basic soules matrices and their applications abstract in this paper we study the properties of the basic soules matrices in r n n which are a special subclass of the n n soules matrices generated via the basic soules basis the basic soules basis has the sign pattern n and it corresponds to the vector e n r n of all 1 s the basic soules matrices are up to a multiple by a positive scalar symmetric and doubly stochastic we begin by investigating the permanents of basic soules matrices next for a nonsingular basic soules matrix a r n n we show that the matrix a a 1 which is known to be a nonsingular m matrix has a basic soules basis of eigenvectors furthermore we obtain explicit formulas for the eigenvalues of a a 1 in terms of the eigenvalues of a finally let a r n n be a basic soules matrix of spectral radius 1 and set q i a by investigating the sign pattern of the off diagonal entries of the group inverse q of q we determine when the perron root is a concave function in each of the off diagonal entries at a

cone volume measure of general centered convex bodies abstract we show that the cone volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition this extends former results obtained in the discrete as well as in the symmetric case and implies among others a conjectured best possible inequality for the u functional of a convex body

dynamical behavior of a one predator and two independent preys system with stochastic perturbations abstract a one predator and two independent preys system with stochastic perturbations is considered first we show that there is a positive solution of this system then we investigate the long time behavior of this system sufficient criteria for extinction and persistence in time average are established moreover it is also shown that this system has a stationary distribution and it is ergodicity finally examples and simulations are carried on to verify these results

stationary distribution and extinction of a stochastic tuberculosis model abstract in this paper we focus on a stochastic tuberculosis model we first obtain the existence of a stationary distribution to the positive solutions by stochastic lyapunov function method then we establish sufficient conditions for extinction of the disease finally some examples and numerical simulations are provided to illustrate our theoretical results

stochastic approximations of perturbed fredholm volterra integro differential equation arising in mathematical neurosciences this paper extends the results of synaptically generated wave propagation through a network of connected excitatory neurons to a continuous model defined by a fredholm volterra integro differential equation fvide which includes memory effects of the past in the propagation stochastic approximation and numerical simulations are discussed

necessary subspace concentration conditions for the even dual minkowski problem abstract we prove tight subspace concentration inequalities for the dual curvature measures c q k of an n dimensional origin symmetric convex body for q n 1 this supplements former results obtained in the range q n

a splitting step algorithm for reflected stochastic differential equations in r 1 a new algorithm which is based on the splitting step idea and the penalization method for reflected stochastic differential equation rsde in the upper half space r 1 is presented in this paper after some important estimates about rsdes and penalization odes are obtained the local pathwise error of the suggested algorithm are considered and an estimate of local error in the 2pth moment is proved under the assumptions of lipschitz continuity and linear growth some numerical experiments based on matlab programs are given to support the suggested algorithm

on single and double soules matrices abstract until now the concept of a soules basis matrix of sign pattern n consisted of an orthogonal matrix r r n n generated in a certain way from a positive n vector which has the property that for any diagonal matrix diag 1 n with 1 n 0 the symmetric matrix a r r t has nonnegative entries only in the present paper we introduce the notion of a pair of double soules basis matrices of sign pattern n which is a pair of matrices p q each in r n n which are not necessarily orthogonal and which are generated in a certain way from two positive vectors but such that pq t i and such that for any of the aforementioned diagonal matrices the matrix a p q t also has nonnegative entries only we investigate the interesting properties which such matrices a have as a preamble to the above investigation we show that the iterates a k r k r k t generated in the course of the qr algorithm when it is applied to a r r t where r is a soules basis matrix of sign pattern n are again symmetric matrices generated by the soules basis matrices r k of sign pattern n which are themselves modified as the algorithm progresses our work here extends earlier works by soules and elsner et al

the logarithmic minkowski problem in analogy with the classical minkowski problem necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone volume measure of the unit ball of a finite dimensional banach space

approximate independence of distributions on spheres and their stability properties let zeta be chosen at random on the surface of the p sphere in mathbb r n 0 p n x in mathbb r n sum n i 1 x i p n if p 2 then the first k components zeta 1 ldots zeta k are for k fixed in the limit as n rightarrow infty independent standard normal considering the general case p 0 the same phenomenon appears with a distribution f p in an exponential class mathscr e f p can be characterized by the distribution of quotients of sums by conditional distributions and by a maximum entropy condition these characterizations have some interesting stability properties some discrete versions of this problem and some applications to de finetti type theorems are discussed

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

a probabilistic approach to the geometry of the lᵨⁿ ball this article investigates by probabilistic methods various geometric questions on b n p the unit ball of ln p we propose realizations in terms of independent random variables of several distributions on b n p including the normalized volume measure these representations allow us to unify and extend the known results of the sub independence of coordinate slabs in b n p as another application we compute moments of linear functionals on b n p which gives sharp constants in khinchine s inequalities on b n p and determines the 2 constant of all directions on b n p we also study the extremal values of several gaussian averages on sections of b n p including mean width and l norm and derive several monotonicity results as p varies applications to balancing vectors in l 2 and to covering numbers of polyhedra complete the exposition

a note on persistence and extinction of a randomized food limited logistic population model this paper addresses the issue of the asymptotic behavior for a non autonomous randomized food limited logistic population model several sufficient conditions are formulated and proved for p moment persistence and extinction of the population as well as in sense of almost sure results show that food limited assumption has an influence on the convergence rate of the solution to the equilibria for the deterministic and stochastic model some previously known results are improved numerical simulations are provided to support the results

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

lp dual curvature measures abstract a new family of geometric borel measures on the unit sphere is introduced special cases include the l p surface area measures which extend the classical surface area measure of aleksandrov and fenchel jessen and l p integral curvature which extends alkesandrov s integral curvature in the l p brunn minkowski theory it also includes the dual curvature measures which are the duals of federer s curvature measures in the dual brunn minkowski theory this partially unifies the classical theory of mixed volumes and the newer theory of dual mixed volumes

stability analysis of numerical schemes for stochastic differential equations stochastic differential equations sdes represent physical phenomena dominated by stochastic processes as for deterministic ordinary differential equations odes various numerical schemes are proposed for sdes in this paper we study the stability of numerical schemes for scalar sdes with respect to the mean square norm which we call ms stability we will show some figures of the ms stability domain or regions for some numerical schemes and present numerical results which confirm it this notion is an extension of absolute stability in numerical methods for odes

filtering of stochastic nonlinear differential systems via a carleman approximation approach this paper deals with the state estimation problem for stochastic nonlinear differential systems driven by standard wiener processes and presents a filter that is a generalization of the classical extended kalman bucy filter ekbf while the ekbf is designed on the basis of a first order approximation of the system around the current estimate the proposed filter exploits a carleman like approximation of a chosen degree v ges 1 the approximation procedure applied to both the state and the measurement equations allows to define an approximate representation of the system by means of a bilinear system for which a filtering algorithm is available from the literature numerical simulations on an example show the improvement in terms of sample error covariance of the filter based on the first order second order and third order system approximations v 1 2 3

on mardia skewness and kurtosis of soules basis matrices in rom simulation abstract relying on an interesting connection between generalized helmert ledermann matrices and soules basis matrices as well as a complete binary tree classification of the latter a recursive determination of the mardia skewness and kurtosis coefficients of soules basis matrices is proposed it is based on a convenient combinatorial representation of soules basis matrices by restricted binary partitions of a natural number into two ordered summands with recursive repetition of this binary partitioning on the summands the obtained simple composition and invariance formulas enable the recursive calculation of these skewness and kurtosis coefficients

robust observer design for ito stochastic time delay systems via sliding mode control this paper deals with the output feedback sliding mode control for ito stochastic time delay systems the system states are unmeasured and the uncertainties are unmatched a sliding mode control scheme is proposed based on the state estimates by utilizing a novel switching function the derivative of the switching function is ensured to be finite variation it is shown that the sliding mode in the estimation space can be attained in finite time the sufficient condition for the asymptotic stability in probability of the overall closed loop stochastic system is derived finally a simulation example is shown to illustrate the proposed method

subspace concentration of dual curvature measures of symmetric convex bodies we prove a tight subspace concentration inequality for the dual curvature measures of a symmetric convex body 2018 international press of boston inc all rights reserved

distributions for the eigenvalues of large random matrices generated from four manifolds in this paper we will first study the spectrum of certain large euclidean random matrices the entries of these matrices are functions of n random points lp norm uniformly sampled in n dimensional lp ball or lp sphere under the setting n n 0 as n and n tend to it is shown that the empirical distributions of eigenvalues of normalized euclidean random matrices generated from the above two manifolds both converge weakly to semicircle law we also investigate certain sample covariance type matrices whose entries are determined by n random positions from an n dimensional lp ellipsoid or its surface when n and n with n n 0 we prove that their empirical spectral distribution converge to the same fixed distribution

global stability of a stochastic predator prey system with infinite delays abstract this paper is concerned with the global asymptotic stability of a stochastic delay predator prey system with beddington deangelis functional response sufficient criteria for the global asymptotic stability of the system are established some simulation figures are provided to show that our model is more realistic than existing models

mean square and asymptotic stability of the stochastic theta method stability analysis of numerical methods for ordinary differential equations odes is motivated by the question for what choices of stepsize does the numerical method reproduce the characteristics of the test equation we study a linear test equation with a multiplicative noise term and consider mean square and asymptotic stability of a stochastic version of the theta method we extend some mean square stability results in saito and mitsui siam j numer anal 33 1996 pp 2254 2267 in particular we show that an extension of the deterministic a stability property holds we also plot mean square stability regions for the case where the test equation has real parameters for asymptotic stability we show that the issue reduces to finding the expected value of a parametrized random variable we combine analytical and numerical techniques to get insights into the stability properties for a variant of the method that has been proposed in the literature we obtain precise analytic expressions for the asymptotic stability region this allows us to prove a number of results the technique introduced is widely applicable and we use it to show that a fully implicit method suggested by kloeden and platen numerical solution of stochastic differential equations springer verlag 1992 has an asymptotic stability extension of the deterministic a stability property we also use the approach to explain some numerical results reported in milstein platen and schurz siam j numer anal 35 1998 pp 1010 1019

cone volume measures of polytopes abstract the cone volume measure of a polytope with centroid at the origin is proved to satisfy the subspace concentration condition as a consequence a conjectured a dozen years ago fundamental sharp affine isoperimetric inequality for the u functional is completely established along with its equality conditions

orthogonal bases that lead to symmetric nonnegative matrices abstract in a paper dating back to 1983 soules constructs from a positive vector x an orthogonal matrix r which has the property that for any nonnegative diagonal matrix with nonincreasing diagonal entries the matrix r rt has all its entries nonnegative independently fiedler in 1988 showed that any symmetric irreducible nonsingular matrix whose powers are all m matrices and hence an mma matrix in the language of friedland hershkowitz and schneider must have an orthogonal matrix of eigenvectors r which has similar properties to those of r here for a given positive n vector x we investigate the structure of all orthogonal matrices r for which for any nonnegative diagonal matrix as above the matrices r rt are nonnegative up to a permutation of its columns each such r corresponds to a binary tree whose vertices are subsets of the set 1 2 n with the property that each vertex has either no successor or exactly two disjoint successors for such orthogonal matrices r and such nonsingular diagonal matrices we show that the set of matrices of the form r rt and the set of inverse mma matrices i e matrices whose inverses are mma matrices coincide using this result we establish a relation between strictly ultrametric matrices and inverse mma matrices finally we show that the qr factorization of r rt for certain such r s has a special sign pattern

the dynamics of a stochastic vaccinated tuberculosis model with treatment abstract in this paper we study a stochastic model with vaccination and treatment to describe the transmission dynamics of tuberculosis firstly by using the stochastic lyapunov analysis method we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model then we obtain sufficient conditions for extinction of the diseases our work greatly improves the results of feng and qiu 2018 finally some examples and numerical simulations are introduced to illustrate our theoretical results

a brunn minkowski theory for coconvex sets of finite volume abstract let c be a closed convex cone in r n pointed and with interior points we consider sets of the form a c k where k c is a closed convex set if a has finite volume lebesgue measure then a is called a c coconvex set and k is called c close the family of c coconvex sets is closed under the addition defined by c a 1 a 2 c a 1 c a 2 we develop first steps of a brunn minkowski theory for c coconvex sets which relates this addition to the notion of volume in particular we establish the equality condition for a brunn minkowski type inequality with reversed inequality sign and introduce mixed volumes and their integral representations for c close sets surface area measures and cone volume measures can be defined in analogy to similar notions for convex bodies they are borel measures on the intersection of the unit sphere with the interior of the polar cone of c we prove a minkowski type uniqueness theorem for c close sets with equal surface area measures concerning minkowski type existence problems we give conditions for a borel measure to be either the surface area measure or the cone volume measure of a c close set these conditions are sufficient in the first case and necessary and sufficient in the second case

dynamical analysis of bayesian inference models for the eriksen task the eriksen task is a classical paradigm that explores the effects of competing sensory inputs on response tendencies and the nature of selective attention in controlling these processes in this task conflicting flanker stimuli interfere with the processing of a central target especially on short reaction time trials this task has been modeled by neural networks and more recently by a normative bayesian account here we analyze the dynamics of the bayesian models which are nonlinear coupled discrete time dynamical systems by considering simplified approximate systems that are linear and decoupled analytical solutions of these allow us to describe how posterior probabilities and psychometric functions depend on model parameters we compare our results with numerical simulations of the original models and derive fits to experimental data showing that agreements are rather good we also investigate continuum limits of these simplified dynamical systems and demonstrate that bayesian updating is closely related to a drift diffusion process whose implementation in neural network models has been extensively studied this provides insight into how neural substrates can implement bayesian computations

generalized helmert ledermann orthogonal matrices and rom simulation abstract deterministic rectangular orthonormal matrices satisfying a hyper plane constraint plays a central role in random orthogonal matrix rom simulation the multivariate skewness and kurtosis sampling properties are encrypted in a given orthonormal matrix we consider a subclass of generalized helmert ledermann ghl orthogonal matrices that have fixed last column are generated by the cayley transform and satisfy the required hyper plane constraint the algebraic structure of ghl orthogonal matrices is determined simple and convenient skewness and kurtosis formulas are obtained we exhibit an asymptotically growing range of variation for skewness and kurtosis which points to an increased flexibility in rom simulation

the logarithmic minkowski problem for polytopes abstract the logarithmic minkowski problem asks for necessary and sufficient conditions for a finite borel measure on the unit sphere so that it is the cone volume measure of a convex body this problem was solved recently by boroczky lutwak yang and zhang for even measures boroczky et al 2013 8 this paper solves the case of discrete measures whose supports are in general position

the central limit problem for convex bodies it is shown that every symmetric convex body which satisfies a kind of weak law of large numbers has the property that almost all its marginal distributions are approximately gaussian several quite broad classes of bodies are shown to satisfy the condition

on the geometry of random convex sets between polytopes and zonotopes abstract in this work we study a class of random convex sets that interpolate between polytopes and zonotopes these sets arise from considering a q t h moment q 1 of an average of order statistics of 1 dimensional marginals of a sequence of n n independent random vectors in r n we consider the random model of isotropic log concave distributions as well as the uniform distribution on an l p n sphere 1 p with respect to the cone probability measure and study the geometry of these sets in terms of the support function and mean width we provide asymptotic formulas for the expectation of these geometric functionals which are sharp up to absolute constants our model includes and generalizes the standard one for random polytopes

simple model for bursting dynamics of neurons neuronal cells in isolation or as an assembly exhibit bursting behavior on two different time scales we introduce a simple one dimensional model which requires only one phase variable to describe the phenomenon of parabolic bursting the analysis in the continuum limit reveals that for any unimodal distribution of frequencies the qualitative properties of the full and the reduced model are identical further we derive analytically an exact low dimensional description of a globally coupled network of bursting oscillators for our model study of the stability for this low dimensional model reveals different dynamical signatures in the parameter space we demonstrate that the structure of the parameter space remains independent of the number of spikes per burst

affine images of isotropic measures necessary and sufficient conditions are given in order for a borel measure on the euclidean sphere to have an affine image that is isotropic a sharp reverse affine isoperimetric inequality for borel measures on the sphere is presented this leads to sharp reverse affine isoperimetric inequalities for convex bodies 2015 international press of boston inc all rights reserved

existence and uniqueness of the solutions and convergence of semi implicit euler methods for stochastic pantograph equations abstract in this paper the sufficient conditions of existence and uniqueness of the solutions for stochastic pantograph equation are given i e the local lipschitz condition and the linear growth condition under the lipschitz condition and the linear growth condition it is proved that the semi implicit euler method is convergence with strong order 1 2

a feasible method for optimization with orthogonality constraints minimization with orthogonality constraints e g x top x i and or spherical constraints e g vert x vert 2 1 has wide applications in polynomial optimization combinatorial optimization eigenvalue problems sparse pca p harmonic flows 1 bit compressive sensing matrix rank minimization etc these problems are difficult because the constraints are not only non convex but numerically expensive to preserve during iterations to deal with these difficulties we apply the cayley transform a crank nicolson like update scheme to preserve the constraints and based on it develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics the efficiency of the proposed algorithms is demonstrated on a variety of test problems in particular for the maxcut problem it exactly solves a decomposition formulation for the sdp relaxation for polynomial optimization nearest correlation matrix estimation and extreme eigenvalue problems the proposed algorithms run very fast and return solutions no worse than those from their state of the art algorithms for the quadratic assignment problem a gap 0 842 to the best known solution on the largest problem tai256c in qaplib can be reached in 5 min on a typical laptop

hybrid legendre polynomials and block pulse functions approach for nonlinear volterra fredholm integro differential equations this paper introduces an approach for obtaining the numerical solution of the nonlinear volterra fredholm integro differential nvfid equations using hybrid legendre polynomials and block pulse functions these hybrid functions and their operational matrices are used for representing matrix form of these equations the main characteristic of this approach is that it reduces nvfid equations to a system of algebraic equations which greatly simplifying the problem numerical examples illustrate the validity and applicability of the proposed method

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

efficient method for computing lower bounds on the p radius of switched linear systems abstract this paper proposes lower bounds on a quantity called l p norm joint spectral radius or in short p radius of a finite set of matrices despite its wide range of applications to for example stability analysis of switched linear systems and the equilibrium analysis of switched linear economical models algorithms for computing the p radius are only available in a very limited number of particular cases the proposed lower bounds are given as the spectral radius of an average of the given matrices weighted via kronecker products and do not place any requirements on the set of matrices we show that the proposed lower bounds theoretically extend and also can practically improve the existing lower bounds a markovian extension of the proposed lower bounds is also presented

dynamics in a predator prey model with space and noise in this paper we presented a predator prey model with spatial diffusion and density dependent noise it was found that the spatial model without noise has spotted pattern however combined with density dependent noise the predator prey model exhibits transition from spotted to labyrinth pattern furthermore when noise intensity and temporal correlation are in appropriate levels the populations will extinct the obtained results suggest that stochastic factors may play an important role in populations dynamics which well enrich the findings in predator prey models

orlicz john ellipsoids abstract the orlicz john ellipsoids which are in the framework of the booming orlicz brunn minkowski theory are introduced for the first time it turns out that they are generalizations of the classical john ellipsoid and the evolved l p john ellipsoids the analog of ball s volume ratio inequality is established for the new orlicz john ellipsoids the connection between the isotropy of measures and the characterization of orlicz john ellipsoids is demonstrated

distributions of eigenvalues of large euclidean matrices generated from lp balls and spheres abstract let x 1 x n be points randomly chosen from a set g r n and f x be a function the euclidean random matrix is given by m n f x i x j 2 n n where is the euclidean distance when n is fixed and n we prove that m n the empirical distribution of the eigenvalues of m n converges to 0 for a big class of functions of f x assuming both n and n go to infinity proportionally we obtain the explicit limit of m n when g is the l p unit ball or sphere with p 1 as corollaries we obtain the limit of a n with a n d x i x j n n and d being the geodesic distance on the ordinary unit sphere in r n we also obtain the limit of a n for the euclidean distance matrix a n x i x j n n the limits are a b v where a and b are constants and v follows the marcenko pastur law the same are also obtained for other examples appeared in physics literature including exp x i x j n n and exp d x i x j n n our results partially confirm a conjecture by do and vu 14

on the l p monge ampere equation abstract for the case where 0 p 1 we prove the existence of solutions of the l p monge ampere equation for arbitrary measures and show that the solution is in general not unique

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

model approximation for fuzzy switched systems with stochastic perturbation in this paper the model approximation problem is investigated for a takagi sugeno fuzzy switched system with stochastic disturbance for a high order considered system our attention is focused on the construction of a reduced order model which not only approximates the original system well with a hankel norm performance but translates it into a lower dimensional fuzzy switched system as well by using the average dwell time approach and the piecewise lyapunov function technique a sufficient condition is first proposed to guarantee the mean square exponential stability with a hankel norm error performance for the error system the model approximation is then converted into a convex optimization problem by using a linearization procedure finally simulations are provided to illustrate the effectiveness of the proposed theory

estimation of moments of sums of independent real random variables for the sum s sum x i of a sequence x i of independent symmetric or nonnegative random variables we give lower and upper estimates of moments of s the estimates are exact up to some universal constants and extend the previous results for particular types of variables x i

the lp minkowski problem for n p 1 abstract chou and wang s existence result for the l p minkowski problem on s n 1 for p n 1 and an absolutely continuous measure is discussed and extended to more general measures in particular we provide an almost optimal sufficient condition for the case p 0 1

numerical solution of a fredholm integro differential equation modelling θ neural networks we propose several approaches to the numerical solution of a new fredholm integro differential equations modelling neural networks a solution strategy based on expansions onto standard cardinal basis functions and collocation is presented comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies

an iterative shifted chebyshev method for nonlinear stochastic ito volterra integral equations abstract in the present work we propose an iterative method based on the shifted chebyshev polynomials for the numerical investigation of the nonlinear stochastic volterra integral equations moreover the convergence of the proposed method is studied the proposed iterative method is fast and easy to implement some numerical examples are given to show the applicability and efficiency of the presented method the numerical results of the proposed method are compared with the reported results in the literature and with the exact solutions if they exist the reported comparison confirm the applicability and high accuracy of the proposed method

stochastic permanence of an siqs epidemic model with saturated incidence and independent random perturbations abstract this article discusses a stochastic siqs epidemic model with saturated incidence we assume that random perturbations always fluctuate at the endemic equilibrium the existence of a global positive solution is obtained by constructing a suitable lyapunov function under some suitable conditions we derive the stochastic boundedness and stochastic permanence of the solutions of a stochastic siqs model some numerical simulations are carried out to check our results

on the lp dual minkowski problem abstract the l p dual curvature measure was introduced by lutwak yang zhang in an attempt to unify the l p brunn minkowski theory and the dual brunn minkowski theory the characterization problem for l p dual curvature measure called the l p dual minkowski problem is a fundamental problem in this unifying theory the l p dual minkowski problem contains the l p minkowski problem and the dual minkowski problem two major problems in modern convex geometry that remain open in general in this paper existence results on the l p dual minkowski problem in the weak sense will be provided moreover existence and uniqueness of the solution in the smooth category will also be demonstrated

dynamical behavior of a stochastic svir epidemic model with vaccination abstract in this paper we investigate the dynamical behavior of svir models in random environments firstly we show that if r 0 s 1 the disease of stochastic autonomous svir model will die out exponentially if r 0 s 1 the disease will be prevail moreover this system admits a unique stationary distribution and it is ergodic when r 0 s 1 results show that environmental white noise is helpful for disease control secondly we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic svir model with periodic parameters finally numerical simulations validate the analytical results

robust variance reduction for random walk methods random walk methods are effective for solving linear partial differential equations in many dimensions especially those involving complex geometries they are based on an equivalence given by a feynman kac formula between an expectation of a functional of a stochastic process and the solution at a point of a partial differential equation the drawback is that the error is proportional only to the square root of the reciprocal of the number of trials efficiency depends critically on variance reduction a general strategy for doing this in the case of stochastic differential equations is proposed by milstein the idea is to introduce a bias in the drift term and to exactly compensate for this by unequal weighting of the trials there is an optimal bias defined in terms of the solution of the partial differential equation which reduces the variance to zero in practice an approximation is used this idea has been tested under the name biased brownian dynamics on the problem of calculating rate constants for diffusion limited reactions the approach is successful in some cases but is less successful in more difficult cases due to the occasional occurrence of a well above average weight proposed and tested here is a weight control algorithm which greatly enhances the effectiveness of biased brownian dynamics

random orthogonal matrix simulation this paper introduces a method for simulating multivariate samples that have exact means covariances skewness and kurtosis we introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices l matrices they may be deterministic parametric or data specific in nature the target moments determine the l matrix then infinitely many random samples with the same exact moments may be generated by multiplying the l matrix by arbitrary random orthogonal matrices this methodology is thus termed rom simulation considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics rom simulation has applications to many problems that are resolved using standard monte carlo methods but no parametric assumptions are required unless parametric l matrices are used so there is no sampling error caused by the discrete approximation of a continuous distribution which is a major source of error in standard monte carlo simulations for illustration we apply rom simulation to determine the value at risk of a stock portfolio

optimal harvesting policy of logistic population model in a randomly fluctuating environment abstract in this paper we investigate the optimal harvest policy of a stochastic logistic population model the value of this study lies in two aspects mathematically we establish a stochastic threshold theorem to govern whether the population persists or not in the case of population persistence we prove the existence uniqueness and global asymptotic stability of the invariant density of the fokker planck equation associated with the sde model and we further show the relation between these two models in addition we give the unique optimal harvesting effort and the corresponding maximum of expectation of sustainable yield which gives us the profile of the optimal harvesting policy of the sde model ecologically we find that big harvesting effort or big intensity of noise will lead the population to extinct risk almost surely in addition we find that under a fixed randomness strategy and proper harvesting the maximum sustainable yield increases systematically as the harvesting effort increases but overexploitation will reduce the level of maximize sustainable yield and eventually make the whole population extinct with probability one hence in order to obtain the optimal harvesting policy we must decrease the harvesting effort and the intensity of noise furthermore we find that our parameter perturbation method in this paper is more beneficial to the exploitation of renewable resources than the classical one given by beddington and may 1977 the results show that different perturbation method can exhibit different stochastic population dynamics

geometric measures in the dual brunn minkowski theory and their associated minkowski problems a longstanding question in the dual brunn minkowski theory is what are the dual analogues of federer s curvature measures for convex bodies the answer to this is provided this leads naturally to dual versions of minkowski type problems what are necessary and sufficient conditions for a borel measure to be a dual curvature measure of a convex body sufficient conditions involving measure concentration are established for the existence of solutions to these problems

superconcentration and randomized dvoretzky s theorem for spaces with 1 unconditional bases abstract let n be a sufficiently large natural number and let b be an origin symmetric convex body in r n in the l position and such that the space r n b admits a 1 unconditional basis then for any e 0 1 2 and for random c e log n log 1 e dimensional subspace e distributed according to the rotation invariant haar measure the section b e is 1 e euclidean with probability close to one this shows that the worst case dependence on e in the randomized dvoretzky theorem in the l position is significantly better than in john s position it is a previously unexplored feature which has strong connections with the concept of superconcentration introduced by s chatterjee in fact our main result follows from the next theorem let b be as before and assume additionally that b has a smooth boundary and e n b n c e n grad b 2 for a small universal constant c 0 where grad b is the gradient of b and n is the standard gaussian measure in r n then for any p 1 c log n the p th power of the norm b p is c log n superconcentrated in the gauss space

some issues in discrete approximate solution for stochastic differential equations abstract an evaluation method for numerical schemes of stochastic differential equations is treated discussing the source of errors in the discrete numerical solution we highlight the effect of pseudo random numbers upon the numerical solution and point out the significance of the independencies of the series of them required in the numerical schemes to discriminate the stochastic and deterministic parts in the errors more clearly we propose a new two dimensional linear test equation of multiplicative type whose analytical solution can be obtained readily our results are illustrated through some numerical examples

dynamics of a stochastic sir epidemic model with saturated incidence in this paper the dynamics of a stochastic sir epidemic model with saturated incidence is investigated firstly we prove that the system has a unique global positive solution with any positive initial value then we verify that random effect may lead the disease to extinction under a simple condition thirdly we establish a sufficient condition for persistence in the mean of the disease moreover we show that there is a stationary distribution to the stochastic system under certain parametric restrictions finally some numerical simulations are carried out to confirm the analytical results

cone volume measure and stability abstract we prove stability results for two central inequalities involving the cone volume measure of a centered convex body the subspace concentration conditions and the u functional volume inequality

relative entropy of cone measures and lp centroid bodies let k be a convex body in r n we introduce a new affine invariant which we call k t hat can be found in three different ways a as a limit of normalized lp affine surface areas b as the relative entropy of the cone measure of k and the cone measure of k c as the limit of the volume difference of k and lp centroid bodies we investigate properties of k and of related new invariant quantities in particular we show new affine isoperimetric inequalities and we show an information inequality for convex bodies

the sharma parthasarathy stochastic two body problem we study the sharma parthasarathy stochastic two body problem introduced by sharma and parthasarathy in dynamics of a stochastically perturbed two body problem proc r soc a 463 979 1003 2007 in particular we focus on the preservation of some fundamental features of the classical two body problem like the hamiltonian structure and first integrals in the stochastic case numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi major axis the eccentricity and the pericenter we also derive a stochastic version of gauss s equations in the planar case

the ergodicity and extinction of stochastically perturbed sir and seir epidemic models with saturated incidence abstract in this paper we include stochastic perturbations into sir and seir epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number r 0 the long time behavior of the two stochastic systems is studied mainly we utilize stochastic lyapunov functions to show under some conditions the solution has the ergodic property as r 0 1 while exponential stability as r 0 1 at last we make simulations to conform our analytical results

the surface measure and cone measure on the sphere of ell_p n we prove a concentration inequality for the l n p norm on the l n p sphere for p q 0 this inequality which generalizes results of schechtman and zinn 2000 is used to study the distance between the cone measure and surface measure on the sphere of l n p in particular we obtain a significant strengthening of the inequality derived by naor and romik 2003 and calculate the precise dependence of the constants that appeared there on p

threshold behavior of a stochastic sis model with levy jumps in this paper the dynamics of a stochastic sis model with levy jumps are investigated we first prove that this model has a unique global positive solution starting from the positive initial value then taking the accumulated jump size into account we find a threshold of the model denoted by r 0 which completely determines the extinction and prevalence of the disease if r 0 1 the disease dies out exponentially with probability one if r 0 1 the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease from the view of epidemiology the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics moreover we find that levy noise can suppress disease outbreak finally we introduce some numerical simulations to support the main results obtained

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

extremum problems for the cone volume functional of convex polytopes abstract lutwak yang and zhang defined the cone volume functional u over convex polytopes in r n containing the origin in their interiors and conjectured that the greatest lower bound on the ratio of this centro affine invariant u to volume v is attained by parallelotopes in this paper we give affirmative answers to the conjecture in r 2 and r 3 some new sharp inequalities characterizing parallelotopes in r n are established moreover a simplified proof for the conjecture restricted to the class of origin symmetric convex polytopes in r n is provided

the lp minkowski problem for polytopes for 0 p 1 abstract necessary and sufficient conditions are given for the existence of solutions to the discrete l p minkowski problem for the critical case where 0 p 1