sharp systolic inequalities for reeb flows on the three sphere the systolic ratio of a contact form alpha on the three sphere is the quantity begin aligned rho mathrm sys alpha frac t min alpha 2 mathrm vol s 3 alpha wedge d alpha end aligned where t min alpha is the minimal period of closed reeb orbits on s 3 alpha a zoll contact form is a contact form such that all the orbits of the corresponding reeb flow are closed and have the same period our first main result is that rho mathrm sys le 1 in a neighbourhood of the space of zoll contact forms on s 3 with equality holding precisely at zoll contact forms this implies a particular case of a conjecture of viterbo a local middle dimensional non squeezing theorem and a sharp systolic inequality for finsler metrics on the two sphere which are close to zoll ones our second main result is that rho mathrm sys is unbounded from above on the space of tight contact forms on s 3

economic reorder point for fuzzy backorder quantity abstract in this paper we consider the backorder inventory problem with fuzzy backorder such that the backorder quantity is a triangular fuzzy number s s 1 s 0 s 2 suppose s and q denote the crisp economic backorder and order quantities respectively in the classical inventory with backorder model according to four order relations of s and s 1 s 0 s 2 s 1 s 0 s 2 we find the membership function g q s z of the fuzzy cost function g q s and their centroid we also obtain the economic order quantity q and the economic backorder quantity s in the fuzzy sense we conclude that after solving the model in the fuzzy sense the total cost is slightly higher than that in the crisp model however it permits better use of the economic fuzzy quantities arising with changes in orders deliveries and sales

ranking fuzzy numbers with integral value abstract ranking fuzzy numbers is important in decision making since very often the alternatives are evaluated by fuzzy numbers in a vague environment a comparison between these fuzzy numbers is indeed a comparison between alternatives this paper proposes a method of ranking fuzzy numbers with integral value the method which is independent of the type of membership functions used and the normality of the functions can rank more than two fuzzy numbers simultaneously it is relatively simple in computation especially in ranking triangular and trapezoidal fuzzy numbers further an index of optimism is used to reflect the decision maker s optimistic attitude discussion on comparative advantages is included

fuzzy models for single period inventory problem in this paper we consider the single period inventory problem in the presence of uncertainties two types of uncertainties one arising from randomness which can be incorporated through a probability distribution and the other from fuzziness which can be characterized by fuzzy numbers are considered we develop two models in one the demand is probabilistic while the cost components are fuzzy and in the other the costs are deterministic but the demand is fuzzy in each the objective is maximization of profit which is fuzzy and optimization is achieved through fuzzy ordering of fuzzy numbers with respect to their total integral values we show that the first model reduces to the classical newsboy problem and therefore an optimal solution is easily available in second model we show that the objective function is concave and hence present a characterization of the optimal solution from which one can readily compute an optimal solution besides discussion of the models a relevant extension is outlined

fuzzy inventory with backorder for fuzzy order quantity this paper investigates a group of computing schemas for economic order quantity as fuzzy values and the corresponding optimal stock quantity of the invenyory with backorder we express the fuzzy order quantity as the normal triangular fuzzy number q1 q0 q2 and then we solve the aforementioned optimization problem under the constraints 0 s q1 q0 q2 where s denotes the optimizing stock quantity we find that after defuzzification the total cost is slightly higher than in the crisp model however it permits better use of the economic fuzzy quantities arising with changes in orders deliveries and sales

an example of convex hamiltonian diffeomorphism where asymptotic distance from identity is strictly greater than the minimal action abstract we construct a convex hamiltonian diffeomorphism on the unit ball of cotangent bundle of t n n 2 where the asymptotic distance from identity is strictly greater than the minimal action

codimension one and two bifurcations in a symmetrical ring network with delay abstract in this paper we discussed all the possible codimension one and partial codimension two bifurcations existing in a symmetrical ring network using the symmetric bifurcation theory of delay differential equations coupled with the representation theory of lie groups and dynamical analysis methods we have not only figured out the pattern of each bifurcation but also predicted the directions and stability analysis of the bifurcated solutions according to structure of the system numerical simulations were then given to verify our theoretical analysis and investigate the complexity of codimension two mode intersections comments were also presented to highlight some future work

an inventory model for single period products with reordering opportunities under fuzzy demand this paper analyzes a single period inventory model of profit maximization with a reordering strategy in an imprecise environment the entire period is divided into two slots and the customer demand is considered as a fuzzy number in situations where the demand in each slot is linguistic in nature and characterized as demand is aboutd the reordering is to be done during the mid season after the early season demand has been observed the objective is to determine the optimal order quantity in maximizing the expected resultant profit by considering the fuzzy demand and reordering strategy in the single period framework the solution procedure is presented using ordering of fuzzy numbers with respect to their possibilistic mean values numerical examples are given to illustrate the efficiency of this strategy

bifurcation and stability analysis of nonlinear waves in dn symmetric delay differential systems abstract in this paper a direct effective computation method is proposed on stability analysis of the bifurcating solutions in symmetric delay differential systems mechanism about multistability there coexist multiple nontrivial equilibria limit cycles is analyzed

floquet multipliers of a metastable rotating wave in a chua yang ring network abstract a ring of n 2 m identical neuron cells with piecewise linear and saturated bidirectional coupling nonlinearities is considered the rotating wave under investigation exists for most values of the coupling parameters 0 and the dominant floquet multiplier is unstable and converges exponentially to 1 in the number of cells the remaining 2 m 2 nontrivial floquet multipliers converge exponentially to 0 a heteroclinic bifurcation curve and also the heteroclinic orbit connections are described by explicit formulas the entire work was motivated by electrical circuit experiments

hofer s l geometry energy and stability of hamiltonian flows part i in this paper we first show that the necessary condition introduced in our previous paper is also a sufficient condition for a path to be a geodesic in the group ham c m of compactly supported hamiltonian symplectomorphisms this applies with no restriction onm we then discuss conditions which guarantee that such a path minimizes the hofer length our argument relies on a general geometric construction the gluing of monodromies and on an extension of gromov s non squeezing theorem both to more general manifolds and to more general capacities the manifolds we consider are quasi cylinders that is spaces homeomorphic tom d2 which are symplectically ruled overd2 when we work with the usual capacity derived from embedded balls we can prove the existence of paths which minimize the length among all homotopic paths provided thatm is semi monotone this restriction occurs because of the well known difficulty with the theory ofj holomorphic curves in arbitrarym however we can only prove the existence of length minimizing paths i e paths which minimize length amongstall paths not only the homotopic ones under even more restrictive conditions onm for example whenm is exact and convex or of dimension 2 the new difficulty is caused by the possibility that there are non trivial and very short loops in ham c m when such lengthminimizing paths do exist we can extend the bialy polterovich calculation of the hofer norm on a neighbourhood of the identity cl flatness

symmetric functional differential equations and neural networks with memory we establish an analytic local hopf bifurcation theorem and a topological global hopf bifurcation theorem to detect the existence and to describe the spatial temporal pattern the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry we apply these general results to obtain the coexistence of multiple large amplitude wave solutions for the delayed hopfield cohen grossberg model of neural networks with a symmetric circulant connection matrix

normal forms for retarded functional differential equations with parameters and applications to hopf bifurcation abstract the paper addresses for retarded functional differential equations fdes with parameters the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity the analysis is based on the theory previously developed for fdes without parameters by considering an extension of a phase space appropriate to the computation of these normal forms as an application the generic hopf bifurcation for scalar retarded fdes is considered

fuzzy production inventory for fuzzy product quantity with triangular fuzzy number abstract in this paper we consider the fundamental production inventory problem such that the product quantity is a triangular fuzzy number q q 1 q 0 g 2 where q1 q0 1 q2 q0 2 suppose q denotes the crisp economic product quantity in the classical production inventory model and we assume 0 1 0 2 or 0 1 0 2 according to two relations of q and q1 q0 q2 q1 f q y of the fuzzy cost function f q and their centroid then obtain the economic product quantity q in the fuzzy sense

euler maclaurin with remainder for a simple integral polytope we give an euler maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope we prove this formula by elementary methods

on the topological properties of symplectic maps in this paper we show that symplectic maps have surprising topological properties in particular we construct an interesting metric for the symplectic diffeomorphism groups which is related but not obviously to the topological properties of symplectic maps and phase space geometry we also prove a certain number of generalised symplectic fixed point theorems and give an application to a hamiltonian system

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

fuzzy multi product constraint newsboy problem in this paper we consider the multi product newsboy problem with fuzzy demands under budget constraint since the demands of products are often fuzzy in real life the profit of the newsboy is fuzzy too we develop three types of models under different criteria evm model dcp model and ccp model in these models the objective functions are to maximize the expected profit of newsboy the chance of achieving a target profit and the profit which satisfies some chance constraints with at least some given confidence level respectively furthermore the hybrid intelligent algorithm based on genetic algorithm and fuzzy simulation is designed for these models and some illustrating examples are given in order to show the application of these proposed models and algorithm

a class of fuzzy rough expected value multi objective decision making model and its application to inventory problems in this paper we concentrate on developing a fuzzy rough multi objective decision making model according to fuzzy rough theory then we prove the existence of a solution of the fuzzy rough multi objective decision making model formulated next we develop an effective algorithm to solve the fuzzy rough expected value multi objective decision making model concerning the inventory problem and prove the convergence of the proposed algorithm finally these are applied to practical inventory problem in which all inventory costs purchasing and selling prices in the objectives and constraints are assumed to be fuzzy rough in nature comparing the results with those from the fuzzy multi objective decision making model we reach that the proposed fuzzy rough multi objective decision making model and algorithm which will be of much use to management and provide significant solutions to construct other inventory models with fuzzy rough variables in real life

normal forms for retarded functional differential equations and applications to bogdanov takens singularity abstract the paper addresses for retarded functional differential equations fdes the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity a phase space appropriate to the computation of these normal forms is introduced and adequate nonresonance conditions for the computation of the normal forms are derived as an application the general situation of bogdanov takens singularity and its versal unfolding for scalar retarded fdes with nondegeneracy at second order is considered both in the general case and in the case of differential delay equations of the form t x t x t 1

the multiplier equation and its application to s solutions of a differential delay equation stability and uniqueness of slowly oscillating periodic solutions are two important questions concerning differential delay equations it is suggested in 6 that these two problems are closely related to each other although many results on the existence of such solutions have been established see 7 and refs therein results on their uniqueness and stability are comparatively few even in the simplest cases a slowly oscillating periodic or sop solution of

on possibilistic mean value and variance of fuzzy numbers dubois and prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions in this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval valued possibilistic mean and investigate its relationship to the interval valued probabilistic mean we also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions which are consistent with the extension principle we also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

geometry of nonlinear connections abstract we show that locally diffeomorphic exponential maps can be defined for any second order differential equation and give a possibly nonlinear covariant derivative for any possibly nonlinear connection we introduce vertically homogeneous connections as the natural correspondents of homogeneous second order differential equations we provide significant support for the prospect of studying nonlinear connections via certain closely associated second order differential equations one of the most important is our generalized ambrose palais singer correspondence

economic order quantity in fuzzy sense for inventory without backorder model abstract this paper investigates a group of computing schemas for economic order quantity as fuzzy values of the inventory without backorder we express the fuzzy order quantity as the normal triangular fuzzy number q 1 q 0 q 2 and then solve the aforementioned optimization problem we find that after defuzzification the total cost is slightly higher than in the crisp model however it permits better use of the economic fuzzy quantities arising with changes in orders deliveries and sales

the geometry of symplectic energy non squeezing theorem which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form r2 x b2 where b2 is a 2 disc this led to hofer s discovery of symplectic capacities which give a way of measuring the size of subsets in symplectic manifolds recently hofer found a way to measure the size or energy of symplectic diffeomorphisms by looking at the total variation of their generating hamiltonians this gives rise to a bi invariant pseudo norm on the group ham m of compactly supported hamiltonian symplectomorphisms of the manifold m the deep fact is that this pseudo norm is a norm in other words the only symplectomorphism on m with zero energy is the identity map up to now this had been proved only for sufficiently nice symplectic manifolds and by rather complicated analytic arguments in this paper we consider a more geometric version of this energy which was first considered by eliashberg and hofer in connection with their study of the extent to which the interior of a region in a symplectic manifold determines its boundary we prove by a simple geometric argument that both versions of energy give rise to genuine norms on all symplectic manifolds roughly speaking we show that if there were a symplectomorphism of m which had too little energy one could embed a large ball into a thin cylinder m x

multi objective decision making model under fuzzy random environment and its application to inventory problems in this paper we concentrate on developing a fuzzy random multi objective model about inventory problems by giving some definitions and discussing some properties of fuzzy random variable we design a method of solving solution sets of fuzzy random multi objective programming problems these are applied to numerical inventory problems in which all inventory costs purchasing and selling prices in the objectives and constraints are assumed to be fuzzy random variables in nature and then the impreciseness of fuzzy random variables in the above objectives and constraints are transformed into fuzzy variables which are similar trapezoidal fuzzy numbers the exact parameters of fuzzy membership function and probability density function can be obtained through fuzzy random simulating the past dates by comparing the results with those from the fuzzy multi objective models we believe that the proposed fuzzy random multi objective model and hybrid intelligent algorithm provide significant solutions to construct other inventory models with fuzzy random variables in real life

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

characteristic multipliers and stability of symmetric periodic solutions of x t g x t 1 on etudie l equation differentielle scalaire a retard x t g x t 1 a retroaction negative on suppose que la fonction non lineaire g est impaire et monotone on demontre que des solutions periodiques x t de type legerement oscillant satisfaisant la condition de symetrie x t x t 2 t r sont non degenerees et ont toutes des multiplicateurs de floquet non triviaux dans le cercle unite

patterns in hierarchical networks of neuronal oscillators with d3 z3 symmetry abstract in this paper we consider a hierarchically organized network composed of three interacting systems each of which consists of three coupled oscillators this hierarchical network is equivariant under the symmetry group d 3 z 3 using the lattice of isotropy subgroups we study the reduced equations restricted to invariant fixed point subspaces and prove that it is possible for the oscillator network to have 4 distinct equilibria or 45 distinct periodic solutions with maximal isotropy subgroups these are classified and their bifurcation directions are determined in terms of the quadratic coefficients and relevant quantities a center manifold reduction from the hierarchical network to the normal form equations is then performed in order to investigate the codimension two bifurcations using this reduction we find a great variety of equilibria periodic and quasi periodic oscillation patterns of maximal and submaximal symmetry which can be classified in a two level pattern hierarchy

a single period inventory model with fuzzy demand abstract the single period inventory models have wide applications in the real world in assisting the decision maker to determine the optimal quantity to order due to lack of historical data the demand has to be subjectively determined in many cases in this paper a single period inventory model for cases of fuzzy demand is constructed the costs considered include the procurement cost shortage cost and holding cost for different fuzzy total cost resulted from different order quantity a method for ranking fuzzy numbers is adopted to find the optimal order quantity in terms of the cost when the profit gained from selling one item is less greater than the loss incurred due to one unsold item the optimal order quantity lies in the range defined for the left shape right shape function of the fuzzy demand if the unit profit is equal to the unit loss then all quantities with a membership grade 1 are optimal to be ordered the methodology of this paper can be applied to construct other inventory models with fuzzy demand

a robust lot sizing problem with ill known demands the paper deals with a lot sizing problem with ill known demands modeled by fuzzy intervals whose membership functions are possibility distributions for the values of the uncertain demands optimization criteria in the setting of possibility theory that lead to choose robust production plans under fuzzy demands are given some algorithms for determining optimal robust production plans with respect to the proposed criteria and for evaluating production plans are provided some computational experiments are presented

frustration stability and delay induced oscillations in a neural network model the effect of time delays on the linear stability of equilibria in an artificial neural network of hopfield type is analyzed the possibility of delay induced oscillations occurring is characterized in terms of properties of the not necessarily symmetric connection matrix of the network such oscillations are possible exactly when the network is frustrated equivalently when the signed digraph of the matrix does not require the perron property nonlinear analysis centre manifold computation of a three unit frustrated network is presented giving the nature of the bifurcations taking place a supercritical hopf bifurcation is shown to occur and a codimension two bifurcation is unfolded

fuzzy inventory with or without backorder for fuzzy order quantity with trapezoid fuzzy number abstract the purpose of this paper is to investigate a group of computing schemas for the economic order quantity as fuzzy values of the inventory with without backorder we express the fuzzy order quantity as the normal trapezoid fuzzy number q 1 q 2 q 3 q 4 and then we solve the aforementioned optimization problem we find that after defuzzification the total cost is slightly higher than in the crisp model however it permits better use of the economic fuzzy quantities arising with changes in orders and deliveries

hopf bifurcating periodic orbits in a ring of neurons with delays in this paper we consider a ring of neurons with self feedback and delays the linear stability of the model is investigated by analyzing the associated characteristic transcendental equation based on the normal form approach and the center manifold theory we derive the formula for determining the properties of hopf bifurcating slowly oscillating periodic orbits for a ring of neurons with delays including the direction of hopf bifurcation stability of the hopf bifurcating slowly oscillating periodic orbits and so on moreover by means of the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups we not only investigate the effect of synaptic delay of signal transmission on the pattern formation but also obtain some important results about the spontaneous bifurcation of multiple branches of periodic solutions and their spatio temporal patterns

finite time stability for a class of fractional order fuzzy neural networks with proportional delay abstract in this paper we consider a class of fuzzy neural networks of fractional order and proportional time delay we derive sufficient conditions for the finite time stability of the considered system using finite time stability theory and fractional calculus and employing differential inequality techniques the results are obtained in terms of simple algebraic inequalities which can be easily verified in the end we give a numerical example to validate the analytical findings

stability of nonlinear waves in a ring of neurons with delays abstract in this paper we consider a ring of identical neurons with self feedback and delays based on the normal form approach and the center manifold theory we derive some formula to determine the direction of hopf bifurcation and stability of the hopf bifurcated synchronous periodic orbits phase locked oscillatory waves standing waves mirror reflecting waves and so on in addition under general conditions such a network has a slowly oscillatory synchronous periodic solution which is completely characterized by a scalar delay differential equation despite the fact that the slowly oscillatory synchronous periodic solution of the scalar equation is stable we show that the corresponding synchronized periodic solution is unstable if the number of the neurons is large or arbitrary even