a discrete dynamic convexized method for nonlinear integer programming in this paper we consider the box constrained nonlinear integer programming problem we present an auxiliary function which has the same discrete global minimizers as the problem the minimization of the function using a discrete local search method can escape successfully from previously converged discrete local minimizers by taking increasing values of a parameter we propose an algorithm to find a global minimizer of the box constrained nonlinear integer programming problem the algorithm minimizes the auxiliary function from random initial points we prove that the algorithm can converge asymptotically with probability one numerical experiments on a set of test problems show that the algorithm is efficient and robust

hopf bifurcation in a delayed reaction diffusion advection population model abstract in this paper we investigate a reaction diffusion advection model with time delay effect the stability instability of the spatially nonhomogeneous positive steady state and the associated hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction diffusion advection model and the model can exhibit oscillatory pattern through hopf bifurcation the effect of advection on hopf bifurcation values is also considered and our results suggest that hopf bifurcation is more likely to occur when the advection rate increases

effects of random motility on microbial growth and competition in a flow reactor the authors investigate the effects of random motility on the ability of a microbial population to survive in pure culture and to be a good competitor for scarce nutrient in mixed culture in a flow reactor model consisting of a nonlinear parabolic system of partial differential equations for pure culture a single population a sharp condition is derived which distinguishes between the two outcomes 1 washout of the population from the reactor or 2 persistence of the population and the existence of a unique single population steady state the simulations suggest that this steady state is globally attracting for the case of two populations competing for scarce nutrient they obtain sufficient conditions for the uniform persistence of the two populations for the existence of a coexistence steady state and for the ability of one population to competitively exclude a rival extensive simulations are reported which suggest that 1 all solutions approach some steady state solution 2 all possible outcomes exhibited by the classical competitive lotka volterra ode model can occur in the model and 3 the outcome of competition between two bacterial strains can depend rather subtly on their respective random motility coefficients

on the existence of solutions to the quadratic mixed integer mean variance portfolio selection problem abstract in the standard mean variance portfolio selection approach several operative features are not taken into account among these neglected aspects one of particular interest is the finite divisibility of the stock assets i e the obligation to buy sell only integer quantities of asset lots whose number is pre established in order to consider such a feature we deal with a suitably defined quadratic mixed integer programming problem in particular we formulate this problem in terms of quantities of asset lots instead of as usual in terms of capital per cent quotas secondly we provide necessary and sufficient conditions for the existence of a non empty mixed integer feasible set of the considered programming problem thirdly we present some rounding procedures for finding in a finite number of steps a feasible mixed integer solution which is better than the one detected by the necessary and sufficient conditions in terms of the value assumed by the portfolio variance finally we perform an extensive computational experiment by means of which we verify the goodness of our approach

evolution of passive movement in advective environments general boundary condition abstract in a previous work 16 lou et al studied a lotka volterra competition diffusion advection system where two species are supposed to differ only in their advection rates and the environment is assumed to be spatially homogeneous and closed no flux boundary condition and showed that weaker advective movements are more beneficial for species to win the competition in this paper we aim to extend this result to a more general situation where the environmental heterogeneity is taken into account and the boundary condition at the downstream end becomes very flexible including the standard dirichlet neumann and robin type conditions as special cases our main approaches are to exclude the existence of co existence positive steady state and to provide a clear picture on the stability of semi trivial steady states where we introduced new ideas and techniques to overcome the emerging difficulties based on these two aspects and the theory of abstract competitive systems we achieve a complete understanding on the global dynamics

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

the simple chemostat with wall growth a model of the simple chemostat which allows for growth on the wall or other marked surface is presented as three nonlinear ordinary differential equations the organisms which are attached to the wall do not wash out of the chemostat this destroys the basic reduction of the chemostat equations to a monotone system a technique which has been useful in the analysis of many chemostat like equations the adherence to and shearing from the wall eliminates the boundary equilibria for a reasonably general model the basic properties of invariance dissipation and uniform persistence are established for two important special cases global asymptotic results are obtained finally a perturbation technique allows the special results to be extended to provide the rest point as a global attractor for nearby growth functions

asymptotic strong duality for bounded integer programming a logarithmic exponential dual formulation a logarithmic exponential dual formulation is proposed in this paper for bounded integer programming problems this new dual formulation possesses an asymptotic strong duality property and guarantees the identification of an optimal solution of the primal problem these prominent features are achieved by exploring a novel nonlinear lagrangian function deriving an asymptotic zero duality gap investigating the unimodality of the associated dual function and ensuring the primal feasibility of optimal solutions in the dual formulation one other feature of the logarithmicexponential dual formulation is that no actual dual search is needed when parameters are set above certain threshold values

global attractors and steady state solutions for a class of reaction diffusion systems abstract we show that weak l p dissipativity implies strong l dissipativity and therefore implies the existence of global attractors for a general class of reaction diffusion systems this generalizes the results of alikakos and rothe the results on positive steady states especially for systems of three equations in our earlier work j differential equations 130 1996 59 91 are improved

on a lotka volterra competition diffusion advection model in general heterogeneous environments abstract we consider a two species lotka volterra competition diffusion advection system which has the combined effect of spatial dispersal advection and spatial variations of resource on the population firstly the existence and global asymptotic stability of the positive equilibrium solution for the logistic model are obtained with the assumption of spatially heterogeneous dispersal advection and resource distribution secondly it is shown that when the diffusion coefficients resource functions and competition rates are all spatially heterogeneous the positive equilibrium solution is globally asymptotically stable when it exists

numerical experience with lower bounds for miqp branch and bound the solution of convex mixed integer quadratic programming miqp problems with a general branch and bound framework is considered it is shown how lower bounds can be computed efficiently during the branch and bound process improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming qp problems that have to be solved the branch and bound approach is also shown to be superior to other approaches in solving miqp problems numerical experience is presented which supports these conclusions

the nonlinear resource allocation problem in this paper we study the nonlinear resource allocation problem defined as the minimization of a convex function over one convex constraint and bounded integer variables this problem is encountered in a variety of applications including capacity planning in manufacturing and computer networks production planning capital budgeting and stratified sampling despite its importance to these and other applications the nonlinear resource allocation problem has received little attention in the literature therefore we develop a branch and bound algorithm to solve this class of problems first we present a general framework for solving the continuous variable problem then we use this framework as the basis for our branch and bound method we also develop reoptimization procedures and a heuristic that significantly improve the performance of the branch and bound algorithm in addition we show how the algorithm can be modified to solve nonconvex problems so that a concave objective function can be handled

a new proof of the garoufalidis le zeilberger quantum macmahon master theorem abstract we propose a new proof of the quantum version of macmahon s master theorem established by garoufalidis le and zeilberger

dynamical behavior of a general reaction diffusion advection model for two competing species it is well known that the studies of the evolution of biased movement along a resource gradient could create very interesting phenomena this paper deals with a general two species lotka volterra competition model for the same resources in an advective nonhomogeneous environment where the individuals are exposed to unidirectional flow advection but no individuals are lost through the boundary it is assumed that the two species have the same population dynamics but different diffusion and advection rates it is shown that at least five scenarios can occur i if one with a very strong biased movement relative to diffusion and the other with a more balanced approach the species with much larger advection dispersal rate is driven to extinction ii if one with a very strong biased movement and the other is smaller compare to its diffusion the two species can coexist since one species mainly pursues resources at places of locally most favorable environments while the other relies on resources from other parts of the habitat iii if both of the species random dispersal rates are sufficiently large respectively small two competing species coexist iv if one with a sufficiently large random dispersal rate and the other with a sufficiently small one two competing species still coexist v if one with a sufficiently small random dispersal rate and the other with a suitable diffusion which causes the extinction of the species with smaller random movement where iii iv and v show the global dynamics of 5 when both of the species dispersal rates are sufficiently large or sufficiently small these results provide a new mechanism for the coexistence of competing species and they also imply that selection is against excessive advection along environmental gradients respectively random dispersal rate and an intermediate biased movement rate respectively random dispersal rate may evolve finally we also apply a perturbation argument to illustrate the evolution of these rates

a weak competition system with advection and free boundaries abstract in order to study the influence of advection speed on the competitive outcomes of two invading species a reaction diffusion advection weak competition system with four free boundaries in one dimensional space is proposed and investigated in the case of small advection speed the explicit classification of the competitive outcomes the estimation of the spreading speed the long time behavior of the solutions and the minimal habitat size which determines whether the species can always spread or not are obtained the results are similar as the case with no advection in the case of large advection speed both two species cannot spread successfully but may virtual spread downstream in the case of medium sized advection speed some competitive outcomes and the long time behaviors of the solutions are also obtained mathematical results suggest that the competitive outcomes which depend on the advection speed and moving parameters are very complicated some criteria for spreading vanishing and virtual spreading are also established in all cases

extensions of the chemostat model with flocculation in this work we study a model of the chemostat where the species are present in two forms isolated bacteria and under an aggregated form like attached bacteria or bacteria in flocks we show that our general model contains a lot of models which were previously considered in the literature assuming that flocculation and deflocculation dynamics are fast with respect to the growth of the species we construct a reduced chemostat like model in which both the growth functions and the apparent dilution rate depend on the density of the species we also show that such a model involving monotonic growth rates may exhibit bistability while it may only occur in the classical chemostat model when the growth rate in non monotonic

multiparametric quantum deformation of the general linear supergroup in the work l d faddeev and his collaborators and subsequently v g drinfeld m jimbo s l woronowicz a new class of hopf algebras was constructed they can be considered as one parametric deformations of either group ring or the universal enveloping algebra of a simple algebraic group in this paper we define and investigate a multiparametric deformation of the general linear supergroup this is the simplest example of some general constructions described in 5 6

a survey of methods for pure nonlinear integer programming the subject of this paper is a classification and discussion of algorithms for solution of nonlinear pure integer programming problems the survey is organized by characterizing the mathematical form of the nonlinear optimization problems addressed by the various algorithms if any method can be used without changes to solve mixed integer nonlinear programming problems that fact is mentioned in the description of the algorithm however algorithms which must be applied only to mixed integer problems are not surveyed

applications of q lagrange inversion to basic hypergeometric series a family of g lagrange inversion formulas is given special cases include quadratic and cubic transformations for basic hypergeometric series the g analogs of the so called strange evaluations are also corollaries some new rogers ramanujan identities are given a connection between the work of rogers and andrews and lagrange inversion is stated

steady states of a leslie gower model with diffusion and advection abstract this paper focuses on a stationary leslie gower model with diffusion and advection firstly some existence conditions of nonconstant positive solutions are obtained by means of the leray schauder degree theory as diffusion and advection of one of the species both tend to infinity we obtain a limiting system which is a semi linear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system is classified

a hierarchy of relaxations for nonlinear convex generalized disjunctive programming we propose a framework to generate alternative mixed integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations we extend the concept of basic steps defined for disjunctive linear programs to the nonlinear case a basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts we show that the strength of the relaxations increases as the number of conjuncts decreases leading to a hierarchy of relaxations we prove that the tightest of these relaxations allows in theory the solution of the disjunctive convex program as a nonlinear programming problem we present a methodology to guide the generation of strong relaxations without incurring an exponential increase of the size of the reformulated mixed integer program finally we apply the theory developed to improve the computational efficiency of solution methods for nonlinear convex generalized disjunctive programs gdp this methodology is validated through a set of numerical examples

the effect of dispersal patterns on stream populations individuals in streams are constantly subject to predominantly unidirectional flow the question of how these populations can persist in upper stream reaches is known as the drift paradox we employ a general mechanistic movement model framework and derive dispersal kernels for this situation we derive thin as well as fat tailed kernels we then introduce population dynamics and analyze the resulting integrodifferential equation in particular we study how the critical domain size and the invasion speed depend on the velocity of the stream flow we give exact conditions under which a population can persist in a finite domain in the presence of stream flow as well as conditions under which a population can spread against the direction of the flow we find a critical stream velocity above which a population cannot persist in an arbitrarily large domain at exactly the same stream velocity the invasion speed against the flow becomes zero for larger velocities the population retreats with the flow

global dynamics of a classical lotka volterra competition diffusion advection system abstract in this paper we study a classical two species lotka volterra competition diffusion advection system where the diffusion and advection rates of two competitors are supposed to be proportional by employing the principal spectral theory we first establish a key a priori estimate on the co existence positive steady state which is a powerful tool to link the local and global dynamics we then further present a complete classification on all possible long time dynamical behaviors by appealing to the theory of monotone dynamical systems lastly we apply these results to a special situation where two species are competing for the same resources and obtain a sharp criteria in term of certain variable parameters for all kinds of global dynamics this work gives a positive answer to the conjecture proposed by lou et al in 34 by considering a more general model under certain conditions and also can be seen as a further development of he and ni 19 for competition diffusion system where we bring new ingredients in the arguments to overcome the difficulty caused by the involvement of advection

persistence of wavefronts in delayed nonlocal reaction diffusion equations we develop a perturbation argument based on existing results on asymptotic autonomous systems and the fredholm alternative theory that yields the persistence of traveling wavefronts for reaction diffusion equations with nonlocal and delayed nonlinearities when the time lag is relatively small this persistence result holds when the nonlinearity of the corresponding ordinary reaction diffusion system is either monostable or bistable we then illustrate this general result using five different models from population biology epidemiology and bio reactors

a spatial sis model in advective heterogeneous environments abstract we study the effects of diffusion and advection for a susceptible infected susceptible epidemic reaction diffusion model in heterogeneous environments the definition of the basic reproduction number r 0 is given if r 0 1 the unique disease free equilibrium dfe is globally asymptotically stable asymptotic behaviors of r 0 for advection rate and mobility of the infected individuals denoted by d i are established and the existence of the endemic equilibrium when r 0 1 is studied the effects of diffusion and advection rates on the stability of the dfe are further investigated among other things we find that if the habitat is a low risk domain there may exist one critical value for the advection rate under which the dfe changes its stability at least twice as d i varies from zero to infinity while the dfe is unstable for any d i when the advection rate is larger than the critical value these results are in strong contrast with the case of no advection where the dfe changes its stability at most once as d i varies from zero to infinity

a pivotal eigenvalue problem in river ecology this paper studies an eigenvalue problem associated with a linear parabolic equation and a coupled ordinary differential equation the existence and the uniqueness of the principal eigenvalue for this eigenvalue problem is first established then the qualitative dependence of the principal eigenvalue with respect to the several parameters involved in the system is analyzed finally these results are applied to a system in flowing habitats with a hydraulic storage zone and light limitation

an approximate algorithm for nonlinear integer programming abstract this paper suggests an approximate algorithm designed to solve nonlinear integer problems this algorithm belongs to the class of component algorithms of feasible integer directions the search for a feasible integer direction is done on the basis of a linear approximation of the objective function and the constraints at the integer points under consideration theoretical analysis is presented as well as experimental investigation using the algorithm for test examples taken from the literature

when is rounding allowed in integer nonlinear optimization abstract in this paper we consider nonlinear integer optimization problems nonlinear integer programming has mainly been studied for special classes such as convex and concave objective functions and polyhedral constraints in this paper we follow an other approach which is not based on convexity or concavity studying geometric properties of the level sets and the feasible region we identify cases in which an integer minimizer of a nonlinear program can be found by rounding up or down the coordinates of a solution to its continuous relaxation we call this property rounding property if it is satisfied it enables us for fixed dimension to solve an integer programming problem in the same time complexity as its continuous relaxation we also investigate the strong rounding property which allows rounding a solution to the continuous relaxation to the next integer solution and in turn yields that the integer version can be solved in the same time complexity as its continuous relaxation for arbitrary dimensions

specializations and extensions of the quantum macmahon master theorem abstract we study some specializations and extensions of the quantum version of the macmahon master theorem derived by garoufalidis le and zeilberger in particular we obtain a t q analogue for the cartier foata noncommutative version and a semi strong t q analogue for the contextual algebra

traveling waves in a bio reactor model with stage structure abstract in this paper the existence and non existence of traveling wave solutions are established for a bio reactor model with stage structure the method to prove the existence of wave solutions is to construct an invariant cone of initial functions defined in a large but bounded domain to apply a fixed point theorem on this cone and then extend to the unbounded spatial domain r by a limiting argument

a free boundary problem of a predator prey model with advection in heterogeneous environment this paper is concerned with a system of reaction diffusion advection equations with a free boundary which arises in a predator prey ecological model in heterogeneous environment the evolution of the free boundary problem is discussed precisely we prove a spreading vanishing dichotomy namely both prey and predator either survive and establish themselves successfully in the new environment or they fail to establish and vanishes eventually furthermore when spreading occurs we obtain an upper bound of the asymptotic spreading speed which is smaller than the minimal speed of the corresponding traveling wave problem

koszulity for nonquadratic algebras abstract it is known that a koszul algebra is defined as being a quadratic algebra with a pure resolution of the ground field in this paper we extend koszulity to algebras whose relations are homogeneous of degree s 2 a cubic artin schelter regular algebra has motivated our work generalized koszulity is connected to lattice distributivity and to confluence a generalized symmetric algebra is proved to be generalized koszul and the bimodule version of the generalized koszul resolution is used for investigating its hochschild homology

non commutative extensions of the macmahon master theorem we present several non commutative extensions of the macmahon master theorem further extending the results of cartier foata and garoufalidis le zeilberger the proofs are combinatorial and new even in the classical cases we also give applications to the s extension and krattenthaler schlosser s q analogue

manin matrices and talalaev s formula in this paper we study properties of lax and transfer matrices associated with quantum integrable systems our point of view stems from the fact that their elements satisfy special commutation properties considered by yu i manin some 20 years ago at the beginning of quantum group theory these are the commutation properties of matrix elements of linear homomorphisms between polynomial rings more explicitly these read 1 elements of the same column commute 2 commutators of the cross terms are equal mij mkl mkj mil e g m11 m22 m21 m12 the main aim of this paper is twofold on the one hand we observe and prove that such matrices which we call manin matrices in short behave almost as well as matrices with commutative elements namely the theorems of linear algebra e g a natural definition of the determinant the cayley hamilton theorem the newton identities and so on and so forth have a straightforward counterpart in the case of manin matrices on the other hand we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability for instance manin matrices and their q analogs include matrices satisfying the yang baxter relation rtt ttr and the so called cartier foata matrices also they enter talalaev s remarkable formulae for the quantum spectral curve and appear in the separation of variables problem and capelli identities we show that theorems of linear algebra after being established for such matrices have various applications to quantum integrable systems and lie algebras e g in the construction of new generators in and in general in the construction of quantum conservation laws in the knizhnik zamolodchikov equation and in the problem of wick ordering we propose in the appendix a construction of quantum separated variables for the xxx heisenberg system

ellipsoid bounds for convex quadratic integer programming solving convex quadratic integer minimization problems by a branch and bound algorithm requires tight lower bounds on the optimal objective value to obtain such dual bounds we follow the approach of c buchheim a caprara and a lodi math program 135 2012 pp 369 395 and underestimate the objective function by another convex quadratic function that can be minimized over the integers by simply rounding its continuous minimizer in geometric terms we approximate the sublevel sets of the original objective function by auxiliary ellipsoids having the strong rounding property introduced by r hu bner and a scho bel european j oper res 237 2014 pp 404 410 we first consider axisparallel ellipsoids corresponding to separable convex quadratic functions and show how to efficiently compute an axisparallel ellipsoid yielding the tightest lower bound both in the situation where the location of the continuous minimizer is given and in the situation where it varies as it happens in a branch and bound approach in the latter case we compute both worst case and average case optimal ellipsoids moreover we consider the class of quasi round ellipsoids from hu bner and scho bel in this case we do not know whether optimal auxiliary ellipsoids can be computed efficiently however we present a heuristic for computing an appropriate quasi round ellipsoid that still yields valid dual bounds it turns out that using this approach within a branch and bound scheme outperforms the approaches based on axisparallel ellipsoid in terms of running times we finally combine both approaches by introducing the concept of quasi axisparallel ellipsoids and present a corresponding extension of the heuristic bound computation

food chain length of a ecological model with prey taxis abstract in this paper we construct a ecological system with prey taxis from the dynamic point of view we analytically and numerically investigate the steady states our results show how the combined action of the death rates chemotaxis diffusivity and conversion efficiency to influence the survival ability of multiple consumer levels in a ecological system with self produced nutriment furthermore the food chain length of our model can be determined by the co existence conditions of all consumer levels numerical simulation corroborates the analytical results

an algorithm for indefinite integer quadratic programming abstract we present an algorithm for finding the global minimum of an indefinite quadratic function over the integers contained in a compact convex set to find this minimum the algorithm first transforms the problem into an equivalent problem with a separable objective function it then uses a branch and bound search on the values of the constraints rather than the variables of the transformed problem

evolution of dispersal in advective homogeneous environment the effect of boundary conditions abstract we consider a single species model and a two species competition model in a one dimensional advective homogeneous environment one interesting feature in these models concerns the boundary condition at the downstream end where the species can be exposed to a net loss of individuals as tuned by a parameter b which measures the magnitude of the loss we first determine necessary and sufficient conditions for the persistence of a single species for general value of b in terms of the critical habitat size and the critical advection rate then for the competition model we assume that two species are identical except their random diffusion rates we obtain complete understanding when 0 b 1 and our result indicates that larger diffusion rate is selected extending an earlier work 20 b 1 however for b 1 the dynamics can be quite different and particularly we illustrate that some intermediate diffusion rate may be selected when b 3 2

uniqueness of traveling wave solutions for a biological reaction diffusion equation abstract the existence of traveling wave solutions for a reaction diffusion which serves as models for microbial growth in a flow reactor and for mathematical epidemiology was previously confirmed however the problem on the uniqueness of traveling wave solutions remains open in this paper we give a complete proof of the uniqueness of traveling wave solutions

branch and bound experiments in convex nonlinear integer programming the branch and bound principle has long been established as an effective computational tool for solving mixed integer linear programming problems this paper investigates the computational feasibility of branch and bound methods in solving convex nonlinear integer programming problems the efficiency of a branch and bound method often depends on the rules used for selecting the branching variables and branching nodes among others the concepts of pseudo costs and estimations are implemented in selecting these parameters since the efficiency of the algorithm also depends on how fast an upper bound on the objective minimum is attained heuristic rules are developed to locate an integer feasible solution to provide an upper bound the different criteria for selecting branching variables branching nodes and heuristics form a total of 27 branch and bound strategies these strategies are computationally tested and the empirical results are presented

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

extension of macmahon s master theorem to pre semi rings an extended version of the classical macmahon s master theorem to algebraicstructures much more general than the field of real numbers namely semi rings and even pre semi rings is proposed due to the fact that many semi rings or pre semi rings are not additive groups such concepts as the determinant of a matrix cannot be used any more and the statement of the result itself has to be significantly different when specialized to the field of real numbers however the extended result is shown to reduce to the classical version of macmahon s master theorem

polyhedral approximation in mixed integer convex optimization generalizing both mixed integer linear optimization and convex optimization mixed integer convex optimization possesses broad modeling power but has seen relatively few advances in general purpose solvers in recent years in this paper we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class our approach is based on constructing polyhedral outer approximations of the convex constraints resulting in a global solution by solving a finite number of mixed integer linear and continuous convex subproblems the key advance we present is to strengthen the polyhedral approximations by constructing them in a higher dimensional space in order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming dcp and for generality and ease of implementation we use conic representations of the convex constraints although our framework requires a manual translation of existing models into dcp form after performing this transformation on the minlplib2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state of the art solvers like bonmin scip and artelys knitro

the evolution of traveling waves in a simple isothermal chemical system modeling quadratic autocatalysis with strong decay abstract in this paper we study a reaction diffusion system for an isothermal chemical reaction scheme governed by a quadratic autocatalytic step a b 2 b and a decay step b c where a b and c are the reactant the autocatalyst and the inner product respectively previous numerical studies and experimental evidences demonstrate that if the autocatalyst is introduced locally into this autocatalytic reaction system where the reactant a initially distributes uniformly in the whole space then a pair of waves will be generated and will propagate outwards from the initial reaction zone one crucial feature of this phenomenon is that for the strong decay case the formation of waves is independent of the amount of the autocatalyst b introduced into the system it is this phenomenon of kpp type which we would like to address in this paper to study the propagation of reactant and autocatalyst analytically we first use the tail behavior of waves to construct a pair of generalized super sub solutions for the approximate system of the autocatalytic reaction system note that the autocatalytic reaction system does not enjoy comparison principle together with a family of truncated problems we can establish the existence of a family of traveling waves with the minimal speed second we use this pair of generalized super sub solutions to show that the propagation of waves is fully determined by the rate of decay of the initial data at infinity in the sense of aronson weinberger formulation which in turn confirms the aforementioned numerical and experimental results

a critical review of discrete filled function methods in solving nonlinear discrete optimization problems many real life problems can be modeled as nonlinear discrete optimization problems such problems often have multiple local minima and thus require global optimization methods due to high complexity of these problems heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems one of the more recent global optimization tools is known as the discrete filled function method nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given some of the most promising filled functions are tested on various benchmark problems numerical results are given for comparison

a system of partial differential equations modeling the competition for two complementary resources in flowing habitats abstract this paper examines a system of reaction diffusion equations arising from a flowing water habitat in this habitat one or two microorganisms grow while consuming two growth limiting complementary essential resources for the single population model the existence and uniqueness of a positive steady state solution is proved furthermore the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values mathematical analysis for the two competing populations is carried out more precisely the long time behavior is determined by using the monotone dynamical system theory when the semi trivial solutions are both unstable it is also shown that coexistence solutions exist by using the fixed point index theory when the semi trivial solutions are both asymptotically stable

global optimization of mixed integer nonlinear programs a theoretical and computational study this work addresses the development of an efficient solution strategy for obtaining global optima of continuous integer and mixed integer nonlinear programs towards this end we develop novel relaxation schemes range reduction tests and branching strategies which we incorporate into the prototypical branch and bound algorithm in the theoretical algorithmic part of the paper we begin by developing novel strategies for constructing linear relaxations of mixed integer nonlinear programs and prove that these relaxations enjoy quadratic convergence properties we then use lagrangian linear programming duality to develop a unifying theory of domain reduction strategies as a consequence of which we derive many range reduction strategies currently used in nonlinear programming and integer linear programming this theory leads to new range reduction schemes including a learning heuristic that improves initial branching decisions by relaying data across siblings in a branch and bound tree finally we incorporate these relaxation and reduction strategies in a branch and bound algorithm that incorporates branching strategies that guarantee finiteness for certain classes of continuous global optimization problems in the computational part of the paper we describe our implementation discussing wherever appropriate the use of suitable data structures and associated algorithms we present computational experience with benchmark separable concave quadratic programs fractional 0 1 programs and mixed integer nonlinear programs from applications in synthesis of chemical processes engineering design just in time manufacturing and molecular design

a competition model for two resources in un stirred chemostat abstract this paper studies a un stirred chemostat with two species competing for two growth limiting non reproducing resources we determine the conditions for positive steady states of the two species and then consider the global attractors of the model in addition we obtain the conditions under which the two populations uniformly strongly persist or go to extinction since the diffusion mechanism with homogeneous boundary conditions inhibits the growth of the organism species it can be understood that the coexistence will be ensured by proportionally smaller diffusions for the two species in particular it is found that both instability and bi stability subcases of the two semitrivial steady states are included in the coexistence region the two populations will go to extinction when both possess large diffusion rates if just one of them spreads faster with the other one diffusing slower then the related semitrivial steady state will be globally attracting the techniques used for the above results consist of the degree theory the semigroup theory and the maximum principle

operator methods and lagrange inversion a unified approach to lagrange formulas on presente une methode generale de demonstration des formules d inversion de lagrange et de leurs variantes on considere le cas de plusieurs variables

q analogues of lagrange inversion abstract an inversion theorem is proved which places into a common setting and extends the work of andrews gessel garsia and garsia and remmel examples of q lagrange inversion are given including new rogers ramanujan type identities

traveling waves solutions of isothermal chemical systems with decay this article studies propagating traveling waves in a class of reaction diffusion systems which include a model of microbial growth and competition in a flow reactor proposed by smith and zhao 17 and isothermal autocatalytic systems in chemical reaction of order m with a decay order n where m and n are positive integers and m n a typical system in autocatalysis is a 2b 3b with rate k1ab2 and b c with rate k2b where m 2 and n 1 involving two chemical species a reactant a and an auto catalyst b whose diffusion coefficients da and db are unequal due to different molecular weights and or sizes here a is the concentration density of a b that of b and c an inert chemical species the two constants k1 and k2 are material constants measuring the relative strength of respective reactions it is shown that there exist traveling waves when m 1 and n 1 with suitable relation between the ratio db da traveling speed c and rate constants k1 k2 on the other hand it is proved that there exists no traveling wave when one of the chemical species is immobile db 0 or n m for all choices of other parameters

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

microbial competition for nutrient and wall sites in plug flow a mathematical model of microbial competition for limiting nutrients and for a limited set of available wall attachment sites in an advection dominated tubular reactor is formulated as a limiting case of the more general model considered in m ballyk and h l smith a flow reactor with wall growth in mathematical models in medical and health sciences m horn g simonett and g webb eds vanderbilt university press nashville tn 1998 the model consists of a system of hyperbolic pde the existence and stability properties of its steady state solutions are investigated both analytically and numerically a surprising finding in the case of two strain competition is the existence of a steady state solution characterized by the segregation of the two bacterial strains to separate nonoverlapping segments along the tubular reactor

existence of traveling waves of auto catalytic systems with decay abstract this article establishes the existence of traveling waves of a class of reaction diffusion systems which model the pre mixed isothermal autocatalytic chemical reaction of order m m 1 between two chemical species a reactant and an auto catalyst and a linear decay moreover our result shows that the set of speed is contained in a bounded interval for any fixed initial value at x this is in strong contrast to either the reaction diffusion systems of autocatalytic chemical reaction of the order m without decay or to the systems which have the same order of decay which were shown by various authors e g 8 13 17 26 that the set of traveling wave speeds contains c for some c 0 the same systems also appear in a mathematical model of microbial growth and competition in a flow reactor see 2 24

impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment abstract in this work we develop a new modeling framework to study the impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment our model is built on a reaction advection diffusion system to represent spatiotemporal dynamics of cholera transmission and incorporates bacterial hyperinfectivity and spatial heterogeneity firstly we define the basic reproduction number r 0 and establish the global threshold dynamics based on r 0 secondly the global attractivity of the unique endemics equilibrium is discussed when the spatial environment is homogeneous and waning cholera immunity advection and intrinsic growth of bacteria are ignored thirdly the dependence of r 0 on model parameters are numerically investigated the theoretical results are obtained for some specific cases our result highlights the importance of hyperinfectivity and its interplay with spatial heterogeneity particularly our findings indicate ignoring hyperinfectivity may underestimate the risk of infection

global stability and pattern formation in a nonlocal diffusive lotka volterra competition model abstract a diffusive lotka volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed the nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species it is shown that when there is no nonlocal intraspecific competition the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive lotka volterra competition model regardless of the strength of nonlocal interspecific competition global stability of nonnegative constant equilibria are proved using lyapunov or upper lower solution methods on the other hand strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity for the weak competition case the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients

evolution of predator prey systems described by a lotka volterra equation under random environment abstract in this paper we consider the evolution of a system composed of two predator prey deterministic systems described by lotka volterra equations in random environment it is proved that under the influence of telegraph noise all positive trajectories of such a system always go out from any compact set of int r 2 with probability one if two rest points of the two systems do not coincide in case where they have the rest point in common the trajectory either leaves from any compact set of int r 2 or converges to the rest point the escape of the trajectories from any compact set means that the system is neither permanent nor dissipative

a reaction advection diffusion system modeling the competition for two complementary resources with seasonality in a flowing habitat abstract in this current paper we investigate a periodic bio reactor model where microorganisms compete for two essential nutrient resource s needed for growth for the single population growth model we show that when the trivial solution is locally asymptotically stable then the single population will be washed out when the trivial solution is unstable there is a unique periodic positive solution which attracts all solutions with nonzero initial data for the two species model we prove that the existence of a periodic coexistence state is possible if each species can invade the semi trivial periodic state established by the other species more precisely if the semi trivial periodic solutions are both unstable there exists at least one periodic coexistence solution numerical work indicates conditions for persistence depend on the flow characteristics advection and diffusivity from our numerical simulations competitive exclusion bistability and coexistence are all observed

on a lotka volterra competition diffusion advection system homogeneity vs heterogeneity abstract as we know interactions between movement and environmental heterogeneity could create very interesting phenomena in population dynamics in this paper based on a lotka volterra competition diffusion advection system we try to reveal the combined effect of movement and spatial variations on the outcome of competition for the purpose of comparison we suppose that the total resources for two populations are fixed at the same level but one distribution is even across space while the other one not our main results suggest that the contest between heterogeneous and homogeneous distribution is very complex either one of the two competitors becomes the final single winner exclusion or both populations coexist eventually coexistence depending closely on the movement rates and the shape of the given resource

dynamics of a periodically pulsed bio reactor model abstract global attractivity and uniform persistence are established for both single species growth and two species competition in a periodically pulsed bio reactor model in terms of principal eigenvalues of the periodic parabolic eigenvalue problem by appealing to the theories of monotone discrete dynamical systems abstract persistence asymptotically periodic semiflows and perturbation of global attractors

global dynamics of a lotka volterra competition diffusion system in advective homogeneous environments abstract in this paper we mainly study a two species competition model in a one dimensional advective homogeneous environment where the two species are identical except their diffusion rates one interesting feature of the model is that the boundary condition at the downstream end represents a net loss of individuals which is tuned by a parameter b to measure the magnitude of the loss when the upstream end has the no flux condition lou and zhou 2015 11 have confirmed that large diffusion rate is more favorable when 0 b 1 here we consider the case where the upstream end has the free flow condition which means that the upstream end is linked to a lake we firstly investigate the corresponding single species model here we establish the existence and uniqueness of positive steady states then for the two species model we find that the parameter b can be regarded as a bifurcation parameter precisely when 0 b 1 large diffusion rate is more favorable while when b 1 small diffusion rate is selected if exists when b 1 the system is degenerate in the sense that there is a compact global attractor consisting of a continuum of steady states