a mathematical model of competition for two essential resources in the unstirred chemostat a mathematical model of competition between two species for two growth limiting essential complementary resources in the unstirred chemostat is considered the existence of a positive steady state solution and some of its properties are established analytically techniques include the maximum principle the fixed point index and numerical simulations the simulations also seem to indicate that there are regions in parameter space for which a globally stable positive equilibrium occurs and that there are other regions for which the model admits bistability and even multiple positive equilibria

coexistence and stability of an unstirred chemostat model with beddington deangelis function this paper deals with an unstirred chemostat model with the beddington deangelis functional response first a sufficient condition to the existence of positive steady state solutions is established second the effect of the parameter b 1 in the beddington deangelis functional response which models mutual interference between species u is considered the result shows that if b 1 is sufficiently large the solution of this model is determined by a limiting equation the main tool used here includes the fixed point index theory the perturbation technique and the bifurcation theory

a generalization of the vidav jorgens perturbation theorem for semigroups and its application to transport theory on considere des semigroupes t t engendres par l operateur de transport a k comme une perturbation du semi groupe s t engendre par a seul on montre que pour un n tous les produits de la forme ks td 1k ks tnd k t i 0 sont strictement singuliers alors s t et t t ont le meme rayon spectral essentiel

asymptotic spectrum of the linear boltzmann equation with general boundary conditions in finite bodies abstract the purpose of this paper is the study of the spectral properties of both streaming operator and transport operator with general boundary conditions in multidimensional bounded geometry we discuss the asymptotic spectrum existence and nonexistence results of eigenvalues in the half plane c re s t h where s t h stands for the spectral bound of the streaming operator t h next we discuss the irreducibility of the transport semigroup in particular we establish that the transport semigroup is irreducible if the boundary operator is strictly positive afterwards we discuss the strict monotonicity of the leading eigenvalue when it exists of the transport operator with respect to different parameters of the equation our analysis is based essentially on results from the theory of positive linear operators

on the leading eigenvalue of neutron transport models abstract we give variational characterizations of the leading eigenvalue of neutron transport like operators the proofs rely on sub and super eigenvalues various bounds of the leading eigenvalue are derived

asymptotic behavior of an unstirred chemostat model with internal inhibitor this paper deals with a chemostat model with an internal inhibitor first the elementary stability and asymptotic behavior of solutions of the system are determined second the effects of the inhibitor are considered it turns out that the parameter which measures the effect of the inhibitor plays a very important role in deciding the stability and longtime behavior of solutions of the system the results show that if is sufficiently large this model has no coexistence solution and one of the semitrivial equilibria is a global attractor when the maximal growth rate a of the species u lies in certain range but when a belongs to another range all positive solutions of this model are governed by a limit problem and two semitrivial equilibria are bistable the main tools used here include monotone system theory degree theory bifurcation theory and perturbation technique

positive solutions of a competition model for two resources in the unstirred chemostat this paper deals with a competition model between two species for two growth limiting and perfectly complementary resources in the unstirred chemostat the main purpose is to determine the exact range of the parameters of two species so that the system possesses positive solutions and to investigate multiple positive steady states of the system the main tools used here include the monotone methods and the topological fixed point theory developed by amann

bayesian methods for censored categorical data abstract bayesian methods are given for finite category sampling when some of the observations suffer missing category distinctions dickey s 1983 generalization of the dirichlet family of prior distributions is found to be closed under such censored sampling the posterior moments and predictive probabilities are proportional to ratios of b c carlson s multiple hypergeometric functions closed form expressions are developed for the case of nested reported sets when bayesian estimates can be computed easily from relative frequencies effective computational methods are also given in the general case an example involving surveys of death penalty attitudes is used throughout to illustrate the theory a simple special case of categorical missing data is a two way contingency table with cross classified count data xij i 1 r j 1 c together with supplementary trials counted only in the margin distinguishing the rows yi i 1 r there could also be further supplementary trials report

weak spectral mapping theorems for c0 groups associated to transport equations in slab geometry abstract we show in this paper that the c 0 groups governing neutron transport equations with reflecting boundary conditions in slab geometry satisfy a weak spectral mapping theorem in any l p spaces 1 p the main part of this paper is dealing with collisionless transport c 0 group while the full transport c 0 group is dealt with by stability arguments

positivity and stability of the essential spectrum for singular transport semigroups with non vacuum boundary conditions in this paper we prove some compactness results for a large class of singular transport equations our approach relies on some comparison results for positive operators our results extend and complete several earlier works we also provide simpler proofs for several known results in the literature

on the classical solutions of the boltzmann equation on etudie le probleme aux valeurs initiales pour l equation de boltzmann on montre que des solutions au sens classique existent pour tout temps si la donnee initiale est assez proche de l equilibre on se restreint a un domaine cubique et on considere seulement la condition aux limites periodique

optimal spectral theory of the linear boltzmann equation we give optimal compactness results in lp spaces 1 p related to spectral theory of general neutron transport equations on spatial domains with finite lebesgue measure

singular one dimensional transport equations on lp spaces we prove the well posedness of the cauchy problem governed by a linear mono energetic singular transport equation i e transport equation with unbounded collision frequency and unbounded collision operator with specular reflecting and periodic boundary conditions on lp spaces the large time behaviour of its solution is also considered we discuss the compactness properties of the second order remainder term of the dyson phillips expansion for a large class of singular collision operators this allows us to evaluate the essential type of the transport semigroup from which the asymptotic behaviour of the solution is derived

on the rate of convergence to equilibrium for the linear boltzmann equation with soft potentials abstract in this work we present several quantitative results of convergence to equilibrium for the linear boltzmann operator with soft potentials under grad s angular cut off assumption this is done by an adaptation of the famous entropy method and its variants resulting in explicit algebraic or even stretched exponential rates of convergence to equilibrium under appropriate assumptions the novelty in our approach is that it involves functional inequalities relating the entropy to its production rate which have independent applications to equations with mixed linear and non linear terms we also briefly discuss some properties of the equation in the non cut off case and conjecture what we believe to be the right rate of convergence in that case

improved estimation in a contingency table independence structure abstract estimation of the cell probabilities in a two way contingency table is considered when it is plausible that the table might have an independence structure relating to the two traits in a classical nonparametric setup the unrestricted maximum likelihood estimators of the cell probabilities are the corresponding sample proportions under the assumption of independence the restricted estimators are the product of the respective row and column sample proportions the latter estimators behave better than the former when independence actually holds but a different picture may emerge for possible departure from the assumed independence structure the restricted estimators may be heavily biased inefficient and even inconsistent for this reason a preliminary test on independence based on the classical contingency chi squared statistic may be conveniently incorporated in the formulation of a preliminary test estimator of the matrix of cell probabilities since typically we have a multiparameter e

global asymptotic behavior of a chemostat model with two perfectly complementary resources and distributed delay a model of the chemostat involving two species of microorganisms competing for two perfectly complementary growth limiting nutrients is considered the model incorporates distributed time delay in the form of integral differential equations in order to describe the time involved in converting nutrient to biomass the delays are included in the nutrient and species concentrations simultaneously a general class of monotone increasing functions is used to describe nutrient uptake sufficient conditions based on biologically meaningful parameters in the model are given that predict competitive exclusion for certain parameter ranges and coexistence for others we prove that the global asymptotic attractivity of steady states of the model is similar to that of the corresponding model without time delays however our results indicate that when the inherent delays are in fact large ignoring them may result in incorrect predictions

a system of resource based growth models with two resources in the unstirred chemostat abstract models of single species growth in the unstirred chemostat on two growth limiting nonreproducing resources are considered for the case of two complementary resources the existence and uniqueness of a positive steady state solution is established it is also proved that the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values for the case of two substitutable resources the existence of a positive steady state solution is determined for a range of the parameter m n techniques include the maximum principle monotone method and global bifurcation theory the longtime behavior of the corresponding limiting system is given for a range of m n in the special case of m n the uniqueness and global attractivity of the positive steady state solution of the original system is established

count data modeling and classification using finite mixtures of distributions in this paper we consider the problem of constructing accurate and flexible statistical representations for count data which we often confront in many areas such as data mining computer vision and information retrieval in particular we analyze and compare several generative approaches widely used for count data clustering namely multinomial multinomial dirichlet and multinomial generalized dirichlet mixture models moreover we propose a clustering approach via a mixture model based on a composition of the liouville family of distributions from which we select the beta liouville distribution and the multinomial the novel proposed model which we call multinomial beta liouville mixture is optimized by deterministic annealing expectation maximization and minimum description length and strives to achieve a high accuracy of count data clustering and model selection an important feature of the multinomial beta liouville mixture is that it has fewer parameters than the recently proposed multinomial generalized dirichlet mixture the performance evaluation is conducted through a set of extensive empirical experiments which concern text and image texture modeling and classification and shape modeling and highlights the merits of the proposed models and approaches

on a system of reaction diffusion equations arising from competition in an unstirred chemostat a system of reaction diffusion equations modeling two species competition in an unstirred chemostat is considered the asymptotic behavior of solutions is given as a function of the parameters and it is determined when neither one or both competing populations survive techniques include the maximum principle theory of uniform persistence in infinite dimensional dynamical systems and the theory of strongly order preserving semidynamical system

bayesian estimation methods for 2 2 contingency tables using mixtures of dirichlet distributions abstract in the estimation of cell probabilities from a 2 2 table a prior distribution is developed that can reflect prior beliefs about the cross classification structure in the table the posterior means using this prior shrink the classical estimates towards the association structure specified a priori by the user closed form approximations to the posterior means and credible regions are developed in the special case where the two variables of the table are believed independent

assessing robustness of intrinsic tests of independence in two way contingency tables for testing nested hypotheses from a bayesian standpoint a desirable condition is that the prior for the alternative model concentrates mass around the smaller or null model for testing independence in contingency tables the intrinsic priors satisfy this requirement furthermore the degree of concentration of the priors is controlled by a discrete parameter t the training sample size which plays an important role in the resulting answer in this article we report on the robustness of the tests of independence for small or moderate sample sizes in contingency tables with respect to intrinsic priors with different degrees of concentration around the null we compare these tests to frequentist tests and other robust bayes tests for large sample sizes robustness is achieved because the intrinsic bayesian tests are consistent examples using real and simulated data are given supplemental materials technical details and data sets are available online

a compactness result for perturbed semigroups and application to a transport model abstract in this paper we are concerned with the compactness properties of remainder terms of the dyson phillips expansion of perturbed semigroups on general banach spaces more specifically we derive conditions which ensure the compactness of the remainder term r n t for some integer n our result applies directly to discuss the time asymptotic behaviour for large times of the solution of a one dimensional transport equation with reentry boundary conditions on l 1 spaces without regularity conditions on the initial data

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results