earliest arrival transshipment and maximum dynamic flow problems are presented. Also, an approximation solution to the latter problem is obtained in polynomial-time.

Description: There is no effective therapeutic or vaccine for Middle East Respiratory Syndrome and this study attempts to find therapy using peptide by establishing a basis for the peptide-protein interactions through in silico docking studies for the spike protein of MERS-CoV. The antimicrobial peptides (AMPs) were retrieved from the antimicrobial peptide database (APD3) and shortlisted based on certain important physicochemical properties. The binding mode of the shortlisted peptides was measured based on the number of clusters which forms in a protein-peptide docking using Piper. As a result, we identified a list of putative AMPs which binds to the spike protein of MERS-CoV, which may be crucial in providing the inhibitory action. It is observed that seven putative peptides have good binding score based on cluster size cutoff of 208. We conclude that seven peptides, namely, AP00225, AP00180, AP00549, AP00744, AP00729, AP00764, and AP00223, could possibly have binding with the active site of the MERS-CoV spike protein. These seven AMPs could serve as a therapeutic option for MERS and enhance its treatment outcome.

Description: In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

Description: The aim of this paper is to study certain subclasses of bi-univalent functions defined by generalized Sãlãgean differential operator related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients and and upper bounds for the Fekete-Szegö functional for the functions in this class. The results proved by various authors follow as particular cases.

Description: In this paper, we consider the Schwartz’s one-factor model for a storable commodity and a futures contract on that commodity. We introduce the analysis of asymptotic arbitrage in storable commodity models by proving that the futures prices process allows asymptotic exponential arbitrage with geometric decaying failure probability. Next, we find by comparison that, under some similar conditions, our result is a corresponding commodity assets (stronger) version of Föllmer and Schachermayer’s result stated in the modeling setting of geometric Ornstein-Uhlenbeck process for financial security assets.

Description: Infectious laryngotracheitis virus (ILTV) is a gallid herpesvirus type 1, a member of the genus Iltovirus. It causes an infection in the upper respiratory tract mainly trachea which results in significant economic losses in the poultry industry worldwide. Vaccination against ILTV produced latent infected carriers’ birds, which become a source of virus transmission to nonvaccinated flocks. Thus this study aimed to design safe multiepitopes vaccine against glycoprotein B of ILT virus using immunoinformatic tools. Forty-four sequences of complete envelope glycoprotein B were retrieved from GenBank of National Center for Biotechnology Information (NCBI) and aligned for conservancy by multiple sequence alignment (MSA). Immune Epitope Database (IEDB) analysis resources were used to predict and analyze candidate epitopes that could act as a promising peptide vaccine. For B cell epitopes, thirty-one linear epitopes were predicted using Bepipred. However eight epitopes were found to be on both surface and antigenic epitopes using Emini surface accessibility and antigenicity, respectively. Three epitopes (190KKLP193, 386YSSTHVRS393, and 317KESV320) were proposed as B cell epitopes. For T cells several epitopes were interacted with MHC class I with high affinity and specificity, but the best recognized epitopes were 118YVFNVTLYY126, 335VSYKNSYHF343, and 622YLLYEDYTF630. MHC-II binding epitopes, 301FLTDEQFTI309,277FLEIANYQV285, and 743IASFLSNPF751, were proposed as promising epitopes due to their high affinity for MHC-II molecules. Moreover the docked ligand epitopes from MHC-1 molecule exhibited high binding affinity with the receptors; BF chicken alleles (BF2 2101 and 0401) expressed by the lower global energy of the molecules. In this study nine epitopes were predicted as promising vaccine candidate against ILTV. In vivo and in vitro studies are required to support the effectiveness of these predicted epitopes as a multipeptide vaccine through clinical trials.

Description: We propose a model which describes the interaction between pest and its natural predator. We assume that pest can be infected with diseases or pathogens such as bacteria, fungi, and viruses. The model is constructed by combining the Leslie-Gower model and S-I epidemic model. It is also considered the effects of pest harvesting. Harvesting in this case is intended to take a number of pests as one of the pest population control strategies. The proposed model will be analyzed dynamically to study its qualitative behaviour. The dynamical analysis includes the determination of all possible equilibrium points and their stability properties. Furthermore we also discuss the implementation of pesticide control where its optimal strategy is determined by Pontryagin’s maximum principle. To support our analytical studies, we perform some numerical simulations and their interpretation.

Description: Aptamer has been long studied as a substitute of antibodies for many purposes. However, due to the exceeded length of the aptamers obtained in vitro, difficulties arise in its manipulation during its molecular conjugation on the matrix surfaces. Current study focuses on computational improvement for aptamers screening of hepatitis B surface antigen (HBsAg) through optimization of the length sequences obtained from SELEX. Three original aptamers with affinity against HBsAg were truncated into five short hairpin structured aptamers and their affinity against HBsAg was thoroughly studied by molecular docking, molecular dynamics (MD) simulation, and Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) method. The result shows that truncated aptamers binding on HBsAg “a” determinant region are stabilized by the dynamic H-bond formation between the active binding residues and nucleotides. Amino acids residues with the highest hydrogen bonds hydrogen bond interactions with all five aptamers were determined as the active binding residues and further characterized. The computational prediction of complexes binding will include validations through experimental assays in future studies. Current study will improve the current in vitro aptamers by minimizing the aptamer length for its easy manipulation.

Description: In this paper we analyze the shape of fattened sets; given a compact set let be its fattened set; we prove a general bound between the perimeter of and the Lebesgue measure of . We provide two proofs: one elementary and one based on Geometric Measure Theory. Note that, by the Flemin–Rishel coarea formula, is integrable for . We further show that for any integrable continuous decreasing function there exists a compact set such that . These results solve a conjecture left open in (Mennucci and Duci, 2015) and provide new insight in applications where the fattened set plays an important role.

Description: In this study, we investigate the topology on -algebras: an algebraic system of propositional logic. We define here the notion of topological -algebras (briefly, -algebras) and some properties are investigated. A characterization of -algebras based on neighborhoods is provided. We also provide a filterbase that generates a unique -topology, making a -algebra in which the filterbase is a neighborhood base of the constant element, provided that the given -algebra is commutative. Finally, we investigate subalgebras of -algebras and introduce the notion of quotient -algebras of the given -algebra.

Description: Background. Familial Mediterranean Fever (FMF) is the most common autoinflammatory disease (AID) affecting mainly the ethnic groups originating from Mediterranean basin. We aimed to identify the pathogenic SNPs in MEFV by computational analysis software. Methods. We carried out in silico prediction of structural effect of each SNP using different bioinformatics tools to predict substitution influence on protein structure and function. Result. 23 novel mutations out of 857 nsSNPs are found to have deleterious effect on the MEFV structure and function. Conclusion. This is the first in silico analysis of MEFV gene to prioritize SNPs for further genetic mapping studies. After using multiple bioinformatics tools to compare and rely on the results predicted, we found 23 novel mutations that may cause FMF disease and it could be used as diagnostic markers for Mediterranean basin populations.

Description: In this work, a novel approach for solving systems of nonsimilar boundary layer equations over a large time domain is presented. The method is a multidomain bivariate spectral local linearisation method (MD-BSLLM), Legendre-Gauss-Lobatto grid points, a local linearisation technique, and the spectral collocation method to approximate functions defined as bivariate Lagrange interpolation. The method is developed for a general system of nonlinear partial differential equations. The use of the MD-BSLLM is demonstrated by solving a system of nonlinear partial differential equations that describe a class of nonsimilar boundary layer equations. Numerical experiments are conducted to show applicability and accuracy of the method. Grid independence tests establish the accuracy, convergence, and validity of the method. The solution for the limiting case is used to validate the accuracy of the MD-BSLLM. The proposed numerical method performs better than some existing numerical methods for solving a class of nonsimilar boundary layer equations over large time domains since it converges faster and uses few grid points to achieve accurate results. The proposed method uses minimal computation time and its accuracy does not deteriorate with an increase in time.

Description: It is well known that locally everywhere onto, totally transitive, and topologically mixing are equivalent on shift of finite type. It turns out that this relation does not hold true on shift of infinite type. We introduce the increasing gap shift and determine its chaotic properties. The increasing gap shift and the sigma star shift serve as counterexamples to show the relation between the three chaos notions on shift of infinite type.

Description: A simple graph is said to be an -covering if every edge of belongs to at least one subgraph isomorphic to . A bijection is an (a,d)--antimagic total labeling of if, for all subgraphs isomorphic to , the sum of labels of all vertices and edges in form an arithmetic sequence where , are two fixed integers and is the number of all subgraphs of isomorphic to . The labeling is called super if the smallest possible labels appear on the vertices. A graph that admits (super) --antimagic total labeling is called (super) --antimagic. For a special , the (super) --antimagic total labeling is called -(super)magic labeling. A graph that admits such a labeling is called -(super)magic. The -shadow of graph ,, is a graph obtained by taking copies of , namely, , and then joining every vertex in ,, to the neighbors of the corresponding vertex in . In this paper we studied the -supermagic labelings of where are paths and cycles.

Description: In the context of binary data mining, for unifying view on probabilistic quality measures of association rules, Totohasina’s theory of normalization of quality measures of association rules primarily based on affine homeomorphism presents some drawbacks. Indeed, it cannot normalize some interestingness measures which are explained below. This paper presents an extension of it, as a new normalization method based on proper homographic homeomorphism that appears most consequent.

Description: The automorphism group of the unitary group has a maximal subgroup of the form of order 20643840. In this paper, Fischer-Clifford theory is applied to the split extension group to construct its character table. Also, class fusion from into the parent group is determined.

Description: This paper is concerned with the blow-up properties of Cauchy and Dirichlet problems of a coupled system of Reaction-Diffusion equations with gradient terms. The main goal is to study the influence of the gradient terms on the blow-up profile. Namely, under some conditions on this system, we consider the upper blow-up rate estimates for its blow-up solutions and for the gradients.

Description: We consider the following problem: where is a bounded set in () with a smooth boundary, ,,, and and belong to for some . In this paper, we assume that a.e. in and without sign condition and then we prove the existence of at least two bounded solutions under the condition that and are suitably small. For this purpose, we use the Mountain Pass theorem, on an equivalent problem to with variational structure. Here, the main difficulty is that the nonlinearity term considered does not satisfy Ambrosetti and Rabinowitz condition. The key idea is to replace the former condition by the nonquadraticity condition at infinity.

Description: Machine learning has undergone a transition phase from being a pure statistical tool to being one of the main drivers of modern medicine. In gastroenterology, this technology is motivating a growing number of studies that rely on these innovative methods to deal with critical issues related to this practice. Hence, in the light of the burgeoning research on the use of machine learning in gastroenterology, a systematic review of the literature is timely. In this work, we present the results gleaned through a systematic review of prominent gastroenterology literature using machine learning techniques. Based on the analysis of 88 journal articles, we delimit the scope of application, we discuss current limitations including bias, lack of transparency, accountability, and data availability, and we put forward future avenues.

Description: Harmonic functions can be constructed using two analytic functions acting as their analytic and coanalytic parts but the prediction of the behavior of convolution of harmonic functions, unlike the convolution of analytic functions, proved to be challenging. In this paper we use the shear construction of harmonic mappings and introduce dilatation conditions that guarantee the convolution of two harmonic functions to be harmonic and convex in the direction of imaginary axis.

Description: By examining whether the individualistic assumptions used in social choice could be used in the aggregation of individual preferences, Arrow proved a key lemma that generalizes the famous Szpilrajn’s extension theorem and used it to demonstrate the impossibility theorem. In this paper, I provide a characterization of Arrow’s result for the case in which the binary relations I extend are not necessarily transitive and are defined on abelian groups. I also give a characterization of the existence of a realizer of a binary relation defined on an abelian group. These results also generalize the well-known extension theorems of Szpilrajn, Dushnik-Miller, and Fuchs.

Description: In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

Description: A graph G is called (a, b)-cycle books B[(Ca, m), (Cb, n), Pt] if G consists of m cycles Ca and n cycles Cb with a common path Pt. In this article we show that the (7, 3)-cycle books B[(C7, 1), (C3, n), P2] admits edge-magic total labeling. In addition we prove that (a, 3)-cycle books B[(Ca, 1), (C3, n), P2] admits super edge-magic total labeling for a = 7 and extends the values of a to 4x − 1 for any positive integer x. Moreover we prove that the (7, 3)-cycle books B[(C7, 2), (C3, n), P2] admits super edge-magic total labeling.

Description: In this paper, an ecoepidemiological deterministic model for the transmission dynamics of maize streak virus (MSV) disease in maize plant is proposed and analysed qualitatively using the stability theory of differential equations.The basic reproduction number with respect to the MSV free equilibrium is obtained using next generation matrix approach. The conditions for local and global asymptotic stability of MSV free and endemic equilibria are established. The model exhibits forward bifurcation and the sensitivity indices of various embedded parameters with respect to the MSV eradication or spreading are determined. Numerical simulation is performed and dispalyed graphically to justify the analytical results.

Description: For a locally compact Hausdorff space K and a Banach space X, let be the Banach space of all X-valued continuous functions defined on K, which vanish at infinite provided with the sup norm. If X is , we denote as . If be an extremely regular subspace of and is an into isomorphism, what can be said about the set-theoretical or topological properties of K and S? Answering the question, we will prove that if X contains no copy of , then the cardinality of K is less than that of S. Moreover, if and is also a subalgebra of , the cardinality of the αth derivative of K is less than that of the αth derivative of S, for each ordinal Finally, if and , then K is a continuous image of a subspace of S. Here, is the geometrical parameter introduced by Jarosz in 1989: As a consequence, we improve classical results about into isomorphisms from extremely regular subspaces already obtained by Cengiz.

Description: We aim through this paper to present an improved variational iteration method (VIM) based on Bernstein polynomials (BP) approximations to be used with transcendental functions. The key benefits gained from this modification are to reach stable and fairly accurate results and, at the same time, to expand the unknown function’s domain in partial differential equations (PDEs). The proposed approach introduces the Bernstein polynomials in the transcendental functions of nonlinear PDEs. A number of examples were included in order to expound the method’s capacity and reliability. From the results, we conclude that the VIM with BP is a powerful mathematical tool that can be applied to solve nonlinear PDEs.

Description: In this study, we work on the Fuchsian group where m is a prime number acting on transitively. We give necessary and sufficient conditions for two vertices to be adjacent in suborbital graphs induced by these groups. Moreover, we investigate infinite paths of minimal length in graphs and give the recursive representation of continued fraction of such vertex.

Description: Automata are machines, which receive inputs, accordingly update their internal state, and produce output, and are a common abstraction for the basic building blocks used in engineering and science to describe and design complex systems. These arbitrarily simple machines can be wired together—so that the output of one is passed to another as its input—to form more complex machines. Indeed, both modern computers and biological systems can be described in this way, as assemblies of transistors or assemblies of simple cells. The complexity is in the network, i.e., the connection patterns between simple machines. The main result of this paper is to show that the range of simplicity for parts as compared to the complexity for wholes is in some sense complete: the most complex automaton can be obtained by wiring together direct-output memoryless components. The model we use—discrete-time automata sending each other messages from a fixed set of possibilities—is certainly more appropriate for computer systems than for biological systems. However, the result leads one to wonder what might be the simplest sort of machines, broadly construed, that can be assembled to produce the behaviour found in biological systems, including the brain.

Description: The unsteady magnetohydrodynamics (MHD) flow of nanofluid with variable fluid properties over an inclined stretching sheet in the presence of thermal radiation and chemical reaction is studied taking into account the effect of variable fluid properties in thermal conductivity and diffusion coefficient. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation. The numerical solutions of the problem are obtained by using the fourth order Runge-Kutta method in line with the shooting technique. It is found that the increase in both thermal conductivity and radiative heat flux decreases the heat transfer rate but increases the skin friction and mass transfer rates. It is further observed that the increase in porosity parameter and magnetic field reduces the skin friction, heat, and mass transfer rates.

Description: About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context.

Description: The representation of analytic functions as convergent series in Jacobi polynomials is reformulated using the Hadamard principal part of integrals for all . The coefficients of the series are given as usual integrals in the classical case (when ) or by their Hadamard principal part when they diverge. As an application it is shown that nonhomogeneous differential equations of hypergeometric type do generically have a unique solution which is analytic at both singular points in .

Description: In this paper, we have considered the generalized growth (-order and -type) in terms of coefficient of the development given in the (n, n)-th Newton-Padé approximant of meromorphic function. We use these results to study the relationship between the degree of convergence in capacity of interpolating functions and information on the degree of convergence of best rational approximation on a compact of (in the supremum norm). We will also show that the order of meromorphic functions puts an upper bound on the degree of convergence.

Description: Aptamer has been long studied as a substitute of antibodies for many purposes. However, due to the exceeded length of the aptamers obtained in vitro, difficulties arise in its manipulation during its molecular conjugation on the matrix surfaces. Current study focuses on computational improvement for aptamers screening of hepatitis B surface antigen (HBsAg) through optimization of the length sequences obtained from SELEX. Three original aptamers with affinity against HBsAg were truncated into five short hairpin structured aptamers and their affinity against HBsAg was thoroughly studied by molecular docking, molecular dynamics (MD) simulation, and Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) method. The result shows that truncated aptamers binding on HBsAg “a” determinant region are stabilized by the dynamic H-bond formation between the active binding residues and nucleotides. Amino acids residues with the highest hydrogen bonds hydrogen bond interactions with all five aptamers were determined as the active binding residues and further characterized. The computational prediction of complexes binding will include validations through experimental assays in future studies. Current study will improve the current in vitro aptamers by minimizing the aptamer length for its easy manipulation.

Description: Infectious laryngotracheitis virus (ILTV) is a gallid herpesvirus type 1, a member of the genus Iltovirus. It causes an infection in the upper respiratory tract mainly trachea which results in significant economic losses in the poultry industry worldwide. Vaccination against ILTV produced latent infected carriers’ birds, which become a source of virus transmission to nonvaccinated flocks. Thus this study aimed to design safe multiepitopes vaccine against glycoprotein B of ILT virus using immunoinformatic tools. Forty-four sequences of complete envelope glycoprotein B were retrieved from GenBank of National Center for Biotechnology Information (NCBI) and aligned for conservancy by multiple sequence alignment (MSA). Immune Epitope Database (IEDB) analysis resources were used to predict and analyze candidate epitopes that could act as a promising peptide vaccine. For B cell epitopes, thirty-one linear epitopes were predicted using Bepipred. However eight epitopes were found to be on both surface and antigenic epitopes using Emini surface accessibility and antigenicity, respectively. Three epitopes (190KKLP193, 386YSSTHVRS393, and 317KESV320) were proposed as B cell epitopes. For T cells several epitopes were interacted with MHC class I with high affinity and specificity, but the best recognized epitopes were 118YVFNVTLYY126, 335VSYKNSYHF343, and 622YLLYEDYTF630. MHC-II binding epitopes, 301FLTDEQFTI309,277FLEIANYQV285, and 743IASFLSNPF751, were proposed as promising epitopes due to their high affinity for MHC-II molecules. Moreover the docked ligand epitopes from MHC-1 molecule exhibited high binding affinity with the receptors; BF chicken alleles (BF2 2101 and 0401) expressed by the lower global energy of the molecules. In this study nine epitopes were predicted as promising vaccine candidate against ILTV. In vivo and in vitro studies are required to support the effectiveness of these predicted epitopes as a multipeptide vaccine through clinical trials.

Description: There is no effective therapeutic or vaccine for Middle East Respiratory Syndrome and this study attempts to find therapy using peptide by establishing a basis for the peptide-protein interactions through in silico docking studies for the spike protein of MERS-CoV. The antimicrobial peptides (AMPs) were retrieved from the antimicrobial peptide database (APD3) and shortlisted based on certain important physicochemical properties. The binding mode of the shortlisted peptides was measured based on the number of clusters which forms in a protein-peptide docking using Piper. As a result, we identified a list of putative AMPs which binds to the spike protein of MERS-CoV, which may be crucial in providing the inhibitory action. It is observed that seven putative peptides have good binding score based on cluster size cutoff of 208. We conclude that seven peptides, namely, AP00225, AP00180, AP00549, AP00744, AP00729, AP00764, and AP00223, could possibly have binding with the active site of the MERS-CoV spike protein. These seven AMPs could serve as a therapeutic option for MERS and enhance its treatment outcome.

Description: About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context.