comparison of fuzzy numbers based on the probability measure of fuzzy events abstract most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only and suffer from lack of discrimination and occasionally conflict with intuition it is true that fuzzy numbers are frequently partial order and cannot be compared however this does not alleviate the need for comparison in practical applications in this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to zadeh it considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions the approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number it is shown that several comparison indices in the literature can be obtained based on the probability present measure approach finally some typical examples are used to compare the various different approaches the different interpretations of the dispersion index under different physical situations are emphasized

the set of limiting distributions for a markov chain with fuzzy transition probabilities abstract using point to set maps and the hausdorf metric we derive the stationary set of distributions for a finite markov chain with fuzzy i e specified within bounds transition probabilities and give two limiting set theorems which are analogous to the ergodic theorems for ordinary stationary markov chains we also describe the testable properties of a fuzzy probability chain which will guarantee existence of a unique limiting set give a test for elements in or arbitrarily close to the limiting set and give a method for approximating the stationary set to any desired degree of accuracy with respect to the hausdorf metric an illustrative example in three dimensions is included

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

spectral statistics for unitary transfer matrices of binary graphs quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits it is proposed here to generalize this approach by considering arbitrary directed graphs with unitary transfer matrices an exponentially increasing contribution to the form factor is identified when performing a diagonal summation over periodic orbit degeneracy classes a special class of graphs so called binary graphs is studied in more detail for these the conditions for periodic orbit pairs to be correlated including correlations due to the unitarity of the transfer matrix can be given explicitly using combinatorial techniques it is possible to perform the summation over correlated periodic orbit pair contributions to the form factor for some low dimensional cases gradual convergence towards random matrix results is observed when increasing the number of vertices of the binary graphs

on the convergence of least squares estimates in white noise the problem of convergence of least squares ls estimates in a stochastic linear regression model with white noise is considered it is well known that if the parameter estimates are known to converge the convergence analysis for many adaptive systems can be rendered considerably less arduous for an important case where the regression vector is a measurable function of the observations and the noise is gaussian it has been shown by using a bayesian embedding argument that the ls estimates converge almost surely for almost all true parameters in the parameter space except for a zero measure set however nothing can be said about a particular given system which is usually the objective it has long been conjectured that such a bad zero measure set in the parameter space does not actually exist a conclusive answer to this important question is provided and it is shown that the set can indeed exist this then shows that to provide conclusive convergence results for stochastic adaptive systems it is necessary to resort to a sample pathwise analysis instead of the bayesian embedding approach

analysis and simulation of fuzzy queues abstract the aim of this paper is to combine the ability of fuzzy sets to represent practical situations with the well known established traditional queuing approaches which are rigorous but the assumptions are frequently too far from reality it is shown that this approach can utilize the advantages of both the fuzzy and probability approaches to make the model more realistic and less restrictive both cut sets and the use of random variables to represent fuzzy numbers are investigated trapezoidal fuzzy numbers are used and the analytical and simulation results are discussed based on actual examples

moments of random matrices and hypergeometric orthogonal polynomials we establish a new connection between moments of n times n random matrices xn and hypergeometric orthogonal polynomials specifically we consider moments mathbb e rm tr x n s as a function of the complex variable s in mathbb c whose analytic structure we describe completely we discover several remarkable features including a reflection symmetry or functional equation zeros on a critical line in the complex plane and orthogonality relations an application of the theory resolves part of an integrality conjecture of cunden et al j math phys 57 111901 2016 on the time delay matrix of chaotic cavities in each of the classical ensembles of random matrix theory gaussian laguerre jacobi we characterise the moments in terms of the askey scheme of hypergeometric orthogonal polynomials we also calculate the leading order n rightarrow infty asymptotics of the moments and discuss their symmetries and zeroes we discuss aspects of these phenomena beyond the random matrix setting including the mellin transform of products and wronskians of pairs of classical orthogonal polynomials when the random matrix model has orthogonal or symplectic symmetry we obtain a new duality formula relating their moments to hypergeometric orthogonal polynomials

quantum graphs a simple model for chaotic scattering we connect quantum graphs with infinite leads and turn them into scattering systems we show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics typical poles delay time and conductance distributions ericson fluctuations and when considered statistically the ensemble of scattering matrices reproduces quite well the predictions of the appropriately defined random matrix ensembles the underlying classical dynamics can be defined and it provides important parameters which are needed for the quantum theory in particular we derive exact expressions for the scattering matrix and an exact trace formula for the density of resonances in terms of classical orbits analogous to the semiclassical theory of chaotic scattering we use this in order to investigate the origin of the connection between random matrix theory and the underlying classical chaotic dynamics being an exact theory and due to its relative simplicity it offers new insights into this problem which is at the forefront of the research in chaotic scattering and related fields

fredholm method for scars a new quasiclassical formula for scars is obtained by using the fredholm method we show that it can be expanded into a formula obtained earlier by agam and fishman the derivation is simple and direct it is also more rigorous and more general than that of agam and fishman it also clarifies the remarkable process of resurgence relating the high order terms based on long orbits to the weyl term whose origin is the zero length orbits

modeling uncertain activity duration by fuzzy number and discrete event simulation this paper introduces how to incorporate fuzzy set theory and a fuzzy ranking measure with discrete event simulation in order to model uncertain activity duration in simulating a real world system especially when insufficient or no sample data are available fuzzy numbers are used to describe uncertain activity durations reflecting vagueness imprecision and subjectivity in the estimation of them a fuzzy ranking measure is merged with an activity scanning simulation algorithm for performing fuzzy simulation time advancement and event selection for simulation experimentation the uses of the fuzzy activity duration and the probability distribution modeled duration are compared through a series of simulation experiments it is observed that the fuzzy simulation outputs are arrived at through only one cycle of fuzzy discrete event simulation still they contain all the statistical information that are produced through multiple cycles of simulation experiments when the probability distribution approach is adopted

on the concept of possibility probability consistency both probability and possibility may be seen as information about an experiment it is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once in this paper some aspects of the concept of possibility probability consistency are studied the consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information we analyse several measures of the degree of consistency and introduce an axiomatic to characterize them

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

scattering reflection and impedance of waves in chaotic and disordered systems with absorption we review recent progress in analysing wave scattering in systems with both intrinsic chaos and or disorder and internal losses when the scattering matrix is no longer unitary by mapping the problem onto a nonlinear supersymmetric model we are able to derive closed form analytic expressions for the distribution of reflection probability in a generic disordered system one of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel the developed theory has far reaching consequences for many quantities of interest including local green functions and time delays in particular we point out the role played by absorption as a sensitive indicator of mechanisms behind the anderson localization transition we also provide a random matrix based analysis of s matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time reversal invariance completing previous works on the subject the results can be applied in particular to the experimentally accessible impedance and reflection in a microwave or an ultrasonic cavity attached to a system of antennas

non weyl microwave graphs one of the most important characteristics of a quantum graph is the average density of resonances l where l denotes the length of the graph this is a very robust measure it does not depend on the number of vertices in a graph and holds also for most of the boundary conditions at the vertices graphs obeying this characteristic are called weyl graphs using microwave networks that simulate quantum graphs we show that there exist graphs that do not adhere to this characteristic such graphs are called non weyl graphs for standard coupling conditions we demonstrate that the transition from a weyl graph to a non weyl graph occurs if we introduce a balanced vertex a vertex of a graph is called balanced if the numbers of infinite leads and internal edges meeting at a vertex are the same our experimental results confirm the theoretical predictions of e b davies and a pushnitski analysis and pde 4 729 2011 and are in excellent agreement with the numerical calculations yielding the resonances of the networks

truncations of random unitary matrices we analyse properties of non hermitian matrices of size m constructed as square submatrices of unitary orthogonal random matrices of size n m distributed according to the haar measure in this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle in the limit of large matrices this ensemble is characterized by the ratio m n for the truncated cue we analytically derive the joint density of eigenvalues and all correlation functions in the strongly non unitary case universal ginibre behaviour is found for n m fixed and n to the universal resonance width distribution with n m open channels is recovered

statistics of time delay and scattering correlation functions in chaotic systems i random matrix theory we consider the statistics of time delay in a chaotic cavity having m open channels in the absence of time reversal invariance in the random matrix theory approach we compute the average value of polynomial functions of the time delay matrix q i s ds de where s is the scattering matrix our results do not assume m to be large in a companion paper we develop a semiclassical approximation to s matrix correlation functions from which the statistics of q can also be derived together these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches

theory of random matrices with strong level confinement orthogonal polynomial approach strongly non gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in the presence and the absence of a hard edge in their energy spectra employing a theory of polynomials orthogonal with respect to exponential weights we calculate with an asymptotic accuracy the two point kernel over all distance scale and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the end points of the spectrum we also obtain the exact expressions for density of levels one and two point green s functions and prove that a universal local relationship exists for the suitably normalized and rescaled connected two point green s function the connection between the structure of the szeg o function entering strong polynomial asymptotics and mean field equation is traced textcopyright 1996 the american physical society

recursion for the smallest eigenvalue density of β wishart laguerre ensemble the statistics of the smallest eigenvalue of wishart laguerre ensemble is important from several perspectives the smallest eigenvalue density is typically expressible in terms of determinants or pfaffians these results are of utmost significance in understanding the spectral behavior of wishart laguerre ensembles and among other things unveil the underlying universality aspects in the asymptotic limits however obtaining exact and explicit expressions by expanding determinants or pfaffians becomes impractical if large dimension matrices are involved for the real matrices beta 1 edelman has provided an efficient recurrence scheme to work out exact and explicit results for the smallest eigenvalue density which does not involve determinants or matrices very recently an analogous recurrence scheme has been obtained for the complex matrices beta 2 in the present work we extend this to beta wishart laguerre ensembles for the case when exponent alpha in the associated laguerre weight function lambda alpha e beta lambda 2 is a non negative integer while beta is positive real this also gives access to the smallest eigenvalue density of fixed trace beta wishart laguerre ensemble as well as moments for both cases moreover comparison with earlier results for the smallest eigenvalue density in terms of certain hypergeometric function of matrix argument results in an effective way of evaluating these explicitly exact evaluations for large values of n the matrix dimension and alpha also enable us to compare with tracy widom density and large deviation results of katzav and castillo we also use our result to obtain the density of the largest of the proper delay times which are eigenvalues of the wigner smith matrix and are relevant to the problem of quantum chaotic scattering

evaluation of the coulomb force via the fredholm integral equation the electrostatic force between two conducting spheres is solved exactly from coulomb s law the force is evaluated in two steps i the charge distribution on each of the spheres is calculated as a function of separation distance by way of a solution to the fredholm integral equation ii the effect of the known charge distribution is integrated to obtain the electrostatic force evaluation of the electrostatic force is fast because the series expression for the charge distribution is super converging a characteristic trait for some fredholm type equations

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

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

parametric nonlinear programming for analyzing fuzzy queues with finite capacity abstract this paper proposes a procedure for constructing the membership functions of the performance measures in finite capacity queueing systems with the arrival rate and service rate being fuzzy numbers the basic idea is to transform a fuzzy queue with finite capacity to a family of conventional crisp queues with finite capacity by applying the cut approach a pair of parametric nonlinear programs is formulated to describe the family of crisp finite capacity 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 real life serve as examples since the performance measures are expressed by membership functions rather than by crisp values more information is provided for designing queueing systems in real life by extending to fuzzy environment the finite capacity queueing models would have wider applications

on consistency of bayes estimates in a certainty equivalence adaptive system the authors analyze a control problem with data generated by the linear regression model where intercept and slope coefficients are unknown they propose a certainty equivalence control rule based on bayes estimates of the intercept and slope coefficients it is shown that the control rule converges to the optimal control rule which requires complete knowledge of intercept and slope coefficients furthermore under the proposed control rule if the total control cost tends to infinity they show that the bayes estimates for slope and intercept are consistent

on the level spacing distribution in quantum graphs we derive a formula for the level spacing probability distribution in quantum graphs we apply it to simple examples and we discuss its relation with previous work and its possible application in more general cases moreover we derive an exact and explicit formula for the level spacing distribution of integrable quantum graphs

classical wave experiments on chaotic scattering we review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems scattering theory has to be applied for a quantitative interpretation of the measurements most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation in all studied examples a quantitative agreement between experiment and theory is achieved to this end it is necessary however to take absorption and imperfect coupling into account concepts that were ignored in most previous theoretical investigations classical phase space signatures of scattering are being examined in a small number of experiments

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

experimental investigation of wigner s reaction matrix for irregular graphs with absorption we use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by t joints to make an experimental study of wigner s reaction k matrix for irregular graphs in the presence of absorption from measurements of the scattering matrix s for each realization of the microwave network we obtain distributions of the imaginary and real parts of k our experimental results are in good agreement with theoretical predictions

brief paper consistency in least squares estimation in a previous paper the convenience of using martingale theory in the analysis of bayesian least squares estimation was demonstrated however certain restrictions had to be imposed on either the feedback structure or on the initial values for the estimation in the present paper these restrictions are removed and necessary and sufficient conditions for strong consistency in a bayesian sense are given for the gaussian white noise case without any assumptions on closed loop stability or on the feedback structure in the open loop case the poles are shown to be consistently estimated almost everywhere and in the closed loop case certain choices of control law are shown to assure consistency finally adaptive control laws are treated and implicit self tuning regulators are shown to converge to the desired control laws

experimental and numerical investigation of the reflection coefficient and the distributions of wigner s reaction matrix for irregular graphs with absorption we present the results of an experimental and numerical study of the distribution of the reflection coefficient p r and the distributions of the imaginary p v and the real p u parts of the wigner reaction k matrix for irregular fully connected hexagon networks graphs in the presence of strong absorption in the experiment we used microwave networks which were built of coaxial cables and attenuators connected by joints in the numerical calculations experimental networks were described by quantum fully connected hexagon graphs the presence of absorption introduced by attenuators was modeled by optical potentials the distribution of the reflection coefficient p r and the distributions of the reaction k matrix were obtained from measurements and numerical calculations of the scattering matrix s of the networks and graphs respectively we show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory

bayesian heuristic for multiperiod control in multiperiod control problems one needs to sequentially choose the value of a set of multiple input variables xn to keep the value of a single output variable yn close to a target t at any stage n the selection of xn poses a difficult dilemma on the one hand xn has to be such that yn xn t 2 is small in expectation on the other hand xn has to be such that it maximizes the amount of information in yn xn about the model relating yn and xn to help keep the value of future y s as close to t as possible the main approach to this problem is through certainty equivalence designs which select xn such that yn xn is estimated to be equal to t instead myopic designs select the xn that would be optimal if yn xn was the last observation to be made we propose designs that improve on certainty equivalence and on myopic designs by searching for the best design in a family that contains both in that way the proposed design reaches a good compromise between the certainty equivalence choice know

universal and nonuniversal properties of wave chaotic scattering systems prediction of the statistics of scattering in typical wave chaotic systems requires combining system specific information with universal aspects of chaotic scattering as described by random matrix theory this rapid communication shows that the average impedance matrix which characterizes such system specific properties can be semiclassically calculated in terms of ray trajectories between ports theoretical predictions are compared with experimental results for a microwave billiard demonstrating that the theory successfully uncovered universal statistics of wave chaotic scattering systems

on retrial queueing model with fuzzy parameters abstract this work constructs the membership functions of the system characteristics of a retrial queueing model with fuzzy customer arrival retrial and service rates the cut approach is used to transform a fuzzy retrial queue into a family of conventional crisp retrial queues in this context by means of the membership functions of the system characteristics a set of parametric non linear programs is developed to describe the family of crisp retrial queues a numerical example is solved successfully to illustrate the validity of the proposed approach because the system characteristics are expressed and governed by the membership functions more information is provided for use by management by extending this model to the fuzzy environment fuzzy retrial queue is represented more accurately and analytic results are more useful for system designers and practitioners

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

statistical distribution of the wigner smith time delay matrix moments for chaotic cavities we derive the joint distribution of the moments trq 1 of the wigner smith matrix for a chaotic cavity supporting a large number of scattering channels n this distribution turns out to be asymptotically gaussian and we compute explicitly averages and covariances the results are in a compact form and have been verified numerically the general methodology of proof and computations has a wide range of applications

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

matrix models for beta ensembles this paper constructs tridiagonal random matrix models for general 0 hermite gaussian and laguerre wishart ensembles these generalize the well known gaussian and wishart models for 1 2 4 furthermore in the cases of the laguerre ensembles we eliminate the exponent quantization present in the previously known models we further discuss applications for the new matrix models and present some open problems

parametric programming approach for batch arrival queues with vacation policies and fuzzy parameters this work constructs the membership functions of the system characteristics of a batch arrival queuing model with vacation policies and fuzzy batch arrival customer service and server vacation rates the cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context by means of the membership functions of the system characteristics a set of parametric nonlinear programs is developed to describe the family of crisp queues with a vacationing server two numerical examples are solved successfully to illustrate the validity of the proposed approach because the system characteristics are expressed and governed by the membership functions more information is provided for use by management by extending this model to the fuzzy environment fuzzy queues with a vacationing server are represented more accurately and the analytic results are more useful for system designers and practitioners

association of scattering matrices in quantum networks algorithms based on operations that associate scattering matrices in series or in parallel analogous to impedance association in a classical circuit are developed here we exemplify their application by calculating the total scattering matrix of several types of quantum networks such as star graphs and a chain of chaotic quantum dots obtaining results with good agreement with the literature through a computational time analysis we compare the efficiency of two algorithms for the simulation of a chain of chaotic quantum dots based on series association operations of i two by two centers and ii three by three ones empirical results point out that the algorithm ii is more efficient than i for small number of open scattering channels a direct counting of floating point operations justifies quantitatively the superiority of the algorithm i for large number of open scattering channels

fuzzy analysis of queueing systems with an unreliable server a nonlinear programming approach abstract this work constructs the membership functions of the system characteristics of a queuing model with an unreliable server in which the arrival rate and the service rate of customers as well as the breakdown rate and repair rate of server are all fuzzy numbers the cut approach is used to transform a fuzzy queue with an unreliable server into a family of conventional crisp queues with an unreliable server by means of the membership functions of the system characteristics a set of parametric nonlinear programs is developed to describe the family of crisp queues with an unreliable server an efficient algorithm is provided to find the optimal solutions at a different possibility level three numerical examples are solved successfully to illustrate the validity of the proposed approach due to the system characteristics being expressed and governed by the membership functions more information is provided for use by management by extending the fuzzy environment the fuzzy queues with an unreliable server can be represented more accurately by using the proposed approach and the analysis results for such queuing model will be useful and significant for system designers and practitioners

strong consistency in stochastic regression models via posterior covariance matrices summary in this paper we use posterior covariance matrices to study the strong consistency of bayes estimators in stochastic regression models under various assumptions on the stochastic regressors the random errors are assumed to form a martingale difference sequence several results are obtained using a recursion satisfied by the sequence of posterior covariance matrices these results suggest that the posterior covariance matrix is a useful tool in studying strong consistency problems in stochastic regression models three examples from sequential design and adaptive control are discussed

explicitly solvable cases of one dimensional quantum chaos we identify a set of quantum graphs with unique and precisely defined spectral properties called regular quantum graphs although chaotic in their classical limit with positive topological entropy regular quantum graphs are explicitly solvable the proof is constructive we present exact convergent periodic orbit expansions for individual energy levels thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete explicit and exact

random matrices close to hermitian or unitary overview of methods and results the paper discusses recent progress in understanding statistical properties of eigenvalues of weakly non hermitian and non unitary random matrices the first type of ensembles is of the form i with being a large random n n hermitian matrix with independent entries deformed by a certain anti hermitian n n matrix i satisfying in the limit of large dimension n the condition tr 2 n tr 2 here can be either a random or just a fixed given hermitian matrix ensembles of such a type with 0 emerge naturally when describing quantum scattering in systems with chaotic dynamics and serve to describe resonance statistics related models are used to mimic complex spectra of the dirac operator with chemical potential in the context of quantum chromodynamics ensembles of the second type arising naturally in scattering theory of discrete time systems are formed by n n matrices with complex entries such that i for 0 this coincides with the circular unitary ensemble and 0 i describes deviation from unitarity our result amounts to answering statistically the following old question given the singular values of a matrix describe the locus of its eigenvalues we systematically show that the obtained expressions for the correlation functions of complex eigenvalues describe a non trivial crossover from wigner dyson statistics of real unimodular eigenvalues typical of hermitian unitary matrices to ginibre statistics in the complex plane typical of ensembles with strong non hermiticity tr 2 tr 2 when n finally we discuss scarce results available on eigenvector statistics for weakly non hermitian random matrices

a unified fluctuation formula for one cut β ensembles of random matrices using a coulomb gas approach we compute the generating function of the covariances of power traces for one cut ensembles of random matrices in the limit of large matrix size this formula depends only on the support of the spectral density and is therefore universal for a large class of models this allows us to derive a closed form expression for the limiting covariances of an arbitrary one cut ensemble as particular cases of the main result we consider the classical gaussian wishart and jacobi ensembles for which we derive previously available results as well as new ones within a unified simple framework we also discuss the connections between the problem of trace fluctuations for the gaussian unitary ensemble and the enumeration of planar maps

reducing nonideal to ideal coupling in random matrix description of chaotic scattering application to the time delay problem we write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with m statistically equivalent channels at nonideal coupling to that for ideal coupling unfolding the phases by their local density leads to universality of their local fluctuations for large m a relation between the partial time delays and diagonal matrix elements of the wigner smith matrix is revealed for ideal coupling this helped us in deriving the joint probability distribution of partial time delays and the distribution of the wigner time delay

experimental simulation of quantum graphs by microwave networks we present the results of experimental and theoretical study of irregular tetrahedral microwave networks consisting of coaxial cables annular waveguides connected by t joints the spectra of the networks were measured in the frequency range 0 0001 16 ghz in order to obtain their statistical properties such as the integrated nearest neighbor spacing distribution and the spectral rigidity d3sld the comparison of our experimental and theoretical results shows that microwave networks can simulate quantum graphs with time reversal symmetry in particular we use the spectra of the microwave networks to study the periodic orbits of the simulated quantum graphs we also present experimental study of directional microwave networks consisting of coaxial cables and faraday isolators for which the time reversal symmetry is broken in this case our experimental results indicate that spectral statistics of directional microwave networks deviate from predictions of gaussian orthogonal ensembles in random matrix theory approaching especially for small eigenfrequency spacing s results for gaussian unitary ensembles experimental results are supported by the theoretical analysis of directional graphs

single value simulation of fuzzy variables abstract the basic ideas of the present paper arise from relations between random sets and fuzzy ones the suggested approach which may be called fuzzy numerical simulation allows for ascribing a precise numerical value to a fuzzy variable by generating a value of a random variable related in some way to the fuzzy variable the so called generative characteristics of a fuzzy variable being the expected value and variance of the generating random variable are introduced the problem of simultaneous generating values of two fuzzy variables is also discussed finally methods of generating when a fuzzy variable is described with a complex body of evidence are presented

extended least squares and their applications to adaptive control and prediction in linear systems herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature the argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators making use of these properties of the adaptive predictors simple modifications of the astrom wittenmark self tuning regulator are proposed and shown to be asymptotically optimal

resurgence in quasi classical scattering in quasi classical studies of closed systems e g a billiard resurgence means that the contribution of long periodic orbits to the spectral determinant can be expressed in terms of composites of short orbits and the resulting expression for the determinant is manifestly real the question has thus long been posed whether something like resurgence applies to a scattering system with its resonances we find here a resurgent expression for wigner s r matrix which gives the s matrix by a cayley transform in which long scattering pseudo orbits are expressed in terms of composites of short pseudo orbits both scattering and periodic and the result is manifestly hermitian giving a unitary expression for the s matrix this is particularly useful in the case that the resonance width is comparable with the resonance spacing the pseudo orbits are defined in terms of a fictitious and to some extent arbitrary closed reference system we relate the results to other formulations we give a simple but non trivial approximation for a particular example which illustrates the phenomenon of resonance trapping

parameter dependent spectral statistics of chaotic quantum graphs neumann versus circular orthogonal ensemble boundary conditions the parameter dependent spectral statistics of totally connected quantum graphs with n 4 30 vertices such as the parametric velocities correlation functions and the distribution of curvatures are studied the inverse participation ratio ipr an important measure of localization effects was also numerically investigated in the calculations we successfully used two different theoretical approaches the first approach was based on the graphs eigenenergies and wave functions calculations while the second one used the eigenphases and the eigenvectors of the bond scattering matrix s k we considered graphs with neumann and circular orthogonal ensemble coe boundary conditions we show that in contrast to large neumann graphs for which the departure of many parameter dependent spectral statistics from the random matrix theory rmt predictions is observed for large coe graphs the spectral statistics and ipr are in good agreement with the rmt predictions

universal statistics of the scattering coefficient of chaotic microwave cavities we consider the statistics of the scattering coefficient s of a chaotic microwave cavity coupled to a single port we remove the nonuniversal effects of the coupling from the experimental s data using the radiation impedance obtained directly from the experiments we thus obtain the normalized scattering coefficient whose probability density function pdf is predicted to be universal in that it depends only on the loss quality factor of the cavity we compare experimental pdfs of the normalized scattering coefficients with those obtained from random matrix theory rmt and find excellent agreement the results apply to scattering measurements on any wave chaotic system

truncated linear statistics associated with the eigenvalues of random matrices ii partial sums over proper time delays for chaotic quantum dots invariant ensembles of random matrices are characterized by the distribution of their eigenvalues lambda 1 ldots lambda n we study the distribution of truncated linear statistics of the form tilde l sum i 1 p f lambda i with p n this problem has been considered by us in a previous paper when the p eigenvalues are further constrained to be the largest ones or the smallest in this second paper we consider the same problem without this restriction which leads to a rather different analysis we introduce a new ensemble which is related but not equivalent to the thinned ensembles introduced by bohigas and pato this question is motivated by the study of partial sums of proper time delays in chaotic quantum dots which are characteristic times of the scattering process using the coulomb gas technique we derive the large deviation function for tilde l large deviations of linear statistics l sum i 1 n f lambda i are usually dominated by the energy of the coulomb gas which scales as sim n 2 implying that the relative fluctuations are of order 1 n for the truncated linear statistics considered here there is a whole region including the typical fluctuations region where the energy of the coulomb gas is frozen and the large deviation function is purely controlled by an entropic effect because the entropy scales as sim n the relative fluctuations are of order 1 sqrt n our analysis relies on the mapping on a problem of p fictitious non interacting fermions in n energy levels which can exhibit both positive and negative effective absolute temperatures we determine the large deviation function characterizing the distribution of the truncated linear statistics and show that for the case considered here f lambda 1 lambda the corresponding phase diagram is separated in three different phases

moments of the wigner delay times the wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system for chaotic systems the statistics of the individual delay times whose average is the wigner time delay are thought to be well described by random matrix theory here we present a semiclassical derivation showing the validity of random matrix results in order to simplify the semiclassical treatment we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies in the semiclassical approximation the elements of the scattering matrix are given in terms of the classical scattering trajectories requiring one to study correlations between sets of such trajectories we describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number this allows us to derive a polynomial equation satisfied by the generating function of the moments along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory we infer that the scattering matrix is unitary to all orders in the semiclassical approximation

families of line graphs and their quantization any directed graph g with n vertices and j edges has an associated line graph l g where the j edges form the vertices of l g we show that the non zero eigenvalues of the adjacency matrices are the same for all graphs of such a family ln g we give necessary and sufficient conditions for a line graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions line graphs may therefore serve as models to study the semiclassical limit of large matrix size of a quantum dynamics on graphs with fixed classical behaviour

convergence of adaptive control schemes using least squares parameter estimates the stability convergence asymptotic optimality and self tuning properties of stochastic adaptive control schemes based on least squares estimates of the unknown parameters are examined it is assumed that the additive noise is i i d and gaussian and that the true system is of minimum phase the bayesian embedding technique is used to show that the recursive least squares parameter estimates converge in general the normal equations of least squares are used to establish that all stable control law designs used in a certainty equivalent i e indirect procedure generally yield a stable adaptive control system four results are given to characterize the limiting behavior precisely a certainty equivalent self tuning regulator is shown to yield strongly consistent parameter estimates when the delay is strictly greater than one even without any excitation in the reference trajectory

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

classical 1d maps quantum graphs and ensembles of unitary matrices we study a certain class of classical one dimensional piecewise linear maps for these systems we introduce an infinite family of markov partitions in equal cells the symbolic dynamics generated by these systems is described by bi stochastic doubly stochastic matrices we analyse the structure of graphs generated from the corresponding symbolic dynamics we demonstrate that the spectra of quantized graphs corresponding to the regular classical systems have locally poissonian statistics while quantized graphs derived from classically chaotic systems display statistical properties characteristic of the circular unitary ensemble even though the corresponding unitary matrices are sparse