gravity coupled with matter and the foundation of non commutative geometry we first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length elementds its unitary representations correspond to riemannian metrics and spin structure whileds is the dirac propagatords x x d 1 whered is the dirac operator we extend these simple relations to the non commutative case using tomita s involutionj we then write a spectral action the trace of a function of the length element which when applied to the non commutative geometry of the standard model will be shown cc to give the sm lagrangian coupled to gravity the internal fluctuations of the non commutative geometry are trivial in the commutative case but yield the full bosonic sector of sm with all correct quantum numbers in this slightly non commutative case the group of local gauge transformations appears spontaneously as a normal subgroup of the diffeomorphism group

discrete spectral triples and their symmetries we classify zero dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure we investigate also whether such spectral triples admit a symmetry arising from the hopf algebra structure of the finite algebra we discuss examples of commutative algebras and group algebras

global stability of an hiv 1 infection model with saturation infection and intracellular delay in this paper an hiv 1 infection model with a saturation infection rate and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated by analyzing the characteristic equations the local stability of an infection free equilibrium and a chronic infection equilibrium of the model is established by using suitable lyapunov functionals and the lasalle invariant principle it is proved that if the basic reproduction ratio is less than unity the infection free equilibrium is globally asymptotically stable if the basic reproduction ratio is greater than unity the chronic infection equilibrium is globally asymptotically stable

analysis of the dynamics of a delayed hiv pathogenesis model in this paper considering full logistic proliferation of cd4 t cells we study an hiv pathogenesis model with antiretroviral therapy and hiv replication time we first analyze the existence and stability of the equilibrium and then investigate the effect of the time delay on the stability of the infected steady state sufficient conditions are given to ensure that the infected steady state is asymptotically stable for all delay furthermore we apply the nyquist criterion to estimate the length of delay for which stability continues to hold and investigate the existence of hopf bifurcation by using a delay t as a bifurcation parameter finally numerical simulations are presented to illustrate the main results

dynamics of virus infection models with density dependent diffusion abstract density dependent diffusion plays an important role in the process of viral infection in this paper we construct mathematical models to investigate the dynamics of the viruses and their control single strain and multi strain viral infections are both considered in this work using the method proposed by pao and ruan 2013 we prove the well posedness of the models by constructing appropriate lyapunov functions we proved the global asymptotical stabilities of the models for the multi strain model we show that when the basic reproduction number for each strain is greater than one all viral strains coexist since the effect of different treatments may result in competitive exclusion it is essential to employ the treatment with combined therapy we find with surprise that the density dependent diffusion of the virus does not influence the global stabilities of the model with homogeneous neumann boundary conditions

weak and classical solutions to predator prey system with cross diffusion abstract in this paper we are concerned with a system of nonlinear partial differential equations modeling a predator prey system with cross diffusion in heterogeneous habitats predators are assumed to feed on preys with a holling type ii functional response to prey density and preys are assumed to follow a logistic growth in the absence of predation the mobility of each classes is assumed to be influenced by the gradient of other classes the existence result is proved by means of an approximation system the faedo galerkin method and the compactness method the global existence of classical solutions is proved under certain restrictions on the coefficients

spatial covariance based downlink beamforming in an sdma mobile radio system on the downlink of an sdma mobile radio system different users who share the same frequency band and time slot have to be spatially separated by beamforming in this paper we analyze an approach to jointly calculate weights in such a way that all users receive their signal with a given signal to noise and interference ratio the computations are based on spatial covariance matrices which describe the user specific channels averaged over the fast fading the presented algorithm succeeds in minimizing the array transmit power while spatially separating the users no matter which rank their spatial covariance matrices have but since it needs to solve a complex nonlinear constrained optimization problem several approximations of this algorithm are presented and compared to each other on the basis of array power complexity and convergence

a differential equation model of hiv infection of cd4 t cells with cure rate abstract a differential equation model of hiv infection of cd4 t cells with cure rate is studied we prove that if the basic reproduction number r 0 1 the hiv infection is cleared from the t cell population and the disease dies out if r 0 1 the hiv infection persists in the host we find that the chronic disease steady state is globally asymptotically stable if r 0 1 furthermore we also obtain the conditions for which the system exists an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

abstract quasilinear parabolic equations on considere des problemes paraboliques quasi lineaires abstraits p 0 u t a t u t u t f t u t t 0 u o u 0 ou u t est une fonction a valeurs dans un espace de banach x on donne des theoremes d existence locale et d unicite pour des solutions classiques et strictes de p 0

global solutions to a class of multi species reaction diffusion systems with cross diffusions arising in population dynamics in this paper an n species strongly coupled cooperating diffusive system is considered in a bounded smooth domain subject to homogeneous neumann boundary conditions employing the method of energy estimates we obtain some conditions on the diffusion matrix and inter specific cooperatives to ensure the global existence and uniform boundedness of a nonnegative solution the globally asymptotical stability of the constant positive steady state is also discussed as a consequence all the results hold true for multi species lotka volterra type competition model and prey predator model

dynamics in a diffusive predator prey system with ratio dependent predator influence abstract a diffusive predator prey system with predator functional response subject to neumann boundary conditions is considered existence nonexistence and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation hopf and steady state bifurcation analyses are carried out in detail these results provide theoretical evidences to the complex spatio temporal dynamics found by numerical simulation

global existence of solutions to a cross diffusion predator prey system with holling type ii functional response this paper is concerned with a cross diffusion system arising in a predator prey population model with holling type ii functional response in a bounded domain with no flux boundary condition employing the energy estimates and gagliardo nirenberg type inequalities to establish w 2 1 bounds uniform in time the global existence and uniform boundedness of solutions for a cross diffusion system are proved the global asymptotic stability of the constant positive steady state is also investigated

downlink mmse transceiver optimization for multiuser mimo systems duality and sum mse minimization we address the problem of minimum mean square error mmse transceiver design for point to multipoint transmission in multiuser multiple input multiple output mimo systems we focus on the problem of minimizing the downlink sum mse under a sum power constraint it is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink mse feasible regions we propose two different optimization frameworks for downlink mmse transceiver design the first one solves an equivalent uplink problem then the result is transferred to the original downlink problem duality ensures that any uplink mmse scheme e g linear mmse reception or mmse decision feedback equalization dfe has a downlink counterpart we propose two globally optimum algorithms based on convex optimization the basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels this strategy exploits that the same mse can be achieved in both links for a given choice of transmit and receive filters this iteration is proven to be convergent

krajewski diagrams and the standard model this paper provides a complete list of krajewski diagrams representing the standard model of particle physics we will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic hilbert space the algebra representations following from the krajewski diagrams are not complete in the sense that the corresponding spectral triples do not necessarily obey to the axiom of poincare duality this defect may be repaired by adding new particles to the model i e by building models beyond the standard model the aim of this list of finite spectral triples up to poincare duality is therefore to provide a basis for model building beyond the standard model

parabolic evolution equations in interpolation and extrapolation spaces on etudie le probleme de cauchy pour des equations d evolution lineaires a t u f t o t t de type parabolique dans un espace de banach x 0 on considere des resultats d existence d unicite et de continuite pour a t u u f t u o t t

evolution equations with dynamic boundary conditions in this paper we study boundary problems with dynamic boundary conditions that is with boundary operators containing time derivatives the equations under consideration are transformed into abstract cauchy problems x cx f and x 0 x 0 abstract theoretical results concerning the operators c are obtained by the study of a naturally arising pseudodifferential operator for existence and uniqueness theorems concerning solutions of parabolic and hyperbolic equations we then apply the theory of semigroups in banach spaces some examples of semilinear and quasilinear problems to which our results apply are given

spatial pattern dynamics due to the fitness gradient flux in evolutionary games we introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory the spatial flux is based on motion due to local gradients in the relative fitness of each strategy providing a game dependent alternative to diffusive coupling we study numerically the development of patterns in one dimension 1d for two strategy games including the coordination game and the prisoner s dilemma and in two dimensions 2d for the rock paper scissors game in 1d we observe modified traveling wave solutions in the presence of diffusion and asymptotic attracting states under a frozen strategy assumption without diffusion in 2d we observe spiral formation and breakup in the frozen strategy rock paper scissors game without diffusion a change of variables appropriate to replicator dynamics is shown to correctly capture the 1d asymptotic steady state via a nonlinear diffusion equation

dynamic theory of quasilinear parabolic equations i abstracts evolution equations on etablit les fondements abstraits pour une theorie dynamique generale pour des problemes aux valeurs limites et initiales quasilineaires

linear precoding via conic optimization for fixed mimo receivers in this paper the problem of designing linear precoders for fixed multiple input multiple output mimo receivers is considered two different design criteria are considered in the first the transmitted power is minimized subject to signal to interference plus noise ratio sinr constraints in the second the worst case sinr is maximized subject to a power constraint it is shown that both problems can be solved using standard conic optimization packages in addition conditions are developed for the optimal precoder for both of these problems and two simple fixed point iterations are proposed to find the solutions that satisfy these conditions the relation to the well known uplink downlink duality in the context of joint transmit beamforming and power control is also explored the proposed precoder design is general and as a special case it solves the transmit rank one beamforming problem simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders

block skew circulant matrices in complex valued signal processing two main lines of approach can be identified in the recent literature on improper signals and widely linear operations the augmented complex formulation based on the signal and its complex conjugate is considered as more insightful since it leads to convenient mathematical formulations for many considered problems moreover it allows an easy distinction between proper and improper signals as well as between linear and widely linear operations on the other hand the composite real representation using the real and imaginary parts of the signal is closer to the actual implementation and it allows to readily reuse results that have originally been derived for real valued signals or proper complex signals in this work we aim at getting the best of both worlds by introducing mathematical tools that make the composite real representation more powerful and elegant the proposed approach relies on a decomposition of real matrices into a block skew circulant and a block hankel skew circulant component by means of various application examples from the field of signal processing for communications we demonstrate the usefulness of the proposed framework

well posedness and stability results for a quasilinear periodic muskat problem abstract we study the muskat problem describing the spatially periodic motion of two fluids with equal viscosities under the effect of gravity in a vertical unbounded two dimensional geometry we first prove that the classical formulation of the problem is equivalent to a nonlocal and nonlinear evolution equation expressed in terms of singular integrals and having only the interface between the fluids as unknown secondly we show that this evolution equation has a quasilinear structure which is at a formal level not obvious and we also disclose the parabolic character of the equation exploiting these aspects we establish the local well posedness of the problem for arbitrary initial data in h s s with s 3 2 2 determine a new criterion for the global existence of solutions and uncover a parabolic smoothing property besides we prove that the zero steady state solution is exponentially stable

a complete description of the qos feasibility region in the vector broadcast channel we characterize the complete quality of service qos feasibility region and present a simple feasibility test for given qos requirements in the gaussian vector broadcast channel while most contributions in the literature recast the qos constraints into requirements for the signal to interference and noise ratios sinrs we convert them into upper bounds for the minimum mean square errors mmses instead and test feasibility in the mmse domain our main contribution is a complete description of the feasible mmse region its closure is shown to be a polytope and we find the complete set of its bounding half spaces noniteratively after a finite number of steps the polytope can easily be converted into any other qos domain like sinr or rate however the simple geometry of the mmse domain is lost in other domains once the bounding half spaces are determined any target mmse tuple can quickly be checked for feasibility by verifying its membership to the interior of the polytope for nondegenerate channels the only relevant bounding half space is essentially the lower bound on the sum mean square error no further computations are necessary contrary to existing feasibility checks which iteratively solve eigenproblems in an alternating optimization framework for every single qos requirement to test for two particular user antenna configurations we find a noniterative closed form solution for the optimum power allocation of the signal to interference ratio sir balancing

global existence and nonexistence for semilinear parabolic systems with nonlinear boundary conditions on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme t u j a jk k u a 0 u f u dans 0 a jk j k u bu 1 u g u sur 0 u 0 u 0 sur ou est un domaine borne de r n n 1 de classe c 2

spatiotemporal patterns in a reaction diffusion model with the degn harrison reaction scheme abstract spatial and temporal patterns generated in ecological and chemical systems have become a central object of research in recent decades in this work we are concerned with a reaction diffusion model with the degn harrison reaction scheme which accounts for the qualitative feature of the respiratory process in a klebsiella aerogenes bacterial culture we study the global stability of the constant steady state existence and nonexistence of nonconstant steady states as well as the hopf and steady state bifurcations in particular our results show the existence of turing patterns and inhomogeneous periodic oscillatory patterns while the system parameters are all spatially homogeneous these results also exhibit the critical role of the system parameters in leading to the formation of spatiotemporal patterns

mse balancing in the mimo bc unequal targets and probabilistic interference constraints second order cone soc restrictions have been widely employed in the design of wireless communication systems to recast precoding optimizations in convex form this paper highlights the flexibility of this framework to handle various transmit power and interference limitations also in the multistream multiple input multiple output broadcast channel with imperfect channel state information at the transmitter in particular we propose an iterative solution for mean square error mse balancing with such constraints via the lagrangian dual formulation the mse balancing criteria contrary to signal to interference plus noise ratio and rate criteria exhibit an interesting property when considering different targets for the receivers users with low target values are strictly prioritized in comparison to users with large mse targets that can even be switched off therefore only a subset of the receivers is served at the solution with stringent limitations for the precoders an example of such stringent limitations are small power constraints and probabilistic interference temperature constraints that set a measurable threshold on the generated interference in a cognitive radio system we provide four different approaches to approximate these probabilistic constraints with deterministic soc constraints and compare their accuracy

on a time dependent bio reactor model with chemotaxis long time dynamics of solutions to a strongly coupled system of parabolic equations modeling the competition in bio reactors with chemotaxis will be studied if the parameters of the system are periodic sufficient conditions for positive periodic solutions will be derived in terms of parabolic eigenvalue problems

uniform boundedness and convergence of solutions to the systems with a single nonzero cross diffusion uniform boundedness and convergence of global solutions are proved for quasilinear parabolic systems with a single nonzero cross diffusion in population dynamics gagliardo nirenberg type inequalities are used in the estimates of solutions in order to establish w12 bounds uniform in time by using the uniform bound convergence of solutions are established for systems with large diffusion coefficients in the weak competition case

prevention of blow up by fast diffusion in chemotaxis abstract in this paper we study a strongly coupled parabolic system with cross diffusion term which models chemotaxis the diffusion coefficient goes to infinity when cell density tends to an allowable maximum value such fast diffusion leads to global existence of solutions in bounded domains for any given initial data irrespective of the spatial dimension which is usually the goal of many modifications to the classical keller segel model the key estimates that make this possible have been obtained by a technique that uses ideas from moser s iterations

invariant manifolds and bifurcation for quasilinear reaction diffusion systems in this paper we consider parameter dependent quasilinear reaction diffusion equations on a bounded domain of r it is our purpose to study the dynamical behavior of solutions to these equations in particular we are interested in the behavior of the solution set if the parameter is changed to be more precise let us assume that sz c r is a bounded domain having a smooth boundary then we consider the parameter dependent equation

dynamics of a bio reactor model with chemotaxis long time dynamics of solutions to a strongly coupled system of parabolic equations modeling the competition in bio reactors with chemotaxis will be studied in particular we show that the dynamical system possesses a global attractor and that it is strongly uniformly persistent if the trivial steady state is unstable using a result of smith and waltman on perturbation of global attractors we also show that the positive steady state is unique and globally attracting

on a cross diffusion system arising in image denoising abstract we study a generalization of a cross diffusion problem deduced from a nonlinear complex variable diffusion model for signal and image denoising we prove the existence of weak solutions of the time independent problem with fidelity terms under mild conditions on the data problem then we show that this translates on the well posedness of a quasi steady state approximation of the evolution problem and also prove the existence of weak solutions of the latter under more restrictive hypothesis we finally perform some numerical simulations for image denoising comparing the performance of the cross diffusion model to other well known denoising methods

global stability and hopf bifurcation of an hiv 1 infection model with saturation incidence and delayed ctl immune response abstract in this paper an hiv 1 infection model with saturation incidence and time delay due to the ctl immune response is investigated by analyzing corresponding characteristic equations the local stability of each of feasible equilibria and the existence of hopf bifurcation at the ctl activated infection equilibrium are established respectively by means of lyapunov functionals and lasalle s invariance principle it is shown that the infection free equilibrium is globally asymptotically stable when the basic reproduction ratio is less than unity when the immune response reproductive ratio is less than unity and the basic reproductive ratio is greater than unity the ctl inactivated infection equilibrium of the system is globally asymptotically stable

stability of runge kutta methods for quasilinear parabolic problems we consider a quasilinear parabolic problem u t q u t u t u t 0 u 0 d where q w d c x x w w c x is a family of sectorial operators in a banach space x with fixed domain d this problem is discretized in time by means of a strongly a stable 0 2 runge kutta method we prove that the resulting discretization is stable under some natural assumptions on the dependence of q w with respect to w our results are useful for studying in l p norms 1 p many problems arising in applications some auxiliary results for time dependent parabolic problems are also provided

global existence analysis of cross diffusion population systems for multiple species the existence of global in time weak solutions to reaction cross diffusion systems for an arbitrary number of competing population species is proved the equations can be derived from an on lattice random walk model with general transition rates in the case of linear transition rates it extends the two species population model of shigesada kawasaki and teramoto the equations are considered in a bounded domain with homogeneous neumann boundary conditions the existence proof is based on a refined entropy method and a new approximation scheme global existence follows under a detailed balance or weak cross diffusion condition the detailed balance condition is related to the symmetry of the mobility matrix which mirrors onsager s principle in thermodynamics under detailed balance and without reaction the entropy is nonincreasing in time but counter examples show that the entropy may increase initially if detailed balance does not hold

a generic approach to qos based transceiver optimization we propose a generic framework for jointly optimizing the transmit power allocation and the adaptive receive strategies in a multiuser network with individual quality of service qos requirements the qos is assumed to be a one to one mapping of the signal to interference plus noise ratio sinr the feasibility of certain target qos depends on the mutual interference and on a given sum power constraint this coupling can be modeled by interference functions which determine how the transmit powers cause interference to the individual users we show fundamental properties like continuity and feasibility for the most general case when the functions are defined by axioms additional properties are shown for the case when the interference functions are based on a parameter dependent coupling matrix which allows to apply techniques from the theory of nonnegative matrices we derive a class of iterative algorithms which exploit the matrix structure the proposed iteration converges monotonically to the global optimum starting from the same initialization it is better than the known fixed point iteration it achieves arbitrary qos values within the qos feasible region

global stability of a diffusive and delayed virus dynamics model with beddington deangelis incidence function and ctl immune response in this paper we study a diffusive and delayed virus dynamics model with beddington deangelis incidence and ctl immune response by constructing lyapunov functionals we show that if the basic reproductive number is less than or equal to one then the infection free equilibrium is globally asymptotically stable if the immune reproductive number is less than or equal to one and the basic reproductive number is greater than one then the immune free equilibrium is globally asymptotically stable if the immune reproductive number is greater than one then the interior equilibrium is globally asymptotically stable

global solutions for quasilinear parabolic systems we present an approach for proving the global existence of classical solutions of certain quasilinear parabolic systems with homogeneous dirichlet boundary conditions in bounded domains with a smooth boundary c 2003 elsevier inc all rights reserved

global dynamics of a diffusive and delayed viral infection model with cellular infection and nonlinear infection rate abstract a diffusive and delayed viral dynamics model which incorporates cell to cell transmission cell mediated immune responses and general nonlinear incidence is investigated by constructing lyapunov functionals it is shown that the global threshold dynamics of the model is fully determined by the basic reproduction numbers of the virus and the immune response r 0 and r 1 the result implies that both the basic reproduction number of the virus and the immune response might be underevaluated without considering either the virus to cell transmission or cell to cell transmission the main results obtained in this paper extend some known results

semigroups and nonlinear evolution equations abstract in the main part of this paper we survey some recent results on a semigroup approach to parabolic equations under nonlinear boundary conditions in particular we give a detailed motivation and a heuristic derivation of a generalized variation of constant formula which is the basis for the whole method in the appendix we prove some new results about semigroups in interpolation and extrapolation spaces

on the stability of equilibria to weakly coupled parabolic systems in unbounded domains abstract we investigate weakly coupled semilinear parabolic systems in unbounded domains of r 2 or r 3 with general nonlinearities we present several sufficient conditions on the nonlinearities which ensure the stability of the zero solution with respect to h 2 perturbations in addition various examples are discussed to illustrate the scope of application of our results

entropic structure and duality for multiple species cross diffusion systems this paper deals with the existence of global weak solutions for a wide class of multiple species cross diffusions systems the existence is based on two different ingredients an entropy estimate giving some gradient control and a duality estimate that gives naturally l 2 control the proof relies on a semi implicit scheme tailored for cross diffusion systems firstly defined by the two authors and collaborators these results are applied to models having an entropy relying on the detailed balance condition recently exhibited by chen et al

on a classification of irreducible almost commutative geometries a second helping we complete the classification of almost commutative geometries from a particle physics point of view given by iochum schucker and stephan j math phys to be published four missing krajewski diagrams will be presented after a short introduction into irreducible nondegenerate spectral triples

korteweg de vries burgers system in rn abstract we study cauchy problem in r n for the korteweg de vries burgers system parabolic regularization technique is used to prove its global in time solvability the regularization effect of the laplacian term is observed for the viscous solutions constructed in the paper asymptotic behavior of weak solutions is discussed next in the language of the global attractors

lorentz positive maps and quadratic matrix inequalities with applications to robust miso transmit beamforming consider a unicast downlink beamforming optimization problem with robust signal to interference plus noise ratio constraints to account for imperfect channel state information at the base station in a multiple input single output miso communication system the convexity of this robust beamforming problem remains unknown a slightly conservative version of the robust beamforming problem is thus studied herein as a compromise it is in the form of a semi infinite second order cone program socp and more importantly it possesses an equivalent and explicit convex reformulation due to a linear matrix inequality lmi description of the cone of lorentz positive maps hence the conservative robust beamforming problem can be efficiently solved by an optimization solver additional robust shaping constraints can also be easily handled to control the amount of interference generated on other co existing users such as in cognitive radio systems

on the mse duality of the broadcast channel and the multiple access channel we present a mean square error mse duality between the broadcast channel and the multiple access channel for multiantenna users communicating with a single base station we introduce three levels of the duality which allow for a problem specific customization with different computational complexities and resolutions the first level preserves the sum mse during the conversion from the uplink to the downlink and vice versa whereas the second level not only keeps the sum mse constant but also ensures the preservation of the individual users mses the third level involves the finest resolution and preserves the individual streams mses and the individual streams signal to interference and noise ratio sinr simultaneously in contrast with hitherto existing mse dualities the proposed sort of duality features a lower complexity since no mse computation detouring is necessary during the conversion to the dual domain and is capable of handling all combinations of active and passive transmitters and receivers moreover we show how two of these three dualities can be exploited to solve the unweighted total sum mse minimization problem and the weighted sum mse minimization in the broadcast channel in an efficient way by revealing the hidden convexity in the first case and drastically reducing the computational complexity in the latter case

quasilinear evolution equations and parabolic systems it is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values provided the boundary conditions are time independent moreover it is shown that in the autonomous case these equations generate local semi flows on appropriate sobolev spaces our results apply in particular to the case of prescribed boundary values dirichlet boundary conditions

holder regularity for certain strongly coupled parabolic systems abstract we present a shorter proof to show holder continuity of bounded solutions to a general class of quasilinear parabolic equations the proof will be extended to obtain regularity results for bounded solutions to certain strongly coupled or cross diffusion quasilinear parabolic systems

on global existence of solutions to a cross diffusion system abstract we consider a strongly coupled nonlinear parabolic system which arises in population dynamics in n dimensional domains n 1 we prove the global existence of classical solutions to the system for n 10

random dispersal versus fitness dependent dispersal abstract this work extends previous work cantrell et al 2008 9 on fitness dependent dispersal for a single species to a two species competition model both species have the same population dynamics but one species adopts a combination of random and fitness dependent dispersal and the other adopts random dispersal global existence of smooth solutions to the time dependent quasilinear parabolic system is studied when a single species has a strong tendency to move up its fitness gradient it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution cantrell et al 2008 9 for the two species competition model if one species has strong tendency to move up its fitness gradient such approximately ideal free dispersal is advantageous relative to random dispersal bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate

global stability and periodic solution of the viral dynamics it is well known that the mathematical models provide very important information for the research of human immunodeficiency virus type 1 and hepatitis c virus hcv however the infection rate of almost all mathematical models is linear the linearity shows the simple interaction between the t cells and the viral particles in this paper we consider the classical mathematical model with saturation response of the infection rate by stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection free steady state we also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

a convergent finite volume method for a model of indirectly transmitted diseases with nonlocal cross diffusion in this paper we are concerned with a model of the indirect transmission of an epidemic disease between two spatially distributed host populations having non coincident spatial domains with nonlocal and cross diffusion the epidemic disease transmission occurring through a contaminated environment the mobility of each class is assumed to be influenced by the gradient of the other classes we address the questions of existence of weak solutions and existence and uniqueness of classical solution by using respectively a regularization method and an interpolation result between banach spaces moreover we propose a finite volume scheme and proved the well posedness nonnegativity and convergence of the discrete solution the convergence proof is based on deriving a series of a priori estimates and by using a general l p compactness criterion finally the numerical scheme is illustrated by some examples

aw1 p estimate for solutions to mixed boundary value problems for second order elliptic differential equations on demontre que sous des hypotheses plutot faibles une solution d un probleme aux valeurs limites mixte pour une equation elliptique d ordre 2 est dans l espace de sobolev w 1 p pour p 2

stable periodic orbits for a class of three dimensional competitive systems abstract it is shown that for a dissipative three dimensional competitive and irreducible system of ordinary differential equations having a unique equilibrium point at which point the jacobian matrix has negative determinant either the equilibrium point is stable or there exists an orbitally stable periodic orbit if in addition the system is analytic then there exists an orbitally asymptotically stable periodic orbit when the equilibrium is unstable the additional assumption of analyticity can be replaced by the assumption that the equilibrium point and every periodic orbit are hyperbolic in this case the morse smale conditions hold and the flow is structurally stable

on global existence for semilinear parabolic systems we present some results on global existence of classical solutions of certain semilinear parabolic systems with homogeneous dirichlet boundary conditions in bounded domains with a smooth boundary relaxing the usual monotonicity assumptions on the nonlinearities

stability properties and hopf bifurcation of a delayed viral infection model with lytic immune response a class of more general delayed viral infection model with lytic immune response is proposed based on some important biological meanings the effect of time delay on stabilities of the equilibria is given the sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium and the local asymptotic stabilities of the no immune response equilibrium are given we also get the sufficient criteria for stability switch of the positive equilibrium numerical simulations are carried out to explain the mathematical conclusions

minimal transmit power in parallel vector broadcast channels with linear precoding we consider the communication over a set of parallel multiple input single output miso broadcast channels with separate linear precoding on each of them in this setup we study the problem of fulfilling per user quality of service constraints expressed in terms of rates using minimal transmit power by means of a dual decomposition approach and a branch and bound algorithm solving the arising nonconvex subproblems we find the so far unknown globally optimal solution for the case of linear precoding with time sharing although prohibitively complex for implementation in a practical system the new power minimization method is highly interesting from a theoretical point of view as it can be used to quantify the performance gap between the outcome of heuristic algorithms and the theoretical limitations of the system with linear transceivers we also extend the approach such that zero forcing constraints can be handled

global dynamics of a viral infection model with a latent period and beddington deangelis response in this paper we study the global dynamics of a viral infection model with a latent period the model has a nonlinear function which denotes the incidence rate of the virus infection in vivo the basic reproduction number of the virus is identified and it is shown that the uninfected equilibrium is globally asymptotically stable if the basic reproduction number is equal to or less than unity moreover the virus and infected cells eventually persist and there exists a unique infected equilibrium which is globally asymptotically stable if the basic reproduction number is greater than unity the basic reproduction number determines the equilibrium that is globally asymptotically stable even if there is a time delay in the infection

uniform holder bounds for a strongly coupled elliptic system with strong competition abstract this article is concerned with a strongly coupled elliptic system modeling the steady state of populations that compete in some region we prove that the solutions are uniformly holder bounded as the competition rate tends to infinity the proof relies on the blow up technique and the monotonicity formula

gradient based power minimization in mimo broadcast channels with linear precoding we study the problem of minimizing the sum transmit power in mutliple input multiple output mimo downlink channels with linear transceivers if per user quality of service qos constraints expressed in terms of rates have to be fulfilled to find a suboptimal solution of the arising non convex optimization problem we introduce new auxiliary variables representing the di vision of the per user rate constraints into per stream rate targets and we optimize these variables by means of gradient projection steps this new method is combined with alternating updates of the transmit and receive filters furthermore the proposed algorithm ensures that the mean square error mse matrices of all users are diagonal and in the course of the execution of the algorithm it is possible that inactive streams get activated if this leads to a decreased sum transmit power in numerical simulations the new algorithm turns out to be superior to the various existing methods since these methods either lead to a higher sum transmit power than the proposed scheme or have a higher computational complexity or make restrictive assumptions on the system parameters

analysis of stability and hopf bifurcation for an hiv infection model with time delay a class of more general hiv infection models with time delay is proposed based on some important biological meanings the effect of time delay on stability of the equilibria of the infection model has been studied and the sufficient criteria for stability switch of the infected equilibrium and the local and global asymptotic stability of the viral free equilibrium are given using the normal form theory and center manifold argument the explicit formulaes which determine the stability the direction and the periodic of bifurcating period solutions are derived numerical simulations are carried out to explain the mathematical conclusions

global existence and stabilization in a degenerate chemotaxis stokes system with mildly strong diffusion enhancement abstract a class of chemotaxis stokes systems generalizing the prototype n t u n n m 1 n n c c t u c c n c u t p u n u 0 is considered in bounded convex three dimensional domains where w 2 is given the paper develops an analytical approach which consists in a combination of energy based arguments and maximal sobolev regularity theory and which allows for the construction of global bounded weak solutions to an associated initial boundary value problem under the assumption that 0 1 m 9 8 moreover the obtained solutions are shown to approach the spatially homogeneous steady state 1 n 0 0 0 in the large time limit this extends previous results which either relied on different and apparently less significant energy type structures or on completely alternative approaches and thereby exclusively achieved comparable results under hypotheses stronger than 0 1

a second order magnus type integrator for quasi linear parabolic problems in this paper we consider an explicit exponential method of classical order two for the time discretisation of quasi linear parabolic problems the numerical scheme is based on a magnus integrator and requires the evaluation of two exponentials per step our convergence analysis includes parabolic partial differential equations under a dirichlet boundary condition and provides error estimates in sobolev spaces in an abstract formulation the initial boundary value problem is written as an initial value problem on a banach space x u t a u t u t 0 t t u 0 given involving the sectorial operator a v d x with domain d c x independent of v v c x under reasonable regularity requirements on the problem we prove the stability of the numerical method and derive error estimates in the norm of certain intermediate spaces between x and d various applications and a numerical experiment illustrate the theoretical results

modeling and mathematical analysis of an initial boundary value problem for hepatitis b virus infection abstract in this work we investigate the hepatitis b virus infection we first derive a nonlinear pde model for the studied biological phenomenon the obtained initial boundary value problem is completely analyzed to begin with the analysis of the model we use lou and zhao lemma concerning globally attractive steady states to prove boundedness of potential solutions then we prove global existence uniqueness and positivity of the solution by a variational method combined with semigroups theory and some other useful tools from functional analysis moreover the basic reproduction number r 0 determining the extinction or the persistence of the hbv infection is thoroughly computed via a new method based on spectral properties of differential operators the residue theorem and some arguments from numerical analysis also the global asymptotical properties of the hbv free equilibrium of the model are derived via a skillful construction of a suitable lyapunov function local stability of the endemic equilibrium of the model is studied as well finally numerical simulations are performed to support the theoretical results obtained

global existence for semilinear parabolic systems on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme u t a t u f t x u du d 2m 1 u dans t 0 b t u 0 sur t 0 u t 0 u 0 sur ou est un domaine de r n

stability and hopf bifurcation in a delayed viral infection model with mitosis transmission in this paper we study a model of hcv with saturation and delay we stablish the local and global stability of system also we stablish the occurrence of a hopf bifurcation we will determine conditions for the permanence of model and the length of delay to preserve stability we present a sensitivity analysis for the basic reproductive number

existence of global solutions for a ratio dependent food chain model with diffusion in this article a ratio dependent food chain model is studied very few mathematical results are known for this model with diffusion first the existence and uniform boundedness of global solutions and stability of the equilibrium points for the model of weakly coupled reaction diffusion type are discussed then we prove the existence of global classical solutions for the model of pde type with cross diffusion when the space dimension n6

global properties of delayed hiv dynamics models with differential drug efficacy in cocirculating target cells the objective of this work is to investigate the qualitative behaviors of three hiv dynamical models with two types of cocirculating target cells and intracellular discrete time delay in the two types of target cells the drug efficacy is assumed to be different the models take into account both short lived infected cells and long lived chronically infected cells the incidence rate of infection is given by bilinear and saturation functional response in the first and second model respectively while it is given by a general function in the third model lyapunov functionals are constructed and lasalle s invariance principle is applied to prove the global asymptotic stability of all equilibria of the models in the first two models we have derived the basic reproduction number r0 it has been proven that the disease free equilibrium is globally asymptotically stable gas when r0 1 and the endemic equilibrium is gas when r0 1 for the third model we have derived r0 and established a set of sufficient conditions for global stability of both disease free and endemic equilibria of the model at the end theoretical results have been checked by numerical simulations