optimal control of non homogenous prey predator models during infinite and finite time intervals we propose a lattice to describe dynamics of two animal species population one being a prey and the other a predator the problem of controlling steady states of non homogenous prey predator model during finite and infinite time intervals is studied using lyapunov bellman technique the optimal control law is derived from the conditions that ensure the asymptotic stabilization of the steady states of this model using bellman s equation the densities of both prey and predator populations are obtained as functions of time graphical and numerical example studies of the obtained results are presented

on the tropical torelli map abstract we construct the moduli spaces of tropical curves and tropical principally polarized abelian varieties working in the category of what we call stacky fans we define the tropical torelli map between these two moduli spaces and we study the fibers tropical torelli theorem and the image of this map tropical schottky problem finally we determine the image of the planar tropical curves via the tropical torelli map and we use it to give a positive answer to a question raised by namikawa on the compactified classical torelli map

qualitative analysis for a ratio dependent predator prey model with disease and diffusion abstract this paper is purported to study a reaction diffusion system arising from a ratio dependent predator prey model with disease we study the dynamical behavior of the predator prey system the conditions for the permanent and existence of steady states and their stability are established we can obtain the bounds for positive steady state of the corresponding elliptic system the non existence results of non constant positive solutions are derived

extending the torelli map to toroidal compactifications of siegel space it has been known since the 1970s that the torelli map m g a g associating to a smooth curve its jacobian extends to a regular map from the deligne mumford compactification overline operatorname m g to the 2nd voronoi compactification overline operatorname a g mathrm vor we prove that the extended torelli map to the perfect cone 1st voronoi compactification overline operatorname a g mathrm perf is also regular and moreover overline operatorname a g mathrm vor and overline operatorname a g mathrm perf share a common zariski open neighborhood of the image of overline operatorname m g we also show that the map to the igusa monoidal transform central cone compactification is not regular for g 9 this disproves a 1973 conjecture of namikawa

comparing perfect and 2nd voronoi decompositions the matroidal locus we compare two rational polyhedral admissible decompositions of the cone of positive definite quadratic forms the perfect cone decomposition and the 2nd voronoi decomposition we determine which cones belong to both the decompositions thus providing a positive answer to a conjecture of alexeev and brunyate invent math doi 10 1007 s00222 011 0347 2 2011 as an application we compare the two associated toroidal compactifications of the moduli space of principal polarized abelian varieties the perfect cone compactification and the 2nd voronoi compactification

adomian decomposition a tool for solving a system of fractional differential equations abstract adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations convergence of the method has been discussed with some illustrative examples in particular for the initial value problem d 1 y 1 d n y n t a y 1 y n t y i 0 c i i 1 n where a a i j is a real square matrix the solution turns out to be y x e 1 n 1 x 1 a 1 x n a n y 0 where e 1 n 1 denotes multivariate mittag leffler function defined for matrix arguments and a i is the matrix having ith row as a i 1 a i n and all other entries are zero fractional oscillation and bagley torvik equations are solved as illustrative examples

the general vector solutions of such linear coupled matrix fractional differential equations by using kronecker structures in this paper we demonstrate how kronecker products and vector operator can be combined beautifully to solve and fit the non homogenous linear matrix fractional differential equations and such coupled linear matrix fractional differential equations the way exists which transform the given coupled matrix fractional differential equations by using kronecker structures into forms for which solutions may be readily computed some important and interesting special cases of the general system of non homogeneous linear matrix fractional differential equations of fractional order are also considered which includes the non homogenous linear fractional dynamical system with delays in control finally a brief comparison between the fractional and integer order vector solutions and some examples are given to illustrate our new approaches

log canonical models for the moduli space of curves the first divisorial contraction in this paper we initiate our investigation of log canonical models for m g as we decrease from 1 to 0 we prove that for the first critical value 9 11 the log canonical model is isomorphic to the moduli space of pseudostable curves which have nodes and cusps as singularities we also show that 7 10 is the next critical value i e the log canonical model stays the same in the interval 7 10 9 11 in the appendix we develop a theory of log canonical models of stacks that explains how these can be expressed in terms of the coarse moduli space

permanence and stability of a diffusive predator prey model with disease in the prey abstract we investigate a 3 dimensional system of the predator prey dynamics with disease for the prey this system is a reaction diffusion model with ratio dependent michaelis menten functional response and diffusion in a bounded domain by applying the comparison principle liapunov function and linearized method we are able to achieve the sufficient conditions of the permanence the global stability of the boundary equilibria and the positive equilibrium and the local stability of the positive equilibrium numerical simulations are also given to illustrate the applications

the nonexistence of certain level structures on abelian varieties over complex function fields let a be a principally polarized abelian variety of dimension g over a number field k the mordell weil theorem tells us that the group a k of k rational points of a is finitely generated in particular the torsion subgroup of a k is finite for the important special case of an elliptic curve e q mazur mal 2 has proved that the torsion subgroup of e q has order 16 in general one would expect the torsion subgroup of a k to have order c g k a constant depending only on the number field k and the dimension g but not

hopf bifurcation and stability of periodic solutions in a delayed eco epidemiological system abstract in this paper a delayed predator prey epidemiological system with disease spreading in predator population is considered by regarding the delay as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the original system at the positive equilibrium the local asymptotic stability of the positive equilibrium and the existence of local hopf bifurcation of periodic solutions are investigated moreover we also study the direction of hopf bifurcations and the stability of bifurcated periodic solutions an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations finally numerical simulations supporting the theoretical analysis are also included

maximum number of frequencies in oscillations generated by fractional order lti systems in this paper relation between the inner dimension of a fractional order lti system and the maximum number of frequencies which exist in oscillations generated by the system is investigated the considered system is defined in pseudo state space form and the orders of its involved fractional derivatives are rational numbers between zero and one first an upper bound is derived for the maximum number of frequencies then using the restricted difference bases concept a new method is introduced to design a multifrequency oscillatory fractional order system finally based on the proposed method some lower bounds are derived for the maximum number of frequencies obtainable in solutions of a fractional order system having a fixed inner dimension

analytical and numerical solutions of a nonlinear alcoholism model via variable order fractional differential equations abstract in this paper we analyze an alcoholism model which involves the impact of twitter via liouville caputo and atangana baleanu caputo fractional derivatives with constant and variable order two fractional mathematical models are considered with and without delay special solutions using an iterative scheme via laplace and sumudu transform were obtained we studied the uniqueness and existence of the solutions employing the fixed point postulate the generalized model with variable order was solved numerically via the adams method and the adams bashforth moulton scheme stability and convergence of the numerical solutions were presented in details numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient therefore by including both the fractional derivatives and finite time delays in the alcoholism model studied we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking

bifurcation analysis of a delayed epidemic model in this paper hopf bifurcation for a delayed sis epidemic model with stage structure and nonlinear incidence rate is investigated through theoretical analysis we show the positive equilibrium stability and the conditions that hopf bifurcation occurs applying the normal form theory and the center manifold argument we derive the explicit formulas determining the properties of the bifurcating periodic solutions in addition we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions to illustrate our theoretical analysis some numerical simulations are also included

vanishing theorems for torsion automorphic sheaves on general pel type shimura varieties abstract we consider the interior cohomology and the hodge graded pieces in the case of the de rham realization of general not necessarily compact pel type shimura varieties with coefficients in the local systems corresponding to sufficiently regular algebraic representations of the associated reductive group for primes p bigger than an effective bound we prove that the f p and z p cohomology groups are concentrated in the middle degree that the z p cohomology groups are free of p torsion and that every f p cohomology class lifts to a z p cohomology class

a new predictor corrector method for fractional differential equations we present a new predictor corrector method to solve non linear fractional differential equations involving caputo derivative the proposed method is compared with the fractional adams method numerous illustrative examples discussed here demonstrate that the new method is more accurate and time efficient a detailed error analysis given points to the higher accuracy of the new method furthermore the proposed method when applied to fractional analog of chaotic system introduced by bhalekar and daftardar gejji unravels the underlying rich dynamics of the system

non existence of finite time stable equilibria in fractional order nonlinear systems we note that in the literature it is often taken for granted that for fractional order system without delays whenever the system trajectory reaches the equilibrium it will stay there in fact this is the well known phenomenon of finite time stability however in this paper we will prove that for fractional order nonlinear system described by caputo s or riemann liouville s definition any equilibrium cannot be finite time stable as long as the continuous solution corresponding to the initial value problem globally exists in addition some examples of stability analysis are revisited and linear lyapunov function is used to prove the asymptotic stability of positive fractional order nonlinear systems

on the kodaira dimensions of hilbert modular varieties f o r m e e r where e l e 9 are of general type let us give the summary of this paper our argument is based on the criterion on the extendability of pluri canonical differential forms developed by tai 13 in w 1 we mainly introduce our notations and reproduce well known facts in w 2 we introduce tai s criterion lemma 2 and proposition 1 which assures that elliptic fixed points almost always satisfy tai s criterion and discuss the extendability of pluri canonical differential forms over such points in w we discuss the extendability over the cusp singularities by means of toroidal compactification 1 and tai s criterion and give some criterion for a

modelling and analysis of a delayed predator prey model with disease in the predator in this paper we study a predator prey model with a transmissible disease spreading in the predator population and a time delay representing the gestation period of the predator by analyzing corresponding characteristic equations the local stability of each of feasible equilibria and the existence of hopf bifurcations at the disease free equilibrium and the coexistence equilibrium are established respectively by means of lyapunov functionals and lasalle s invariance principle sufficient conditions are derived for the global stability of the predator extinction equilibrium and the disease free equilibrium and the global attractiveness of the coexistence equilibrium of the system respectively numerical simulations are carried out to support the theoretical analysis

on the kodaira dimension of orthogonal modular varieties we prove that up to scaling there are only finitely many integral lattices l of signature 2 n with n ge 21 or n 17 such that the modular variety defined by the orthogonal group of l is not of general type in particular when n ge 108 every modular variety defined by an arithmetic group for a rational quadratic form of signature 2 n is of general type we also obtain similar finiteness in n ge 9 for the stable orthogonal groups as a byproduct we derive finiteness of lattices admitting reflective modular form of bounded vanishing order which proves a conjecture of gritsenko and nikulin

analysis of a three species eco epidemiological model abstract this paper formulates and analyzes a predator prey model with disease in the prey mathematical analyses of the model equations with regard to invariance of nonnegativity boundedness of solutions nature of equilibria permanence and global stability are analyzed it is also shown that for some parameter values the positive equilibrium is asymptotically stable but for other parameter values it is unstable and a surrounding periodic solution appears by hopf bifurcation a concluding discussion with numerical simulation is then presented

qualitative analysis for a diffusive predator prey model with a transmissible disease in the prey population in this paper we study a diffusive predator prey model with a transmissible disease in the prey population we offer a complete discussion of the dynamical properties under the homogeneous neumann boundary condition we analyze local and global stabilities of nonnegative constant steady states and long time behaviors of the positive solutions moreover we study the existence nonexistence and bifurcation of nonconstant positive stationary solutions finally some numerical simulations are presented to support and strengthen our analytical analysis

a three dimensional ball quotient in this paper we determine a very particular example of a picard modular variety of general type on its non singular models there exist many holomorphic differential forms in a forthcoming paper we will show that one can construct calabi yau manifolds by considering quotients of this variety and resolving singularities

the class of the locus of intermediate jacobians of cubic threefolds we study the locus of intermediate jacobians of cubic threefolds within the moduli space mathcal a 5 of complex principally polarized abelian fivefolds and its generalization to arbitrary genus the locus of abelian varieties with a singular odd two torsion point on the theta divisor assuming that this locus has expected codimension g which we show to be true for g 5 and conjecturally for any g we compute the class of this locus and of its closure in the perfect cone toroidal compactification mathcal a g mathrm perf in the chow homology and the tautological ring

undamped oscillations generated by hopf bifurcations in fractional order recurrent neural networks with caputo derivative in this paper a fractional order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated such as the stability hopf bifurcations and undamped oscillations the stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate order neural network based on the stability analysis the critical values of the fractional order are identified where hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state then the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate order networks meanwhile it is shown that the incommensurate order neural network can also exhibit a hopf bifurcation as the network parameter passes through a critical value which can be determined exactly the frequency and amplitude of bifurcated oscillations are determined

stability analysis of a sis model with stage structured and distributed maturation delay abstract we consider a sis model with stage structure in which the maturation delay is modeled as a distribution to allow for the possibility that individuals may take different amounts of time to mature general birth function and incidence rate are used the basic reproductive number r 0 to determine whether the disease is extinct or not is found furthermore we obtain sufficient conditions of globally asymptotical stability for the disease free equilibrium and the endemic equilibrium

ecoepidemic models with disease incubation and selective hunting in this paper we consider ecoepidemic models in which the basic demographics is represented by predator prey interactions with the disease modeled by an sei system at first we consider a basic lotka volterra type of interaction then we also introduce competition for resources among individuals of the prey population several variations of the model are presented in which the prey intra specific population pressure assumes different forms depending on the virulence of the disease indeed the latter may affect the exposed and infected individuals so much that they may not be able to compete with the sound ones for resources a further distinguishing feature of this investigation lies in the way in which the predator actively selects the prey for hunting for instance in some cases predators may discard the diseased ones as less palatable while in other situations they would instead search expressly for the infected since these are weaker individuals and thus easier to hunt the equilibria of the systems are analyzed showing that in some cases bifurcations arise contrary to what happens to similar classical holling type i ecoepidemic models these persistent oscillations seem to be triggered by the number of subpopulations present in the system which is larger than those introduced in the former models counting also the latent class furthermore adding predation to an sei epidemic model has profound effects on the stability of its equilibria in particular once the predators are introduced into an sei epidemic at a stable endemic equilibrium their presence destabilizes this equilibrium making the previous stable conditions unrecoverable

on integral solutions of some nonlocal fractional differential equations with nondense domain abstract in this paper we prove the existence and uniqueness of integral solution for some nondensely defined fractional semilinear differential equation with nonlocal conditions the results are obtained by means of fixed point methods we also give some examples of such problems

the zero section of the universal semiabelian variety and the double ramification cycle we study the chow ring of the boundary of the partial compactification of the universal family of principally polarized abelian varieties ppav we describe the subring generated by divisor classes and we compute the class of the partial compactification of the universal zero section which turns out to lie in this subring our formula extends the results for the zero section of the universal uncompactified family the partial compactification of the universal family of ppav can be thought of as the first two boundary strata in any toroidal compactification of ag our formula provides a first step in a program to understand the chow groups of a g especially of the perfect cone compactification by induction on genus by restricting to the image of mg under the torelli map our results extend the results of hain on the double ramification cycle answering eliashberg s question

solving systems of fractional differential equations using differential transform method this paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method the fractional derivatives are described in the caputo sense the application of differential transform method developed for differential equations of integer order is extended to derive approximate analytical solutions of systems of fractional differential equations the solutions of our model equations are calculated in the form of convergent series with easily computable components some examples are solved as illustrations using symbolic computation the numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations the method introduces a promising tool for solving many linear and nonlinear fractional differential equations

numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis in this paper a system of nonlinear fractional differential equations fdes are considered they have been solved by legendre wavelets method combining with its operational matrix however there are no articles about solving this system using wavelets method the main purpose of this technique is to transform the initial equations into a nonlinear system of algebraic equations which can be solved easily the convergence and error analysis are presented to show the correctness and feasibility of method proposed for solving the above mentioned problem finally the applicability and efficiency of the mentioned approach are demonstrated by three numerical examples

hopf bifurcation in an eco epidemic model abstract this paper deals with prey predator system where the prey population is infected with a microparasite predator functional response is assumed to be holling type i all the feasible equilibrium points of the system are obtained and the condition for the existence of positive interior equilibrium point is also determined the criteria for both local stability and instability involving system parameters are derived the criterion for existence of hopf type small periodic oscillation is shown the condition for survival of all the population is investigated we have developed a necessary and sufficient criteria for uniform persistence finally the numerical verifications of analytic results are done

the long time behavior of a predator prey model with disease in the prey by stochastic perturbation in this paper we formulate a predator prey model with disease in the prey by stochastic perturbation using lyapunov analysis methods we discuss the asymptotic behavior of this solution furthermore we investigate whether that there exists a stationary distribution for this system and if it has the ergodic property finally we make simulations to illustrate our analytical results

a predator prey disease model with immune response in infected prey abstract in this paper a predator prey disease model with immune response in the infected prey is formulated the basic reproduction number of the within host model is defined and it is found that there are three equilibria extinction equilibrium infection free equilibrium and infection persistent equilibrium the stabilities of these equilibria are completely determined by the reproduction number of the within host model furthermore we define a basic reproduction number of the between host model and two predator invasion numbers predator invasion number in the absence of disease and predator invasion number in the presence of disease we have predator and infection free equilibrium infection free equilibrium predator free equilibrium and a co existence equilibrium we determine the local stabilities of these equilibria with conditions on the reproduction and invasion reproduction numbers finally we show that the predator free equilibrium is globally stable

the kodaira dimension of the moduli of k3 surfaces the global torelli theorem for projective k3 surfaces was first proved by piatetskii shapiro and shafarevich 35 years ago opening the way to treating moduli problems for k3 surfaces the moduli space of polarised k3 surfaces of degree 2d is a quasi projective variety of dimension 19 for general d very little has been known hitherto about the kodaira dimension of these varieties in this paper we present an almost complete solution to this problem our main result says that this moduli space is of general type for d 61 and for d 46 50 54 57 58 60

bifurcation of an eco epidemiological model with a nonlinear incidence rate abstract a predator prey system with disease in the prey is considered assume that the incidence rate is nonlinear we analyse the boundedness of solutions and local stability of equilibria by using bifurcation methods and techniques we study bogdanov takens bifurcation near a boundary equilibrium and obtain a saddle node bifurcation curve a hopf bifurcation curve and a homoclinic bifurcation curve the hopf bifurcation and generalized hopf bifurcation near the positive equilibrium is analyzed one or two limit cycles is also discussed

a point set whose space of triangulations is disconnected in this paper we explicitly construct a triangulation of a 6 dimensional point configuration of 324 points which admits no geometric bistellar operations or flips for short this triangulation is an isolated element in the graph of triangulations of the point configuration it has been a central open question in polytope combinatorics in the last decade whether point configurations exist for which this graph is not connected see e g 37 question 1 2 and 48 challenge 3 we also construct a 234 dimensional polytope with 552 vertices whose graph of triangulations has an isolated element our construction is likely to have an impact in algebraic geometry too via the connections between lattice polytopes and toric varieties 21 23 31 43 for example in 2 section 2 and 24 section 4 the different authors study algebraic schemes based on the poset of subdivisions of an integer point configuration the connectivity of these schemes and of the graph of triangulations are equivalent see section 4 3 in particular corollary 4 9 the graph of triangulations is also related to the baues poset which appears in oriented matroid theory zonotopal tilings and hyperplane arrangements so our result has implications in these areas let a be a finite point set in the real affine space r a polyhedral subdivision of a is a geometric polyhedral complex with vertices in a which covers the convex hull of a if all the cells are simplices then it is a triangulation more combinatorial definitions are convenient if a is not in convex position i e if some element of a is not a vertex of the convex hull see definitions 4 1 and 1 1 for details and also 6 21 chapter 7 36 47 chapter 9 or the monograph in preparation 14 there are at least the following three ways to give a structure to the collection of all triangulations of a point configuration a a flips geometric bistellar operations or flips are the minimal changes which can be made in a triangulation of a to produce a new one see definition 1 3 a particular case is the familiar diagonal edge flip in two dimensional triangulations of frequent use in computational geometry and geometric combinatorics

the nef cone of toroidal compactifications of cal a _4 the moduli space of principally polarised abelian 4 folds can be compactified in several different ways by toroidal methods here we consider in detail the igusa compactification and the second voronoi compactification we describe in both cases the cone of nef cartier divisors the proof depends on a detailed description of the voronoi compactification which makes it possible to proceed by induction using the known description of the nef cone for compactifications of mathcal a 3 the igusa compactification has a non mathbb q factorial singularity which is resolved by a single blow up this resolution is the voronoi compactification the exceptional divisor e is a toric fano variety of dimension 9 the other boundary divisor d corresponds to degenerations with corank 1 after imposing a level structure in order to avoid certain technical complications we show that the closure of d in the voronoi compactification maps to the voronoi compactification of mathcal a 3 the toric description of the exceptional divisor allows us to describe the map in sufficient detail to estimate the intersection numbers needed this inductive process is only valid for the voronoi compactification the result for the igusa compactification is deduced from the voronoi compactification

dynamic behavior of an eco epidemic system with impulsive birth in the paper we investigate an eco epidemic system with impulsive birth the conditions for the stability of infection free periodic solution are given by applying floquet theory of linear periodic impulsive equation and we give the conditions of persistence by constructing a consequence of some abstract monotone iterative schemes by using the method of coincidence degree a set of sufficient conditions are derived for the existence of at least one strictly positive periodic solution finally numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level thus we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels

a ratio dependent predator prey model with disease in the prey in this paper a ratio dependent predator prey system with disease in the prey is formulated and analyzed mathematical analyses of the model equations with regard to invariance of nonnegativity boundedness of solutions nature of equilibria permanence and global stability are analyzed specially we shall show that ratio dependent predator prey models are rich in boundary dynamics and most importantly we shall show that a periodic solution can occur whether the system is permanent or not that is there are solutions which tend to disease free equilibrium while bifurcating periodic solution exists

log minimal model program for the moduli space of stable curves the first flip we give a geometric invariant theory git construction of the log canonical model m g a of the pairs m g ad for a 7 10 7 10 for small q we show that m g 7 10 is isomorphic to the git quotient of the chow variety of bicanonical curves m g 7 10 is isomorphic to the git quotient of the asymptotically linearized hilbert scheme of bicanonical curves in each case we completely classify the semi stable curves and their orbit closures chow semistable curves have ordinary cusps and tacnodes as singularities but do not admit elliptic tails hilbert semistable curves satisfy further conditions e g they do not contain elliptic chains we show that there is a small contraction m g 7 10 m g 7 10 that contracts the locus of elliptic bridges moreover by using the git interpretation of the log canonical models we construct a small contraction m g 7 10 m g 7 10 that is the mori flip of

brief paper a proof for non existence of periodic solutions in time invariant fractional order systems the aim of this note is to highlight one of the basic differences between fractional order and integer order systems it is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals as a result a limit cycle cannot be expected in the solution of these systems our investigation is based on caputo s definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems

analysis of a system of nonautonomous fractional differential equations involving caputo derivatives abstract we discuss existence uniqueness and stability of solutions of the system of nonlinear fractional differential equations d i y i t f i t y 1 y n y i k c k i 1 i n 1 k m i where m i i m i 1 and d i denotes caputo fractional derivative linear and nonlinear systems have been solved using banach fixed point theorem

stability and hopf bifurcation analysis of an eco epidemic model with a stage structure abstract in this paper an eco epidemiological model with a stage structure is considered the asymptotical stability of the five equilibria the existence of stability switches about positive equilibrium is investigated it is found that hopf bifurcation occurs when the delay passes though a critical value some explicit formulae determining the stability and the direction of the hopf bifurcation periodic solutions bifurcating from hopf bifurcations are obtained by using the normal form theory and center manifold theory some numerical simulations for justifying the theoretical analysis are also provided finally biological explanations and main conclusions are given

integral inequalities of systems and the estimate for solutions of certain nonlinear two dimensional fractional differential systems this paper generalizes the results for the constructions of explicit bounds and the qualitative properties for the solutions of certain two dimensional fractional differential systems established in a recent paper of the authors the main generalizations come from an elementary inequality and by means of the modification of medved s de singular approach

complete moduli in the presence of semiabelian group action i prove the existence and describe the structure of moduli space of pairs p consisting of a projective variety p with semiabelian group action and an ample cartier divisor on it satisfying a few simple conditions every connected component of this moduli space is proper a component containing a projective toric variety is described by a configuration of several polytopes the main one of which is the secondary polytope on the other hand the component containing a principally polarized abelian variety provides a moduli compactification of a g the main irreducible component of this compactification is described by an infinite periodic analog of the secondary polytope and coincides with the toroidal compactification of a g for the second voronoi decomposition

a mathematical study of an eco epidemiological system on disease persistence and extinction perspective a prey predator system with nonlinear incidence rate of the disease in prey is described the dynamical behavior of the system is investigated at each equilibrium point sufficient conditions are derived for the uniformly strong persistence of the system results are obtained to extract the criteria for disease persistence and extinction a prey predator system with disease in prey is proposed the proposed system is an extension of the model analyzed by bhattacharyya and mukhopadhyay 2011 which did not consider the density of fish population as a dynamic variable which significantly influence the dynamics of the system the coexistence equilibria of the system is determined and the dynamic behavior of the system is investigated around coexistence equilibria incidence rate of the disease is considered as a bifurcation parameter to examine the occurrence of hopf bifurcation in the neighborhood of the co existing equilibria sufficient conditions are derived for the global stability of the system around coexistence equilibria uniform strong persistence of the system is discussed in order to ensure long term survival of the species the obtained results are useful to extract the criteria for disease extinction and persistence finally some numerical simulations are given to verify the analytical results and the system is analyzed through graphical illustrations

linear dependence among siegel modular forms theorems are given which describe when high enough vanishing at the cusps implies that a siegel modular cusp form is zero formerly impractical computations become practical and examples are given in degree four vanishing order is described by kernels a type of polyhedral convex hull

existence of periodic solutions for periodic eco epidemic models with disease in the prey abstract for an eco epidemic model with disease in the prey and periodic coefficients it is conjectured in niu et al 2011 5 that when the infected prey is permanent there is a positive periodic orbit that is globally asymptotically stable in the interior of r 3 in this paper we prove the existence part of the conjecture for a large family of periodic systems

on a system of differential equations with fractional derivatives arising in rod theory we study a system of equations with fractional derivatives that arises in the analysis of the lateral motion of an elastic column fixed at one end and loaded by a concentrated follower force at the other end we assume that the column is positioned on a viscoelastic foundation described by a constitutive equation of fractional derivative type the stability boundary is determined it is shown that as in the case of an elastic winkler type of foundation the stability boundary remains the same as for the column without a foundation thus with the solution analysed here the column exhibits the so called hermann smith paradox

asymptotic behavior of a three species eco epidemiological model perturbed by white noise abstract this paper considers a three species eco epidemiological model perturbed by white noise stochastic stability and long time behavior around the equilibrium of deterministic eco epidemiological model are analyzed by lyapunov methods numerical simulations for a set of parameter values are presented to illustrate the analytical findings

the uniformization of the moduli space of principally polarized abelian 6 folds author s alexeev valery donagi ron farkas gavril izadi elham ortega angela abstract abstractstarting from a beautiful idea of kanev we construct a uniformization of the moduli space mathcal a 6 of principally polarized abelian 6 folds in terms of curves and monodromy data we show that the general principally polarized abelian variety of dimension 6 is a prym tyurin variety corresponding to a degree 27 cover of the projective line having monodromy the weyl group of the e 6 lattice along the way we establish numerous facts concerning the geometry of the hurwitz space of such e 6 covers including 1 a proof that the canonical class of the hurwitz space is big 2 a concrete geometric description of the hodge hurwitz eigenbundles with respect to the kanev correspondence and 3 a description of the ramification divisor of the prym tyurin map from the hurwitz space to mathcal a 6 in the terms of syzygies of the abel prym tyurin curve

optimal control of stochastic lattice of prey predator models we propose a stochastic lattice model to describe the dynamics of two animal species population one being a prey and the other a predator the system follows a stochastic dynamics composed of three markovain processes the first one describes the birth of prey the second describes the death of prey and simultaneous birth of predator the third describes spontaneous death of predator the master equation is used to derive the time evolution of one and two site correlations the stability of the stationary states of one site correlations is studied the optimal control functions that ensure the asymptotic stability of unstable stationary states are derived in the case of one site approximation the densities of the vacant sites prey sites and predator sites are obtained as functions of time for the controlled model

a nonlocal and time delayed reaction diffusion eco epidemiological predator prey model abstract in this paper we propose and investigate a nonlocal and time delayed reaction diffusion predator prey model with disease spread in the prey which incorporates spatial heterogeneity and assimilation lag of consumed prey biomass into predator biomass the si type subsystem of prey without predator is first studied and we establish the threshold dynamics in terms of the basic reproduction number based on epidemiology then we show a series of sufficient conditions for the co existence of prey and predator species the global extinction of predator species and the global extinction of both the prey and predator species finally a special example is explored via numerical simulations where the influences of nonlocal effect spatial heterogeneity and time delay on the invasion of the predator species are probed

stability and hopf bifurcation of a mathematical model describing bacteria fish interaction in marine environment abstract in this work we present and study a model of a host parasite system in marine environment which describes the population dynamics of fish tilapia which can be infected by botulinum the mathematical model is structured by levels of infection using the characteristic curves method we transform the model into a system of distributed delay differential equations we study the existence of hopf bifurcation following the method presented by hassard et al 1981 5 we prove analytically the stability of limit cycle periodic solutions we present numerical and computer simulations of the model

solving a system of nonlinear fractional differential equations using adomian decomposition adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations dxiyi x ni x y1 yn yi k 0 cki 0 k i 1 i n and dxi denotes caputo fractional derivative some examples are solved as illustrations using symbolic computation

periodic and almost periodic solution for a non autonomous epidemic predator prey system with time delay in this paper we studied a non autonomous predator prey system with discrete time delay where there is epidemic disease in the predator by using some techniques of the differential inequalities and delay differential inequalities we proved that the system is permanent under some appropriate conditions when all the coefficients of the system is periodic we obtained the existence and global attractivity of the positive periodic solution by mawhin s continuation theorem and constructing a suitable lyapunov functional furthermore when the coefficients of the system are not absolutely periodic but almost periodic sufficient conditions are also derived for the existence and asymptotic stability of the almost periodic solution

global analysis and numerical simulations of a novel stochastic eco epidemiological model with time delay abstract in this paper a new stochastic eco epidemiological model is proposed and investigated and the high dimensional model includes time delay and a general incidence rate which make the study more complex first the existence and uniqueness of the global positive solution with any positive initial value are verified second using stochastic analysis methods and some differential inequality techniques we explore the long time asymptotic properties of the stochastic delayed system furthermore we prove that the solution of the stochastic delayed system has a unique stationary distribution and it has ergodic property third the sufficient conditions of permanence in mean or extinction for the ecological populations are obtained finally we introduce a series of computer simulations to show the performance of the theoretical results

a numerical scheme for two dimensional optimal control problems with memory effect a new formulation for multi dimensional fractional optimal control problems is presented in this article the fractional derivatives which are coming from the formulation of the problem are defined in the riemann liouville sense some terminal conditions are imposed on the state and control variables whose dimensions need not be the same a numerical scheme is described by using the grunwald letnikov definition to approximate the riemann liouville fractional derivatives the set of fractional differential equations which are obtained after the discretization of the time domain are solved within the grunwald letnikov approximation to obtain the state and the control variable numerically a two dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme

a predator prey model with disease in the prey after the seminal models of vito volterra and alfred james lotka in the mid 1920s for predator prey interactions mutualist and competitive mechanisms have been studied extensively in the recent years by researchers there are so many references in this context we have just cited here some books e g see 14 16 18 and the refer ences therein similarly after the pioneering work of kermack mckendrick on sirs susceptible infective removal susceptible epidemiological models have also received much attention from scientists relevant references in this context are also vast and we shall again mention here some books see 1 2 4 to mention a few but little attention has been paid so far to merge these two important areas of research see 7 21 in this paper we shall put emphasis in such an eco epidemiological system we consider a three species eco epidemiological system namely sound prey suscep tible infected prey infective and predator we consider the case when the predator mainly eats the infected prey this is in accordance with a previous model by hadeler and freedman 7 which describes a predator prey model where the prey is infected by a parasite and the prey in turn infects the predator with that parasite the infec tion weakens the prey and increases its susceptibility to predation while no predator impairing elect is accounted for while the paper is mainly theoretical and does not address any specific situation the reader may and several examples in 7 we derive persistence and extinction conditions of the populations and we also determine conditions for which the system enters a hopf type bifurcation moreover we observe that the bifurcated branches are supercritical in some parametric region space in a special case when the predator response function is a holling type ii function

diseased prey predator model with general holling type interactions choice of interaction function is one of the most important parts for modelling a food chain many models have been proposed as a diseased prey predator model with holling type i or type ii or type iii interactions but there is no model with general holling type interactions in this paper we study a diseased prey predator model with general holling type interactions local stability conditions of equilibrium points are derived we obtain the permanence and impermanence conditions of the system the conditions for global stability of the system are also derived the system exhibits limit cycle period 2 higher periodic oscillations and chaotic behaviour for different values of holling parameters one parameter bifurcation analysis is done with respect to general holling parameters and infection rate we utilize the matcont package to analyse the detailed bifurcation scenario as the two important interaction parameters are varied it is interesting to note that a diseased system becomes a disease free system for proper choice of interaction functions our results give an idea for constructing a realistic food chain model through proper choice of general holling parameters

classicite en theorie de hida in this article we prove an effective classicity theorem in hida s theory we focus more precisely on the case of the symplectic group and siegel modular forms we also prove that certain mod p siegel modular forms lift to characteristic zero and study carefully the divisibility by p of certain hecke operators