an automata theoretic decision procedure for the propositional mu calculus the propositional mu calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of fischer and ladner the infinite looping construct of streett and the game logic of parikh we give an elementary time decision procedure using a reduction to the emptiness problem for automata on infinite trees a small model theorem is obtained as a corollary

the greatest fixed points and rational omega tree languages abstract rational omega tree languages are defined by extending the notion of rational or regular expressions for languages and their properties are investigated they are characterized by means of greatest fixed points of certain functions and are shown to be precisely the omega tree languages recognized by rabin s special automata a simple normal form for rational omega tree languages is also presented

an interpolating by pass to pareto optimality in intuitionistic fuzzy technique for a eoq model with time sensitive backlogging abstract this article fuzzyfies eoq crisp model with backlogged while demand of the customers varies with selling price and promotional effort the demand rate in stock out situation decreases with duration of the shortage period and it comes back to its initial rate since promotional effort continues the cost function consists of set up cost inventory cost shortage cost and cost for promotional effort the coefficient vectors of the concerned minimization cost function are considered as fuzzy numbers which are transformed into interval numbers then the interval objective function has been transformed into a classical multi objective eoq model using intuitionistic fuzzy technique a comparative study on pareto optimality and optimality under lagrange s interpolating polynomial function has been made illustrating numerical example

simple modules of the witten woronowicz algebra abstract it was proved in v v bavula d a jordan trans amer math soc 353 2 2001 769 794 that witten s second deformation and woronowicz s deformation are isomorphic algebras for a class of generalized weyl algebras including the two deformations above simple modules are being classified up to irreducible elements of certain noncommutative euclidean rings

optimization of fuzzy production inventory models in this paper we introduce two fuzzy production inventory models with fuzzy parameters for crisp production quantity or for fuzzy production quantity the fuzzy total production inventory costs of these models under the fuzzy arithmetical operations of function principle are proposed the final purpose is to find optimal solutions of these models by using graded mean integration representation method for defuzzifing fuzzy total production inventory cost and by using extension of the lagrangean method for solving inequality constrain problem furthermore we find that the optimal solutions are all crisp real numbers in addition when the fuzzy parameters fuzzy inventory cost fuzzy demand fuzzy setup cost fuzzy demand rate and fuzzy production rate are all crisp real numbers the optimal solutions of our proposed models can be specified to meet classical production inventory models

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

backorder fuzzy inventory model under function principle in this paper the fuzzy inventory model is discussed especially in the case of permitting backorder under the fuzzy environment of fuzzy demand fuzzy order cost fuzzy inventory cost and fuzzy backorder cost we use the function principle instead of the extension principle to calculate the total fuzzy inventory cost we also apply the median rule to find the optimal economic order quantity eoq and shortage quantity

simulating alternating tree automata by nondeterministic automata new results and new proofs of the theorems of rabin mcnaughton and safra abstract we give a proof that alternating tree automata can be simulated by nondeterministic tree automata which yields new complexity results and a unified proof of the theorems of rabin mcnaughton and safra we also give a simple axiomatic framework for uniformizing strategies

equivalences and transformations of regular systems applications to recursive program schemes and grammars abstract this work presents a unified theory of recursive program schemes context free grammars grammars on arbitrary algebraic structures and in fact recursive definitions of all kind by means of regular systems the equivalences of regular systems associated with either all their solutions or their least solutions in all domains of appropriate type satisfying a set of algebraic laws expressed by equations are systematically investigated and characterized in some cases in terms of system transformations by folding unfolding and rewriting according to the equational algebraic laws grammars are better characterized in terms of polynomial systems which are regular systems involving the operation of set union and the same questions are raised for them we also examine conditions insuring the uniqueness of the solution of a regular or of a polynomial system this theory applies to grammars of many kinds which generate trees graphs etc we formulate some classical transformations of context free grammars in terms of correct transformations which only use folding unfolding and algebraic laws and we immediately obtain their correctness

a single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints abstract this paper develops a mathematical model for a single period multi product manufacturing system of stochastically imperfect items with continuous stochastic demand under budget and shortage constraints after calculating expected profit in general form in terms of density functions of the demand and percentage of imperfectness particular expressions for those density functions are considered here the constraints are of three types i both are stochastic ii one stochastic and other one imprecise fuzzy and iii both imprecise the stochastic constraints have been represented by chance constraints and fuzzy constraints in the form of possibility necessity constraints stochastic and fuzzy constraints are transformed to equivalent deterministic ones using here and now approach and fuzzy relations respectively the deterministic problems are solved using a non linear optimization technique generalized reduced gradient method the model is illustrated through numerical examples sensitivity analyses on profit functions due to different permitted aspiration and confidence levels are presented

the alternation hierarchy in fixpoint logic with chop is strict too fixpoint logic with chop extends the modal calculus with a sequential composition operator which results in an increase in expressive power we develop a game theoretic characterisation of its model checking problem and use these games to show that the alternation hierarchy in this logic is strict the structure of this result follows the lines of arnold s proof showing that the alternation hierarchy in the modal calculus is strict over the class of binary trees

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

de concini kac filtration and gelfand tsetlin generators for quantum gln abstract in this note we compute the leading term with respect to the de concini kac filtration of u q gl n of a generating set for the quantum gelfand tsetlin subalgebra

quantification de la localisation de dixmier de u sln 1 c resume in this article we extend to the quantum case the classical result of dixmier according to which up to localization the enveloping algebra of sl n 1 c is a central polynomial extension of the enveloping algebra of some parabolic subalgebra in fact the latter has a semiinvariant element d by which it is sufficient to localize to obtain the result the methods we use here are quite different from those used by dixmier indeed in the quantum case the powers of the indeterminate q would make calculations similar to those of dixmier much too complicated on the other hand when we use the rosso form which allows us to work in the hopf dual of q sl n 1 c the calculations become much easier than they would be in q sl n 1 c

continuous review inventory model in mixed fuzzy and stochastic environment in this paper we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting since demand plays an important role in such type of inventory systems we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand after fuzzifying the random lead time demand we consider the annual average demand as a fuzzy random variable we provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value since the expected value of a fuzzy random variable is a fuzzy quantity a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution a numerical example is presented to illustrate the proposed model

galois orders in skew monoid rings abstract we introduce a new class of noncommutative rings galois orders realized as certain subrings of invariants in skew semigroup rings and develop their structure theory the class of galois orders generalizes classical orders in noncommutative rings and contains many important examples such as the generalized weyl algebras the universal enveloping algebra of the general linear lie algebra associated yangians and finite w algebras

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

fuzzy periodic review system with fuzzy random variable demand in this paper a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously a model has been developed with customer demand assumed to be a fuzzy random variable the lead time has been assumed to be a constant the lead time demand and the lead time plus one period s demand have also been assumed to be fuzzy random variables a methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized a numerical example has been presented to illustrate the model

fixed point characterization of context free languages several concepts of context freeness of sets of finite infinite words are characterized by means of greatest solutions of systems of equations of the form xi gi i 1 n where gi is a not necessarily finite union of monomials consideration of the systems with the components gi context free regular or finite leads to characterizations of the following classes of languages the kleene closure of the family of context free languages algebraic languages infinitely generated by context free grammars in the sense of nivat 1977 and cantor like topological closures of context free languages respectively

the gelfand kirillov conjecture and gelfand tsetlin modules for finite w algebras abstract we address two problems with the structure and representation theory of finite w algebras associated with general linear lie algebras finite w algebras can be defined using either kostant s whittaker modules or a quantum hamiltonian reduction our first main result is a proof of the gelfand kirillov conjecture for the skew fields of fractions of finite w algebras the second main result is a parameterization of finite families of irreducible gelfand tsetlin modules using gelfand tsetlin subalgebra as a corollary we obtain a complete classification of generic irreducible gelfand tsetlin modules for finite w algebras

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

fixed point characterization of infinite behavior of finite state systems abstract infinite behavior of nondeterministic finite state automata running over infinite trees or more generally over elements of an arbitrary algebraic structure is characterized by a calculus of fixed point terms interpreted in powerset algebras these terms involve the least and greatest fixed point operators and disjunction as the only logical operation a tight correspondence is established between a hierarchy of rabin indices of automata and a hierarchy induced by alternation of the least and greatest fixed point operators it is shown that in the powerset algebra of trees constructed from a set of functional symbols the fixed point hierarchy is infinite unless all the symbols are unary i e trees are words it is also shown that an interpretation of a closed fixed point term in any powerset algebra can be factorized through the interpretation of this term in the powerset algebra of trees from which it is deduced that the question whether a term denotes always can be answered in polynomial time

a multi objective decision making model with fuzzy rough coefficients and its application to the inventory problem in this paper we concentrate on developing a fuzzy rough multi objective decision making model according to uncertainty theory we present some equivalent models and a traditional algorithm based on an interactive fuzzy satisfying method which is similar to the interactive fuzzy rough satisfying method in order to obtain a satisfying solution for the decision maker in addition the technique of fuzzy rough simulation is applied to deal with general fuzzy rough objective functions and fuzzy rough constraints which are usually difficult to convert into their equivalents furthermore combined with the techniques of fuzzy rough simulation a genetic algorithm using the compromise approach is designed for solving a fuzzy rough multi objective programming problem finally a model is applied to an inventory problem to illustrate the usefulness of the proposed model and algorithm and then a sensitivity analysis is made