laguerre type derivatives dobinski relations and combinatorial identities we consider properties of the operators d r m ar a a m which we call generalized laguerre type derivatives with r 1 2 m 0 1 where a and a are boson annihilation and creation operators respectively satisfying a a 1 we obtain explicit formulas for the normally ordered form of arbitrary taylor expandable functions of d r m with the help of an operator relation that generalizes the dobinski formula coherent state expectation values of certain operator functions of d r m turn out to be generating functions of combinatorial numbers in many cases the corresponding combinatorial structures can be explicitly identified

new q deformed coherent states with an explicitly known resolution of unity we construct a new family of q deformed coherent states zq where 0 q 1 these states are normalizable on the whole complex plane and continuous in their label z they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated stieltjes power moment problem and expressed in terms of one of the two jacksons s q exponentials they also permit exact evaluation of matrix elements of physically relevant operators we use this to show that the photon number statistics for the states is sub poissonian and that they exhibit quadrature squeezing as well as an enhanced signal to quantum noise ratio over the conventional coherent state value finally we establish that they are the eigenstates of some deformed boson annihilation operator and study some of their characteristics in deformed quantum optics

dynamics of predator prey system with fading memory abstract a predator prey model with fading memory for general holling type functional response is proposed the fading memory term is used with the hypothesis that the predator s growth rate at present depends on the recent past quantities of prey the effects of predator harvesting is also considered in the model the model is analysed theoretically as well as numerically two parameter bifurcation analysis are done and the existence of hopf point bifurcation is identified both supercritical and subcritical hopf bifurcations are obtained with the variation of system parameters maximum sustainable yield with respect to harvesting effort is also determined it is to be observed that the system dynamics is very rich in presence of fading memory the obtained results may be useful in the field of agriculture and fishery

renewal reward processes with fuzzy rewards and their applications to t age replacement policies the application of fuzzy set theory to renewal reward processes is proposed in this paper the reward is modeled as a fuzzy random variable a theorem which presents the long run average fuzzy reward per unit time is stated a procedure to obtain the best t age replacement policy with fuzzy cost structure is developed the original problem is transformed into a nonlinear program in order to evaluate the membership of the long run average fuzzy cost per unit time

a continuous time dynamic fuzzy system i a limit theorem abstract a continuous time dynamic fuzzy system with possibility transition is constructed and a differential of fuzzy states is given by paths a limit theorem for fuzzy states is discussed under a contractive condition on fuzzy relations

optimal control of harvest and bifurcation of a prey predator model with stage structure abstract this paper describes a prey predator model with stage structure for prey the adult prey and predator populations are harvested in the proposed system the dynamic behavior of the model system is discussed it is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account state feedback controller is incorporated to stabilize the model system in case of positive economic interest harvesting of prey and predator population are used as controls to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource the pontryagin s maximum principle is used to characterize the optimal controls the optimality system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

the time average reward for some dynamic fuzzy systems abstract in this paper by using a fuzzy relation we define a dynamic fuzzy system with a bounded convex fuzzy reward on the positive orthant r n of an n dimensional euclidean space as a measure of the system s performance we introduce the time average fuzzy reward which is characterized by the limiting fuzzy state under the contractive properties of the fuzzy relation in the one dimensional case the average fuzzy reward is expressed explicitly by the functional equations concerning the extreme points of its cuts also a numerical example is given to illustrate the theoretical results

a continuous time dynamic fuzzy system ii fuzzy potentials abstract this paper is a sequel of yoshida 9 fuzzy potentials are introduced in a continuous time dynamic fuzzy system and a fuzzy relational differential equation is given to characterize the fuzzy potentials

permanence and stability of a stage structured predator prey model abstract a predator prey model with a stage structure for the predator which improves the assumption that each individual predator has the same ability to capture prey is proposed it is assumed that immature individuals and mature individuals of the predator are divided by a fixed age and that immature predators do not have the ability to attack prey we obtain conditions that determine the permanence of the populations and the extinction of the populations furthermore we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model by exploiting the monotonicity of one equation of the model we obtain conditions for the global attractivity of the positive equilibrium which allow for long delay as long as the predator birth rate is large or the death rate of immature predators is small by constructing liapunov functionals we also obtain conditions under which the positive equilibrium is globally stable when the delay is small

stability and bifurcation analysis of a stage structured predator prey model with time delay abstract in this paper we proposed and analyzed a prey predator system with stage structured for the predator population a time delay is incorporated due to the gestation for the matured predator all the possible non negative equilibria are obtained and their local as well as global behavior are studied choosing delay as a bifurcation parameter the existence of the hopf bifurcation of the system has been investigated moreover we use the normal form method and the center manifold theorem to examine the direction of the hopf bifurcation and the nature of the bifurcating periodic solution some numerical simulations are given to support the analytical results some interesting conclusions are obtained from our analysis and it is given at the end of the paper

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

on non selective harvesting of a multispecies fishery incorporating partial closure for the populations highlightswe describe a prey predator fishery model incorporating partial closure for the populations the criterion for the existence of interior equilibrium point local and global stability of the system are derived the existence of bionomic equilibrium is discussed the optimal system is derived and solved numerically using an iterative method with runge kutta fourth order scheme numerical simulations are carried out to verify the analytically proved results a prey predator type fishery model incorporating partial closure for the populations is described in this paper the proposed model deals with a problem of non selective harvesting of a prey predator system in which both the prey and the predator species obey logistic law of growth the predator dependent beddington deangelis type functional response is taken into consideration dynamic behavior of the system is analyzed partial closure for the populations is considered as a controlling instrument to regulate the harvesting of the populations a dynamic framework towards the optimal utilization of the resource is developed using pontryagin s maximum principle the optimal system is numerically solved using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem results are analyzed with the help of graphical illustrations

a fuzzy ordering on multi dimensional fuzzy sets induced from convex cones a fuzzy ordering for fuzzy sets on rn is presented by a fuzzy relation on rn rn which is induced by closed convex cones the suitability of the fuzzy order is discussed using the axioms a1 a7 in fuzzy sets and systems 118 2001 375 for fuzzy sets on rn which are incomparable with respect to the fuzzy order a method to evaluate the degree of satisfaction regarding the fuzzy order is presented by using a subsethood degree approximation by discrete cases is discussed for numerical calculation on the degree of the fuzzy order numerical examples are also given to illustrate our idea

dobinski type relations and the log normal distribution we consider sequences of generalized bell numbers b n n 1 2 which can be represented by dobinski type summation formulae i e b n 1 c k 0 p k n d k with p k a polynomial d k a function of k and c const they include the standard bell numbers p k k d k k c e their generalizations br r n r 2 3 appearing in the normal ordering of powers of boson monomials p k k r k d k k c e variants of ordered bell numbers bo p n p k k d k p 1 p k c 1 p p 1 2 etc we demonstrate that for t positive integers t 0 b n2 n t is the nth moment of a positive function on 0 which is a weighted infinite sum of log normal distributions

global dynamics and bifurcation in a stage structured prey predator fishery model with harvesting abstract this paper describes a prey predator model with stage structure for predator and selective harvesting effort on predator population the holling type ii functional response function is taken into consideration all the equilibria of the proposed system are determined and the behavior of the system is investigated near them local stability of the system is analyzed geometric approach is used to derive the sufficient conditions for global stability of the system the occurrence of hopf bifurcation of the model system in the neighborhood of the co existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource pontryagin s maximum principle is used to characterize the optimal control the optimal system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

hopf bifurcation and global stability for a delayed predator prey system with stage structure for predator abstract in this paper a delayed predator prey system with stage structure for predator is proposed and studied it is found that the time delay is harmless for permanence of the stage structured system if 1 we show that the unique positive equilibrium is locally asymptotically stable when time delay is sufficiently small while loss of stability by a hopf bifurcation can occur as the delay increases

on constructions of algebraic space time codes with am psk constellations satisfying rate diversity tradeoff constructions of space time codes having amplitude modulated phase shift keying am psk constellations are presented in this paper the first construction termed p radii construction is obtained by extending hammons dyadic dual radii construction to the cases when the size of the constellation is a power of a prime p p ges 2 the resultant code is optimal with respect to the rate diversity tradeoff and has an am psk constellation with signal points distributed over p concentric circles in the complex plane i e there are p radii also contained in this paper is the identification of rich classes of nontrivial subset subcodes of the newly constructed space time codes and it is shown that these subset subcodes are again all optimal finally a new generalization of the super unified construction by hammons is presented it is shown that codes obtained from several previously known constructions are subset subcodes of the one derived from this generalized construction

stability and bifurcation in plant pathogens interactions we consider a plant pathogen interaction model and perform a bifurcation analysis at the threshold where the pathogen free equilibrium loses its hyperbolicity we show that a stimulatory inhibitory host response to infection load may be responsible for the occurrence of multiple steady states via backward bifurcations we also find sufficient conditions for the global stability of the pathogen present equilibrium in case of null or linear inhibitory host response the results are discussed in the framework of the recent literature on the subject

on convexity of fuzzy sets and fuzzy relations abstract various kinds of set theoretic operations produce new fuzzy sets and fuzzy relations from old ones what are the convexities of these sets and relations this is the problem discussed herein

a limit theorem in some dynamic fuzzy systems abstract in this paper using a fuzzy relation we define a dynamic fuzzy system with a compact state space by introducing a contraction property we study the limit of a sequence of fuzzy states and obtain a theorem for the existence and uniqueness of the solution of a fuzzy relational equation as an application we deal with a dynamic fuzzy system with a terminal fuzzy gain and give some characterizations for the fuzzy expected gain a numerical example is given to comprehend our idea in this paper

a potential of fuzzy relations with a linear structure the unbounded case this paper is a sequel to yoshida et al 1993 in which the potential theory for linear fuzzy relations on the positive orthant r n is considered in the class of fuzzy sets with a compact support under the contractive assumption in this paper potential treatment for unbounded fuzzy sets is developed without the assumption of contraction and compactness the objective of this paper is to give the existence and the characterization of potentials for linear fuzzy relations under some reasonable conditions also introducing a partial order in fuzzy sets we prove riesz decomposition theorem in the fuzzy potential theory the proofs are shown by using only the linear structure and the monotonicity of fuzzy relations in the one dimensional case the potential and its cuts are explicitly calculated numerical examples are given to comprehend further discussions

the effect of state dependent delay and harvesting on a stage structured predator prey model we propose and analyze a stage structured predator prey model in which the time from birth to maturity is directly related to the number of individuals present individuals mature more quickly when there are fewer of them around the state dependent time delay is taken to be an increasing differentiable bounded function in this research we study the dynamics of our model analytically we present results on positivity and boundedness of all populations criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given in order to observe the effect of state dependent maturation delay local stability analysis around all equilibria of the proposed model is discussed due to variation of maturation delay also global stability of trivial and the boundary equilibria is investigated using liapunov functional and lasalle invariant principle to investigate the effect of state dependent maturation delay and the harvesting effort of all species we carried out numerical simulations

effects of supplying alternative food in a predator prey model with harvesting in this paper we propose a tritrophic predator prey model with harvesting where the top predator population is partially supported with alternative food we report the consequences of providing alternative food to the top predator in a top predator harvested model the extinction criterion for top predator population local stability of equilibrium points and persistence conditions are discussed theoretically pontryagins maximum principle is used to characterize the optimal control of harvesting we have derived the condition of hopf bifurcation by varying harvesting effort the bifurcation diagrams of the system with respect to harvesting effort in presence of alternative food are given our analysis show that alternative food can prevent top predator extinction risk at higher harvesting effort and plays a vital role for biological conservation of species

an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards abstract this paper deals with an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards and shows that the optimal discounted fuzzy reward is characterized by a unique solution of a fuzzy relational equation we define a fuzzy expectation with a density given by fuzzy goals and we estimate discounted fuzzy rewards by the fuzzy expectation this paper characterizes the optimal fuzzy expected value and gives an optimal stopping time

hierarchical dobinski type relations via substitution and the moment problem we consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson a a 1 monomials of the form exp a ra r 1 2 under the composition of their exponential generating functions they turn out to be of sheffer type we demonstrate that two key properties of these sequences remain preserved under substitutional composition a the property of being the solution of the stieltjes moment problem and b the representation of these sequences through infinite series dobinski type relations we present a number of examples of such composition satisfying properties a and b we obtain new dobinski type formulae and solve the associated moment problem for several hierarchically defined combinatorial families of sequences

dobinski type relations some properties and physical applications we introduce a generalization of the dobinski relation through which we define a family of bell type numbers and polynomials for all these sequences we find the weight function of the moment problem and give their generating functions we provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the kerr hamiltonian

mittag leffler coherent states we create a family of boson coherent states using the functions of mittag leffler ml e z 0 and their generalizations e z 0 instead of exponentials these states are shown to satisfy the usual requirements of normalizability continuity in the label and the resolution of unity with a positive weight function this last quantity is found for arbitrary 0 as a solution of an associated stieltjes moment problem in addition for m 1 2 3 and 1 corresponding to em z we propose and analyse special q deformations 0 q1 of the functions em z which serve as a tool to define q deformed coherent states of ml type we provide the expressions for expectation values of physical quantities for all the above states we discuss physical properties of these states noting that they are squeezed the ml coherent states are sub poissonian in nature whereas the q deformed ml states can be sub and super poissonian depending on q all these states are shown to be eigenstates of deformed boson operators whose commutation relations are given

a potential of fuzzy relations with a linear structure the contractive case abstract in this paper we develop a potential theory of fuzzy relations on the positive orthant in a euclidean space by introducing a linear structure for fuzzy relations the existence of a potential and its characterization by fuzzy relational equation are derived under the assumption of contraction and compactness in the one dimensional unimodal case a potential is given explicity also a numerical example is shown to illustrate our approaches

a fuzzy approach to markov decision processes with uncertain transition probabilities in this paper markov decision models with uncertain transition matrices which allow a matrix to fluctuate at each step in time is described by the use of fuzzy sets we find a pareto optimal policy maximizing the infinite horizon fuzzy expected discounted reward fedr over all stationary policies under some partial order the pareto optimal policies are characterized by maximal solutions of an optimal inclusion including efficient set functions as a numerical example a machine maintenance problem is considered

local bifurcations and feasibility regions in differential algebraic systems the dynamics of a large class of physical systems such as the general power system can be represented by parameter dependent differential algebraic models of the form x spl dot f and 0 g typically such constrained models have singularities this paper analyzes the generic local bifurcations including those which are directly related to the singularity the notion of a feasibility region is introduced and analyzed it consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability it is shown that generically loss of stability at the feasibility boundary is caused by one of three different local bifurcations namely the saddle node and hopf bifurcations and a new bifurcation called the singularity induced bifurcation which is analyzed precisely here for the first time the latter results when an equilibrium point is at the singular surface under certain transversality conditions the change in the eigenstructure of the system jacobian at the equilibrium is established and the local dynamical structure of the trajectories near this bifurcation point is analyzed

dynamic programming for fuzzy systems with fuzzy environment abstract a dynamic programming functional equation for a multi stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation this is an extension of the bellman zadeh model

on fuzzy convexity and parametric fuzzy optimization abstract in this paper some different types of convexity and generalized convexity of fuzzy sets are defined and their properties are studied a general fuzzy nonlinear programming problem is formulated with application of the concept of convexity

modeling and dynamical analysis of a triple delayed prey predator scavenger system with levy jumps abstract in this paper a hybrid triple delayed prey predator scavenger system with commercial harvesting and levy jumps is established where both maturation delay for prey population and gestation delays for predator and scavenger population are considered for deterministic system positivity and uniform permanence of solution are discussed local stability analysis of deterministic system around interior equilibrium is investigated due to variations of triple time delays for stochastic system without time delay sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed for stochastic system with triple time delays existence and uniqueness of global positive solution are studied by constructing appropriate lyapunov functions asymptotic behavior of the hybrid stochastic system with triple time delays and levy jumps is discussed numerical simulations are supported to illustrate theoretical results

continuous time fuzzy decision processes with discounted rewards a continuous time decision process with fuzzy transitions which is termed fuzzy decision process is discussed from a viewpoint of a dynamic fuzzy system by the authors the discounted total reward is given by a fuzzy number and is discussed by the fuzzy max order this paper gives the optimality equation for the fuzzy decision model by a fuzzy differential equation the optimization problem of the discounted total rewards is also discussed by a fuzzy expectation generated from a fuzzy goal and an optimal policy and the permissible range of the decision maker s optimal expected payoffs are given for this problem also an illustrated example is given to explain the idea of the paper

an approach to stopping problems of a dynamic fuzzy system we formulate a stopping problem for dynamic fuzzy systems concerning with fuzzy decision environment it could be regarded as a natural fuzzification of non fuzzy stopping problem with a deterministic dynamic system the validity of the approach by cuts of fuzzy sets will be discussed in constructing one step look ahead policy of an optimal fuzzy stopping time a numerical example is given to illustrate the theoretical results and to show a merit to use fuzzy stopping times in dynamic fuzzy systems

dynamics in a ratio dependent predator prey model with predator harvesting abstract the objective of this paper is to study systematically the dynamical properties of a ratio dependent predator prey model with nonzero constant rate predator harvesting it is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena including the bifurcation of cusp type of codimension 2 i e bogdanov takens bifurcation the subcritical and supercritical hopf bifurcations these results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in d xiao l jennings bifurcations of a ratio dependent predator prey system with constant rate harvesting siam appl math 65 2005 737 753 biologically it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction and remove the singularity of the origin which was regarded as pathological behavior for a ratio dependent predator prey model in p yodzis predator prey theory and management of multispecies fisheries ecological applications 4 2004 51 58

fuzzy stopping in continuous time dynamic fuzzy systems in a continuous time dynamic fuzzy system a stopping problem regarding fuzzy rewards is discussed using fuzzy stopping times the fuzzy rewards are evaluated by an expectation generated from a linear ranking function the optimality equations for the optimal fuzzy rewards are given by variational inequalities and an optimal fuzzy stopping time is constructed under assumptions of monotonicity and regularity for stopping rules a numerical example is given to discuss that fuzzy stopping times are better than non fuzzy ones in comparison between the fuzzy stopping models and the non fuzzy ones

markov type fuzzy decision processes with a discounted reward on a closed interval abstract we formulate a new multi stage decision process with markov type fuzzy transition which is termed markov type fuzzy decision process in the general framework of the decision process both of state and action are assumed to be fuzzy itself the transition of states is defined using the fuzzy relation with markov property and the discounted total reward is described as a fuzzy number on a closed bounded interval to discuss the optimization problem a partial order of convex fuzzy numbers is introduced in this paper the discounted total reward associated with an admissible stationary policy is characterized by a unique fixed point of the contractive mapping moreover the optimality equation for the fuzzy decision model is derived under some continuity conditions also an illustrated example is given to explain the theoretical results and the computation in the paper

analysis of predator prey models with continuous threshold harvesting abstract we formulate an alternative form of threshold harvesting and investigate its properties within the framework of a predator prey model our formulation accounts for economic constraints and is defined as a continuous harvesting function of the predator species theoretical and numerical analysis indicate that our formulation which we call continuous threshold policy ctp can help improve undesirable behavior of the predator prey ecosystem our study includes uniform boundedness of solutions stability of equilibria and periodic orbits bifurcations and heteroclinic orbits

quantum field theory of partitions given a sequence of numbers an it is always possible to find a set of feynman rules that reproduce that sequence for the special case of the partitions of the integers the appropriate feynman rules give rise to graphs that represent the partitions in a clear pictorial fashion these feynman rules can be used to generate the bell numbers b n and the stirling numbers s n k that are associated with the partitions of the integers

dynamic analysis of fractional order singular holling type ii predator prey system abstract in this paper a fractional order singular fos predator prey model with holling type ii functional response has been introduced and the mathematical behavior of the model from the aspect of local stability is investigated through the fractional calculus and economic theory a new and more realistic predator prey model has been extended and the solvability condition is presented besides numerical simulations are considered to illustrate the effectiveness of the numerical method and confirm the theoretical results to explore the impacts of fractional order and economic interest on the presented system in biological context it is found that the presence of fractional order in the differential model can improve the stability of the solutions and enrich the dynamics of system in addition singular models exhibit more complicated dynamics rather than standard models especially the bifurcation phenomena which can reveal the instability mechanism of systems