resolutions of fat point ideals involving eight general points of p2 abstract the main result theorem 1 provides an algorithm for determining the minimal free resolution of fat point subschemes of p 2 involving up to eight general points of arbitrary multiplicities the resolutions obtained hold for any algebraically closed field independent of the characteristic the algorithm works by giving a formula in nice cases and a reduction to the nice cases otherwise the algorithm which does not involve grobner bases is very fast partial information is also obtained in certain cases with n 8

conditions imposed by tacnodes and cusps the study of linear systems of algebraic plane curves with fixed imposed singularities is a classical subject which has recently experienced important progress the horace method introduced by a hirschowitz has been successfully exploited to prove many h1 vanishing theorems even in higher dimension other specialization techniques which include degenerations of the plane are due to z ran and c ciliberto and r miranda g m greuel c lossen and e shustin use a local specialization procedure together with the horace method to give the first asymptotically proper general existence criterion for singular curves of low degree in this paper we develop a specialization method which allows us to compute the dimension of several linear systems as well as to substantially improve the bounds given by greuel lossen and shustin for curves with tacnodes and cusps

analysis of a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation abstract in this paper we consider a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation we show there is a unique positive solution to the system with positive initial value and mainly investigate the long time behavior of the system condition for the system to be extinct is given and persistent condition is established at last numerical simulations are carried out to support our results

on bounding the number of generators for fat point ideals on the projective plane abstract let x be the surface obtained by blowing up general points p1 pn of the projective plane over an algebraically closed ground field k and let l be the pullback to x of a line on the plane if c is a rational curve on x with c l d then for every t there is a natural map c o c t x o x l c o c t d given by multiplication on simple tensors the ranks of such maps are determined as a function of t d and m where m is the largest multiplicity of c at any of the points pi if i is the ideal defining the fat point subscheme z m1p1 mnpn p2 and is the least degree in which i has generators then the ranks of the maps c o c t x o x l c o c t d can be used for bounding the number of generators of i in degrees t 1

new criteria on persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching abstract this paper concerns persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching by using some novel stochastic analysis techniques sufficient criteria for the partial permanence and partial extinction are established some novel sufficient conditions on persistence in mean and extinction are also obtained nontrivial examples are provided to illustrate our results

periodic solution for a non autonomous lotka volterra predator prey model with random perturbation abstract this paper studies a stochastic non autonomous lotka volterra predator prey model we prove that there exists at least one positive periodic solution under some simple and reasonable conditions in addition we obtain sufficient conditions for persistence in mean and extinction for the stochastic non autonomous system our method and results are new and the ideas could be used to study other types of non autonomous stochastic predator prey systems

stationary distribution of stochastic population systems under regime switching abstract this paper is concerned with n species model of facultative mutualism in random environments the environment variability in this study is characterized with both white noise and color noise modeled by markovian switching we established new sufficient conditions that ensuring that the system model is positive recurrent we also showed the existence of a unique ergodic stationary distribution the presented results are demonstrated by numerical simulations

dynamics of stochastic delay lotka volterra systems with impulsive toxicant input and levy noise in polluted environments in this paper two stochastic delay lotka volterra systems i e competition system and predator prey system with impulsive toxicant input and levy noise in polluted environments are proposed and investigated under some simple assumptions sufficient and necessary criteria for stability in time average and extinction of each population are established the thresholds between stability in time average and extinction of each model are obtained some recent results are improved and extended greatly

competitive lotka volterra population dynamics with jumps abstract this paper considers competitive lotka volterra population dynamics with jumps the contributions of this paper are as follows a we show that a stochastic differential equation sde with jumps associated with the model has a unique global positive solution b we discuss the uniform boundedness of the p th moment with p 0 and reveal the sample lyapunov exponents c using a variation of constants formula for a class of sdes with jumps we provide an explicit solution for one dimensional competitive lotka volterra population dynamics with jumps and investigate the sample lyapunov exponent for each component and the extinction of our n dimensional model

on competitive lotka volterra model in random environments focusing on competitive lotka volterra model in random environments this paper uses regime switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem subject to the random changes of the external environment it is demonstrated that the growth rates of the population sizes of the species are bounded above moreover certain long run average limits of the solution are examined from several angles a partial stochastic principle of competitive exclusion is also derived finally simple examples are used to demonstrate our findings

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

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

periodic solution for stochastic non autonomous multispecies lotka volterra mutualism type ecosystem we give sufficient conditions for the existence of positive periodic solution we give sufficient conditions for the global attractiveness of the periodic solution we prove that all species will be extinct if the intensity of noise is large enough the results are illustrated by computer simulations the paper characterizes some qualitative dynamic properties of a stochastic non autonomous multi species mutualism model with continuous periodic parameters using khasminskii theory of stability with suitable lyapunov functions and m matrices sufficient conditions are established to guarantee existence of positive periodic solutions to the system we also provide conditions for the global attractiveness of the latter or extinction of all species for sufficiently high volatility levels results are finally supported by numerical computations

periodic solutions and stationary distribution of mutualism models in random environments abstract this paper is concerned with mutualism models in random environments for the periodic mutualism model disturbed by white noise using has minskii theory of periodic solution we show that this model admits a nontrivial positive periodic solution then sufficient conditions for the existence and global attractivity of the boundary periodic solutions are established for the mutualism model disturbed by both white noise and telephone noise sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the solution are established finally examples are introduced to illustrate the results developed

limit cycles for the competitive three dimensional lotka volterra system abstract in the first part of this paper it is proved that the number of limit cycles of the competitive three dimensional lotka volterra system in r 3 is finite if this system has not any heteroclinic polycycles in r 3 in the second part of this paper a 3d competitive lotka volterra system with two small parameters is discussed this system always has a heteroclinic polycycle with three saddles it is proved that there exists one parameter range in which the system is persistence and has at least two limit cycles and there exists other parameter ranges in which the system is not persistence and has at least one limit cycle

global stability of almost periodic solution of multispecies mutualism system with time delays and impulsive effects abstract this paper discusses an almost periodic multispecies lotka volterra mutualism system with time delays and impulsive effects by using the theory of comparison theorem and constructing a suitable lyapunov functional sufficient conditions which guarantee the existence and uniqueness and global asymptotical stability of almost periodic solution of this system are obtained the results of this paper is completed new an suitable example indicates the feasibility of the main results

the total coordinate ring of a smooth projective surface in 5 cox introduced the homogeneous coordinate ring of a toric variety which is a polynomial ring that allows to show that such a variety behaves like a projective space in many ways an analogous to that ring can also be defined for a smooth projective variety x over an algebraically closed field k such that linear and numerical equivalence coincide for divisors on x condition which is assumed for all varieties considered in this paper indeed let us fix li i 1 a z basis of pic x and set n n1 n2 nr z and dn ri 1 nili by regarding the vector spaces h 0 x ox dn f k divx f dn 0 0 as k subvector spaces of the function field k of x the total coordinate ring of x or the cox ring of x is defined as the graded k subalgebra of k

dynamics of a stochastic heroin epidemic model abstract in this paper we investigate a stochastic heroin epidemic model by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the extinction of the drug users moreover we also establish sufficient conditions for the existence of ergodic stationary distribution to the model which reveals that the drug users will persist the sensitivity analysis indicates that prevention would be more important than cure

comparing stochastic lotka volterra predator prey models abstract the phenomenology of population extinction is one of the central themes in population biology which it is an inherently stochastic event in the present investigation we study this problem for three different stochastic models built from a single lotka volterra deterministic model more concretely we study their mean extinction time which satisfies the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients hence we can only compute numerical approximations we suggest a finite element method using freefem our analysis and numerical results allow us to conclude that there are important differences between the three models these differences enable us to choose the most natural way to turn a the deterministic model into a stochastic model

on the projective normality of double coverings over a rational surface abstract we study the projective normality of a minimal surface x which is a ramified double covering over a rational surface s with dim k s 1 in particular horikawa surfaces the minimal surfaces of general type with k x 2 2 p g x 4 are of this type up to resolution of singularities let be the covering map from x to s we show that the z 2 invariant adjoint divisors k x r a are normally generated where the integer r 3 and a is an ample divisor on s

periodic solution for a stochastic non autonomous competitive lotka volterra model in a polluted environment abstract in this paper we consider a stochastic non autonomous competitive lotka volterra model in a polluted environment we derive sufficient criteria for the existence and global attractivity of the boundary periodic solutions furthermore we obtain conditions for the existence and global attractivity of a nontrivial positive periodic solution finally we make simulations to illustrate our analytical results

asymptotic behavior of a food chain model with stochastic perturbation abstract in this article asymptotic behavior of a stochastic food chain model is analyzed first of all we consider the dynamic of the deterministic system by analyzing the equilibria and their stability conditions then by lyapunov analysis methods we show that the system has a unique positive solution after that the stochastic stability and its long time behavior around the equilibriums of the deterministic system is given later we obtain the stochastic system and its corresponding deterministic system have similar properties when the white noise is small and then we show the conditions that there is a stationary distribution of the system which implies that the system is permanent at last we make simulations to verify the results of our analysis

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

on the first infinitesimal neighborhood of a linear configuration of points in p2 abstract we consider the following open questions fix a hilbert function h that occurs for a reduced zero dimensional subscheme of p 2 among all subschemes x with hilbert function h what are the possible hilbert functions and graded betti numbers for the first infinitesimal neighborhood z of x i e the double point scheme supported on x is there a minimum h min and maximum h max such function the numerical information encoded in h translates to a type vector which allows us to find unions of points on lines called linear configurations with hilbert function h we give necessary and sufficient conditions for the hilbert function and graded betti numbers of the first infinitesimal neighborhoods of all such linear configurations to be the same even for those h for which the hilbert functions or graded betti numbers of the resulting double point schemes are not uniquely determined we give one depending only on h that does occur we prove the existence of h max in general and discuss h min our methods include liaison techniques

some results on rational surfaces and fano varieties this is the publisher s version also available electronically from http www degruyter com view j crll 2001 2001 issue 538 crll 2001 068 crll 2001 068 xml

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

resolutions of ideals of any six fat points in p2 the graded betti numbers of the minimal free resolution and also therefore the hilbert function of the ideal of a fat point subscheme z of p2 are determined whenever z is supported at any 6 or fewer distinct points all results hold over an algebraically closed field k of arbitrary characteristic

the ergodic property and positive recurrence of a multi group lotka volterra mutualistic system with regime switching abstract in this paper we consider a stochastic multi group lotka volterra mutualistic system under regime switching it is well known that the population is forced to expire when the perturbation is sufficiently large the main aim here is to investigate its ergodic property and positive recurrence by stochastic lyapunov functions under small perturbation which can be used to explain some recurring phenomena in practice and thus provide a good description of permanence the mean of the stationary distribution is estimated simulations are also carried out to confirm our analytical results

big rational surfaces we prove that the cox ring of a smooth rational surface with big anticanonical class is finitely generated we classify surfaces of this type that are blow ups of mathbb p 2 at distinct points lying on a possibly reducible cubic

global stability and stochastic permanence of a non autonomous logistic equation with random perturbation abstract this paper discusses a randomized non autonomous logistic equation d n t n t a t b t n t d t t d b t where b t is a 1 dimensional standard brownian motion in d q jiang n z shi a note on non autonomous logistic equation with random perturbation j math anal appl 303 2005 164 172 the authors show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0 we show that this equation is stochastically permanent and the solution n p t is globally attractive provided a t b t and t are continuous t periodic functions a t 0 b t 0 and min t 0 t a t max t 0 t 2 t by the way the similar results of a generalized non autonomous logistic equation with random perturbation are yielded

asymptotic behavior of a stochastic non autonomous predator prey system with jumps in this paper a two species stochastic non autonomous food chain predator prey system with jumps is proposed and studied the asymptotic properties of the system are examined sufficient conditions for extinction non persistence in the mean weak persistence in the mean and weak persistence of the system are established results show that levy jumps are disadvantageous for the persistence of the populations furthermore we also show that the solution is stochastically ultimate bounded under certain conditions some examples together with numerical simulations are introduced to illustrate our main results

analysis of a stochastic autonomous mutualism model abstract an autonomous lotka volterra mutualism system with random perturbations is investigated under some simple conditions it is shown that there is a decreasing sequence k which has the property that if 1 1 then all the populations go to extinction i e lim t x i t 0 1 i n if k 1 k 1 then lim t x j t 0 j k 1 n whilst the remaining k populations are stable in the mean i e lim t t 1 0 t x i s d s a positive constant i 1 k if n 1 then all the species are stable in the mean sufficient conditions for stochastic permanence and global asymptotic stability are also established

stationary distribution and extinction of a stochastic ratio dependent predator prey system with stage structure for the predator abstract in this paper we deal with a stochastic predator prey model with stage structure for predator population and ratio dependent functional response the proposed mathematical model consists of a system of three stochastic differential equations to stimulate the interactions between prey population immature predator and mature predator population we first establish sufficient conditions for the existence and uniqueness of the positive solutions by constructing an appropriate lyapunov function then we extend the existence of stationary distribution under certain parametric restrictions we also obtain the sufficient conditions for extinction of the predator populations finally numerical simulations have been carried out to validate our analytical findings

stochastic lotka volterra models with multiple delays abstract this paper investigates the asymptotic behavior of the stochastic lotka volterra model with multiple delays by using certain matrix techniques some results on nonexplosion boundedness and pathwise estimation of the model are investigated

stability in distribution of a stochastic predator prey system with s type distributed time delays abstract this paper concerns the dynamics of a stochastic predator prey lotka volterra system with s type distributed time delays sufficient conditions for the stability in distribution of the solutions sds to the system are obtained the results show that the dynamic scenarios of the sds are completely characterized by two parameters 1 2 among which 1 is just related to the environmental noise while 2 is closely related to both time delays and environmental noises if 2 0 then the distributions of prey predator converge weakly to a unique ergodic invariant distribution ueid if 1 0 2 then the predator goes to extinction while the distributions of prey converge weakly to a ueid if 0 1 then both the predator and prey go to extinction

a note on nonautonomous logistic equation with random perturbation abstract this paper discusses a randomized nonautonomous logistic equation d n t n t a t b t n t d t t d b t where b t is 1 dimensional standard brownian motion we show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0

cox rings of surfaces and the anticanonical iitaka dimension abstract in this paper we investigate the relation between the finite generation of the cox ring r x of a smooth projective surface x and its anticanonical iitaka dimension k x

positivity of line bundles on general blow ups of p2 abstract let x be the blow up of p 2 at r general points p 1 p r p 2 we study line bundles on x given by plane curves of degree d passing through p i with multiplicity at least m i motivated by results in 39 we establish conditions for ampleness very ampleness and global generation of such line bundles

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

birational morphisms of rational surfaces abstract a fairly complete characterization on anticanonical rational surfaces of the divisor classes whose sections define birational morphisms is given most results are proven over an algebraically closed field of arbitrary characteristic

fisher transformations for correlations corrected for selection and missing data the validity of a test is often estimated in a nonrandom sample of selected individuals to accurately estimate the relation between the predictor and the criterion we correct this correlation for range restriction unfortunately this corrected correlation cannot be transformed using fisher sz transformation and asymptotic tests of hypotheses based on small or moderate samples are not accurate we developed a fisherr toz transformation for the corrected correlation for each of two conditions a the criterion data were missing due to selection on the predictor the missing data were mar and b the criterion was missing at random not due to selection the missing data were mcar the twoz transformations were evaluated in a computer simulation the transformations were accurate and tests of hypotheses and confidence intervals based on the transformations were superior to those that were not based on the transformations

the effects of time dependent delays on global stability of stochastic lotka volterra competitive model abstract in this paper a stochastic lotka volterra competitive model with time dependent delays is investigated sufficient conditions for global asymptotic stability of the positive equilibrium are established the obtained result demonstrates that time dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system

permanence of hybrid competitive lotka volterra system with levy noise abstract this paper concerns stochastic permanence of a hybrid competitive lotka volterra system with levy noise sufficient conditions of stochastic permanence are obtained by combining stochastic analytical techniques with m matrix analysis

the criteria for globally stable equilibrium in n dimensional lotka volterra systems abstract in this paper a set of sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium point in various submodels of the classic n dimensional lotka volterra system the submodels are the following systems competition cooperative or predator prey chain system and competition cooperative or predator prey model between one and multispecies the criteria in this paper are in explicit forms of the parameters and thus are easily verifiable

on the long time behavior of non autonomous lotka volterra models with diffusion via the sub supertrajectory method abstract in this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non autonomous lotka volterra systems in all the three cases of competition symbiosis or prey predator in particular under some conditions on the parameters we prove the existence of a unique nondegenerate global solution for these models which attracts any other complete bounded trajectory thus we generalize the existence of a unique strictly positive stable stationary solution from the autonomous case and we extend to lotka volterra systems the result for scalar logistic equations to this end we present the sub supertrajectory tool as a generalization of the now classical sub supersolution method in particular we also conclude pullback and forwards permanence for the above models

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing results

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

seshadri constants and very ample divisors on algebraic surfaces a broadly applicable geometric approach for constructing nef divisors on blow ups of algebraic surfaces at n general points is given it works for all surfaces in all characteristics for any n this construction is used to obtain substantial improvements for currently known lower bounds for n point seshadri constants remarks are included about a range of applications to classical problems involving linear systems on p 2

on hybrid competitive lotka volterra ecosystems abstract this paper is concerned with competitive lotka volterra model in random environments it uses regime switching diffusion to model the dynamic of population sizes of n different species in a ecosystem subject to the random changes of the external environment we show that the positive solution of the associated stochastic differential equation does not explode in finite time with probability 1 moreover we demonstrate that the solution is stochastically bounded continuous and has finite moments furthermore we obtain certain asymptotic results regarding large time behavior and present some numerical experimental results

stationary distribution and periodic solutions for stochastic holling leslie predator prey systems abstract the stochastic autonomous and periodic predator prey systems with holling and leslie type functional response are investigated for the autonomous system we prove that there exists a unique stationary distribution which is ergodic by constructing a suitable lyapunov function under relatively small white noise the result shows that stationary distribution doesn t rely on the existence and the stability of the positive equilibrium in the undisturbed system furthermore for the corresponding non autonomous system we show that there exists a positive periodic markov process under relatively weaker condition finally numerical simulations illustrate our theoretical results

permanence and asymptotic behaviors of stochastic predator prey system with markovian switching and levy noise abstract this paper concerns the dynamics of a stochastic predator prey system with markovian switching and levy noise first the existence and uniqueness of global positive solution to the system is proved then by combining stochastic analytical techniques with m matrix analysis sufficient conditions of stochastic permanence and extinction are obtained furthermore for the stochastic permanence case by means of four constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated finally our conclusions are illustrated through an example

stochastic delay lotka volterra model we reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay lotka volterra model but will also make the solutions to be stochastically ultimately bounded to reveal these interesting facts we stochastically perturb the delay lotka volterra model x t diag x1 t xn t b ax t into the ito form dx t diag x1 t xn t b ax t dt x t dw t and show that although the solution to the original delay equation may explode to infinity in a finite time with probability one that of the associated stochastic delay equation does not we also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix a

asymptotically log fano varieties abstract motivated by the study of fano type varieties we define a new class of log pairs that we call asymptotically log fano varieties and strongly asymptotically log fano varieties we study their properties in dimension two under an additional assumption of log smoothness and give a complete classification of two dimensional strongly asymptotically log smooth log fano varieties based on this classification we formulate an asymptotic logarithmic version of calabi s conjecture for del pezzo surfaces for the existence of kahler einstein edge metrics in this regime we make some initial progress towards its proof by demonstrating some existence and non existence results among them a generalization of matsushima s result on the reductivity of the automorphism group of the pair and results on log canonical thresholds of pairs one by product of this study is a new conjectural picture for the small angle regime and limit which reveals a rich structure in the asymptotic regime of which a folklore conjecture concerning the case of a fano manifold with an anticanonical divisor is a special case

optimal control strategy for an impulsive stochastic competition system with time delays and jumps abstract driven by both white and jump noises a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated by using the comparison theorem of stochastic differential equations and limit superior theory sufficient conditions for persistence in mean and extinction of two species are established in addition we obtain that the system is asymptotically stable in distribution by using ergodic method furthermore the optimal harvesting effort and the maximum of expectation of sustainable yield esy are derived from hessian matrix method and optimal harvesting theory of differential equations finally some numerical simulations are provided to illustrate the theoretical results

coexistence and exclusion of stochastic competitive lotka volterra models abstract this work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive lotka volterra model the conditions obtained are close to necessary in addition convergence in distribution of positive solutions of the model is also established a number of numerical examples are given to illustrate our results

stochastic lotka volterra systems with levy noise abstract this paper is concerned with stochastic lotka volterra models perturbed by levy noise firstly stochastic logistic models with levy noise are investigated sufficient and necessary conditions for stochastic permanence and extinction are obtained then three stochastic lotka volterra models of two interacting species perturbed by levy noise i e predator prey system competition system and cooperation system are studied for each system sufficient and necessary conditions for persistence in the mean and extinction of each population are established the results reveal that firstly both persistence and extinction have close relationships with levy noise secondly the interaction rates play very important roles in determining the persistence and extinction of the species

analysis on stochastic delay lotka volterra systems driven by levy noise abstract in this paper two types of stochastic lotka volterra systems i e competition system and predator prey system with time delays and levy noise are discussed for each model we establish sufficient and necessary criteria for stability in time average and extinction of each population the thresholds between stability in time average and extinction of each model are obtained some recent results are improved and extended significantly these results point out that i time delays are harmless for stability in time average and extinction of our model ii both stability in time average and extinction have close relationships with levy noise iii the interaction rates play significant roles in determining the stability in time average and extinction of the populations

resolutions of ideals of quasiuniform fat point subschemes of the notion of a quasiuniform fat point subscheme z p 2 is introduced and conjectures for the hilbert function and minimal free resolution of the ideal i defining z are put forward in a large range of cases it is shown that the hilbert function conjecture implies the resolution conjecture in addition the main result gives the first determination of the resolution of the mth symbolic power i m n of an ideal defining n general points of p 2 when both m and n are large in particular for infinitely many m for each of infinitely many n and for infinitely many n for every m 2 resolutions in other cases such as fat points with tails are also given except where an explicit exception is made all results hold for an arbitrary algebraically closed field k as an incidental result a bound for the regularity of i m n is given which is often a significant improvement on previously known bounds

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

existence of periodic solutions for a periodic mutualism model on time scales abstract by using mawhin s continuation theorem of coincidence degree theory sufficient criteria are obtained for the existence of periodic solutions of the mutualism model x t r 1 t k 1 t 1 t exp y t 2 t y t 1 exp y t 2 t y t exp x t 1 t x t y t r 2 t k 2 t 2 t exp x t 1 t x t 1 exp x t 1 t x t exp y t 2 t y t where r i k i i c t r i k i i 1 2 i i c t r t i 1 2 r i k i i i i i 1 2 are functions of period 0

infinitesimal deformations of rational surface automorphisms if x is a rational surface without nonzero holomorphic vector field and f is an automorphism of x we study in several examples the zariski tangent space of the local deformation space of the pair x f

asymptotic stability of a stochastic may mutualism system abstract this paper deals with a mutualism system in random environments in which the cooperation of two species is guaranteed depending on increasing the carrying capacity of each other mathematically we obtain the existence and uniqueness of a stable stationary distribution by means of markov semigroup theory and fokker planck equation in addition we prove that densities of the distributions for the solutions converge in l 1 to an invariant density under appropriate conditions numerical simulations are also presented to illustrate the theoretical results

an improved correction for range restricted correlations under extreme monotonic quadratic nonlinearity and heteroscedasticity standardized tests are frequently used for selection decisions and the validation of test scores remains an important area of research this paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples existing formulas for direct range restriction require three assumptions 1 the criterion variable is missing at random 2 a linear relationship between independent and dependent variables and 3 constant error variance or homoscedasticity the results in this paper demonstrate that the standard approach for correcting restricted correlations is severely biased in cases of extreme monotone quadratic nonlinearity and heteroscedasticity this paper offers at least three significant contributions to the existing literature first a method from the econometrics literature is adapted to provide more accurate estimates of unrestricted correlations second derivations establish bounds on the degree of bias attributed to quadratic functions under the assumption of a monotonic relationship between test scores and criterion measurements new results are presented on the bias associated with using the standard range restriction correction formula and the results show that the standard correction formula yields estimates of unrestricted correlations that deviate by as much as 0 2 for high to moderate selectivity third monte carlo simulation results demonstrate that the new procedure for correcting restricted correlations provides more accurate estimates in the presence of quadratic and heteroscedastic test score and criterion relationships

population dynamical behavior of lotka volterra system under regime switching in this paper we investigate a lotka volterra system under regime switching dx t diag x 1 t x n t b r t a r t x t dt s r t db t where b t is a standard brownian motion the aim here is to find out what happens under regime switching we first obtain the sufficient conditions for the existence of global positive solutions stochastic permanence and extinction we find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the markov chain the limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients finally the main results are illustrated by several examples

estimating correlations with missing data a bayesian approach the posterior distribution of the bivariate correlation is analytically derived given a data set wherex is completely observed buty is missing at random for a portion of the sample interval estimates of the correlation are then constructed from the posterior distribution in terms of highest density regions hdrs various choices for the form of the prior distribution are explored for each of these priors the resulting bayesian hdrs are compared with each other and with intervals derived from maximum likelihood theory

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea