on the existence of local strong solutions to chemotaxis shallow water system with large data and vacuum abstract in this paper motivated by the chemotaxis navier stokes system arising from mathematical biology 43 a modified shallow water type chemotactic model is derived for large initial data allowing vacuum the local existence of strong solutions together with the blow up criterion is established

basic theory of f bounded quantification abstract system f bounded is a second order typed lambda calculus where the basic features of object oriented languages can be naturally modelled f bounded extends the better known system f in a way that provides an immediate solution for the treatment of the so called binary methods although more powerful than f and also quite natural system f bounded has only been superficially studied from a foundational perspective and many of its essential properties have been conjectured but never proved in the literature the aim of this paper is to give a solid foundation to f bounded by addressing and proving the key properties of the system in particular transitivity elimination completeness of the type checking semi algorithm the subject reduction property for reduction conservativity with respect to system f and antisymmetry of a full subsystem are considered and various possible formulations for system f bounded are compared finally a semantic interpretation of system f bounded is presented based on partial equivalence relations

aggregation blowup and collapse the abc s of taxis in reinforced random walks in many biological systems movement of an organism occurs in response to a diffusible or otherwise transported signal and in its simplest form this can be modeled by diffusion equations with advection terms of the form first derived by patlak bull of math biophys 15 1953 pp 311 338 however other systems are more accurately modeled by random walkers that deposit a nondiffusible signal that modifies the local environment for succeeding passages in these systems one example of which is the myxobacteria the question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates davis probab theory related fields 84 1990 pp 203 229 has studied this question for a certain class of random walks and here we extend this analysis to the continuum limit of such walks we first derive several general classes of partial differential equations that depend on how the movement rules are

optimal mean square state and parameter estimation for stochastic linear systems with poisson noises this paper presents the mean square state and parameter estimation problem for stochastic linear systems with unknown multiplicative and additive parameters over linear observations where unknown parameters are considered poisson processes the original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states the obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters performance of the designed optimal state filter and parameter identifier is verified for both stable and unstable stochastic linear systems and compared against the mean square estimator designed for polynomial systems with white gaussian noises

global existence and large time behavior for a two dimensional chemotaxis shallow water system abstract this paper concerns the chemotaxis shallow water system in two dimensional whole spaces we first establish the global existence of strong solution under the condition that the initial data are close to the constant equilibrium state in h n r 2 n 3 framework then the optimal time decay rates of the global solution are obtained by the method of energy estimates if the initial data belong to h s r 2 0 s 1 additionally

linear filtering for bilinear stochastic differential systems with unknown inputs investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance whose statistics are completely unknown a linear filter is proposed based on a suitable decomposition of the state of the bilinear system into two components the first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm no a priori information on the disturbance is required for the filter implementation the proposed filter is robust with respect to the unknown input in that the covariance of the estimation error is not affected by such input numerical simulations show the effectiveness of the proposed filter

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

exact finite dimensional filters for maximum likelihood parameter estimation of continuous time linear gaussian systems in this paper we derive a new class of finite dimensional filters for integrals and stochastic integrals of moments of the state for continuous time linear gaussian systems apart from being of significant mathematical interest these new filters can be used with the expectation maximization em algorithm to yield maximum likelihood estimates of the model parameters

how far do chemotaxis driven forces influence regularity in the navier stokes system the chemotaxis navier stokes system nt u n n n c c ct u c c nf c ut u u u p n u 0 0 1 is considered under boundary conditions of homogeneous neumann type for n and c and dirichlet type for u in a bounded convex domain r with smooth boundary where w and and f are sufficiently smooth given functions generalizing the prototypes const and f s s for s 0 it is known that for all suitably regular initial data n0 c0 and u0 satisfying 0 6 n0 0 c0 0 and u0 0 a corresponding initial boundary value problem admits at least one global weak solution which can be obtained as the pointwise limit of a sequence of solutions to appropriately regularized problems the present paper shows that after some relaxation time this solution enjoys further regularity properties and thereby complies with the concept of eventual energy solutions which is newly introduced here and which inter alia requires that two quasi dissipative inequalities are ultimately satisfied moreover it is shown that actually for any such eventual energy solution n c u there exists a waiting time t0 0 with the property that n c u is smooth in t0 and that n x t n0 c x t 0 and u x t 0 hold as t uniformly with respect to x this resembles a classical result on the three dimensional navier stokes system asserting eventual smoothness of arbitrary weak solutions thereof which additionally fulfill the associated natural energy inequality in consequence our results inter alia indicate that under the considered boundary conditions the possibly destabilizing action of chemotactic cross diffusion in does not substantially affect the regularity properties of the fluid flow at least on large time scales

global existence and large time behavior for a two dimensional chemotaxis navier stokes system abstract this paper concerns the coupled chemotaxis navier stokes system in the two dimensional setting such a system was proposed in 19 to describe the collective effects arising in bacterial suspensions in fluid drops under some basic assumptions on the parameter functions k and the potential function which are consistent with those used by the experimentalists but weaker than those appeared in the known mathematical works we establish the global existence of weak solutions and classical solutions for both the cauchy problem and the initial boundary value problem supplemented with some initial data for the initial boundary value problem we also assert that the solution converges in large time to the spatially homogeneous equilibrium n 0 0 0 with n 0 1 n 0 x d x our results also show that the large diffusion of the cell density or the chemical concentration can rule out the finite time blow up even though the navier stokes fluid is included

strong normalization of mlf via a calculus of coercions ml f is a type system extending ml with first class polymorphism as in system f the main goal of the present paper is to show that ml f enjoys strong normalization i e it has no infinite reduction paths the proof of this result is achieved in several steps we first focus on xml f the church style version of ml f and show that it can be translated into a calculus of coercions terms are mapped into terms and instantiations into coercions this coercion calculus can be seen as a decorated version of system f so that the simulation result entails strong normalization of xml f through the same property of system f we then transfer the result to all other versions of ml f using the fact that they can be compiled into xml f and showing there is a bisimulation between the two we conclude by discussing what results and issues are encountered when using the candidates of reducibility approach to the same problem

a proof of strong normalization for f 2 f ω and beyond abstract we present an evaluation technique for proving strong normalization sn we use the technique to give sn proofs for f2 f bounded quantification subtypes and f the evaluation technique derives sn as a corollary of the soundness of the typing rules under an appropriate evaluation semantics the evaluation semantics yields simpler type sets than those used in the earlier sn proofs the type sets discussed here form a complete lattice under classical union and intersection the simplified type sets allow a simplified treatment of a variety of type constructors

brief filtering on nonlinear time delay stochastic systems in this paper we address the filtering problem for a general class of nonlinear time delay stochastic systems the purpose of this problem is to design a full order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square both filter analysis and synthesis problems are considered sufficient conditions are proposed for the existence of desired exponential filters which are expressed in terms of the solutions to algebraic riccati inequalities involving scalar parameters the explicit characterization of the desired filters is also derived a simulation example is given to illustrate the design procedures and performances of the proposed method

new results on h filtering for fuzzy systems with interval time varying delays this paper investigates the problem of h filtering for continuous takagi sugeno t s fuzzy systems with an interval time varying delay in the state based on the delay partitioning idea a new approach is proposed for solving this problem which can achieve much less conservative feasibility conditions the attention is focused on the design of an h filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the h attenuation level from disturbance to estimation error is below a prescribed scalar the constructed lyapunov krasovskii functional by applying the delay partitioning method can potentially guarantee the obtained delay dependent conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software finally an example is illustrated to show the reduction in conservatism of the proposed filter design method

termination of system f bounded a complete proof abstract systemf bounded is a second order typed calculus with subtyping which has been defined to carry out foundational studies about the type systems of object oriented languages the almost recursive nature of the essential feature of this system makes one wonder whether it retains the strong normalization property with respect to first and second order reduction of systemf we prove that this is the case the proof is carried out to the last detail to allow the reader to be convinced of its correctness

new approach to mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems this paper revisits the problem of mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems differing from previous results in the quadratic framework the filter design makes full use of the parameter dependent stability idea not only is the filter dependent of the parameters which are assumed to reside in a polytope and be measurable online but in addition the lyapunov matrices are different for the entire polytope domain as well as for different channels with respect to the mixed performances these ideas are realized by introducing additional slack variables to the well established performance conditions and by employing new bounding techniques which results in a much less conservative filter design method a numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method

decay estimates of the coupled chemotaxis fluid equations in r 3 abstract in this paper we are concerned with a chemotaxis navier stokes model arising from biology which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations with transport and external force the optimal convergence rates of classical solutions to the chemotaxis navier stokes system for small initial perturbation around constant states are obtained by pure energy method under the assumption the initial data belong to h s h n n 3 0 s 3 2 the h s 0 s 3 2 negative sobolev norms are shown to be preserved along time evolution compared to the result in 5 we obtain the optimal decay rates of the higher order spatial derivatives of the solutions

the lp decay estimates for the chemotaxis shallow water system abstract in this paper we consider the large time behavior of solution for the chemotaxis shallow water system in two dimension by the method of frequency decomposition first we construct the green s function of the linearized system and get the corresponding estimates for low frequency part then we introduce an energy method we named double cycle method to get the decay rate for high frequency part due to the dissipative mechanism of this system the high frequency part decays faster than the low frequency part

long time behavior of the solution to a parabolic elliptic system abstract in this paper we are concerned with a parabolic elliptic model for biological fluid transportation networks with the large diffusivity and activation our investigations reveal that local existence of the unique classical solution to the correspondinginitial boundary value problem can always be achieved in the n dimensional setting with n 3 moreover we show that this local solution can be extended to a global one as long as the source term and the initial data are made small enough in a suitable sense and that the classical solution converges exponentially to a trivial steady state meanwhile we present that the smallness condition on the initial data can be removed in the one dimensional setting our result implies that we cannot expect network formation when the diffusivity is sufficiently large which is a first step toward a qualitative analysis for the role of diffusion in biological transportation networks

long time behavior of solution for the compressible nematic liquid crystal flows in r 3 abstract in this paper we investigate the global existence and long time behavior of classical solution for the compressible nematic liquid crystal flows in three dimensional whole space first of all the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in h n r 3 n 3 framework then one establishes algebraic time decay for the classical solution by weighted energy method finally the algebraic decay rate of classical solution in l p r 3 norm with 2 p and optimal decay rate of their spatial derivative in l 2 r 3 norm are obtained if the initial perturbation belong to l 1 r 3 additionally

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

robust switching type h filter design for linear uncertain systems with time varying delay this paper is concerned with the problem of robust h filter design for a class of linear uncertain systems with time varying delay the uncertainty parameters are supposed to be time varying unknown but bounded which appear affinely in the matrices of the considered system model based on linear matrix inequality lmi method and switching laws a new switching type filter is designed to guarantee the asymptotic stability and h performance level of the filtering error systems the key feature is that the new proposed filter parameters are switching between certain fixed gains automatically via the designed switching law it is shown that the new filter design method is less conservative than the traditional fixed gain filter design method an example is given to illustrate the validity of the proposed design

existence results for chemotaxis shallow water system with degenerate viscosity coefficients and initial vacuum abstract this paper is concerned with the cauchy problem of the chemotaxis shallow water system with degenerate viscosity coefficients a local existence of the unique regular solution is established when the initial data are arbitrarily large and include vacuum moreover a beal kate majda type blow up criterion is provided

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective