implementing dempster s rule for hierarchial evidence this article gives an algorithm for the exact implementation of dempster s rule in the case of hierarchical evidence this algorithm is computationally efficient and it makes the approximation suggested by gordon and shortliffe unnecessary the algorithm itself is simple but its derivation depends on a detailed understanding of the interaction of hierarchical evidence

on the number of nodes in n dimensional cubature formulae of degree 5 for integrals over the ball in this note cubature formulae of degree 5 are studied for n dimensional integrals over the ball with constant weight function we apply the method of reproducing kernel to show that the existence of such formulae attaining the best known lower bound is equivalent to the existence of tight spherical 5 designs the known results concerning spherical 5 designs show that the lower bound for the integral under consideration will not be attained in general the bound will be attained for n 2 3 7 23 and possibly for n 2p 1 2 2 p 5 in all other cases the bound must be increased at least by 1 in particular stroud s formulae for n 4 5 6 7 are minimal

balancing survival and extinction in nonautonomous competitive lotka volterra systems abstract we generalise and unify some recent results about extinction in n th order nonautonomous competitive lotka volterra systems for each r n we show that if the coefficients are continuous bounded by strictly positive constants and satisfy certain inequalities then any solution with strictly positive initial values has the property that n r of its components vanish whilst the remaining r components asymptotically approach a canonical solution of an r dimensional restricted system in other words r of the species being modeled survive whilst the remaining n r are driven to extinction

behavioral analysis of a nonlinear three staged population model with age size structure we present and analyze a nonlinear egg juvenile adult model in which eggs and juveniles are structured by age while adults by size the model consists of three first order partial differential equations with initial and boundary conditions existence and uniqueness of nonnegative solutions to the state system are investigated by the method of characteristics and a comparison principle extinction or persistence conditions of the population are obtained via the upper lower solution technique our investigation extends some results in the literature

asymmetric cubature formulae with few points in high dimension for symmetric measures let mu be a positive measure on mathbb r d invariant under the group of reflections and permutations and let m be a natural number we describe a method to construct cubature formulae of degree m with respect to mu with n positive weights and n points in the support of mu and such that n grows at most like dm with the dimension d we apply this method to classical measures to explicitly construct cubature formulae of degree 5 with the number of points growing at most like d3

a finite difference approximation for a coupled system of nonlinear size structured populations abstract we study a quasilinear nonlocal hyperbolic initial boundary value problem that models the evolution of n size structured subpopulations competing for common resources we develop an implicit finite difference scheme to approximate the solution of this model the convergence of this approximation to a unique bounded variation weak solution is obtained the numerical results for a special case of this model suggest that when subpopulations are closed under reproduction one subpopulation survives and the others go to extinction moreover in the case of open reproduction survival of more than one population is possible

abstract linear partial differential equations related to size structured population models with diffusion abstract we study abstract linear partial differential equations in banach spaces and or banach lattices related to size structured population models with spatial diffusion and their dual problems we introduce mild solutions through semigroup theory and characteristic method and investigate differentiability of mild solutions existence of a unique mild solution is shown also a comparison result is obtained as well as the boundedness of mild solutions is investigated in the banach lattice setting furthermore we consider the dual problems and then we introduce weak solutions and establish their uniqueness

a monotone approximation for a nonlinear nonautonomous size structured population model we develop a monotone approximation based on upper and lower solutions technique for solving a nonlinear nonautonomous size structured model with competition between individuals such an approximation results in the existence and uniqueness of the solution for the model problem it also provides a practicable and efficient numerical scheme furthermore we establish a first order convergence result and present a numerical example

stability and regularity results for a size structured population model in the present paper a nonlinear size structured population dynamical model with size and density dependent vital rate functions is considered the linearization about stationary solutions is analyzed by semigroup and spectral methods in particular the spectrally determined growth property of the linearized semigroup is derived from its long term regularity these analytical results make it possible to derive linear stability and instability results under biologically meaningful conditions on the vital rates the principal stability criteria are given in terms of a modified net reproduction rate

on minimal cubature formulae of small degree for spherically symmetric integrals the aim of this paper is to develop the existence and nonexistence problem of a cubature formula of degree 4k 1 for a spherically symmetric integral which attains the moller lower bound for this purpose we bring together the theory of euclidean design in combinatorics and that of reproducing kernels in numerical analysis we show that if there exists a minimal formula of degree 4k 1 then the nodes are distributed into k 1 concentric spheres including the origin and the weights in the formula are a constant on each concentric sphere we particularly focus on the cases of degrees 5 and 9 we show the equivalence between a minimal formula of degrees 5 and 4 and a spherical tight 5 and 4 design we also prove that there exists no minimal formula of degree 9 for some classical weights such as the gaussian weight on mathbb r d the radial exponential weight on mathbb r d and the jacobi weight on b d

constructing cubature formulae by the method of reproducing kernel we examine the method of reproducing kernel for constructing cubature formulae on the unit ball and on the triangle in light of the compact formulae of the reproducing kernels that are discovered recently several new cubature formulae are derived

fdm for multi dimensional nonlinear coupled system of parabolic and hyperbolic equations a finite difference method fdm for multi dimensional nonlinear coupled system of parabolic and hyperbolic equations is studied nonlinear coupled property is fully considered variant techniques of discrete functional analysis such as summation by parts and deductive reasoning are used to make prior estimates the fd scheme is uniquely solvable and unconditionally stable with the approximation property of the scheme the convergence is obtained with a rate of o h 2 dt 2 order

modeling and estimation problems for structured heterogeneous populations abstract we propose a modeling strategy for structured populations in which individuals are not necessarily identical the heterogeneity is obtained by modeling the population as comprising homogeneous subpopulations by using a vector measure we combine the subpopulations with an abstract integral to obtain the density of the population furthermore we develop an approximation framework for fitting this model to observed population data

cubature on wiener space it is well known that there is a mathematical equivalence between solving parabolic partial differential equations pdes and the integration of certain functionals on wiener space monte carlo simulation of stochastic differential equations sdes is a naive approach based on this underlying principle in finite dimensions it is well known that cubature can be a very effective approach to integration we discuss the appropriate extension of this idea to wiener space in the process we develop high order numerical schemes valid for high dimensional sdes and semi elliptic pdes

a size structured population model with dispersion abstract we propose a model for size structured populations which allows growth rates to vary with individuals growth rate distribution across all possible growth rates after establishing existence and uniqueness of the solutions of our model equations we present a numerical algorithm for computing the solutions and prove its convergence finally we show that this approximation scheme can be used for estimating the growth rate distribution from size structured population data and illustrate the applicability of our ideas by an example

fisher type inequalities for euclidean t designs the notion of a euclidean t design is analyzed in the framework of appropriate inner product spaces of polynomial functions some fisher type inequalities are obtained in a simple manner by this method the same approach is used to deal with certain analogous combinatorial designs

on cubature formulae of degree 4k 1 attaining moller s lower bound for integrals with circular symmetry the structure of cubature formulae of degree 4k 1 whose number of nodes is equal to moller s lower bound is investigated for integrals with circular symmetry a simple criterion is derived for the existence of such formulae it shows that fork 1 moller s lower bound can always be attained with radon s formulae it also allows to prove that for several integrals with circular symmetry and several values ofk 1 moller s lower bound cannot be attained

existence uniqueness and monotone approximation for an erythropoiesis age structured model we develop a monotone approximation to the solution of an age structured model which describes the regulation of erythropoiesis the process in which red blood cells are developed the convergence of this approximation to the unique solution of the model is also established

a nonlinear model of population dynamics containing an arbitrary number of continuous structure variables a nonlinear model is presented for the dynamics of a population in which each individual is characterized by its chronological age and by an arbitrary finite number of additional structure variables the nonlinearities are introduced by assuming that the birth and loss processes as well as the maturation rates of individuals are controlled by a functional of the population density the model is a generalization of the classical sharpe lotka mckendrick model of age structured population growth the nonlinear age structured model of gurtin and maccamy and the age size structured cell population model of bell and anderson based on a reformulation of the model in terms of a coupled system of equations the existence for all positive time of unique solutions to the model is proved using a contraction mapping argument the existence of equilibrium solutions is discussed and sufficient conditions are proved for the local asymptotic stability of equilibria using results from the theory of strongly continuous

a fully discretized approximation scheme for size structured population models an efficient algorithm for computing solutions to a class of models for size structured populations is presented furthermore some numerical examples are discussed

stability results for a size structured population model with resources dependence and inflow it is undoubted that the survival of individuals of populations is dependent on resources e g foods we formulate a system of integro differential equations to model the dynamics of a size structured and resources dependent population a kind of inflow of newborn individuals from external environment is considered the resource dependence is incorporated through the size growth mortality fertility and feeding rates of the target population the existence of the stationary size distributions are discussed and the linear stability is investigated by means of the semigroup theory and the characteristic equation technique some sufficient conditions for stability instability of stationary states are obtained and two examples and the corresponding simulations are presented

extinction in nonautonomous t periodic competitive lotka volterra system a nonautonomous t periodic competitive lotka volterra system of n species is considered it is shown that if the coefficients are t periodic continuous and satisfy certain inequalities then any solution with strictly positive initial conditions has the property that all but one of its components vanish while the remaining component approaches the canonical solution of a certain logistic differential equation

a nonautonomous juvenile adult model well posedness and long time behavior via a comparison principle a nonautonomous nonlinear continuous juvenile adult model where juveniles and adults depend on different resources is developed it is assumed that juveniles are structured by age while adults are structured by size existence uniqueness results are proved using the monotone method based on a comparison principle established in this paper conditions on the model parameters that lead to extinction or persistence of the population are obtained via the upper lower solution technique

a new approach for the existence problem of minimal cubature formulas based on the larman rogers seidel theorem in this paper we consider the existence problem of minimal cubature formulas of degree 4k 1 for spherically symmetric integrals we prove that for a minimal formula in sufficiently high dimensional space there exists some concentric sphere on which the inner product of any two distinct points is rational by using this result we prove that for any d ge 2 there exist no d dimensional minimal formulas of degrees 13 and 21 for some special integral

stability and instability of equilibria of an equation of size structured population dynamics in this paper we consider a quasilinear equation with a nonlinear boundary condition modelling the dynamics of a biological population structured by size we suppose vital rates depending on the total population this hypothesis introduces some nonlinearities on the equation and on the boundary condition we study the existence and uniqueness of solution of the initial value problem and the existence of stationary solutions after we calculate the spectrum of the linearization at an equilibrium and we study its local stability