global analysis of multi host and multi vector epidemic models abstract we formulate a multi group and multi vector epidemic model in which hosts dynamics is captured by staged progression s e i r framework and the dynamics of vectors is captured by an si framework the proposed model describes the evolution of a class of zoonotic infections where the pathogen is shared by m host species and transmitted by p arthropod vector species in each host the infectious period is structured into n stages with a corresponding infectiousness parameter to each vector species we determine the basic reproduction number r 0 2 m n p and investigate the dynamics of the systems when this threshold is less or greater than one we show that the dynamics of the multi host multi stage and multi vector system is completely determined by the basic reproduction number and the structure of the host vector network configuration particularly we prove that the disease free equilibrium is globally asymptotically stable gas whenever r 0 2 m n p 1 and a unique strongly endemic equilibrium exists and is gas if r 0 2 m n p 1 and the host vector configuration is irreducible that is either the disease dies out or persists in all hosts and all vector species

vibration of arbitrarily shaped triangular plates with elastically restrained edges abstract a solution method is proposed for the vibration analysis of arbitrarily shaped triangular plates with elastically restrained edges an arbitrarily shaped triangular plate is first mapped into a right angled isosceles triangular plate and subsequently stretched to form a square plate by padding to it another right angled isosceles triangular plate of near zero thickness the displacement function is then expressed as a two dimensional fourier cosine series supplemented by several one dimensional series introduced to improve the convergence and accuracy of the displacement solution regardless of the shapes and boundary conditions of the triangular plate the final stiffness and mass matrices can always be calculated analytically which makes the current solution method highly efficient in implementations numerical examples are presented to verify the applicability of the proposed method to triangular plates of different shapes and perhaps more importantly different boundary conditions the current method can be easily extended to plates with heterogeneous material properties variable thickness non uniform elastic restraints etc

three dimensional vibration analysis of circular and annular plates via the chebyshev ritz method abstract a three dimensional free vibration analysis of circular and annular plates is presented via the chebyshev ritz method the solution procedure is based on the linear small strain three dimensional elasticity theory selecting chebyshev polynomials which can be expressed in terms of cosine functions as the admissible functions a convenient governing eigenvalue equation can be derived through the ritz method according to the geometric properties of circular and annular plates the vibration is divided into three distinct categories axisymmetric vibration torsional vibration and circumferential vibration each vibration category can be further subdivided into the antisymmetric and symmetric ones in the thickness direction convergence and comparison study demonstrated the high accuracy and efficiency of the present method the present approach shows a distinct advantage over some other ritz solutions in that stable numerical operation can be guaranteed even when a large number of admissible functions is employed therefore not only lower order but also higher order eigenfrequencies can be obtained by using sufficient terms of the chebyshev polynomials finally some valuable results for annular plates with one or both edges clamped are given and discussed in detail

three dimensional vibration analysis of cantilevered and completely free isosceles triangular plates the free vibration of cantilevered and completely free isosceles triangular plates based on exact three dimensional elasticity theory is investigated the actual plate domain is first mapped onto a basic cubic domain then the ritz method is applied to derive the eigenfrequency equation from the strain energy and the kinetic energy of the plate a set of chebyshev polynomial series multiplied by a boundary function chosen to satisfy the essential geometry boundary conditions of the plate is developed as the admissible functions of each displacement component the convergence and comparison studies show that rather accurate results can be obtained by using this approach the effects of thickness to width ratio and apex angle on eigenfrequencies of the plates are studied in detail sets of valuable results are presented which may serve as the benchmark values for future numerical techniques in thick plate vibration analysis data for the completely free isosceles triangular plates are presented for the first time

accurate analytical solution for free vibration of the simply supported triangular plate exploiting the superposition method developed earlier by the author a highly accurate analytical type solution is obtained for the free vibration of the general simply supported triangular plate a new technique is introduced for the orderly storage of eigenvalues it is shown how advantage can be taken of the more easily obtained isosceles triangular plate solutions accurate eigenvalues are tabulated for a wide range of plate geometries this represents the first accurate and comprehensive treatment of this problem to appear in the literature a b d e h k k m w

compact formulations as a union of polyhedra we explore one method for finding the convex hull of certain mixed integer sets the approach is to break up the original set into a small number of subsets find a compact polyhedral description of the convex hull of each subset and then take the convex hull of the union of these polyhedra the resulting extended formulation is then compact its projection is the convex hull of the original set and optimization over the mixed integer set is reduced to solving a linear program over the extended formulation the approach is demonstrated on three different sets a continuous mixing set with an upper bound and a mixing set with two divisible capacities both arising in lot sizing and a single node flow model with divisible capacities that arises as a subproblem in network design

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

dynamics of a multigroup sis epidemic model with standard incidence rates and markovian switching abstract in this paper we investigate a multigroup sis epidemic model with standard incidence rates and markovian switching first of all we establish sufficient conditions for extinction of the diseases then we obtain sufficient conditions for persistence in the mean of the diseases in addition in the case of persistence we obtain sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic lyapunov function with regime switching

three dimensional vibration analysis of a torus with circular cross section the free vibration characteristics of a torus with a circular cross section are studied by using the three dimensional small strain elasticity theory a set of three dimensional orthogonal coordinates system comprising the polar coordinate r at each circular cross section and the circumferential coordinate around the ring is developed each of the displacement components ur and w in the r and directions respectively is taken as a product of the chebyshev polynomials in the r direction and the trigonometric functions in the and directions eigenfrequencies and vibration mode shapes have been obtained via a three dimensional displacement based extremum energy principle upper bound convergence of the first seven eigenfrequencies accurate to at least six significant figures is obtained by using only a few terms of the admissible functions the eigenfrequency responses due to variation of the ratio of the radius of the ring centroidal axis to the cross sectional radius are investig

two group sir epidemic model with stochastic perturbation a stochastic two group sir model is presented in this paper the existence and uniqueness of its nonnegative solution is obtained and the solution belongs to a positively invariant set furthermore the globally asymptotical stability of the disease free equilibrium is deduced by the stochastic lyapunov functional method if r 0 1 which means the disease will die out while if r 0 1 we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average in addition the intensity of the fluctuation is proportional to the intensity of the white noise when the white noise is small we consider the disease will prevail at last we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments

two group infection age model including an application to nosocomial infection in this article we analyze the global asymptotic behavior of a two group si susceptible infected epidemic model with age of infection we prove that the model exhibits the traditional threshold behavior where the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than one and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one we conclude the paper by presenting an application to nosocomial infections moreover some numerical simulations are presented for this application

global dynamic analysis of a model for vector borne diseases on bipartite networks abstract in this paper an sis si model on bipartite networks for vector borne disease is developed the basic reproduction number r 0 is identified and analyzed the global dynamics are completely determined by the reproduction number r 0 it is shown that if r 0 1 the disease free equilibrium is globally asymptotically stable if r 0 1 there is a unique endemic equilibrium which is globally asymptotically stable finally numerical simulations are performed to validate the theoretical results and reveal the influence of network structure on basic reproduction number the transmission scale and propagation speed

accurate free vibration analysis of right triangular plates with one free edge abstract an accurate analytical type analysis of the free vibration of right triangular plates with one free edge has been achieved by the superposition method a number of modifications to the theoretical procedure as described earlier have had to be introduced these modifications are described in detail computed eigenvalues for the first four free vibration modes of plates with all possible combinations of classical boundary conditions are presented this represents to the author s knowledge the first accurate comprehensive treatment of this set of problems

lyapunov functions and global stability for age structured hiv infection model we study the basic age structured population model describing the hiv infection process which is defined by pdes the model allows the production rate of viral particles and the death rate of productively infected cells to vary and depend on the infection age by using the direct lyapunov method and constructing suitable lyapunov functions dynamical properties of the age structured model without or with drug treatment are established the results show that the global asymptotic stability of the infection free steady state and the infected steady state depends only on the basic reproductive number determined by the burst size further we establish mathematically that the typical ode and dde delay differential equation models of hiv infection are equivalent to two special cases of the above pde models

an element free imls ritz method for numerical solution of three dimensional wave equations abstract this paper presents an element free based numerical approach for solving three dimensional wave equations based on the ritz minimization procedure the method involves the use of a set of orthogonal shape functions to approximate its field variables in this study an improved moving least squares imls is used to generate sets of orthogonal shape functions that reduced the number of unknown coefficients in the trial functions the entire approximation procedure can be easily implemented numerically the accuracy of the approximation can be enhanced by increasing the number of nodes used in the computation as the result of the above procedures a final algebraic equation system is derived through discretizing the constructed functional the functional is established by enforcing the dirichlet boundary conditions via the penalty approach the simplicity and applicability of the element free method are demonstrated by solving several selected linear and nonlinear three dimensional wave equations besides the convergence study the present results are compared with the available published solutions from the literature where possible verifying the accuracy efficiency and reliability of the imls ritz method

three dimensional vibration analysis of thick rectangular plates using chebyshev polynomial and ritz method this paper describes a method for free vibration analysis of rectangular plates with any thicknesses which range from thin moderately thick to very thick plates it utilises admissible functions comprising the chebyshev polynomials multiplied by a boundary function the analysis is based on a linear small strain three dimensional elasticity theory the proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions a very simple and general programme has been compiled for the purpose for a plate with geometric symmetry the vibration modes can be classified into symmetric and antisymmetric ones in that direction in such a case the computational cost can be greatly reduced while maintaining the same level of accuracy convergence studies and comparison have been carried out taking square plates with four simply supported edges as examples it is shown that the present method enables rapid convergence stable numerical operation and very high computational accuracy parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail with respect to different thickness side ratios aspect ratios and poissons ratios these results may serve as benchmark solutions for validating approximate two dimensional theories and new computational techniques in future 2002 elsevier science ltd all rights reserved

on the dynamics of a class of multi group models for vector borne diseases abstract the resurgence of vector borne diseases is an increasing public health concern and there is a need for a better understanding of their dynamics for a number of diseases e g dengue and chikungunya this resurgence occurs mostly in urban environments which are naturally very heterogeneous particularly due to population circulation in this scenario there is an increasing interest in both multi patch and multi group models for such diseases in this work we study the dynamics of a vector borne disease within a class of multi group models that extends the classical bailey dietz model this class includes many of the proposed models in the literature and it can accommodate various functional forms of the infection force for such models the vector host host vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases under the assumption that the contact network is strongly connected we can define the basic reproductive number r 0 and show that this system has only two equilibria the so called disease free equilibrium dfe and a unique interior equilibrium usually termed the endemic equilibrium ee that exists if and only if r 0 1 we also show that if r 0 1 then the dfe equilibrium is globally asymptotically stable while when r 0 1 we have that the ee is globally asymptotically stable

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

3 d vibration analysis of generalized super elliptical plates using chebyshev ritz method the three dimensional free vibration of generalized super elliptical plates is analysed based on the exact small strain and linear elasticity theory the ritz method is applied to derive the frequency equation the triplicate chebyshev polynomial series form the backbones of the admissible functions as modified by a characteristic boundary function to ensure the satisfaction of geometric boundary conditions of the plate utilizing the symmetry of the plate under consideration eight distinct vibration modes can be classified and individually solved while maintaining the same level of accuracy the accuracy of the present method has been examined by the convergence and comparison studies the effect of geometric parameters on vibration behaviour of the generalized super elliptical plates with free and fixed perimeters have been studied for different powers thickness ratios and aspect ratios

three dimensional free vibration analysis of plates using the h p version of the finite element method the h p version of the finite element method based on a pentahedral p element is applied to three dimensional free vibrations of plates the element s new hierarchical shape functions are expressed in terms of the shifted legendre orthogonal polynomials the accuracy of the solution can be improved by simultaneously refining the mesh and increasing the polynomial order the method is capable of providing a full frequency spectrum including both the in plane and the out of plane modes results of frequency calculations are first found for a skew plate on a soft edge support and a cantilevered right isosceles triangular plate and comparisons are made with other methods results are also found for a square plate on a hard edge support and comparisons are made with two dimensional plate theories furthermore highly accurate values for a free hexagonal plate are presented for the first time

three dimensional vibration analysis of functionally graded material sandwich plates abstract free vibration of functionally graded material sandwich rectangular plates with simply supported and clamped edges is studied based on the three dimensional linear theory of elasticity two common types of fgm sandwich plates namely the sandwich with fgm facesheet and homogeneous core and the sandwich with homogeneous facesheet and fgm core are considered the three displacements of the plates are expanded by a series of chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions the natural frequencies are obtained by ritz method rapid convergence is observed in this study the natural frequencies of simply supported power law fgm sandwich plates are compared with results from different two dimensional plate theories parametric study is performed for varying volume fraction layer thickness ratios thickness length ratios and aspect ratios of the sandwich plates

global stability of infectious disease models using lyapunov functions two systematic methods are presented to guide the construction of lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics specifically a matrix theoretic method using the perron eigenvector is applied to prove the global stability of the disease free equilibrium while a graph theoretic method based on kirchhoff s matrix tree theorem and two new combinatorial identities are used to prove the global stability of the endemic equilibrium several disease models in the literature and two new cholera models are used to demonstrate the applications of these methods

three dimensional vibration analysis of functionally graded material plates in thermal environment free vibration of functionally graded material rectangular plates with simply supported and clamped edges in the thermal environment is studied based on the three dimensional linear theory of elasticity simply supported and clamped fgm plates with temperature dependent material properties subjected to uniform temperature rise linear temperature rise and nonlinear temperature rise are considered the three displacements of the plates are expanded by a series of chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions the natural frequencies are obtained by ritz method the numerical results of the present approach are compared with the results of other researchers for the validation parametric study is performed for supported conditions temperature fields volume fraction indices of fgm plates

buckling of rectangular mindlin plates subjected to partial in plane edge loads using the radial point interpolation method this paper considers the elastic buckling of rectangular mindlin plates that are subjected to partially distributed in plane edge loadings a numerical algorithm based on the radial point interpolation method rpim is proposed for the solution of such plates the pre buckling stresses are first determined using the rpim based on a two dimensional 2 d elastic plane stress problem the buckling load intensity factors for rectangular plates that incorporate these predetermined pre buckling stresses are then computed via the rpim based on the mindlin plate theory numerical examples of the plates with various boundaries and subjected to different partially distributed in plane edge loadings are presented shear locking of the buckling load is studied the results demonstrate the high accuracy of the proposed rpim

the free flexural vibration of right triangular isotropic and orthotropic plates abstract a simple straighforward rayleigh ritz analysis is given for the determination of an eigenproblem for the free flexural vibration of thin right triangular plates having any combination of the classical free simply supported or clamped boundary conditions simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals the analysis is developed for specially orthotropic plates but numerical results are given primarily for the isotropic case

polyhedra for lot sizing with wagner whitin costs we examine the single item lot sizing problem with wagner whitin costs over ann period horizon i e pt ht pt 1 fort 1 n 1 wherept ht are the unit production and storage costs in periodt respectively so it always pays to produce as late as possible

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing results

the stability of stochastic coupled systems with time varying coupling and general topology structure we introduce a class of novel stochastic coupled systems in which the coupling structure is time varying and the topology structure is not strongly connected and first establish the system on a digraph with a time varying weight matrix motivated by du and li 2014 we give a hierarchical method to deal with digraphs without strong connectivity and establish the corresponding hierarchical algorithm to realize this approach also an example is given to illustrate our hierarchical algorithm and its feasibility in the sequel based on the theory of asymptotically autonomous systems kirchhoff s matrix tree theorem and lyapunov method several moment exponential stability criteria are presented including a lyapunov type theorem and a coefficient type criterion furthermore theoretical results are applied to stochastic coupled oscillators with time varying coupling structure sctcs and the stability criterion of sctcs is obtained finally the effectiveness of theoretical results is illustrated by two numerical examples

strong formulations of robust mixed 0 1 programming we introduce strong formulations for robust mixed 0 1 programming with uncertain objective coefficients we focus on a polytopic uncertainty set described by a budget constraint for allowed uncertainty in the objective coefficients we show that for a robust 0 1 problem there is an tight linear programming formulation with size polynomial in the size of an tight linear programming formulation for the nominal 0 1 problem we give extensions to robust mixed 0 1 programming and present computational experiments with the proposed formulations

three dimensional elasticity solutions to vibration of cantilevered skewed trapezoids an accurate three dimensional elasticity model for determining the free vibration response of skewed trapezoidal plates is presented the method is formulated on the basis of a linear small strain three dimensional elasticity theory with the ritz minimization procedure the solution method uses sets of uniquely defined one and twodimensional polynomial functions to approximate the trial displacements in the thickness and surface directions respectively these functions are orthogonally generated and have been proven to be highly efficient and numerically stable the proposed technique yields natural frequencies and mode shapes for a wide range of cantilevered skewed trapezoidal plates of arbitrary planform the accuracy of these results whenever possible is validated through comparison with the analytical and experimental data parametric investigations on the vibration behavior of cantilevered trapezoidal plates with respect to different thickness ratios skew angles and chord ratios have been carried out for the first time the presence of surface parallel symmetric thickness modes for these plates is demonstrated in vivid three dimensional mode shape plots

global stability of multigroup epidemic model with group mixing and nonlinear incidence rates in this paper we introduce a basic reproduction number for a multigroup seir model with nonlinear incidence of infection and nonlinear removal functions between compartments then we establish that global dynamics are completely determined by the basic reproduction number r0 it shows that the basic reproduction number r0 is a global threshold parameter in the sense that if it is less than or equal to one the disease free equilibrium is globally stable and the disease dies out whereas if it is larger than one there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population finally two numerical examples are also included to illustrate the effectiveness of the proposed result

three dimensional vibration analysis of cantilevered skew plates three dimensional 3 d free vibration of cantilevered thick skew plates is analyzed based on the exact linear and small strain elasticity theory the skew domain of the plate is mapped onto a cubic domain a set of triplicate chebyshev polynomials multiplied by a boundary function is developed as the trial functions of each displacement components using the ritz method the eigenvalue equation is derived from the strain energy and kinetic energy of the plate the vibration modes are divided into the antisymmetric and symmetric ones in the thickness direction therefore can be studied individually the convergence study shows that the first eight frequency parameters for each mode categories can be obtained with an accuracy of at least four significant figures the effect of geometric parameters such as skew angle aspect ratio and span thickness ratio on frequency parameters is studied the results are compared with those obtained by using the algebraic polynomials as trial functions and the 3 d finite element solutions respectively it is shown that the chebyshev polynomials can provide better numerical stability than the algebraic polynomials especially for the plates with large skew angle the present results can serve as the benchmark data for the accuracy evaluation of other computational techniques

global stability of the endemic equilibrium in infinite dimension lyapunov functions and positive operators abstract the global stability of the endemic equilibrium is shown for an endemic model with infinite dimensional population structure using a volterra like lyapunov function and the krein rutman theorem

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

analyzing two dimensional sine gordon equation with the mesh free reproducing kernel particle ritz method abstract we consider an analysis of the non linear two dimensional sine gordon sg equation the analysis is performed using the mesh free reproducing kernel particle ritz method kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

global stability of two group sir model with random perturbation abstract in this paper we discuss the two group sir model introduced by guo li and shuai h b guo m y li z shuai global stability of the endemic equilibrium of multigroup sir epidemic models can appl math q 14 2006 259 284 allowing random fluctuation around the endemic equilibrium we prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large in addition the stability condition is obtained by the construction of lyapunov function finally numerical simulations are presented to illustrate our mathematical findings

the sequential knapsack polytope in this paper we describe the convex hull of all solutions of the integer bounded knapsack problem in the special case when the weights of the items are divisible the corresponding inequalities are defined via an inductive scheme that can also be used in a more general setting

global dynamics of a general class of multistage models for infectious diseases we propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages the models can describe disease progression through multiple latent or infectious stages as in the case of hiv and tuberculosis amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment the models also incorporate general nonlinear incidences and general nonlinear forms of population transfer among stages under biologically motivated assumptions we derive the basic reproduction number r 0 and show that the global dynamics are completely determined by r 0 if r 0 leq 1 the disease free equilibrium is globally asymptotically stable and the disease dies out if r 0 1 then the disease persists in all stages and a unique endemic equilibrium is globally asymptotically stable

global stability of multi group epidemic models with distributed delays abstract we investigate a class of multi group epidemic models with distributed delays we establish that the global dynamics are completely determined by the basic reproduction number r 0 more specifically we prove that if r 0 1 then the disease free equilibrium is globally asymptotically stable if r 0 1 then there exists a unique endemic equilibrium and it is globally asymptotically stable our proof of global stability of the endemic equilibrium utilizes a graph theoretical approach to the method of lyapunov functionals

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

global analysis of new malaria intrahost models with a competitive exclusion principle in this paper we propose a malaria within host model with k classes of age for the parasitized red blood cells and n strains for the parasite we provide a global analysis for this model a competitive exclusion principle holds if mathcal r 0 the basic reproduction number satisfies mathcal r 0 leq 1 then the disease free equilibrium is globally asymptotically stable on the contrary if mathcal r 0 1 then generically there is a unique endemic equilibrium which corresponds to the endemic stabilization of the most virulent parasite strain and to the extinction of all the other parasites strains we prove that this equilibrium is globally asymptotically stable on the positive orthant if a mild sufficient condition is satisfied

three dimensional vibrations of cantilevered right triangular plates abstract the first known three dimensional continuum vibration solutions for cantilevered right triangular plates with variable thickness are obtained using the ritz method assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete reasonably accurate natural frequencies are calculated for low aspect ratio right triangular thin plates having arbitrary values of thickness taper ratios in the spanwise direction detailed numerical studies show that a three dimensional analysis is essential to monitoring coupled mode sensitivities in the variation of non dimensional natural frequencies with increasing thickness taper ratio upper bound results obtained using the present method are compared with those obtained by other investigators using ordinary beam theories two dimensional finite element and finite difference procedures and experimental methods this unified comparison of upper and lower bound solutions is presented here with the aim of bracketing the exact analytical solution of the subject problem

an improved moving least squares ritz method for two dimensional elasticity problems we propose an improved moving least squares ritz imls ritz method with its element free framework developed for studying two dimensional elasticity problems using the imls approximation for the field variables the discretized governing equations of the problem are derived via the ritz procedure in the imls an orthogonal function system with a weight function is employed as the basis for construction of its displacement field by using the element free imls ritz method solutions of the two dimensional elasticity problems are obtained the applicability of the element free imls ritz method is illustrated through three selected example problems the convergence characteristics of the method are examined by varying the number of nodes and geometric parameters of these examples the accuracy of the method is validated by comparing the computed results with the efg and exact solutions

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed