β expectation and β content tolerance limits for balanced one way anova random model this article discusses procedures for computing tolerance limits for a population consisting of many batches the results of mee and owen 1983 for one sided content tolerance limits are extended to the two sided case in addition expectation tolerance limit procedures are presented the procedures given for the case in which the ratio of the between and within variances is known are exact whereas the procedures derived for settings in which the ratio is unknown involve an approximation

periodic solutions of a periodic lotka volterra system with delays a lotka volterra periodic delay model with m predators and n preys is studied in this paper sufficient conditions for the global existence of a positive periodic solutions of this delay model are obtained by means of topological degree finally a suitable example is given to illustrate that the conditions of the main theorem are feasible

permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

one sided tolerance limits for balanced and unbalanced random effects models a simple analytical approach for constructing one sided content confidence tolerance limits is proposed for general random effects models with normal data in both balanced and unbalanced data scenarios the approach is based on an approximation to the noncentral t distribution and modified large sample methods for constructing confidence bounds on functions of variance components an alternative bootstrap adjusted limit is also proposed the performance of the analytical and bootstrap adjusted limits is assessed via simulation techniques the results indicate that the analytical limit is generally somewhat conservative but is often less conservative than an existing analytical approach and may provide substantially shorter interval lengths particularly for smaller sample sizes and larger values of the bootstrap adjusted limit generally maintains the nominal confidence level and yields shorter interval lengths though it can be anticonservative for small sample sizes this article has supplementa

on the periodic solutions of periodic multi species kolmogorov type competitive system with delays and feedback controls abstract in this paper we consider a periodic multi species kolmogorov type competitive system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive periodic solution of the system are obtained as application the existence of the positive periodic solution of a kind of nonlinear competitive model with delays and feedback controls is discussed

large momentum properties and wilson short distance expansion in non perturbative field theory large momentum properties and wilson zimmerman short distance expansion are established via phase space analysis for the weakly coupled massive gross neveu model in dimension 2 methods are applicable more generally

non holonomicity of the s matrix and green functions in quantum field theory a direct algebraic proof in some simple situations a criterion of non holonomicity of thes matrix and green functions in some basic simple situations of relativistic quantum field theory previously established in an indirect way or with supplementary assumptions is reobtained from unitarity equations by a direct and general algebraic argument

asymptotic behaviour of the stochastic gilpin ayala competition models abstract in this paper we investigate a stochastic gilpin ayala competition system which is more general and more realistic than the classical lotka volterra competition system we discuss the asymptotic behaviour in detail of the stochastic gilpin ayala competition system and comparing the classical lotka volterra with gilpin ayala competition system we find that the latter has better properties

dynamics of non autonomous stochastic gilpin ayala competition model with time varying delays in this paper the non autonomous stochastic gilpin ayala competition model with time dependent delay is considered we prove existence and uniqueness of the global positive solution and various properties of that solution such as boundedness moment and pathwise estimation extinction non persistence in time average and weak persistence in addition we give a special case of the considered system and impose its properties all studied features are natural requirements from the biological point of view furthermore examples with numerical simulations are given to illustrate our results

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

2 particle asymptotic completeness and bound states in weakly coupled quantum field theories rigorous results on poles of the 2 and 4 point functions which yield 2 particle asymptotic completeness and give information on the presence or absence of 2 particle bound states and resonances are presented for weakly coupled even and non even field theories with mass gap in space time dimensiond 2 3 and for related hypothetical theories in dimension 4 methods used are more convenient and more general than those used previously with more limited results forp 2 theories

bethe salpeter kernel and short distance expansion in the massive gross neveu model the bethe salpeter kernel is defined non perturbatively for the weakly coupled massive gross neveu model its large momentum properties are established they are used to justify subtracted bethe salpeter equations initially proposed for 44 by k symanzik and in turn to give non perturbative proofs of the wilson short distance expansion at first order and of 2 particle asymptotic completeness and related results

dynamics in a periodic competitive model with stage structure in this paper we consider a time delayed periodic system which describes the competition among mature populations by appealing to theories of monotone dynamical systems periodic semiflows and uniform persistence we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion

two sided tolerance limits for balanced random effects anova models in this article we derive two sided approximate content tolerance limits for multiway balanced random effects models we provide factors obtained from numerical integration that can be used to obtain content tolerance intervals we describe methods for extending the results to nested models and discuss the use of the tabled tolerance factors for exact intervals for simple random samples when we have an independent estimate of the variance we demonstrate the procedure with an experimental design used to evaluate the firing time precision in a high explosives system

convergence conditions for some classes of nonlinear systems abstract systems of differential equations with nonlinearities of a sector type and almost periodic perturbations are studied with the aid of the lyapunov direct method conditions are found under which the considered systems admit globally asymptotically stable almost periodic solutions moreover it is shown that the proposed approach permits us to derive new convergence conditions for some models of neural networks and generalized lotka volterra models of population dynamics an example is presented to demonstrate the effectiveness of the obtained results

tolerance intervals for the distribution of true values in the presence of measurement errors a tolerance interval procedure for the distribution n 2 1 2 2 is derived based on the mutually independent statistics s 2 1 and s 2 2 which are distributed as follows has a normal distribution with mean and variance 2 1 n n 1 s 2 1 2 1 is chi squared with n 1 df and n 2 s 2 1 2 2 is chi squared with n 2 df application to the construction of tolerance intervals for the distribution of true values when observations are contaminated with measurement errors is explained this includes the problem of constructing tolerance intervals in some growth curve models numerical examples are given to illustrate the procedures

periodicity in a food limited population model with toxicants and state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

dynamics of a class of nonautonomous semi ratio dependent predator prey systems with functional responses abstract in this paper we investigate the dynamics of a class of the so called semi ratio dependent predator prey interaction models with functional responses based on systems of nonautonomous differential equations with time dependent parameters the functional responses are classified into five types and typical examples of each type are provided then we establish sufficient criteria for the boundedness of solutions the permanence of system and the existence uniqueness and globally asymptotic stability of positive periodic solution and positive almost periodic solution some conclusive discussion is presented at the end of this paper

asymptotic completeness and multiparticle structure in field theories ii theories with renormalization the gross neveu model the ideas developed in part i ref 1 are applied to the recently constructed massive gross neveu model we define in this case an irreducible kernel satisfying a regularized bethe salpeter equation which is convenient to derive asymptotic completeness in the 2 particle region as in part i the method ailows direct graphical definition of general irreducible kernels and is well suited to the analysis of asymptotic completeness and related results in more general energy regions a large part of the paper is devoted to a new self contained construction via phase space expansion of the gross neveu model the presentation is somewhat simpler than previous ones is more complete on some points and is best suited to our purposes

permanence of a delayed non autonomous gilpin ayala competition model abstract in this paper we consider a delayed non autonomous n species gilpin ayala competitive system which is more general and more realistic then classical lotka volterra competition model by means of ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the permanence of the system it is shown that our result is the generalization of those of zhao et al j d zhao j f jiang a c lazer the permanence and global attractivity in a nonautonomous lotka volterra system nonlinear analysis real world applications 5 4 2004 265 276 our results also supplement the results of fan and wang m fan k wang global periodic solutions of a generalized n species gilpin ayala competition model computer and mathematics with applications 40 2000 1141 1151

β expectation and β content tolerance limits for balanced one way anova random model b expectation and b content tolerance limits for balanced one way anova random model

global attractivity of an almost periodic n species nonlinear ecological competitive model abstract by using comparison theorem and constructing suitable lyapunov functional we study the following almost periodic nonlinear n species competitive lotka volterra model x i t x i t r i t j 1 n a i j t x j i j t j 1 n b i j t x j i j t i j t j 1 n c i j t x i i i t x j i j t a set of sufficient conditions is obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model as applications some special competition models are studied again our new results improve and generalize former results examples and their simulations show the feasibility of our main results

permanence of a discrete nonlinear n species cooperation system with time delays and feedback controls a discrete nonlinear n species cooperation system with time delays and feedback controls is considered in this paper sufficient conditions which ensure the permanence of the system are obtained it is shown that these conditions are weaker than those of chen f d chen permanence of a discrete n species cooperation system with time delays and feedback controls appl math comput 186 2007 23 29 that is our investigation shows that the additional condition in chen s paper is not necessary

positive periodic solution of a kind of nonlinear food chain system a nonlinear periodic food chain predator prey model is proposed in this paper which can be seen as the modification of the traditional lotka volterra food chain system sufficient conditions which guarantee the existence of the positive periodic solution of the system are obtained

on a periodic multi species ecological model a periodic predator prey model with m predators and n preys is proposed in this paper which can be seen as the modification of the traditional lotka volterra model by using comparison theorem the ultimately bounded region of the system is obtained by using comparison theorem and brouwer fixed point theorem sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained finally by constructing a suitable lyapunov function some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system the results obtained here generalized the main results of j d zhao w c chen global asymptotic stability of a periodic ecological model applied mathematics and computation 147 3 2004 881 892

some analyticity properties arising from asymptotic completeness in quantum field theory it is well known that two particle unitarity of the s matrix in quantum field theory implies modulo regularity assumptions second sheet analyticity for the 2 body scattering amplitude here this is first used to prove off mass shell analyticity for the 4 point function in a complex neighborhood of any real mass shell point under the 3 particle threshold then this is applied to the study of the 5 and 6 point functions near the real mass shell of 2 3 and 3 3 processes below the 4 particle threshold the results are those suggested by perturbation theory apart from the 3 particle cut and away from some submanifolds the advantage of this method which could presumably be extended to the exploitation ofn particle unitarity is that the regularity assumptions only refer to the physical scattering amplitudes

global attractivity of the periodic lotka volterra system a lotka volterra periodic model withm predators andn preys is studied in this paper a set of easily verifiable sufficient conditions that guarantee the existence uniqueness and global attractivity of the positive periodic solutions is obtained finally a suitable example is given to illustrate that the conditions of the main theorem are feasible

positive periodic solutions of nonautonomous functional differential systems abstract considered is the periodic functional differential system with a parameter x t a t x t x t f t x t using the eigenvalue problems of completely continuous operators we establish some criteria on the existence of positive periodic solutions moreover we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions which are compared with existing ones

adaptive control of linear singular time invariant single input single output systems with external point delay this paper is devoted to the robust adaptive control of solvable single input single output impulse free linear time invariant singular dynamic systems of known orders and unknown parameterizations subject to single external point delays the control law is of pole placement type and based on input output measurements and parametrical estimation only the parametrical estimation algorithm incorporates adaptation dead zones to prevent against potential instability caused by disturbances and unmodeled dynamics the weierstrass canonical form is investigated in detail concerning the properties of controllability and observability via testable conditions of the given arbitrary state space realization of the same order robust closed loop stability is proved under similar conditions to those used for nonsingular standard systems

permanence of a nonlinear prey competition model with delays abstract a nonlinear periodic predator prey model with m preys and n m predators and delays is studied which can be seen as the modification of the traditional lotka volterra prey competition model two sets of sufficient conditions which guarantee the permanence of the system are obtained one set is delay independent while the other set is delay dependent our results supplement those obtained by chen et al f d chen x d xie j l shi existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays journal of computational and applied mathematics 194 2 2006 368 387

the qualitative analysis of n species nonlinear prey competition systems in this paper we consider an n species nonlinear prey competition system using the differential inequality theorem and the v function method we obtain some sufficient conditions for the permanence and global asymptotic stability of the system

a different consideraton about the globally asymptotically stable solution of the periodic n competing species problem abstract we consider the volterra lotka equations for n competing species n 2 in which the right hand sides are periodic in time we show that conditions given by k gopalsamy j austral math soc ser b 27 1985 66 72 which imply the existence of a periodic solution with positive components also imply the uniqueness and asymptotic stability of the solution

stochastic gilpin ayala competition model with infinite delay abstract in this paper we study the stochastic gilpin ayala competition model with an infinite delay we verify that the environmental noise included in the model does not only provide a positive global solution there is no explosion in a finite time but this solution is also stochastically ultimately bounded we obtain certain asymptotic results regarding a large time behavior

one and two sided tolerance intervals for general balanced mixed models and unbalanced one way random models in this article we develop procedures for one and two sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi squared random variables the proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available however this study focuses on situations involving unbalanced data specific attention is given to the unbalanced one way random model it is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward some practical examples are given to illustrate the proposed procedures furthermore detailed statistical simulation studies are conducted to evaluate their performance showing that the proposed procedures can be recommended for practical use

regularized and renormalized bethe salpeter equations some aspects of irreducibility and asymptotic completeness in renormalizable theories results on the links between 2 particle irreducibility and asymptotic completeness are presented in the framework of a renormalized bethe salpeter formalism introduced recently by j bros from an axiomatic viewpoint for the most simple class of renormalizable theories these results which involve therenormalized 2 particle irreducible kernelg i e from the perturbative viewpoint the sum of renormalized feynman amplitudes of 2 particle irreducible graphs in the channel considered complement the general quasi equivalence previously established by bros forregularized non renormalized bethe salpeter kernels on the one hand a formal derivation of 2 particle asymptotic completeness from the irreducibility ofg is given on the other hand the links between regularized and renormalized kernels are investigated this analysis provides in particular a converse derivation up to some assumptions of the 2 particle irreducibility ofg from asymptotic completeness as a byproduct it also provides a more explicit justification of previous heuristic derivations by k symanzik of integral equations betweenf and various differences of values ofg and a simple alternative derivation of the recently proposed renormalized bethe salpeter equation

diagonal riccati stability and applications abstract we consider the question of diagonal riccati stability for a pair of real matrices a b a necessary and sufficient condition for diagonal riccati stability is derived and applications of this to two distinct cases are presented we also describe some motivations for this question arising in the theory of generalised lotka volterra systems

global positive periodic solutions of periodic n species competition systems abstract in this paper an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n species lotka volterra type and gilpin ayala type competition systems is obtained it improves a series of the well known sufficiency theorems in the literature about the problems mentioned above the method is based on a well known fixed point theorem in a cone of banach space this approach can be applied to more general competition systems

improved factors for one sided tolerance limits for balanced one way anova random model abstract we investigate in this article various techniques for determining a tolerance limit such that the probability is that at least a proportion p of a population produced in batches exceeds that limit if the variance ratio is known one may obtain exact tolerance limits for settings where the variance ratio is not necessarily known we describe a procedure based on the satterthwaite approximation for obtaining conservative tolerance limits the factors based on the satterthwaite approximation are smaller than those obtained using the procedure of lemon 1977

periodic solution of a lotka volterra predator prey model with dispersion and time delays a periodic lotka volterra predator prey model with dispersion and time delays is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory and by means of a suitable lyapunov functional a set of easily verifiable sufficient conditions are derived for the existence uniqueness and global stability of positive periodic solutions of the system sufficient conditions are also established for the uniform persistence of the system numerical simulations are presented to illustrate our main results

asymptotic completeness and multiparticle structure in field theories the ideas developed in part i ref 1 are applied to the recently constructed massive gross neveu model we define in this case an irreducible kernel satisfying a regularized bethe salpeter equation which is convenient to derive asymptotic completeness in the 2 particle region as in part i the method allows direct graphical definition of general irreducible kernels and is well suited to the analysis of asymptotic completeness and related results in more general energy regions

asymptotic properties of stochastic hybrid gilpin ayala system with jumps this paper focuses on studying the dynamics of the stochastic gilpin ayala model under regime switching with jumps the aim is to analyze what happens under the perturbations of regime switching and jumps some asymptotic properties are investigated and sufficient conditions for stochastic permanence extinction non persistence in the mean and weak persistence are provided the critical value among the extinction non persistence in the mean and weak persistence is obtained our results demonstrate that the dynamics of the model have close relations with the jumps and the stationary distribution of the markov chain

unitarity equations and structure of thes matrix at them particle threshold in a theory with purem m interaction the structure of thes matrix at them partical thresholds m 2 of am m process m 2 inv dimensional space time is determined in a theory with a simplified unitarity equation corresponding to a purem m interaction if m 1 v 1 is odd a two sheeted square root type structure is obtained as in the usual case of two particle thresholds in dimension 4 the nature of the singularity is more complicated if m 1 v 1 is even e g m 3 in dimension 4 results obtained in this case include an orthogonal decomposition of the scattering functiont with nonholomic eigenvalues of the form 1 2i ln b i 1 where m 2 s andb i is uniform around 0 and a related infinite expansion oft in powers of ln involving an on shell irreducible kernelu which is the analogue for m 1 v 1 even of zimmerman sk matrix

on a nonlinear nonautonomous predator prey model with diffusion and distributed delay in this paper a nonlinear nonautonomous predator prey model with diffusion and continuous distributed delay is studied where all the parameters are time dependent the system which is composed of two patches has two species the prey can diffuse between two patches but the predator is confined to one patch we first discuss the uniform persistence and global asymptotic stability of the model after that by constructing a suitable lyapunov functional some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained an example shows the feasibility of our main results

on a delayed nonautonomous ratio dependent predator prey model with holling type functional response and diffusion abstract a two species periodic ratio dependent predator prey model with holling type functional response and diffusion is investigated three different sets of sufficient conditions one set is diffusive independent and the other two sets are diffusive dependent which ensure the permanence of the system and a set of sufficient condition which ensure the extinction of the predator species are obtained examples together with their numeric simulations show the feasibility of the main results

global attractivity in an almost periodic multi species nonlinear ecological model abstract a nonlinear almost periodic predator prey model with n preys and m predators is studied in this paper which can be seen as the modification of the traditional multi species lotka volterra predator prey model for general nonautonomous case by using the differential inequality theory we obtain the sufficient conditions which guarantee the uniform persistence and nonpersistence of the system after that by constructing a suitable lyapunov function some sufficient conditions are obtained which ensure the global attractivity of the system for almost periodic case by constructing a suitable lyapunov function sufficient conditions which guarantee the existence of an unique globally attractive positive almost periodic solution of the system are obtained examples together with their numeric simulations show the feasibility of our main results

coexistence states for periodic competitive kolmogorov systems abstract we prove the existence of positive periodic solutions for a class of nonautonomous competitive periodic kolmogorov systems which generalize the may leonard model a necessary and sufficient condition is also obtained

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

permanence and extinction for a nonlinear diffusive predator prey system abstract in this paper we consider a non autonomous predator prey system in a poor patchy environment under the assumption that the intrinsic growth rates of the species may be negative sufficient conditions are obtained for the permanence and extinction of the system considered

polymers in a weak random potential in dimension four rigorous renormalization group analysis correlation functions of the edwards model of polymers at weak coupling are defined and studied at the critical point in dimension four by a rigorous renormalization group method which validates at any order perturbative renormalization group results on their behaviour at large distances remainders are controlled by a new argument which enlarges the use of methods of constructive field theory to models of statistical physics

almost periodic dynamics of a delayed three level food chain model abstractthis paper is concerned with the dynamics of a three level food chain model with time delays by means of mawhin s continuation theorem of coincidence degree theory we investigate the existence of positive almost periodic solutions in a three level food chain model with time delays a set of sufficient conditions for the existence of at least one positive almost periodic solution of the model is obtained in addition the global asymptotical stability of the almost periodic solution of the above model is also studied finally two examples and simulations are also given to illustrate the main results in this paper

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

phase space analysis and particle structure in field theory progress in the last few years in constructive field theory has included 1 the construction of three dimensional non abelian gauge theories in a finite volume 2 the construction of models that are asymptotically free or have a nontrivial fixed point 3 a new presentation of perturbation theory yielding old and new large order estimates and 4 asymptotic completeness for renormalizable models in the two particle region the existence of multiparticle structure equations in the euclidean region provided that the coupling constant goes to zero as the energy increases these equations yield formally the asymptotic completeness in obtaining most of these results the phase space expansion pioneered by glimm and jaffe plays a crucial role the first part of this review is a description of the phase space expansion in the ecole polytechnique version the second part is devoted to the construction of models the third part treats perturbation theory and the last part deals with asymptotic completeness

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

confidence prediction and tolerance in linear mixed models the literature about prediction interval pi and tolerance interval ti in linear mixed models is usually developed for specific designs which is a main limitation to their use this paper proposes to reformulate the two sided pi to be generalizable under a wide variety of designs one random factor nested and crossed designs for multiple random factors and balanced or unbalanced designs this new methodology is based on the hessian matrix namely the inverse of observed fisher information matrix and is built with a cell mean model the degrees of freedom for the total variance are calculated with the generalized satterthwaite method and compared to the kenward roger s degrees of freedom for fixed effects construction of two sided tis are also detailed with one random factor and two nested and two crossed random variables an extensive simulation study is carried out to compare the widths and coverage probabilities of confidence intervals ci pis and tis to their nominal levels it shows excellent coverage whatever the design and the sample size are finally these cis pis and tis are applied to two real data sets one from orthopedic surgery study intralesional resection risk and the other from assay validation study during vaccine development

new methods for one sided tolerance limits for a one way balanced random effects anova model the problem of determining one sided tolerance limits or equivalently one sided confidence limits on a quantile of a normal population with variance 2 2 b 2 b is considered in this article the tolerance limits are obtained using data from a one way balanced randomeffects sample from this population two procedures are introduced a simple approximate method based on an asymptotic expansion and a computer intensive procedure that provides very nearly the nominal confidence in the presence of the nuisance variance component ratio for the computer intensive procedure tables are provided that eliminate the need for most of the computation for some important situations tolerance limits for strength are routinely used in structural design material strength particularly for composite materials often exhibits considerable between batch variability a tolerance limit that provides nearly the nominal confidence is usually preferable to a conservative limit since a conservative tolerance limit undere

new conditions on the existence and stability of periodic solution in lotka volterra s population system in this paper we revisit the famous periodic lotka volterra competitive system some new and interesting sufficient conditions are obtained to guarantee the existence and global asymptotic stability of the periodic solution in the lotka volterra competitive system our method is based on mawhin s coincidence degree matrix s spectral theory and some new estimation techniques for the priori bounds of unknown solutions to the equation lx lambda nx due to this new method our new results are much different from the known results in the previous literature finally some examples and their simulations show the feasibility of our results

dynamic behaviors of a delay differential equation model of plankton allelopathy in this paper we consider a modified delay differential equation model of the growth of n species of plankton having competitive and allelopathic effects on each other we first obtain the sufficient conditions which guarantee the permanence of the system as a corollary for periodic case we obtain a set of delay dependent condition which ensures the existence of at least one positive periodic solution of the system after that by means of a suitable lyapunov functional sufficient conditions are derived for the global attractivity of the system for the two dimensional case under some suitable assumptions we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation examples show the feasibility of the main results

one sided tolerance limits in balanced and unbalanced one way random models based on generalized confidence intervals we consider the problem of deriving one sided tolerance intervals in the one way random model with balanced as well as unbalanced data under the usual normality assumptions the problems investigated deal with the computation of such intervals for the observable random variable as well as the unobservable random effect in the one way random model the tolerance limits are derived using the concept of a generalized confidence interval some approximations are derived for the tolerance limits and their performance is investigated by simulation the simulation results show that the proposed tolerance limits are quite satisfactory for practical use

irreducible kernels and nonperturbative expansions in a theory with purem m interaction recent results on the structure of thes matrix at them particle threshold m 2 in a simplifiedm m scattering theory with no subchannel interaction are extended to the green functionf on the basis of off shell unitarity through an adequate mathematical extension of some results of fredholm theory local two sheeted or infinite sheeted structure off arounds m 2 depending on the parity of m 1 1 where 0 is the mass and is the dimension of space time off shell definition of the irreducible kernelu which is the analogue of thek matrix in the two different parity cases m 1 1 odd or even and related local expansion off for m 1 1 even in powers of ln m 2 s it is shown that each term in this expansion is the dominant contribution to a feynman type integral in which each vertex is a kernelu the links between the kernelu and bethe salpeter type kernelsg of the theory are exhibited in both parity cases as also the links between the above expansion off and local expansions in the bethe salpeter type framework off in terms of feynman type integrals in which each vertex is a kernelg and which include both dominant and subdominant contributions

one sided and two sided tolerance intervals in general mixed and random effects models using small sample asymptotics the computation of tolerance intervals in mixed and random effects models has not been satisfactorily addressed in a general setting when the data are unbalanced and or when covariates are present this article derives satisfactory one sided and two sided tolerance intervals in such a general scenario by applying small sample asymptotic procedures in the case of one sided tolerance limits the problem reduces to the interval estimation of a percentile and accurate confidence limits are derived using small sample asymptotics in the case of a two sided tolerance interval the problem does not reduce to an interval estimation problem however it is possible to derive an approximate margin of error statistic that is an upper confidence limit for a linear combination of the variance components for the latter problem small sample asymptotic procedures can once again be used to arrive at an accurate upper confidence limit in the article balanced and unbalanced data situations are treated separately and

permanence and global attractivity of the discrete gilpin ayala type population model in this paper we propose a discrete gilpin ayala competition model and a discrete gilpin ayala type multispecies competition predator model for general nonautonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained an example together with its numeric simulations shows the feasibility of the main results

periodic solutions for delay lotka volterra competition systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for the periodic distributed delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t 0 t ij k ij s u j t s ds i 1 2 n and the periodic state dependent delay lotka volterra competition system du i t dt u i t r i t a ii t u i t j 1 j i n a ij t u j t j t u 1 t u n t i 1 2 n where ri aii 0 aij 0 j i i j 1 2 n are continuous periodic functions tij 0 j i i j 1 2 n kij c tij 0 0 0 tijkij s ds 1 j i i j 1 2 n i c rn 1 r and i i 1 2 n are periodic with respect to their first arguments respectively

three body asymptotic completeness for p φ 2 models we consider weakly coupled even p 2 models that do not have a two body bound state and prove asymptotic completeness on the subspace of states with mass between 3m a and 4m b wherea andb are positive functions tending to zero with the analytic structure of the six point function integrated over the three incoming momenta shows only two landau singular manifolds plus normal thresholds associated to three particle processes

dynamic of a non autonomous predator prey system with infinite delay and diffusion in the present paper a nonlinear non autonomous predator prey dispersion model with continuous delay is studied sufficient conditions which guarantee the existence of a periodic positive solution are obtained by using gaines and mawhin s continuation theorem of coincidence degree theory moreover globally asymptotically stability of the system is also obtained by means of a suitable lyapunov functional the applications show that these criteria are easily verified

periodicity in a logistic type system with several delays with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of the following several delays logistic type system du t dt u t a t j 1mb j t u t t j t q j where a t b j t are positive periodic continuous functions with periodic w 0 t j t are nonnegative continuous periodic functions with periodic w 0 after that by constructing a suitable lyapunov functional some sufficient conditions which guarantee the stability of the positive periodic solutions are obtained

periodicity in a nonlinear predator prey system on time scales with state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a nonlinear state dependent delays predator prey system on time scales

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model