design of a fuzzy finite capacity queuing model based on the degree of customer satisfaction analysis and fuzzy optimization due to uncontrollable factors the parameters in the queuing models may be uncertain and so in this paper we present the design of a fuzzy finite capacity queuing model in which the arrival pattern and the service pattern follow an exponential distribution under uncertain parameter as for the design of the system the criterion of optimization proposed is aimed at the optimum selection of the number of servers with the goal of providing a high degree of satisfaction to clients when they join the system this optimization process will be solved through markov chains with fuzzy state the validity of the procedure proposed to incorporate fuzzy data in this queuing system is confirmed by a fuzzy simulation experiment of the differential equations which govern the behaviour of the model by the bontempi s qua si iii algorithm the extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informative results and wider knowledge on the behaviour of the system since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information that is why the finite capacity queuing models with uncertain data can have a broader range of applications

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

the yang mills equations on the universal cosmos global existence and regularity of solutions for the yang mills equations on the universal cosmos m which has the form r1 s3 for each of an 8 parameter continuum of factorizations of m as time space are treated by general methods the cauchy problem in the temporal gauge is globally soluble in its abstract evolutionary form with arbitrary data for the field potential in l2 r s3 l2 r 1 s3 where r is an integer 1 and l2 r denotes the class of sections whose first r derivatives are square integrable if r 1 the problem is soluble locally in time when r is 3 or more the solution is identifiable with a classical one if infinite the solution is in c m these results extend earlier work and approaches 1 5 solutions of the equations on minkowski space time m0 extend canonically modulo gauge transformations to solutions on m provided their cauchy data are moderately smooth and small near spatial infinity precise asymptotic structures for solutions on m0 follow and in turn imply various decay estimates thus the energy in regions uniformly bounded in direction away from the light cone is o x0 5 where x0 is the minkowski time coordinate analysis solely in m0 8 9 earlier yielded the estimate o x0 2 applicable to the region within the light cone similarly it follows that the action integral for a solution of the yang mills equations in m0 is finite in fact absolutely convergent

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

analysis in space time bundles iii higher spin bundles the universal cosmos m is the unique four dimensional globally causal space time manifold to which the dirac and maxwell equations among others maximally and covariantly extend a systematic treatment is presented of general fields over m of arbitrary spin considered are fields induced from all irreducible representation of the isotropy group scale extended poincare group to g the connected causal group of m restricted to any species of such fields the k invariant canonical dirac operator k maximal essentially compact subgroup of g is shown g covariant for a unique conformal weight a normalized k finite basis for such fields is constructed the basis actions thereon of the dirac operator infinitesimal generators of g discrete symmetries second order casimir and the essentially unique third order noncentral quantum number enveloping algebra element invariant under k are derived composition series under g of a class of these field spaces namely the extension to m of the relativistic fields considered by bargman and wigner or arbitrary spin and conformal weight are determined distinguishing by invariance and causality features alone the essentially conventional positive energy mass 0 subspaces and massive invariant sub quotient spaces whose unitarity under g is given a new proof the completely positive subclass cf below of representations is determined a more detailed treatment of spin one bundles vector and two form of arbitrary conformal weight is included the exterior derivative transformations are diagonalized and the conformally invariant massive spin one scalar product is identified with a mathematical version of the conventional electromagnetic field lagrangian

relations between perron frobenius results for matrix pencils two different generalizations of the perron frobenius theory to the matrix pencil ax bx are discussed and their relationships are studied in one generalization which was motivated by economics the main assumption is that b a 1a is nonnegative in the second generalization the main assumption is that there exists a matrix x 0 such that a bx the equivalence of these two assumptions when b is nonsingular is considered for b 1a 1 a complete characterization involving a condition on the di graph of b 1a is proved it is conjectured that the characterization holds for b 1a 1 and partial results are given for this case

optimizing a priority discipline queueing model using fuzzy set theory the aim of this paper is to provide a more realistic description of priority discipline queueing models by using fuzzy set theory it develops and optimizes two fuzzy queueing models with priority discipline a model with nonpreemptive priorities system and a model with preemptive priorities system denoted by m i m i 1 and m i f i 1 the first symbol is for a queueing system where arrivals and services from a single server follow a poisson process with fuzzy parameter and the last symbol is for a queueing model with arrivals follows a poisson process with fuzzy rate and fuzzy deterministic service rate zadeh s extension principle is the basic approach to this research into fuzzy stochastic processes our results are the basis for a discussion of optimal selection of priority discipline two fuzzy queueing systems that are commonly found in real situations are solved and serve as examples that highlight the validity of the procedure we propose fuzzy queueing models are more realistic than the crisp queues that are commonly used in reality furthermore extending queueing models to the fuzzy environment widens their scope of application

the revised method of ranking fuzzy numbers with an area between the centroid and original points in 2002 chu and tsao proposed a method to rank fuzzy numbers they employed an area between the centroid and original points to rank fuzzy numbers however there were some problems with the ranking method in this paper we want to indicate these problems of chu and tsao s method and then propose a revised method which can avoid these problems for ranking fuzzy numbers since the revised method is based on the chu and tsao s method it is easy to rank fuzzy numbers in a way similar to the original method

analysis in space time bundles iv natural bundles deforming into and composed of the same invariant factors as the spin and form bundles abstract we study two interesting new bundles over the universal cosmos m or maximal isotropic space time which may be physically applicable the treatment is from a homogeneous vector bundle point of view and uses the notation and some of the results of the treatment in papers i iii s m paneitz and i e segal j funct anal 47 1982 78 142 49 1982 335 414 54 1983 18 22 of conventional bundles over m the spannor bundle deforms into essentially the usual spinor bundle as a conformally invariant parameter that may be interpreted as the space curvature becomes arbitrarily small from a minkowski space standpoint however the spannors involve a nontrivial action of space time translations that deforms into a trivial action in the spinor limit and also have more complex transformation properties under discrete symmetries also studied are the plyors consisting of the dual to the bundle product of the spannors with themselves composition series for the spannor and plyor section spaces are treated relative to the conformal group and irreducible subquotients are identified with certain that occur in conventional bundles in particular factors corresponding to the maxwell and massless dirac equations and which may represent certain of the observed elementary particles are determined a gauge and conformally invariant nonlinear coupling between spannors and plyors constituting essentially a generalization of that used in quantum electrodynamics is developed and an associated invariant nonlinear partial differential equation is derived covariant and causal quantization for spannors as fermions and plyors as bosons is formulated algebraically the present treatment is basically mathematical but physical motivations and possible interpretations are briefly noted

on using a cuts to evaluate fuzzy equations abstract consider an equation y f x1 xn where the extension principle is used to find y f x 1 x n when we subtitute fuzzy numbers x i for the xi 1 i n if x i denotes an cut of x i then we argue that for only certain simple equations will one obtain y equal to f x 1 x n where f is evaluated using interval arithmetic

a mathematical programming approach to the machine interference problem with fuzzy parameters abstract machine interference is an important problem frequently encountered in production and manufacturing operations such as semiconductor manufacturing and maintenance operations due to uncontrollable factors parameters in the machine interference problem may be fuzzy this paper proposes a mathematical programming approach to construct the membership function of the performance measure of the machine interference system with the machine breakdown rate and the service rate being fuzzy numbers on the basis of the extension principle a pair of mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy performance measure at possibility level by enumerating different values of the membership function of the system performance measure is constructed a numerical example is solved successfully to demonstrate the validity of the proposed approach since the performance measure is completely described by a membership function rather than by a crisp value the fuzziness of input parameters is conserved completely thus more information is provided for designing manufacturing systems the successful extension of machine interference models to fuzzy environments permits machine interference models to have wider practical applications

ranking fuzzy numbers based on decomposition principle and signed distance by using the decomposition principle and the crisp ranking system on r we construct a new ranking system for fuzzy numbers which is very realistic and also matching our intuition as in r

optimal selection of the service rate for a finite input source fuzzy queuing system finite input source queuing models have a wide range of applications in many practical situations and are frequently found in machine maintenance and repair operations owing to uncontrollable factors finite input source queuing problems parameters may contain uncertainty that is why to begin with in this paper it is proposed the analysis development and design of a fuzzy queuing model with finite input source in which the arrival pattern as well as the service pattern follow an exponential distribution under uncertain parameter in order to design the system the established optimization criterion consists in determining the optimal number of servers so as to minimize the expected total cost function per unit time to choose among uncertain alternatives three techniques to make decisions under uncertainty are proposed this type of systems has a finite waiting line as a result the system of differential equations that governs the model s behaviour consists of a finite number of equations in the second place this feature of the finite input source queuing systems enables us to bring forward in this paper two new contributions i in the first one the following doubt has been raised and solved if the convergence of the probabilities email protected i t obtained from the fuzzy differential equations that govern the behaviour of the finite source system is worked out does the result match the steady state fuzzy probabilities obtained by applying zadeh s extension principle to the classic queuing model and ii it has been performed a fuzzy simulation experiment on the differential equations using bontempi s qua si iii algorithm this enables us to know the time evolution of the probabilities email protected i t and its convergence on the one hand on the other we can compare the results of the simulation to those analytically obtained by applying zadeh s extension principle this way the validity of the proposed procedure for the simulation is verified by means of the theoretical results the extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informing results and wider knowledge on the behaviour of the system since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information that is why the finite input source queuing models with uncertain data can be of more use and can have a broader range of applications

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

real spinor fields and the electroweak interaction the space of real spinor fields of a given massm 0 in minkowski space is the direct sum of two irreducibly invariant subspaces under the connected poincare groupp these subspaces admit uniquep invariant positive energy complex unitarizable structures in terms of which they are unitarily and canonically equivalent to the conventional left electron and right positron subspaces defined by the dirac equation space reversalpand time reversaltactp covariantly as antiunitary operators on the real fields they also extend to the complex fields in terms of whichpexchanges the two subspaces whiletacts separately on each whenm 0 the identical formalism produces a rigorous version of the conventional neutrino formalism the restriction to the real context of the conventional spinor vector interaction is equivalent to the conventionalv ainteraction together with a computationally equivalent form of quantum electrodynamics in which the right electron and left electron are redundant

spinor currents as vector particles abstract we study a prototype for the problem of determining the irreducible factors of the spaces spanned by currents between homogeneous vector bundles more specifically let g denote the conformal group of minkowski space time m 0 or more precisely su 2 2 it is shown that the positive energy unitary g irreducible massive factors of the one form bundle over the conformal compactification of m 0 are bundle equivalent to spaces spanned by currents of the spinor bundle this has the interpretation that the z particle may be modelled by the representation of g of lowest k type lkt 3 emsp14 1 2 1 2 where k su 1 su 2 su 2 and m j j refers to the representation in which the lowest eigenvalue of the su 1 generator is m while j and j are the spins of the left and right su 2 representations in particular this z representation is bundle equivalent to the representation of g in a space of currents between neutrinos of lkt 3 2 0 1 2 and antineutrinos of lkt 3 2 1 2 0 the w particle representation may similarly be modelled by the representation of g of lowest k type 4 0 0 the only other massive positive energy unitary factor of the one form bundle in particular the w is equivalent to a space of currents between the electron of lkt 5 2 0 1 2 and the antineutrino these results are consistent with the possibility that all quasi stable elementary particles may be modelled by similar subspaces of bundle products

elementary queueing theory based on possibility theory abstract we consider a queueing system with multiple parallel servers finite or infinite system capacity and calling source but whose arrivals and service completions are governed by a possibility distribution changes in the number of customers in the system is modeled by a transition matrix and powers of under max min product produce if it converges the steady state possibility distribution results are applied to the machine servicing problem to determine the most economical size of the repair crew

parametric nonlinear programming approach to fuzzy queues with bulk service this paper proposes a procedure to construct the membership functions of the performance measures in bulk service queuing systems with the arrival rate and service rate are fuzzy numbers the basic idea is to transform a fuzzy queue with bulk service to a family of conventional crisp queues with bulk service by applying the cut approach on the basis of cut representation and the extension principle a pair of parametric nonlinear programs is formulated to describe that family of crisp bulk service queues via which the membership functions of the performance measures are derived to demonstrate the validity of the proposed procedure two fuzzy queues often encountered in transportation management are exemplified since the performance measures are expressed by membership functions rather than by crisp values they completely conserve the fuzziness of input information when some data of bulk service queuing systems are ambiguous thus the proposed approach for vague systems can represent the system more accurately and more information is provided for designing queuing systems in real life by extending to fuzzy environment the bulk service queuing models would have wider applications

time value of delays in unreliable production systems with mixed uncertainties of fuzziness and randomness abstract this paper proposes a parametric programming approach to address the notion of the time value of delays in the presence of mixed random and fuzzy uncertainties that result from unreliable systems to consider different types of delay time values the system states are appropriately and carefully identified and defined and a cost based fuzzy decision model that incorporates several unreliability factors is constructed then the proposed model is transformed into a pair of nonlinear programs parameterized by the possibility level to identify the lower and upper bounds on the minimal total cost per unit time at and thus construct the membership function to provide analytical expressions a special case with analytical results is also presented in contrast to existing studies the results derived from the proposed solution procedure conserve the fuzziness of the input information representing a significant difference from the crisp results obtained using approaches based on probability theory the results indicate that the proposed approach can provide more precise information to managers and improve decision making in practical system design

group inverses of m matrices associated with nonnegative matrices having few eigenvalues abstract we continue here earlier investigations of the structure of group generalized inverses a of singular and irreducible m matrices a ri m where m is an n n nonnegative and irreducible matrix whose spectral radius is r and where m is assumed to belong to one of several special classes of nonnegative matrices we now focus on cases where m has only a few distinct eigenvalues we are particularly interested in instances of such matrices m which cause all or almost all of the off diagonal entries of the corresponding a to be nonpositive we then apply our results to the study of the sign pattern of the off diagonal entries of the group generalized inverse of a ri m where m comes from one of the following families of nonnegative matrices 1 the magic square of order n 4k generated by matlab 2 the doubly regular tournament matrices the latter type is an example of a special type of a nonnegative matrix m for which the group inverse of the associated m matrix satisfies a a t for some 0

harmonic analysis on spannors the spannor representation of the universal covering group of the conformal group of minkowski space time is studied herein it is an example of an indecomposable representation various parallelizations for spannors are described normalized k finite basis fields for the spannors are introduced and a computation of the actions of the scale generator and other generators of the conformal group on these basis fields is given the irreducibility of all irreducible composition factors is established and it is decided which ones are infinitesimally unitary two sets of generators for maximal abelian subalgebras of the enveloping algebra of the conformal group are introduced the action of one of the sets on k finite basis fields in the spannor representation is studied this is important for understanding of the problem of degeneracy in the spannor representation since k types occur with multiplicity 2 many calculations make use of the lowest highest weight module structures of the unitarizable and positive negative energy irreducible composition factors and thus many of our results and techniques can be used to initiate a study of the quantum deformations of the associated lie algebra representations results on the poincare content of the unitarizable irreducible composition factors are stated and unitary equivalences between certain of these factors are established

a characterization of the extension principle abstract we provide an alternative characterization of the extension principle of fuzzy sets this characterization is based upon using relations to represent mappings we apply this new characterization to develop an extension for non deterministic mappings

derivatives of the perron root at an essentially nonnegative matrix and the group inverse of an m matrix abstract the results of the work in this paper can be divided into two major parts in the first part we develop formulae using group inverses of irreducible m matrices for the second order partial derivatives with respect to the entries of the perron root r at an essentially nonnegative and irreducible matrix a we use these formulae to obtain explicit expressions for the matrices 2 r a ij 2 and 2 r a ii jj and examine these expressions at some special cases when for example in addition to a being essentially nonnegative and irreducible a is row stochastic or a is of rank 1 and so on in the second major part of this paper we investigate for a singular and irreducible m matrix q a certain matrix g which is a positive diagonal scaling of the group inverse q of q we show for instance that z gz 0 for all real vectors z and use this result and some of the formulae obtained in the first part of the paper to provide a matrix theoretic proof of a theorem due to j e cohen math proc cambridge philos soc 86 1979 343 350 which states that for an essentially nonnegative and irreducible matrix a the perron root is a convex function of the main diagonal of a

global stability in diallelic migration selection models abstract for diallelic migration selection models in continuous time with arbitrary migration in either discrete or continuous space a sufficient condition for the existence of a globally asymptotically stable equilibrium is established as a special case this condition includes concavity of the mean selection coefficient

the preference order of fuzzy numbers abstract many fuzzy number ranking approaches are developed in the literature for multiattribute decision making problems almost all of the existing approaches focus on quantity measurement of fuzzy numbers for ranking purpose in this paper we consider the ranking process to determine a decision maker s preference order of fuzzy numbers a new ranking index is proposed to not only take quantity measurement but incorporate quality factor into consideration for the need of general decision making problems for measuring quantity several cuts of fuzzy numbers are used a signal noise ratio is defined to evaluate quality of a fuzzy number this ratio considers the middle point and spread of each cut of fuzzy numbers as the signal and noise respectively a fuzzy number with the stronger signal and the weaker noise is considered better moreover the associated levels are treated as the degree of belief about the cut and used as weights in the index for strengthening the influence of cut with higher levels the membership functions of fuzzy numbers are not necessarily to be known beforehand while applying this index only a few left and right boundary values of cuts of fuzzy numbers are required we have proved the feature of the proposed index in a particular case several examples are also used to illustrate the feature and applicability in ranking fuzzy numbers

a stochastic approximation algorithm with varying bounds many optimization problems that are intractable with conventional approaches will yield to stochastic approximation algorithms this is because these algorithms can be used to optimize functions that cannot be evaluated analytically but have to be estimated for instance through simulation or measured thus stochastic approximation algorithms can be used for optimization in simulation unfortunately the classical stochastic approximation algorithm sometimes diverges because of unboundedness problems we study the convergence of a variant of stochastic approximation defined over a growing sequence of compact sets we show that this variant converges under more general conditions on the objective function than the classical algorithm while maintaining the same asymptotic convergence rate we also present empirical evidence that shows that this algorithm sometimes converges much faster than the classical algorithm

ranking and defuzzification methods based on area compensation abstract we present some interesting properties related to the area compensation procedure to compare fuzzy numbers it has been proved that this method produces more than a fuzzy interval order it induces a ranking of fuzzy numbers some further results are given about the transitivity property and about computational aspects extensions to non normal fuzzy numbers and fuzzy quantities are also proposed

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 sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

ranking of fuzzy numbers by sign distance several different strategies have been proposed for ranking of fuzzy numbers these include methods based on the coefficient of variation cv index distance between fuzzy sets centroid point and original point and weighted mean value each of these techniques has been shown to produce non intuitive results in certain cases in this paper we propose a modification of the distance based approach called the sign distance which is both efficient to evaluate and able to overcome the shortcomings of the previous techniques the calculation of the proposed method is far simpler than the other approaches

a simple approximation of productivity scores of fuzzy production plans this paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans the procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational

an approximate approach for ranking fuzzy numbers based on left and right dominance this study presents an approximate approach for ranking fuzzy numbers based on the left and right dominance the proposed approach only requires a few left and right spreads at some levels of fuzzy numbers to determine the respective dominance of one fuzzy number over the other the total dominance is then determined by combining the left and right dominance based on a decision maker s optimistic perspectives such a dominance is useful in ranking the fuzzy numbers when membership functions cannot be acquired the approach proposed herein is relatively simple in terms of computational efforts and is efficient when ranking a large quantity of fuzzy numbers by using a few left and right spreads two groups of examples demonstrate the accuracy and applicability of the proposed approach

ludwig elsner and his contributions to core applied and numerical linear algebra ludwig elsner was bona on 17 january 1939 in grog strehlitz upper silesia in germany he studied mathematics physics and astronomy at the universities of hamburg and freiburg and received his diploma in mathematics in 1963 at the university of hamburg as a member of the lively and inspiring group of lothar collatz in hamburg he worked on his ph d while holding a position at the computing center of the university of hamburg he received his ph d in 1965 and became an assistant professor at collatz institute of applied mathematics at the university of hamburg for six years during this period he spent one year 1968 1969 as senior officer at the csir in pretoria south africa in 1971 ludwig eisner became associate professor at the university of erlangen where he worked at the institute for applied mathematics until 1976 since 1976 he has been a full professor at the university of bielefeld where he has built up the numerical analysis group among many other activities in bielefeld he has twice been chairman of the department of mathematics and has planned and formed the numerical analysis group of the sonderforschungsbereich diskrete strukturen in der mathematik which since 1989 has attracted many specialists in linear algebra and numerical linear algebra to work with eisner in bielefeld numerous publications prove the success of these collaborative efforts

on convexity properties of the spectral radius of nonnegative matrices abstract elementary matrix theoretic proofs are given for the following well known results r d max re an eigenvalue of a d and s d ln e d a are convex here d is diagonal a a nonnegative n n matrix and the spectral radius

analysis in space time bundles i general considerations and the scalar bundle abstract mathematical features involved in the systematic development of elementary particle theory on an alternative cosmos space time are presented bundles representative of physical fields are studied in the unique variant of minkowski space m 0 enjoying similar properties of causality and symmetry the universal cosmos m is the universal cover of the causal compactification of m 0 the bundles studied are induced from representations of the scale extended poincare group which forms the isotropy group in m of the universal cover g s u 2 2 of the connected component of the group of all causal transformations on m discrete symmetries and higher dimensional cases are also discussed the primary focus is on the temporal evolution especially stability involving positivity of the energy wave equations implicative of finite propagation velocity and the unitarity and or composition series of associated actions of g general spin bundles on m are treated parallelized and correlated with bundles on m 0 associated covariant wave equations and the spectral resolution of fundamental quantum numbers are studied in detail in the scalar case

a pilot model in two dimensions for conformally invariant particle theory abstract the two dimensional analog of the mathematical model for elementary particles treated in this journal vol 75 1 57 is developed with greater explicitness than in the four dimensional case preliminary to quantization in part i the section space of the complex spannor bundle is studied invariant subspaces invariant forms and irreducible positive energy factors under the connected conformal group are determined transformation properties under discrete symmetries are also treated relations to the spinor bundle are treated the dirac operator is a canonical transform of the quadratic casimir on the spannor bundle and the section spaces have the same invariant factors at the same time the spinors constitute a deformation of the spannors two natural parallelizations of the spannor bundle and their intertwining operator are computed the irreducible factors of the spannor section space under the conformal group are determined by their restrictions to minkowski space and this group acts continuously in the l2 topology in contrast to its action on the spinor section space

a note on the perturbation of positive matrices by normal and unitary matrices abstract in a recent paper neumann and sze considered for an n n nonnegative matrix a the minimization and maximization of a s the spectral radius of a s as s ranges over all the doubly stochastic matrices they showed that both extremal values are always attained at an n n permutation matrix as a permutation matrix is a particular case of a normal matrix whose spectral radius is 1 we consider here for positive matrices a such that a n is a nonnegative matrix for all normal matrices n whose spectral radius is 1 the minimization and maximization problems of a n as n ranges over all such matrices we show that the extremal values always occur at an n n real unitary matrix we compare our results with a less recent work of han neumann and tastsomeros in which the maximum value of a x over all n n real matrices x of frobenius norm n was sought

an index for ordering fuzzy numbers abstract a new index that is useful for ordering ranking of fuzzy numbers is proposed to use this index the membership functions of fuzzy numbers need not be normal or convex properties of this index and its relationship to the 1981 yager s index are explained a numerical comparison between the proposed and four other ordering procedures is presented

a scaled stochastic approximation algorithm consider a stochastic system of such complexity that its performance can only be evaluated by using simulation or direct experimentation to optimize the expected performance of such systems as a function of several continuous input parameters decision variables we present a scaled stochastic approximation algorithm for finding the zero root of the gradient of the response function in each iteration of the scaled algorithm two independent gradient estimates are sampled at the current estimate of the optimal input parameter vector to compute a scale free estimate of the next search direction we establish sufficient conditions to ensure strong consistency and asymptotic normality of the resulting estimator of the optimal input parameter vector strong consistency is also established for a variant of the scaled algorithm with kesten s acceleration an experimental performance comparison of the scaled algorithm and the classical robbins monro algorithm in two simple queueing systems reveals some of the practical advantages of the scaled algorithm

analysis in space time bundles ii the spinor and form bundles abstract the structures of the spin and form bundles over the universal cosmos m and their relations with corresponding bundles over the minkowski space m 0 canonically imbedded in m are treated wave equations covariant with respect to the causal group g of m are studied their solution manifolds and other stable essentially positive energy invariant subspaces of the section spaces of the bundles are determined and the indecomposability of relevant invariant subspace chains is shown explicit parallelizations of the bundles are applied to the dirac and maxwell equations on m a basis for spinor fields that diagonalizes a complete set of k covariant quantum numbers k maximal essentially compact subgroup of g is developed local multilinear invariants of bundles over m are treated and specialized to convergent mathematical versions of the fermi and yukawa interaction lagrangians that are g invariant for the appropriate conformal weights

a new approach for ranking of trapezoidal fuzzy numbers ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems several strategies have been proposed for ranking of fuzzy numbers each of these techniques have been shown to produce non intuitive results in certain cases in this paper we will introduce a new approach for ranking of trapezoidal fuzzy numbers based on the left and the right spreads at some a levels of trapezoidal fuzzy numbers the calculation of the proposed method is far simpler and easier finally some comparative examples are used to illustrate the advantage of the proposed method

nonnegative alternating circulants leading to m matrix group inverses abstract let c be the set of all an n n nonnegative irreducible alternating circulant matrices we characterize a subset c of c such that if b c and the perron root of b is r then the group inverse ri b of the singular and irreducible m matrixri b is also an m matrix this is equivalent to the fact that for each such b the perron root at b is a concave function in each of the off diagonal entries the characterization for the case when n is odd presents more difficulties than for the case when n is even so the two cases are treated separately

conformal extension of massive wave functions abstract we extend from the massless to the massive case the canonical conformal mapping of solutions of wave equations in two dimensional minkowski space m 0 into the universal cover m of the conformal compactification m of m 0 there is a continuous poincare covariant map from the space of solutions of the klein gordon equation in m 0 to the dual of the space of analytic vectors for the action of the conformal group g su 1 1 su 1 1 on massive fields in m the extensions satisfy a corresponding wave equation in m as in the case of massless equations the extended solutions are periodic under the generator of the infinite cyclic center of the conformal group g in m the analysis involves the determination of the action of the chronometric temporal evolution i e the one parameter group of nonlinear transformations generated by the center of the maximal essentially compact subgroup of g on the fourier transforms of wave functions in minkowski space the analytic continuation of this evolution to complex times of positive imaginary part is represented by a hilbert schmidt operator whose kernel is determined in closed form fields of higher conformal weight associated with other discrete series representations of g are also treated in this respect

orlovsky s concept of decision making with fuzzy preference relation further results orlovsky s concept of decision making on a finite set of alternatives with a fuzzy preference relation is analysed several theorems which extend the possible effective application of that concept for optimization of many decision problems are formulated and proved new fuzzy relations are developed and their basic properties are investigated

ranking fuzzy numbers with an area between the centroid point and original point abstract to improve the ranking method of lee and li 1 cheng 2 proposed the coefficient of variation cv index shortcomings are also found in the cv index cheng 2 also proposed the distance method to improve the ranking method of murakami et al however the distance method is not sound either moreover the cv index contradicts the distance method in ranking some fuzzy numbers therefore to overcome the above shortcomings we propose ranking fuzzy numbers with the area between the centroid point and original point

on the spectral radius of positive operators on banach sequence spaces abstract let k 1 k n be infinite non negative matrices that define operators on a banach sequence space given a function f 0 0 0 of n variables we define a non negative matrix f k 1 k n and consider the inequality r f k 1 k n 1 n r k 1 r k n where r denotes the spectral radius we find the largest function f for which this inequality holds for all k 1 k n we also obtain an infinite dimensional extension of the result of cohen asserting that the spectral radius is a convex function of the diagonal entries of a non negative matrix

solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method abstract this paper proposes a mathematical programming method to construct the membership functions of the fuzzy objective value of the cost based queueing decision problem with the cost coefficients and the arrival rate being fuzzy numbers on the basis of zadeh s extension principle three pairs of mixed integer nonlinear programs minlp parameterized by the possibility level are formulated to calculate the lower and upper bounds of the minimal expected total cost per unit time at through which the membership function of the minimal expected total cost per unit time of the fuzzy objective value is constructed to provide a suitable optimal service rate for designing queueing systems the yager s ranking index method is adopted two numerical examples are solved successfully to demonstrate the validity of the proposed method since the objective value is completely expressed by a membership function rather than by a crisp value it conserves the fuzziness of the input information thus more information is provided for designing queueing systems the successful extension of queueing decision models to fuzzy environments permits queueing decision models to have wider applications in practice

stochastic optimization by simulation numerical experiments with the m m 1 queue in steady state this paper gives numerical illustrations of the behavior of stochastic approximation combined with different derivative estimation techniques to optimize a steady state system it is a companion paper to l ecuyer and glynn 1993 which gives convergence proofs for most of the variants experimented here the numerical experiments are made with a simple m m 1 queue which while simple serves to illustrate the basic convergence properties and possible pitfalls of the various techniques

convergence of powers of s transitive fuzzy matrices abstract natural powers via max min multiplication of s transitive fuzzy matrices are considered it is shown that they oscillate with period equal to 2 this is an extension of the convergence property concerning max min transitive fuzzy matrices

ranking fuzzy numbers with maximizing set and minimizing set abstract up to now these are five methods of ranking n fuzzy numbers in order but these methods contain some confusions and occasionally conflict with intuition this paper introduces the concept of maximizing set and minimizing set to decide the ordering value of each fuzzy number and uses these values to determine the order of the n fuzzy numbers in addition we give a method for calculating the ordering value of each fuzzy number with triangular trapezoidal and two sided drum like shaped membership functions

analysis of fuzzy queues abstract a general approach for queuing systems in a fuzzy environment is proposed based on zadeh s extension principle the possibility concept and fuzzy markov chains to illustrate the approach analytical results for m f 1 and fm fm 1 systems are presented fuzzy queues are much more realistic than the commonly used crisp queues in many practical situations a simple numerical example is also presented