hardness of solving relational equations minimal solutions play a crucial role in describing all solutions of relational equations for this reason the problem of computing minimal solutions has for long been examined the literature contains several algorithms for computing minimal solutions recently contributions regarding computational complexity of the problem itself appeared the complexity aspect is clearly of fundamental importance however the existing results contain serious flaws in this paper we inspect the existing contributions clarify the flaws examine the problem of complexity of computing minimal solutions prove that there is no efficient algorithm computing all minimal solutions and discuss further ramifications of our observations

correlation functions in the itzykson zuber model then point function for the integral over unitary matrices with itzykson zuber measure is reduced to the integral over the gelfand tzetlin table the integrand for genericn is given by linear exponential times the rational function forn 2 and in some cases forn 2 later in fast is the polynomial and this allows to give an explicit and simple expression for all 2 point and a set ofn point functions for the most generaln point function a simple linear differential equation is constructed

measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

on the minimal solutions of max min fuzzy relational equations in this paper the minimal solutions of max min fuzzy relational equations are investigated a sufficient and necessary condition for discriminating whether a given solution is minimal or not is shown furthermore we propose a new algorithm for computing all minimal solutions less than or equal to a given one

linear objective function optimization with fuzzy relation equation constraints regarding max av composition in this paper an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max av composition is presented the solution set of such a fuzzy relation equations is a non convex set in this paper firstly we discuss the feasible solution set with two schemes and secondly study relationship between maximum and minimum points and also the feasible points as well furthermore an algorithm and few concrete examples are presented in order to optimize linear objective function

on some integrals over the u n unitary group and their large n limit the integral over the u n unitary group i du exp tr au bu is re examined various approaches and extensions are first reviewed the second half of the paper deals with more recent developments relation with integrable toda lattice hierarchy diagrammatic expansion and combinatorics and what they teach us on the large n limit of log i

solutions of fuzzy relation equations based on continuous t norms this study is concerned with fuzzy relation equations with continuous t norms in the form atr b where a and b are the fuzzy subsets of x and y respectively email protected xxy is a fuzzy relation and t is a continuous t norm the problem is how to determine a from r and b first an if and only if condition of being solvable is presented novel algorithms are then presented for determining minimal solutions when x and y are finite the proposed algorithms generate all minimal solutions for the equations making them efficient solving procedures

deriving minimal solutions for fuzzy relation equations with max product composition this work considers fuzzy relation equations with max product composition the critical problem in solving such equations is to determine the minimal solutions when an equation is solvable however this problem is np hard and difficult to solve a v markovskii on the relation between equations with max product composition and the covering problem fuzzy sets and systems 153 2005 261 273 this work first examines the attributes of a solvable equation and characteristics of minimal solutions then reduces the equation to an irreducible form and converts the problem into a covering problem for which minimal solutions are correspondingly determined furthermore for theoretical and practical applications this work presents a novel method for obtaining minimal solutions the proposed method easily derives a minimal solution and obtains other minimal solutions from this predecessor using a back tracking step the proposed method is compared with an existing algorithm and some applications are described in detail

asymptotics of unitary and orthogonal matrix integrals abstract in this paper we prove that in small parameter regions arbitrary unitary matrix integrals converge in the large n limit and match their formal expansion secondly we give a combinatorial model for our matrix integral asymptotics and investigate examples related to free probability and the hciz integral our convergence result also leads us to new results of smoothness of microstates we finally generalize our approach to integrals over the orthogonal group

linear optimization problem constrained by fuzzy max min relation equations fang and li introduced the optimization model with a linear objective function and constrained by fuzzy max min relation equations they converted this problem into a 0 1 integer programming problem and solved it using the jump tracking branch and bound method subsequently wu et al improved this method by providing an upper bound on the optimal objective value and presented three rules for simplifying the computation of an optimal solution this work presents new theoretical results concerning this optimization problem they include an improved upper bound on the optimal objective value improved rules for simplifying the problem and a rule for reducing the solution tree accordingly an accelerated approach for finding the optimal objective value is presented and represents an improvement on earlier approaches its potential applications are discussed

generalized lyapunov schmidt reduction for parametrized equations at near singular points abstract the lyapunov schmidt reduction is generalized such that it uniformly handles bothperfect and imperfect singularities the results presented need neither very precise information about the location of the near singularities nor a precise knowledge of near null spaces

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

minimal solutions of general fuzzy relation equations on linear carriers an algebraic characterization abstract this paper considers a general fuzzy relation equation which has minimal solutions if it is solvable in this case an algebraic characterization is introduced which provides an interesting method to compute minimal solutions in this general setting moreover a comparison with other frameworks is also given

on absolute moments of characteristic polynomials of a certain class of complex random matrices the integer moments of the spectral determinant det zi w 2 of complex random matrices w are obtained in terms of the characteristic polynomial of the positive semidefinite matrix ww for the class of matrices w au where a is a given matrix and u is random unitary this work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results are discussed in this context

resolution of fuzzy relational equations method algorithm and software with applications analytical methods and algorithms for inverse problem resolution of fuzzy linear systems of equations in some bl algebras godel algebra in case of max min and min max compositions and goguen algebra in case of max product composition are presented algorithms with software realization for solving fuzzy linear systems of equations are proposed applications include fuzzy optimization with fuzzy linear systems of equation constraint fuzzy machines and covering problem

inertial manifolds for nonlinear evolutionary equations abstract in this paper we introduce the concept of an inertial manifold for nonlinear evolutionary equations in particular for ordinary and partial differential equations these manifolds which are finite dimensional invariant lipschitz manifolds seem to be an appropriate tool for the study of questions related to the long time behavior of solutions of the evolutionary equations the inertial manifolds contain the global attractor they attract exponentially all solutions and they are stable with respect to perturbations furthermore in the infinite dimensional case they allow for the reduction of the dynamics to a finite dimensional ordinary differential equation

noisy dynamic simulations in the presence of symmetry data alignment and model reduction abstract we process snapshots of trajectories of evolution equations with intrinsic symmetries and demonstrate the use of recently developed eigenvector based techniques to successfully quotient out the degrees of freedom associated with the symmetries in the presence of noise our illustrative examples include a one dimensional evolutionary partial differential the kuramoto sivashinsky equation with periodic boundary conditions as well as a stochastic simulation of nematic liquid crystals which can be effectively modeled through a nonlinear smoluchowski equation on the surface of a sphere this is a useful first step towards data mining the symmetry adjusted ensemble of snapshots in search of an accurate low dimensional parametrization and the associated reduction of the original dynamical system we also demonstrate a technique vector diffusion maps that combines in a single formulation the symmetry removal step and the dimensionality reduction step

unattainable solutions of a fuzzy relation equation in a fuzzy relation equation the properties of the solution set have been investigated especially when the basic spaces are all finite sets however when the basic spaces are infinite a few properties are known in this paper we use the concepts of attainability and unattainability of a solution to clarify some properties of the solution set and show the condition for existence of a partially attainable solution and an unattainable one

random matrix ensembles with column row constraints ii we analyze statistical properties of a complex system subjected to conditions which manifests through specific constraints on the column row sum of the matrix elements of its hermitian operators the presence of additional constraints besides real symmetric nature leads to new correlations among their eigenfunctions hinders a complete delocalization of dynamics and affects the eigenvalues too the statistical analysis of the latter indicates the presence of a new universality class analogous to that of a special type of brownian ensemble appearing between poisson and gaussian orthogonal ensemble

concentration of the kirchhoff index for erdos renyi graphs given an undirected graph the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors summing these distances over all pairs of nodes yields the so called kirchhoff index of the graph which measures its overall connectivity in this work we consider erdos renyi random graphs since the graphs are random their kirchhoff indices are random variables we give formulas for the expected value of the kirchhoff index and show it concentrates around its expectation we achieve this by studying the trace of the pseudoinverse of the laplacian of erdos renyi graphs for synchronization a class of estimation problems on graphs our results imply that acquiring pairwise measurements uniformly at random is a good strategy even if only a vanishing proportion of the measurements can be acquired

preserving symmetries in the proper orthogonal decomposition the proper orthogonal decomposition pod also called karhunen loeve expansion has been recently used in turbulence to derive optimally fast converging bases of spatial functions leading to efficient finite truncations whether a finite number of these modes can be used in numerical simulations to derive an accurate finite set of ordinary differential equations over a certain range of bifurcation parameter values still remains an open question it is shown here that a necessary condition for achieving this goal is that the truncated system inherit the symmetry properties of the original infinite dimensional system in most cases this leads to a systematic involvement of the symmetry group in deriving a new expansion basis called the symmetric pod basis the kuramoto sivashinsky equation with periodic boundary conditions is used as a paradigm to illustrate this point of view however the conclusion is general and can be applied to other equations such as the navier stokes equations the complex g

solution algorithms for fuzzy relational equations with max product composition the conditions for the existence of an inverse solution to the max min composition of fuzzy relational equations have been well documented since the original work by sanchez 30 31 these same existence theorems have been extended to the t norm composition of relational equations in which the max product composition is a member 5 13 26 several studies 8 15 24 33 34 38 have shown that the max min operator may not always be the most desirable fuzzy relational composition and in fact the max product operator was superior in these instances this paper reviews the algorithms necessary to determine the complete solution of the inverse for fuzzy relational equations with max product composition

multi adjoint relation equations definition properties and solutions using concept lattices this paper generalizes fuzzy relation equations following the multi adjoint philosophy moreover the solutions of these general fuzzy relation equations and the concepts of a multi adjoint property oriented concept lattice are related and several results are obtained from the theory of concept lattices as a consequence of this relevant relation more properties about these general equations can be proven from the theory of concept lattices and the algorithms developed to compute concept lattices can be used to obtain solutions furthermore an interesting application to fuzzy logic programming has been introduced in which an important problem in this topic has been interpreted in terms of solving a multi adjoint relation equation

approximate inertial manifolds for the kuramoto sivashinsky equation analysis and computations abstract we evaluate several alternative methods for the approximation of inertial manifolds for the one dimensional kuramoto sivashinsky equation kse a method motivated by the dynamics originally developed for the navier stokes equation is adapted for the kse rigorous error estimates are obtained and compared to those of other methods introduced in the literature formal relationships between these other methods and the one introduced here are established numerical bifurcation diagrams of the various approximate inertial forms for the kse are presented we discuss the correspondence between the rigorous error estimates and the accuracy of the computational results these methods can be adapted to other dissipative partial differential equations

on approximate inertial manifolds to the navier stokes equations abstract recently the theory of inertial manifolds has shown that the long time behavior the dynamics of certain dissipative partial differential equations can be fully discribed by that of a finite ordinary differential system although we are still unable to prove existence of inertial manifolds to the navier stokes equations we present here a nonlinear finite dimensional analytic manifold that approximates closely the global attractor in the two dimensional case and certain bounded invariant sets in the three dimensional case this approximate manifold and others allow us to introduce modified galerkin approximations

on the relation between fuzzy max archimedean t norm relational equations and the covering problem the problem of solving a system of fuzzy relational equations with max archimedean t norm composition is studied it is shown that this problem is closely related to the covering problem which belongs to the class of np hard problems it is proved that there is a one to one correspondence between the minimal solutions of the equations and the irredundant coverings as previously discovered by markovskii on the relation between equations with max product composition and the covering problem fuzzy sets and systems 153 2005 261 273 for fuzzy relational equations with max product composition since max product composition is a special case of max archimedean t norm composition this work extends markovskii s work to fuzzy relational equations with max archimedean t norm composition an extension of markovskii s algorithm is implemented yielding a processing time linearly proportional to the square of the number of minimal solutions

minimizing a linear objective function under a fuzzy max t norm relation equation constraint the work examines the feasibility of minimizing a linear objective function subject to a max t fuzzy relation equation constraint where t is a continuous archimedean t norm conventional methods for solving this problem are significantly improved by first separating the problem into two sub problems according to the availability of positive coefficients this decomposition is thus more easily handled than in previous literature next based on use of the maximum solution of the constraint equation the sub problem with non positive coefficients is solved and the size of the sub problem with positive coefficients reduced as well this step is unique among conventional methods owing to its ability to determine as many optimal variables as possible additionally several rules are developed for simplifying the remaining problem finally those undecided optimal variables are obtained using the covering problem rather than the branch and bound methods three illustrative examples demonstrate that the proposed approach outperforms conventional schemes its potential applications are discussed as well

some properties of sup min fuzzy relational equations on infinite domains abstract this paper deals with a sup min fuzzy relational equation on infinite domains some properties of its solution set will be obtained in particular a necessary and sufficient condition describing the attainable solution resp the unattainable solution is formulated in the end the solution set will be given under some conditions

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

do we need minimal solutions of fuzzy relational equations in advance minimal solutions play a crucial role in description of all solutions to a fuzzy relational equation the reason is that all solutions form a convex set with respect to fuzzy set inclusion therefore having all extremal solutions we can represent the entire solution set as a union of intervals bounded from above by the greatest solution and from below by the minimal solutions however when computing the intervals we obtain many duplicate solutions the obvious question is as follows is there another way of representing the solution set for instance without the need of having all the minimal solutions in advance we provide the positive answer to this question

solution sets of finite fuzzy relation equations with sup inf composition over bounded brouwerian lattices this paper considers the resolution of finite fuzzy relation equations with sup inf composition over a bounded brouwerian lattice the solution sets of finite fuzzy relation equations on a bounded brouwerian lattice are described in a similar way as those of linear spaces of n dimensional vectors in linear algebra

optimization of fuzzy relational equations with max av composition max min and max product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations both are members in the class of max t norm composition in this study the max av composition is considered for the same optimization model which does not belong to the max t norm composition however max av composition generates some properties of the solution set that are similar to the max product composition thanks to these properties a simple value matrix with rules can be applied to reduce problem size thus this study proposes an efficient procedure for obtaining optimal solutions without decomposing the problem into two sub problems or finding all the potential minimal solutions

minimizing a linear objective function under a max t norm fuzzy relational equation constraint this paper aims to solve the problem of minimizing a linear objective function subject to a max t fuzzy relational equation constraint with t a continuous t norm this study makes two contributions first two extensions are given based on the results in fang et al where the max min or max product fuzzy relational equation constraint is considered second a procedure for solving optimization problems with the max archimedean t norm fuzzy relational equation constraint is provided a numerical example is provided to illustrate the procedure

solution to the covering problem this work is motivated by recent investigations that reveal the intractability of the covering problem current methods for solving this problem lack an explicit procedure therefore they are of limited value this work presents the steps for solving such problems using a novel algorithm the search performance is better than that achieved in other works some numerical examples are presented to demonstrate the performance and to compare it with the performance of other methods the proposed algorithm can be utilized to solve fuzzy relation equations that exhibit the zero or greatest property

explicit construction of an inertial manifold for a reaction diffusion equation abstract an inertial manifold is constructed for the scalar reaction diffusion equation u t vu xx u with a cubic nonlinearity uniform bounds are obtained for the number of zeros along solutions to the variational equations satisfied by the difference of two elements on the unstable manifolds of equilibria this uniformity leads to the global parameterization of the attractor as a function defined in the linear unstable manifold of the least stable equilibrium by the introduction of local techniques near each equilibrium we succeed in constructing an inertial manifold of lowest possible dimension

solving linear optimization problems with max star composition equation constraints in this paper an optimization model with a linear objective function subject to a system of fuzzy relation composition equations is presented since the non empty feasible solution set of the fuzzy relation equations is generally a non convex set the conventional linear programming method will not be suitable for solving such a problem therefore an efficient solution procedure for such problems appears to be necessary in this paper firstly we characterize the feasible solution set and then introduce two efficient procedures for solving the problem finally two concrete examples are included for more details

developments in random matrix theory in this introduction to the journal of physics a special issue on random matrix theory we give a review of the main historical developments in random matrix theory a short summary of the papers that appear in this special issue is also given

on fuzzy relational equations and the covering problem previous studies have shown that fuzzy relational equations fres based on either the max continuous archimedean t norm or the max arithmetic mean composition can be transformed into the covering problem which is an np hard problem exploiting the properties common to the continuous archimedean t norm and the arithmetic mean this study proposes a generalization of them as the u norm enabling fres that are based on the max continuous u norm composition also to be transformed into the covering problem this study also proposes a procedure for transforming the covering problem into max product fres consequently max continuous u norm fres can be solved by extending any procedure for solving either the covering problem or max product fres

on the variation in the cohomology of the symplectic form of the reduced phase space is called the momentum mapping of the hamiltonian t action given 1 1 the condition 1 2 just means that t acts along the fibers of j for the basic definitions and properties of non commutative hamiltonian group actions see am the results of this paper can easily be extended to hamiltonian actions of arbitrary compact connected lie groups by applying our results to the action of its maximal toms and using the equivariance of the momentum mapping for some more details see the remarks at the end of sect 2 we will assume throughout this paper that the momentum map is proper that is j i u is compact for each compact subset u of t now let r be a regular value of j that is t j tmm t is surjective for all meye j 1 4 then ye is a smooth submanifold of m compact because

an efficient procedure for solving a fuzzy relational equation with max archimedean t norm composition in the literature a necessary condition for minimal solutions of a fuzzy relational equation with max product composition shows that each of its components is either zero or the corresponding component s value of the greatest solution in this paper we first extend this necessary condition to the situation with max archimedean triangular norm t norm composition based on this necessary condition we then propose rules to reduce the problem size so that the complete set of minimal solutions can be computed efficiently furthermore rather than work with the actual equations we employ a simple matrix whose elements capture all of the properties of the equations in finding the minimal solutions numerical examples with specific cases of the max archimedean t norm composition are provided to illustrate the procedure

2 matrix versus complex matrix model integrals over the unitary group as triangular integrals we prove that the 2 hermitian matrix model and the complex matrix model obey the same loop equations and as a byproduct we find a formula for itzykzon zuber type integrals over the unitary group integrals over u n are rewritten as gaussian integrals over triangular matrices and then computed explicitly that formula is an efficient alternative to the former shatashvili s formula

łukasiewicz transform and its application to compression and reconstruction of digital images we define the lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an mv algebra then we describe the lukasiewicz transform based ltb algorithm for image processing demonstrating its applicability

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

resolution of finite fuzzy relation equations abstract general schemes for solving fuzzy relation equations with finite sets are derived in this paper the relationship between the results derived here and those of previous publications regarding this subject is also discussed

vector diffusion maps and the connection laplacian we introduce vector diffusion maps vdm a new mathematical framework for organizing and analyzing massive high dimensional data sets images and shapes vdmis a mathematical and algorithmic generalization of diffusion maps and other nonlinear dimensionality reduction methods such as lle isomap and laplacian eigenmaps while existing methods are either directly or indirectly related to the heat kernel for functions over the data vdm is based on the heat kernel for vector fields vdm provides tools for organizing complex data sets embedding them in a low dimensional space and interpolating and regressing vector fields over the data in particular it equips the data with a metric which we refer to as the vector diffusion distance in the manifold learning setup where the data set is distributed on a low dimensional manifold embedded in we prove the relation between vdm and the connection laplacian operator for vector fields over the manifold 2012 wiley periodicals inc

some properties of angular integrals we find new representations for itzykson zuber like angular integrals for arbitrary in particular for the orthogonal group o n the unitary group u n and the symplectic group sp 2n we rewrite the haar measure integral as a flat lebesge measure integral and we deduce some recursion formulae on n the same methods give also shatashvili s type moments finally we prove that in agreement with brezin and hikami s observation the angular integrals are linear combinations of exponentials whose coefficients are polynomials in the reduced variables xi xj yi yj

diffusion maps and coarse graining a unified framework for dimensionality reduction graph partitioning and data set parameterization we provide evidence that nonlinear dimensionality reduction clustering and data set parameterization can be solved within one and the same framework the main idea is to define a system of coordinates with an explicit metric that reflects the connectivity of a given data set and that is robust to noise our construction which is based on a markov random walk on the data offers a general scheme of simultaneously reorganizing and subsampling graphs and arbitrarily shaped data sets in high dimensions using intrinsic geometry we show that clustering in embedding spaces is equivalent to compressing operators the objective of data partitioning and clustering is to coarse grain the random walk on the data while at the same time preserving a diffusion operator for the intrinsic geometry or connectivity of the data set up to some accuracy we show that the quantization distortion in diffusion space bounds the error of compression of the operator thus giving a rigorous justification for k means clustering in diffusion space and a precise measure of the performance of general clustering algorithms

equation free galerkin free pod assisted computation of incompressible flows we present a galerkin free proper orthogonal decomposition pod assisted computational methodology for numerical simulations of the long term dynamics of the incompressible navier stokes equations the approach is based on the equation free framework we use short appropriate initialized bursts of full direct numerical simulations dns of the navier stokes equations to observe estimate and accelerate through projective integration the evolution of the flow dynamics the main assumption is that the long term dynamics of the flow lie on a low dimensional attracting and invariant manifold which can be parametrized not necessarily spanned by a few pod basis functions we start with a discussion of the consistency and accuracy of the approach and then illustrate it through numerical examples two dimensional periodic and quasi periodic flows past a circular cylinder we demonstrate that the approach can successfully resolve complex flow dynamics at a reduced computational cost and that it can capture the long term asymptotic state of the flow in cases where traditional galerkin pod models fail the approach trades the overhead involved in developing pod galerkin and pod nonlinear galerkin codes for the repeated yet short and on demand use of an existing full dns simulator moreover since in this approach the pod modes are used to observe rather than span the true system dynamics the computation is much less sensitive than pod galerkin to values of the system parameters e g the reynolds number and the particular simulation data ensemble used to obtain the pod basis functions

on the relation between equations with max product composition and the covering problem systems of equations with max product composition are considered it is shown that solving these equations is closely related with the covering problem which belongs to the category of np hard problems it is proved that minimal solutions of equations correspond to irredundant coverings in terms of the covering problem the conditions of compatibility of equations of redundancy of equations of uniqueness of solution of uniqueness of minimal solution are determined concepts of essential non essential semi essential and super essential variables are suggested ways of simplification of a covering problem and methods of its solving are considered

linear optimization of bipolar fuzzy relational equations with max łukasiewicz composition according to the literature a linear optimization problem subjected to a system of bipolar fuzzy relational equations with max ukasiewicz composition can be translated into a 0 1 integer linear programming problem and solved using integer optimization techniques however the technique of integer optimization may involve hight computation complexity to improve computational efficiency for solving such an optimization problem this paper proves that each component of an optimal solution obtained from such an optimization problem can either be the corresponding component s lower bound or upper bound value because of this characteristic a simple value matrix with some simplified rules can be proposed to reduce the problem size first a simple solution procedure is then presented for determining optimal solutions without translating such an optimization problem into a 0 1 integer linear programming problem two examples are provided to illustrate the simplicity and efficiency of the proposed algorithm

addendum to on the variation in the cohomology of the symplectic form of the reduced phase space here we have used the notation rlx for the inner product of the vector field x with the form a and ix m x j m for the x component of a in an earlier paper 4 it was shown that the push forward j dm of the liouville measure dm on m under the momentum mapping j is a piecewise polynomial measure on moreover in case x has isolated isolated zeros on m an explicit formula for the integral

solving nonlinear optimization problems with fuzzy relation equation constraints abstract an optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented since the solution set of the fuzzy relation equations is in general a non convex set when it is not empty conventional nonlinear programming methods are not ideal for solving such a problem in this paper a genetic algorithm ga is proposed this ga is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations the individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations the construction of test problems is also developed to evaluate the performance of the proposed algorithm

correlation functions of harish chandra integrals over the orthogonal and the symplectic groups the harish chandra correlation functions i e integrals over compact groups of invariant monomials prod operatorname tr x p 1 varomega y q 1 varomega dagger x p 2 cdots with the weight exp tr x y are computed for the orthogonal and symplectic groups we proceed in two steps first the integral over the compact group is recast into a gaussian integral over strictly upper triangular complex matrices with some additional symmetries supplemented by a summation over the weyl group this result follows from the study of loop equations in an associated two matrix integral and may be viewed as the adequate version of duistermaat heckman s theorem for our correlation function integrals secondly the gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions

infinite fuzzy relation equations with continuous t norms this study develops a concept of infinite fuzzy relation equations with a continuous t norm it extends the work by xiong and wang q q xiong x p wang some properties of sup min fuzzy relational equations on infinite domains fuzzy sets and systems 151 2005 393 402 we describe attainable respectively unattainable solutions which are closely related to minimal solutions to the equations it is shown that a solution set comprises both attainable and unattainable solutions the study offers a characterization of these solutions under some assumptions the solution set is presented and discussed two applications are also given

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

a motion compression reconstruction method based on max t norm composite fuzzy relational equations a motion compression reconstruction method based on max t norm composite fuzzy relational equations mcf is proposed where into intra pictures i pictures and predictive pictures p pictures of the original motion are compressed by uniform and non uniform coders respectively the non uniform coders of the proposed method can preserve edge information of p pictures on the compressed image to perform an effective compression reconstruction of the p pictures a design method of non uniform coders is proposed based on an overlap level of fuzzy sets and a fuzzy equalization an experiment using 10 p pictures confirms that the root mean square error of the reconstructed images obtained by the proposed non uniform coders is decreased to 89 4 of that one of the uniform coders under the condition that compression rate the ratio between the file size of compressed image and original one is 0 0057 two test motions tennis and woman 100 frames are compressed and reconstructed by the proposed mcf

reconstruction equations and the karhunen loeve expansion for systems with symmetry we present a method for applying the karhunen loeve decomposition to systems with continuous symmetry the techniques in this paper contribute to the general procedure of removing variables associated with the symmetry of a problem and related ideas have been used in previous works both to identify coherent structures in solutions of pdes and to derive low order models via galerkin projection the main result of this paper is to derive a simple and easily implementable set of reconstruction equationswhich close the system of odes produced by galerkin projection the geometric interpretation of the method closely parallels techniques used in geometric phases and reconstruction techniques in geometric mechanics we apply the method to the kuramoto sivashinsky equation and are able to derive accurate models of considerably lower dimension than are possible with the traditional karhunen loeve expansion