single variable term semi latticized fuzzy relation geometric programming with max product operator considering the practical application background in peer to peer network system we investigate the single variable term semi latticized fuzzy relation geometric programming with max product operator in this paper based on the characteristics of the objective function and feasible domain we develop a matrix approach to deal with the proposed problem a step by step algorithm is proposed to find an optimal solution without solving all the minimal solutions of the constraint two examples are given to illustrate the feasibility and efficiency of the algorithm

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

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

nonlinear network description for many body quantum systems in continuous space we show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units using this wave function in variational monte carlo simulations of liquid 4 mathrm he in two and three dimensions we typically find a tenfold increase in accuracy over currently used wave functions furthermore subsequent stages of the iteration procedure define a set of increasingly good wave functions each with its own variational energy and variance of the local energy extrapolation to zero variance gives energies in close agreement with the exact values for two dimensional 4 mathrm he we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form a feature shared with the shadow wave function but now joined by much higher accuracy we also achieve significant progress for liquid 3 mathrm he in three dimensions improving previous variational and fixed node energies

the spectral gap for some spin chains with discrete symmetry breaking we prove that for any finite set of generalized valence bond solid gvbs states of a quantum spin chain there exists a translation invariant finite range hamiltonian for which this set is the set of ground states this result implies that there are gvbs models with arbitrary broken discrete symmetries that are described as combinations of lattice translations lattice reflections and local unitary or anti unitary transformations we also show that all gvbs models that satisfy some natural conditions have a spectral gap the existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics this general scheme is interesting in its own right and threfore although the basic idea is not new we present it in a system independent setting the results are illustrated with a number of examples

transfer matrix renormalization group method for general markov random fields abstract we seek the numerical calculation of partition functions of general markov random fields mrfs on an infinitely long twisted cylindrical lattice by using the transfer matrix renormalization group tmrg method the tmrg is a variant of the density matrix renormalization group dmrg which automatically truncates the hilbert space so that the properties of large systems can be precisely calculated while the dimension of the renormalized hilbert space remains constant we apply the tmrg to the decimation of the fundamental transfer matrix that we have proposed previously for general mrfs instead of the standard s e scheme for tmrg we propose a new e s e scheme and propose an alternative method for selecting the renormalized basis specifically the new e s e scheme keeps those singular value decomposition svd components of the fundamental transfer matrix that are relevant for the perron state and truncates the other irrelevant ones results for the ising model show that our method exhibits very impressive accuracy under a rather restricted computational resource simulations for another four general mrfs demonstrate that our tmrg method is superior to the classical monte carlo method in accuracy computational speed and in the possibility of treating a much larger system

thermodynamic model of social influence on two dimensional square lattice case for two features abstract we propose a thermodynamic multi state spin model in order to describe equilibrial behavior of a society our model is inspired by the axelrod model used in social network studies in the framework of the statistical mechanics language we analyze phase transitions of our model in which the spin interaction j is interpreted as a mutual communication among individuals forming a society the thermal fluctuations introduce a noise t into the communication which suppresses long range correlations below a certain phase transition point t t large scale clusters of the individuals who share a specific dominant property are formed the measure of the cluster sizes is an order parameter after spontaneous symmetry breaking by means of the corner transfer matrix renormalization group algorithm we treat our model in the thermodynamic limit and classify the phase transitions with respect to inherent degrees of freedom each individual is chosen to possess two independent features f 2 and each feature can assume one of q traits e g interests hence each individual is described by q 2 degrees of freedom a single first order phase transition is detected in our model if q 2 whereas two distinct continuous phase transitions are found if q 2 only evaluating the free energy order parameters specific heat and the entanglement von neumann entropy we classify the phase transitions t t q in detail the permanent existence of the ordered phase the large scale cluster formation with a non zero order parameter is conjectured below a non zero transition point t t q 0 5 in the asymptotic regime q

some results on the resolution of fuzzy relation equations abstract in this paper two special cases of the solution of the inverse problem are investigated the necessary and sufficient conditions for the existence of a solution such that the upper bound is the unit vector and for a unique solution of the inverse problem equal to the unit vector are presented an algorithmic approach which derives the output vector and the state matrix in each one of these cases is also proposed

multidomain spectral solution of the euler gas dynamics equations abstract we present interface treatments for computing the euler gas dynamics equations by a multidomain chebyshev spectral collocation method these treatments are suitable for use at the corners of subdomains and for patched or overlapping subdomains they can be applied to interfaces placed in subsonic supersonic or transonic regions of a flow computed results indicate that the solutions are spectrally accurate can be more accurate and more efficient than a single domain calculation and that reflections of waves at interfaces are not significant

probabilistic low rank factorization accelerates tensor network simulations of critical quantum many body ground states we provide evidence that randomized low rank factorization is a powerful tool for the determination of the ground state properties of low dimensional lattice hamiltonians through tensor network techniques in particular we show that randomized matrix factorization outperforms truncated singular value decomposition based on state of the art deterministic routines in time evolving block decimation tebd and density matrix renormalization group dmrg style simulations even when the system under study gets close to a phase transition we report linear speedups in the bond or local dimension of up to 24 times in quasi two dimensional cylindrical systems

solving a linear programming problem with the convex combination of the max min and the max average fuzzy relation equations abstract in this paper we introduce a fuzzy operator constructed by the convex combination of two known operators max min and max average compositions h j zimmermann fuzzy set theory and it s application kluwer academic publishers boston dordrecht london 1999 this operator contains some properties of the two known compositions when it generates the feasible region for linear optimization problems we investigate linear optimization problems whose feasible region is the fuzzy sets defined with this operator thus firstly the structure of these fuzzy regions is considered and then a method to solve the linear optimization problems with fuzzy equation constraints regarding this operator is presented

solving the master equation without kinetic monte carlo in multiscale modeling of heterogeneous catalytic processes one crucial point is the solution of a markovian master equation describing the stochastic reaction kinetics usually this is too high dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic monte carlo method in this study we break the curse of dimensionality for the direct solution of the markovian master equation by exploiting the tensor train format for this purpose the performance of the approach is demonstrated on a first principles based reduced model for the co oxidation on the ruo2 110 surface we investigate the complexity for increasing system size and for various reaction conditions the advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness

spectral solution of the viscous blunt body problem 2 multidomain approximation we present steady solutions of high speed viscous flows over blunt bodies using a multidomain chebyshev spectral collocation method the region within the shock layer is divided into subdomains so that internal layers can be well resolved in the interiors of the subdomains the solution is approximated by chebyshev collocation at interfaces between subdomains the advective terms are upwinded and the viscous terms are treated by a penalty method the method is applied to five flows in the mach number range 5 25 and reynolds number range from 2 x 10 3 to 83 x 10 4 based on nose radius results are compared with experimental data and to a finite difference solution

linear optimization with bipolar max min constraints we consider a generalization of the linear optimization problem with fuzzy relational in equality constraints by allowing for bipolar max min constraints i e constraints in which not only the independent variables but also their negations occur a necessary condition to have a non empty feasible domain is given the feasible domain if not empty is algebraically characterized a simple procedure is described to generate all maximizers of the linear optimization problem considered and is applied to various illustrative example problems

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

computational considerations for the simulation of shock induced sound the numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm because it requires the ability to propagate disturbances of small amplitude and short wavelength the demands are particularly high when shock waves are involved because the chosen algorithm must also resolve discontinuities in the solution the extent to which a high order accurate shock capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified such a study is initiated in this work a fourth order accurate essentially nonoscillatory eno method is used to investigate the solutions of inviscid compressible flows with shocks the design order of accuracy is achieved in the smooth regions of a steady state quasi one dimensional test case however in an unsteady test case only first order results are obtained downstream of a sound shock interaction the difficulty in obtaining a globally high order accurate solution in such a case with a shock capturing method is demonstrated through the study of a simplified linear model problem some of the difficult issues and ramifications for aeroacoustic simulations of flows with shocks that are raised by these results are discussed

shock fitted multidomain solution of supersonic flows abstract shock fitting is presented as a way to compute shocks with spectral methods with fitting spectral approximation is performed on smooth portions of the flow and a precise description of a discontinuous shock is possible coupled with spectral domain decomposition one has the ability to resolve efficiently and without stretching transformations boundary layers and other regions in the flow where increased local resolution is needed a supersonic blunt body problem is solved to provide an example of the use of the approach comparisons between computations and experimental measurements are made for body surface quantities shock shape and body normal direction profiles

relational equations in totally ordered lattices and their complete resolution abstract the set of all solutions of a composite fuzzy relation equation of sanchez inform and control 30 1976 defined on finite spaces is studied by determining and characterizing all the lower solutions of such an equation

increasing continuous operations in fuzzy max equations and inequalities abstract in this paper solutions of fuzzy systems of equations a x b and systems of inequalities a x b a x b are considered where a 0 1 m n b 0 1 m stands for max product and x 0 1 n is an unknown vector in this paper the families of all solutions are described during the last thirty years this problem was considered by many authors our goal is to achieve the most general assumptions for which sets of solutions systems of equations and inequalities are the union of lattice intervals especially a method of determination of all minimal solutions in such systems is indicated as a result the families of all solutions of fuzzy systems of inequalities a x b and a x b are described as the main part of these results the method of determination of the family of all minimal solutions in max system of equations with an increasing operation continuous on the second argument is presented

density matrix renormalization group study of the correlation function of the bilinear biquadratic spin 1 chain using the recently developed density matrix renormalization group approach we study the correlation function of the spin 1 chain with quadratic and biquadratic interactions this allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue combining our results with other studies we predict three phases in the region where the quadratic and biquadratic terms are both positive

solving fuzzy relation equations with a linear objective function abstract an optimization model with a linear objective function subject to a system of fuzzy relation equations is presented due to the non convexity of its feasible domain defined by fuzzy relation equations designing an efficient solution procedure for solving such problems is not a trivial job in this paper we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0 1 integer programming with a branch and bound solution technique after presenting our solution procedure a concrete example is included for illustration purpose

on the outflow conditions for spectral solution of the viscous blunt body problem the purpose of this paper is to study and identify suitable outflow boundary conditions for the numerical simulation of viscous supersonic hypersonic flow over blunt bodies governed by the compressible navier stokes equations with an emphasis motivated primarily by the use of spectral methods without any filtering the subsonic supersonic composition of the outflow boundary requires a dual boundary treatment for well posedness all compatibility relations modified to undertake the hyperbolic parabolic behaviour of the governing equations are used for the supersonic part of the outflow regarding the unknown downstream information in the subsonic region different subsonic outflow conditions in the sense of the viscous blunt body problem are examined a verification procedure is conducted to make out the distinctive effect of each outflow condition on the solution detailed comparisons are performed to examine the accuracy and performance of the outflow conditions considered for two model geometries of different surface curvature variations numerical simulations indicate a noticeable influence of pressure from subsonic portion to supersonic portion of the boundary layer it is demonstrated that two approaches for imposing subsonic outflow conditions namely 1 extrapolating all flow variables and 2 extrapolation of pressure along with using proper compatibility relations are more suitable than the others for accurate numerical simulation of viscous high speed flows over blunt bodies using spectral collocation methods

another modification from two papers of ghodousian and khorram and khorram et al abstract in this paper we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max min and the max average composition and the max star composition respectively they have been proposed by ghodousian and khorram a ghodousian e khorram solving a linear programming problem with the convex combination of the max min and the max average fuzzy relation equations appl math comput 180 2006 411 418 and khorram et al e khorram a ghodousian a abbasi molai solving linear optimization problems with max star composition equation constraints appl math comput 179 2006 654 661 respectively firstly we show that the tabular method algorithm in the first paper and the first procedure in the second paper may not lead to the optimal solutions of the two models in some cases secondly we generalize the proposed algorithm by abbasi molai and khorram a abbasi molai e khorram a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian appl math comput 190 2007 1161 1167 to solve the two models in fact it modifies the presented algorithms in the two papers finally some numerical examples are given to illustrate the purposes

global coefficient adjustment method for neumann condition in explicit chebyshev collocation method and its application to compressible navier stokes equations the present paper consists of two parts in part 1 a new technique of treating neumann boundary conditions with an explicit chebyshev collocation method is developed any neumann boundary condition can be satisfied by adjusting all the chebyshev coefficients of a solution which results in a small influence on the solution and its derivatives except at the boundary comparisons between the new technique and several traditional ones are made for a one dimensional advection diffusion problem which confirms the superiority of the new technique the spectral accuracy of the new technique is also demonstrated in part 2 a chebyshev collocation code for the compressible navier stokes equations is developed to solve the high speed flows around a sphere good resolutions are obtained in the boundary layer by using the new technique and comparison between the calculation and the experiment shows good agreement

elucidating reaction mechanisms on quantum computers with rapid recent advances in quantum technology we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers here we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems using the open problem of biological nitrogen fixation in nitrogenase as an example we discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms to significantly increase their accuracy and enable hitherto intractable simulations our resource estimates show that even when taking into account the substantial overhead of quantum error correction and the need to compile into discrete gate sets the necessary computations can be performed in reasonable time on small quantum computers our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources

spectral solution of the viscous blunt body problem the viscous blunt body problem is solved with a shock fitted chebyshev spectral method no explicit artificial viscosity or filtering is needed to obtain smooth converged solutions the method is applied to two problems first results for the flow over a right circular cylinder in the mach number range of 5 5 6 0 are compared with experimental data second a solution for a mach 25 flow over a hyperbolic cone is compared with a viscous shock layer calculation

optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by dubois prade family of t norms abstract in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated in doing so the feasible region is formed by the intersection of two inequality fuzzy systems and dubois prade family of t norms which are considered as fuzzy composition the most well known continuous t norms are archimedean such as frank yager hamacher sugeno weber and schweizer sklar family an interesting family of t norms that is not archimedean has been introduced by dubois and prade in this paper the resolution of the feasible region of the problem is initialy investigated when it is defined with max duboise prade composition a necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility of the problem moreover two procedures have also been presented with the aim of simplifying the current linear problems a method is proposed to generate random feasible max dubois prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem finally an example is described to illustrate this algorithm

fundamental limitations in the purifications of tensor networks we show a fundamental limitation in the description of quantum many body mixed states with tensor networks in purification form namely we show that there exist mixed states which can be represented as a translationally invariant ti matrix product density operator valid for all system sizes but for which there does not exist a ti purification valid for all system sizes the proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states the result also holds for classical states

parallelization strategies for density matrix renormalization group algorithms on shared memory systems shared memory smp parallelization strategies for density matrix renormalization group dmrg algorithms enable the treatment of complex systems in solid state physics we present two different approaches by which parallelization of the standard dmrg algorithm can be accomplished in an efficient way the methods are illustrated with dmrg calculations of the two dimensional hubbard model and the one dimensional holstein hubbard model on contemporary smp architectures the parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential dmrg calculations

symmetry respecting real space renormalization for the quantum ashkin teller model we use a simple real space renormalization group approach to investigate the critical behavior of the quantum ashkin teller model a one dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously this approach which is based on exploiting the on site symmetry of the model has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse field ising model our investigation explores this approach in more generality in a model in which the critical behavior has a richer structure but which reduces to the simpler ising case at a special point we demonstrate that the correlation length critical exponent as predicted from this real space renormalization group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality near the ising special point the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods although the accuracy decreases away from the decoupled ising model point

finitely correlated states on quantum spin chains we study a construction that yields a class of translation invariant states on quantum spin chains characterized by the property that the correlations across any bond can be modeled on a finite dimensional vector space these states can be considered as generalized valence bond states and they are dense in the set of all translation invariant states we develop a complete theory of the ergodic decomposition of such states including the decomposition into periodic neel ordered states the ergodic components have exponential decay of correlations all states considered can be obtained as local functions of states of a special kind so called purely generated states which are shown to be ground states for suitably chosen finite range vbs interactions we show that all these generalized vbs models have a spectral gap our theory does not require symmetry of the state with respect to a local gauge group in particular we illustrate our results with a one parameter family of examples which are not isotropic except for one special case this isotropic model coincides with the one dimensional antiferromagnet recently studied by affleck kennedy lieb and tasaki

a generalization of the injectivity condition for projected entangled pair states we introduce a family of tensor network states that we term semi injective projected entangled pair states pepss they extend the class of injective pepss and include other states like the ground states of the aklt and the czx models in square lattices we construct parent hamiltonians for which semi injective pepss are unique ground states we also determine the necessary and sufficient conditions for two tensors to generate the same family of such states in two spatial dimensions using this result we show that the third cohomology labeling of symmetry protected topological phases extends to semi injective pepss

standardized pseudospectral formulation of the inviscid supsersonic blunt body problem a highly accurate pseudospectral numerical approximation to the generalized coordinate nonconservative form of the euler equations is implemented for supersonic flow over an axisymmetric blunt body geometry shock fitting is employed to maintain global accuracy and minimize the corrupting influence of numerical viscosity the variables in the euler equations as well as the physical grid coordinates are collocated via lagrange interpolating polynomials and the problem is then cast in the standard form of a large system of ordinary differential equations dx d q x which can be solved using standard solution techniques that do not require an explicit criteria for the minimum time step code verification is performed by demonstrating through a series of grid refinement tests that the error in the approximation to a taylor maccoll solution converges to 10 12 grid refinement tests for flow over a blunt body show convergence of the numerical error also to 10 12 the code is validated for supersonic flow over a blunt body by comparison with the modified newtonian approximation for the surface pressure distribution and empirical predictions for the shock shape the ability of the method to capture unsteady flow phenomena is demonstrated on the problem of a planar acoustic wave interacting with an attached shock

convergence of powers for a fuzzy matrix with convex combination of max min and max arithmetic mean operations fuzzy matrices have been proposed to represent fuzzy relations on finite universes since thomason s paper in 1977 showing that powers of a max min fuzzy matrix either converge or oscillate with a finite period conditions for limiting behavior of powers of a fuzzy matrix have been studied it turns out that the limiting behavior depends on the algebraic operations employed which usually in the literature includes max min max product max archimedean t norm max t norm max arithmetic mean operations respectively in this paper we consider the powers of a fuzzy matrix with convex combination of max min and max arithmetic mean operations we show that the powers of such a fuzzy matrix are always convergent

a quantum version of wielandt s inequality in this paper wielandt s inequality for classical channels is extended to quantum channels that is an upper bound to the number of times a channel must be applied so that it maps any density operator to one with full rank is found using this bound dichotomy theorems for the zero error capacity of quantum channels and for the matrix product state mps dimension of ground states of frustration free hamiltonians are derived the obtained inequalities also imply new bounds on the required interaction range of hamiltonians with unique mps ground state

addition min fuzzy relation inequalities with application in bittorrent like peer to peer file sharing system abstract the data transmission mechanism in bittorrent like peer to peer p2p file sharing systems may be reduced to some addition min fuzzy relation inequalities the solution set of addition min fuzzy relation inequalities plays an important role in the corresponding optimization problem in this paper we study some properties of the solutions to such system convexity of the solution set and number of minimal solutions are discussed with comparison to those of the classical max t fuzzy relation equations or inequalities besides vertex solution and variable ordering minimal solution are also investigated with application in bittorrent like p2p file sharing system two numerical examples are given to illustrate the feasibility and efficiency of the algorithm for solving the variable ordering solution

spectral methods for the euler equations the blunt body problem revisited we solve the blunt body problem using shock fitting and a chehyshev spectral collocation method careful attention is paid to the boundary and shock acceleration equations

leximax minimum solution of addition min fuzzy relation inequalities abstract addition min fuzzy relation inequalities are introduced to characterize the peer to peer p2p network system in order to decrease the network congestion considering both efficiency and fairness we define the leximax minimum solution for system of addition min fuzzy relation inequalities the leximax optimality refines both pareto optimality and max optimality for solving the leximax minimum solution concepts of minimum zero point and minimax value are defined with corresponding resolution algorithms i e algorithms i and ii based on these two algorithms algorithm iii is further developed to find the unique leximax minimum solution numerical examples illustrate the validity of our proposed algorithms

low rank tensor recovery via iterative hard thresholding abstract we study extensions of compressive sensing and low rank matrix recovery matrix completion to the recovery of low rank tensors of higher order from a small number of linear measurements while the theoretical understanding of low rank matrix recovery is already well developed only few contributions on the low rank tensor recovery problem are available so far in this paper we introduce versions of the iterative hard thresholding algorithm for several tensor decompositions namely the higher order singular value decomposition hosvd the tensor train format tt and the general hierarchical tucker decomposition ht we provide a partial convergence result for these algorithms which is based on a variant of the restricted isometry property of the measurement operator adapted to the tensor decomposition at hand that induces a corresponding notion of tensor rank we show that subgaussian measurement ensembles satisfy the tensor restricted isometry property with high probability under a certain almost optimal bound on the number of measurements which depends on the corresponding tensor format these bounds are extended to partial fourier maps combined with random sign flips of the tensor entries finally we illustrate the performance of iterative hard thresholding methods for tensor recovery via numerical experiments where we consider recovery from gaussian random measurements tensor completion recovery of missing entries and fourier measurements for third order tensors

relaxation times in the asep model using a dmrg method we compute the largest relaxation times for the totally asymmetric exclusion process tasep with open boundary conditions with a dmrg method this allows us to reach much larger system sizes than in previous numerical studies we are then able to show that the phenomenological theory of the domain wall indeed predicts correctly the largest relaxation time for large systems besides we can obtain results even when the domain wall approach breaks down and show that the kpz dynamical exponent z 3 2 is recovered in the whole maximal current phase

on manifolds of tensors of fixed tt rank recently the format of tt tensors hackbusch and kuhn in j fourier anal appl 15 706 722 2009 oseledets in siam j sci comput 2009 submitted oseledets and tyrtyshnikov in siam j sci comput 31 5 2009 oseledets and tyrtyshnikov in linear algebra appl 2009 submitted has turned out to be a promising new format for the approximation of solutions of high dimensional problems in this paper we prove some new results for the tt representation of a tensor u in mathbb r n 1 times cdots times n d and for the manifold of tensors of tt rank underline r as a first result we prove that the tt or compression ranks r i of a tensor u are unique and equal to the respective separation ranks of u if the components of the tt decomposition are required to fulfil a certain maximal rank condition we then show that the set mathbb t of tt tensors of fixed rank underline r locally forms an embedded manifold in mathbb r n 1 times cdots times n d therefore preserving the essential theoretical properties of the tucker format but often showing an improved scaling behaviour extending a similar approach for matrices conte and lubich in m2an 44 759 2010 we introduce certain gauge conditions to obtain a unique representation of the tangent space mathcal t u mathbb t of mathbb t and deduce a local parametrization of the tt manifold the parametrisation of mathcal t u mathbb t is often crucial for an algorithmic treatment of high dimensional time dependent pdes and minimisation problems lubich in from quantum to classical molecular dynamics reduced methods and numerical analysis 2008 we conclude with remarks on those applications and present some numerical examples

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

a renormalization group theory of cultural evolution abstract we present a theory of cultural evolution based upon a renormalization group scheme we consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment these representations are built around the most important degrees of freedom of their world cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequate order parameter as the importance of social interactions increases or agents become more intelligent we observe and quantify a series of dynamic phase transitions by which cultural coherence advances in the society a similar phase transition may explain the so called cultural explosion in human evolution some 50 000 years ago

multidomain spectral solution of compressible viscous flows abstract we develop a nonoverlapping multidomain spectral collocation method to solve compressible viscous flows at the interfaces the advection terms are treated with a characteristic correction method the diffusion terms are treated with a penalty method spectral accuracy is demonstrated on linear model problems in one and two space dimensions the method is applied to a subsonic and a supersonic flow over a flat plate the results are compared to solutions of the boundary layer equations which show that two digit accuracy in the adiabatic plate temperature is obtained with 16 points in the boundary layer for a freestream mach number of two a second application is to a transonic flow in a two dimensional converging diverging nozzle where the computed results are compared to experimental data

lexicographic optimal solution of the multi objective programming problem subject to max product fuzzy relation inequalities abstract it is shown in this paper that the emission base stations in wireless communication can be reduced into a system of fuzzy relation inequalities with max product composition for optimal management in such system we introduce the fuzzy relation multi objective programming concept of feasible index set fis is defined based on which a novel algorithm named fis algorithm is developed to find the unique lexicographic optimal solution of the proposed problem with polynomial computational complexity applying this method we needn t to find out all the minimal solutions of the constraint a numerical application example is provided to illustrate the feasibility and efficiency of the fis algorithm

quasioptimality of maximum volume cross interpolation of tensors we consider a cross interpolation of high dimensional arrays in the tensor train format we prove that the maximum volume choice of the interpolation sets provides the quasioptimal interpolation accuracy that differs from the best possible accuracy by the factor which does not grow exponentially with dimension for nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms we justify the theoretical results and measure speed and accuracy of the proposed algorithm with numerical experiments

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

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

further contributions to the study of finite fuzzy relations equations abstract an interesting property of the schein rank of a fuzzy matrix stressed by k h kim and f w roush is formalized as definition of the basis of a set of fuzzy vectors defined over a commutative semiring with respect to another set of fuzzy vectors we apply this definition and another related concept in the setting of finite fuzzy relation equations in particular we give a sufficient condition for the existence of the smallest solution of a max min fuzzy equation

a linear programming approach for minimizing a linear function subject to fuzzy relational inequalities with addition min composition in this paper we study an optimization problem of minimizing a linear function subject to fuzzy relational inequalities with the addition min composition this optimization setting has recently been proposed to model the network cogestion issue when a bittorrent like peer to peer file sharing system is used for data transmission in a 2014 paper a pseudominimal index pmi based approach was proposed to search for an optimal solution it turns out that the pmi based approach may require to solve several to many linear programming problems in order to get an optimal solution in this paper we point out that the feasible domain is indeed convex and we only need to solve a single linear programming problem to generate an optimal solution for the original optimization problem furthermore our approach could be extended to the case with a nonlinear continuous objective function

spectral methods for the euler equations ii chebyshev methods and shock fitting on exprime chaque composante de la vitesse dans les equations d euler par une somme de polynomes de tchebycheff qui constitue une fonction d interpolation on utilise les expressions spectrales ainsi obtenues pour calculer plusieurs ecoulements gazeux bidimensionnels par la methode d ajustement d ondes de choc selon cette methode les conditions initiales correspondent a une onde de choc plane normale a un ecoulement supersonique et on determine la forme veritable de l onde a l aide des formules de rankine hugoniot qui expriment les conditions aux limites

a modified pso algorithm for linear optimization problem subject to the generalized fuzzy relational inequalities with fuzzy constraints fri fc in this paper optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t norm is considered as fuzzy composition and fuzzy inequality replaces ordinary inequality in the constraints unlike most optimization algorithms in fuzzy relational inequalities with fuzzy constraints fri fc we find a near feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp ordinary inequality constraints such solutions are called super optima in this paper subsequently an algorithm is proposed to find a super optimum with pre specified desirable infeasibility for this purpose we firstly study some structural properties of the fri fc problem and present a new formulization that is independent of t norms used in the constraints of the problem this new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters however it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super optimum under a certain sufficient condition finally a modified pso is presented in which the ability of pso to solve unconstrained problems with continuous domain the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized fri fc problems the modified pso algorithm has been applied to the generalized fri fc problem defined with ten well known continuous t norms additionally an idea of the fri fc problems as outer approximators for fri problems with ordinary inequalities is also investigated

optimal vector based algorithm for solving min max programming subject to addition min fuzzy relation inequality optimal management model in bittorrent like peer to peer p2p file sharing system can be reduced into a min max programming problem subject to addition min fuzzy relation inequality to deal with such problem we introduce the concept of optimal vector besides a novel optimal vector based ovb algorithm is developed to find a minimal optimal solution based on practical application consideration solution obtained by the ovb algorithm is theoretically demonstrated to be better than or equal to that obtained by the existing method advantage of our proposed ovb algorithm is illustrated by detailed numerical examples

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure