the induction coefficient of induced representation theory its algebra and an analytic expression the induction coefficient is defined as the element of a matrix reducing the induced representation into irreducible constituents the authors give the algebra of these coefficients and a closed analytic expression in terms of matrix elements of coset representatives the consequences of this choice are derived and the importance of some of these results for the racah wigner coupling algebra of the symmetric and unitary groups noted

recursive calculation of transformation factors in terms of primitive factors the authors present an algorithm for recursively calculating coupling recoupling induction and similar coefficients in terms of the primitive coefficients the algorithm is shown to be complete for any compact group they use the 6 j symbol as an example for describing their algorithm but the algorithm applies to a wide class of group theoretic transformation factors

calculus for interval valued functions using generalized hukuhara derivative and applications this paper is devoted to studying differential calculus for interval valued functions by using the generalized hukuhara differentiability which is the most general concept of differentiability for interval valued functions conditions examples and counterexamples for limit continuity integrability and differentiability are given special emphasis is set to the class f t c g t where c is an interval and g is a real function of a real variable here the emphasis is placed on the fact that f and g do not necessarily share their properties underlying the extra care that must be taken into account when dealing with interval valued functions two applications of the obtained results are presented the first one determines a delta method for interval valued random elements in the second application a new procedure to obtain solutions to an interval differential equation is introduced our results are relevant to fuzzy set theory because the usual fuzzy arithmetic extension functions and mathematical analysis are done on a cuts which are intervals

random walks on combs we develop techniques to obtain rigorous bounds on the behaviour of random walks on combs using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length we also calculate exactly the spectral dimension of some fixed non translationally invariant combs we relate the spectral dimension to the critical exponent of the mass of the two point function for random walks on random combs and compute mean displacements as a function of walk duration we prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension

some properties of a random walk on a comb structure abstract we analyze transport properties of a random walk on a comb structure which serves as a model for a random walk on the backbone of a percolation cluster it is shown that the random walk along the x axis which is the analog of the backbone exhibits anomalous diffusion in that x 2 n n 1 2 and the expected number of x sites visited is proportional to n 1 4 for large n the distribution function is found to be a two dimensional gaussian if a field in the x direction so that diffusion is asymmetric the expected displacement is found to be asymptotically proportional to n 1 2

on the linear equation method for the subduction problem in symmetric groups we focus on the transformation matrices between the standard young yamanouchi basis of an irreducible representation for the symmetric group sn and the split basis adapted to the direct product subgroups we introduce the concept of subduction graph and show that it conveniently describes the combinatorial structure of the equation system arisen from the linear equation method thus we can outline an improved algorithm to solve the subduction problem in symmetric groups by a graph searching process we conclude by observing that the general matrix form for multiplicity separations resulting from orthonormalization can be expressed in terms of sylvester matrices relative to a suitable inner product in the multiplicity space

a new approach to linear interval differential equations as a first step toward solving fuzzy differential abstract this study uses a concept of interval differentiability which was recently introduced to formulate interval initial value problems involving linear interval differential equations differently from the approaches that use the gh differentiability this study does not make use of a criterion of choice for switching points in order to obtain solutions for such problems the method herein presented provides solutions in a simple straightforward and computationally tractable way moreover these solutions are intuitive because they coincide with the solutions given by a differential inclusion method the efficiency and practicality of our approach are illustrated through some examples that have appeared in other articles

biased random walks on random combs we develop rigorous analytic techniques to study the behaviour of biased random walks on combs this enables us to calculate exactly the spectral dimension of random comb ensembles for any bias scenario in the teeth or spine two specific examples of random comb ensembles are discussed the random comb with nonzero probability of an infinitely long tooth at each vertex on the spine and the random comb with a power law distribution of tooth lengths we also analyse transport properties along the spine for these probability measures

functionals of brownian motion localization and metric graphs we review several results related to the problem of a quantum particle in a random environment in an introductory part we recall how several functionals of brownian motion arise in the study of electronic transport in weakly disordered metals weak localization two aspects of the physics of the one dimensional strong localization are reviewed some properties of the scattering by a random potential time delay distribution and a study of the spectrum of a random potential on a bounded domain the extreme value statistics of the eigenvalues then we mention several results concerning the diffusion on graphs and more generally the spectral properties of the schrodinger operator on graphs the interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated finally we consider a two dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices we recall the connection between spectral properties of this model and winding functionals of planar brownian motion

relations between cumulants in noncommutative probability abstract we express classical free boolean and monotone cumulants in terms of each other using combinatorics of heaps pyramids tutte polynomials and permutations we completely determine the coefficients of these formulas with the exception of the formula for classical cumulants in terms of monotone cumulants whose coefficients are only partially computed

anomalous diffusion and charge relaxation on comb model exact solutions abstract the random walks on the comb structure are considered it is shown that due to fingers a diffusion has an anomalous character that is an r m s displacement depends on time by a power way with exponent 1 2 the generalized diffusion equation for an anomalous case is deduced it essentially differs from a usual diffusion equation in the continuity equation form instead of the first time derivative the time derivative of fractal order 1 2 appears in the second part the charge relaxation on the comb structure is studied a non maxwell character is established the reason is that the electric field has three components but a charge may relax only along some conducting lines

brownian excursions on combs in this paper we use techniques from ito excursion theory to analyze brownian motion on generalized combs ito excursion theory is a little known area of probability theory and we therefore present a brief introduction for the uninitiated a general method for analyzing transport along the backbone of the comb is demonstrated and the specific case of a comb whose teeth are scaling branching trees is examined we then present a recursive method for evaluating the distribution of the first passage times on hierarchical combs

1 2 order fractional fokker planck equation on comblike model from the generalized scheme of random walks on the comblike structure it is shown how a 1 2 order fractional fokker planck equation can be derived the operator method for the moments associated with the distribution function p x t is used to solve the resulting equation also the anomalous diffusion along the backbone of the structure has been considered

the interval eigenvalue problem using constraint interval analysis with an application to linear differential equations abstract we study the interval eigenvalue problem and its application to stability theory of interval linear differential equations the interval eigenvalue problem is studied from a constraint interval representation affording advantages not found in previous approaches

reaction diffusion wave fronts on comblike structures from the hamilton jacobi formalism an explicit expression for the speed of wave front propagation along the backbone of comblike structures is obtained this expression through the waiting time distribution function takes into account the number of sites and their distribution in the secondary branches our theoretical results are supported by numerical simulations of the reaction random walk process on the structure finally a more complex situation such as the peano basin structure is also considered both theoretically and numerically exhibiting a good agreement too

unified continuum description for sub diffusion random walks on multi dimensional comb model abstract the anisotropic sub diffusion random walks on multi dimensional comb structure model have been studied in the continuum approximation the problem is that in the considered model mean square displacements on different directions have different power temporal dependencies so this case essentially differs from usual anisotropic diffusion case and it is not obviously how to describe such a diffusion by a unified way nevertheless the unified continuum description for such random walks has been developed as result the new generalization of fick s law for diffusion current has been obtained for anisotropic anomalous sub diffusion random walks in multi dimensional case namely it has been shown that the effective diffusion coefficient in the generalized fick s law has new operator form components of diffusion tensor instead of constant values have the fractional order temporal derivatives

on the growth of bounded trees bounded infinite graphs are defined on the basis of natural physical requirements when specialized to trees this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two we verify that this bound is saturated by a class of random trees in which case we also derive explicit expressions for the growth probabilities

non gaussian random walks the authors present an explicit expression for the probability distribution for the position of a continuous time random walker in an arbitrary number of dimensions when the interjump density has a long time tail in contrast to earlier results which require numerical inversion of a fourier integral they replace this numerical procedure by one that relies on the method of steepest descents their results are applied to diffusion on a comb and on a percolation cluster generated on a cayley tree at criticality and are confirmed numerically

bounds on eigenvalues of real and complex interval matrices we present a cheap and tight formula for bounding real and imaginary parts of eigenvalues of real or complex interval matrices it outperforms the classical formulae not only for the complex case but also for the real case in particular it generalizes and improves the results by rohn 1998 5 and hertz 2009 19 the main idea behind is to reduce the problem to enclosing eigenvalues of symmetric interval matrices for which diverse methods can be utilized the result helps in analysing stability of uncertain dynamical systems since the formula gives sufficient conditions for testing schur and hurwitz stability of interval matrices it may also serve as a starting point for some iteration methods

unequal twins probability distributions do not determine everything it is the common lore to assume that knowing the equation for the probability distribution function pdf of a stochastic model as a function of time tells the whole picture defining all other characteristics of the model we show that this is not the case by comparing two exactly solvable models of anomalous diffusion due to geometric constraints the comb model and the random walk on a random walk we show that though the two models have exactly the same pdfs they differ in other respects like their first passage time distributions their autocorrelation functions and their aging properties

first encounters on combs we consider two random walkers embedded in a finite two dimension comb and we study the mean first encounter time mfet evidencing mainly numerically different scalings with the linear size of the underlying network according to the initial position of the walkers if one of the two players is not allowed to move then the first encounter problem can be recast into a first passage problem mfpt for which we also obtain exact results for different initial configurations by comparing mfet and mfpt we are able to figure out possible search strategies and in particular we show that letting one player be fixed can be convenient to speed up the search as long as we can finely control the initial setting while for a random setting on average letting one player rest would slow down the search

generalized diffusion equation for anisotropic anomalous diffusion motivated by studies of comblike structures we present a generalization of the classical diffusion equation to model anisotropic anomalous diffusion we assume that the diffusive flux is given by a diffusion tensor acting on the gradient of the probability density where each component of the diffusion tensor can have its own scaling law we also assume scaling laws that have an explicit power law dependence on space and time solutions of the proposed generalized diffusion equation are consistent with previously derived asymptotic results for the probability density on comblike structures

diffusion on random comb structure effective medium approximation abstract the random walks on comb model of percolation clusters are studied the generalized diffusion equations in the form of fractal temporal derivatives are deduced the random distributions of fingers over lengths gaussian and power are studied in the effective medium approximation

diffusion on a random comb distribution function of the survival probability we investigate the distribution functionq p describing the survival probability on a comb consisting of a backbone with lateral randomly disconnected infinite branches two different regimes are analyzed in some detail i at short times q p is shown to have a self similar structure devil s staircase ii at large times this function becomes smooth and tends toward a rather well defined unit step function the disorder averaged survival probability is expected to decrease ast 3 4 at large times whereas the relative fluctuations of the sample dependentp0 t display a very slow decay in time going to zero liket 1 8

generating relations for reducing matrices i ordinary representations auxiliary groups are constructed that make it possible to reduce the multiplicity problem and to derive consistent generating relations for the elements of reducing matrices three examples are worked out to illustrate the general scheme

analytic study of a model of diffusion on a random comblike structure abstract we present an analytic study of a model of diffusion on a random comblike structure in which no bias field does exist neither along the backbone nor along the branches for any given disordered structure our analytic treatment allows to compute in an exact manner the asymptotic behaviour at large time of the probability of presence of the particle at its initial site and on the backbone and of the particle position and dispersion the expressions of these quantities are shown to coincide asymptotically with those derived in simple mean field treatments the results for any given sample do not depend on the particular configuration self averaging property the behaviours strongly depend on the distribution of the lengths of the branches with an exponential distribution transport is normal while anomalous diffusion may take place for a power law distribution when long branches are present with a sufficiently high weight

correspondence analysis with fuzzy data the fuzzy eigenvalue problem this paper constitutes a first step towards an extension of correspondence analysis with fuzzy data fca at this stage our main objective is to lay down the algebraic foundations for this fuzzy extension of the usual correspondence analysis a two step method is introduced to convert the fuzzy eigenvalue problem to an ordinary one we consider a fuzzy matrix as the set of its cuts each such cut is an interval valued matrix viewed as a line segment in the matrix space in this way line segments of cut matrices are transformed into intervals of eigenvalues therefore the two step method is essentially a reduction of the fuzzy eigenvalue problem to an ordinary one we illustrate the fca fuzzy eigenvalue problem with a simple numerical example we hope upon the completion of this project in near future to be able to supply the necessary tools for the end user of the correspondence analysis with fuzzy data

toy model of fractional transport of cancer cells due to self entrapping a simple mathematical model is proposed to study the influence of cell fission on transport the model describes fractional in time tumor development which is a one dimensional continuous time random walk the model is relevant for consideration of both solid and diffusive cancers

coefficients of fractional parentage for u m p n q u m n u p q and u m n u m u n the outer product reduction coefficients orc which reduce the representation rep induced from the irreps of the permutation groups s f1 and s f2 into the irreps of s f1 f2 are shown to be the indirect coupling coefficients for the u m p n q u m n u p q irreducible basis the non standard orc for reducing the rep induced from the non standard irreps of s f13 s f1 s f3 and s f24 s f2 s f4 into that of s f s f12 s f34 with fij fi fj f f12 f34 are identified with the u f u f12 u f34 clebsch gordan coefficient for the special gel fand bases of u f12 and u f34 the u m p n q u m n u p q cfp as well as its special case the u m p u m u p cfp are identified with the s f s f12 s f34 outer product isoscalar factor the u m n u m u n cfp are obtained from the u m n u m u n cfp by simply changing all the partition labels for u n into their conjugates interchanging rows with columns and taking into account a phase change the cfp can be calculated from the orc numerical values of the one body cfp for systems with up to six particles are tabulated

the fractional fokker planck equation on comb like model abstract the fractional fokker planck equation were used to describe the anomalous diffusion in external fields is derived using a comb like structure as a background model for the force free case the distribution function associated with space dependence diffusion coefficient along the backbone of the structure are obtained in a closed form of h function the operator method has been used to solve the fractional fokker planck equation taking the external field into account

symmetric and unitary group representations i duality theory an extension of the schur weyl duality connecting the representations of the symmetric and unitary groups is given the schur weyl basis is constructed using annihilation and creation operators three factorisation lemmas are derived their importance lies in the fact that they relate the phase freedoms within the racah wigner algebra of the symmetric groups and the unitary groups extensions of the regge symmetries are also given these are expressed in five duality relations

mesoscopic description of random walks on combs combs are a simple caricature of various types of natural branched structures which belong to the category of loopless graphs and consist of a backbone and branches we study continuous time random walks on combs and present a generic method to obtain their transport properties the random walk along the branches may be biased and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone we analyze the overall diffusion properties along the backbone and find normal diffusion anomalous diffusion and stochastic localization diffusion failure respectively depending on the characteristics of the continuous time random walk along the branches and compare our analytical results with stochastic simulations

generating relations for reducing matrices ii corepresentations the auxiliary group approach developed in paper 1 r dirl p kasperkovitz m i aroyo j n kotzev and m angelova tjurkedjieva j math phys 27 37 1986 is generalized for the case of corepresentations of antiunitary groups it allows us to reduce the multiplicity problem and to derive consistent generating relations for the elements of the reducing matrices for coreps two examples are worked out to illustrate the general scheme

scaling of the first passage time and the survival probability on exact and quasi exact self similar structures the authors calculate the asymptotic behaviour of the moments of the first passage time and survival probability for random walks on an exactly self similar tree and on a quasi self similar comb by applying an exact decimation approach to the master equations for the hierarchical comb a transition from ordinary to anomalous diffusion occurs at r 2 where r is the ratio of teeth length in successive iterations of the structure in the anomalous regime r 2 the positive integer moments of the first passage time tq scale as ltau q with tau q 1 2q 1 ln r ln 2 where l is the linear distance from input to output the asymptotic behaviour of the survival probability is studied using both scaling theory and by a direct solution of the master equations they find that the characteristic time t in the asymptotic exponential decay of the survival probability exp t t scales as t approximately ltau with tau ln r2 ln 2 i e tau is distinct from tau 1 however substantial corrections to this asymptotic form for tau exist and these are needed to account for the recent simulation data of havlin and matan 1988

similarity transformations of irreducible corepresentations in wigner canonical form the general form of the matrices that transform an irreducible corepresentation coirrep into an equivalent one where both representations are assumed to be in the form proposed by wigner is analyzed for the three types of coirreps in addition the relation of these transformations to inner automorphisms of the corresponding group algebras is clarified

anomalous diffusion on a fractal mesh we present exact analytical results for properties of anomalous diffusion on a fractal mesh the fractal mesh structure is a direct product of two fractal sets one belonging to a main branch of backbones the other to the side branches of fingers both fractal sets are constructed on the entire infinite y and x axes we suggest a special algorithm in order to construct such sets out of standard cantor sets embedded in the unit interval the transport properties of the fractal mesh are studied in particular subdiffusion along the backbones is obtained with the dispersion relation x 2 t t where the transport exponent 1 has been observed as well when the environment is controlled by means of a memory kernel

generating relations for reducing matrices iii kronecker products in the first two of this series of papers r dirl et al j math phys 27 37 1986 m i aroyo et al ibid 27 2236 1986 a systematic method to calculate the elements of reducing matrices has been developed in this paper this auxiliary group approach is adapted to multiple kronecker products three examples are worked out to illustrate the efficiency of generating relations and the proposed reduction of the multiplicity problem

some properties of a fractal time continuous time random walk in the presence of traps the ctrw has often been applied to problems related to transport in a statistically homogeneous disordered medium which means that there are no traps or reflecting boundaries to be found in the medium two physical applications one to the migration of photons in a turbid medium and the second to the theory of diffusion controlled reactions in a random medium suggest that it might be useful to study properties of the ctrw particularly as they refer to survival probability in the presence of a trap or a trapping surface we calculate a number of these properties when the pausing time density is asymptotically proportional to a stable law i e t t 1 as t t where 0 1 a forthcoming paper will establish the correspondence between properties of the ctrw and proprties of random walkers on a fractal with trapping boundaries

cutting decimation renormalization for diffusive and vibrational dynamics on fractals abstract recently we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics this phenomenon we call dynamical dimension splitting is related to the lack of exact decimation invariance for these structures which turn out to be invariant under a more complex cutting decimation transform in this paper we study in details the dynamical dimension splitting on these fractals analyzing the mathematical properties of the cutting decimation transform our results clarify how the splitting arises from the cutting transform and show that the dynamical dimension degeneracy is a very peculiar consequence of exact decimability

type adapted subduction matrices if an irreducible representation is restricted to a subgroup it becomes reducible in general the matrices transforming this reducible representation into a direct sum of irreducible constituents are called subduction matrices their structure is discussed for real complex and quaternionic representations where all these representations are assumed to show a peculiar structure characteristic for the type of this representation character test 0 the choice of these type adapted representations a convention possible for all compact groups considerably reduces the number of parameters needed to fix a subduction matrix

the symmetric group algebraic formulas for some sf 6j symbols and sf sf1 sf2 3jm symbols explicit rank dependent expressions have been obtained for some symmetric group sf 6j symbols and some sf sf1 sf2 3jm symbols using butler s recursion method a key point in deriving these results is the use of the reduced notation introduced by murnaghan to label irreps various symmetries of the 6j and 3jm symbols have been imposed these include the complex conjugation permutation and transpose conjugation we incorporate a new symmetry that arises from the occurrence of the two isomorphic direct product groups sf1 sf2 and sf2 sf1 as subgroups of sf in relation to the tables of 6j and 3jm symbols presented a discussion is given of the symmetric group unitary group duality

levy processes on a generalized fractal comb comb geometry constituted of a backbone and fingers is one of the most simple paradigm of a two dimensional structure where anomalous diffusion can be realized in the framework of markov processes however the intrinsic properties of the structure can destroy this markovian transport these effects can be described by the memory and spatial kernels in particular the fractal structure of the fingers which is controlled by the spatial kernel in both the real and the fourier spaces leads to the levy processes levy flights and superdiffusion this generalization of the fractional diffusion is described by the riesz space fractional derivative in the framework of this generalized fractal comb model levy processes are considered and exact solutions for the probability distribution functions are obtained in terms of the fox h function for a variety of the memory kernels and the rate of the superdiffusive spreading is studied by calculating the fractional moments for a special form of the memory kernels we also observed a competition between long rests and long jumps finally we considered the fractal structure of the fingers controlled by a weierstrass function which leads to the power law kernel in the fourier space this is a special case when the second moment exists for superdiffusion in this competition between long rests and long jumps

generalized time dependent schrodinger equation in two dimensions under constraints we investigate a generalized two dimensional time dependent schrodinger equation on a comb with a memory kernel a dirac delta term is introduced in the schrodinger equation so that the quantum motion along the x direction is constrained at y 0 the wave function is analyzed by using green s function approach for several forms of the memory kernel which are of particular interest closed form solutions for the cases of dirac delta and power law memory kernels in terms of fox h function as well as for a distributed order memory kernel are obtained further a nonlocal term is also introduced and investigated analytically it is shown that the solution for such a case can be represented in terms of infinite series in fox h functions green s functions for each of the considered cases are analyzed and plotted for the most representative ones anomalous diffusion signatures are evident from the presence of the power law tails the normalized green s functions obtained in this work are of broader interest

calculating symmetric group split standard transformation coefficients using the block selective method a proof the split basis for the symmetric group sn is adapted to sn and to the product subgroup sn a sa the entries in the matrix that transforms between the split basis representation and the standard young yamanouchi yy basis the split standard transformation coefficients are closely related to a particle coefficients of fractional parentage recently the block selective conjecture was proposed for calculating the coefficients the conjecture implies that the transformation matrix is directly related to the representation matrix in the yy basis of a cycle permutation we present a proof of this conjecture

field induced drift and trapping in percolation networks the authors study the effects of a bias producing external field on a random walk on the infinite cluster in the percolation problem there are two competing physical effects drift and trapping which result in a drift velocity nu which rises and then falls as the field increases they study these effects on a one dimensional lattice with random length branches and on the diluted bethe lattice they calculate nu in the first model with a maximum allowed length for each branch in the limit that this cutoff length becomes infinite they find that the velocity vanishes identically above a finite critical value of the field for the bethe lattice they derive an upper bound on the critical field which varies as p pc 1 2 as the percolation concentration pc is approached in the one dimensional model they also investigate the anomalous regime in which the velocity vanishes they discuss the distribution of steady state times required to traverse n sites and find that it can be described in terms of a stable distribution of index x with superimposed oscillations the index x of the stable distribution is given by l xi where xi is a characteristic branch length and l is a bias induced length which describes the exponential buildup of the steady state density of particles towards the end of a branch

symmetries of group subgroup transformation factors for coupling subduction and induction group subgroup gh transformation theory uses g transformation coefficients and gh transformation factors to describe the relationship between the various bases of representation space of any group decomposed into irreducible representation spaces of the group and its subgroups the representation spaces may be formed by the processes of coupling subduction or induction the authors further develop this gh transformation theory with the study of the various symmetries complex conjugation transposition and associativity of the gh transformation factor emphasising the origins of each symmetry and a hierarchy within these symmetries a method of calculation is given for certain transformation factors the results and methods presented here generalise those of the racah wigner coupling algebra

3jm and 6j tables for some bases of su6 and su3 tables of 6j symbols for su6 and su3 and tables of 3jm factors for su6 contains implies su2 su3 su3 contains implies u1 su2 and su3 contains implies so3 are presented the tables are computer produced using a program that implements the building up principle in a general form these tables are useful for calculations in high energy nuclear and solid state physics some other tabulations contain errors and none uses all the symmetries available the n independence of sun results is discussed by using the various symmetric group unitary group duality relations

a class of linear differential dynamical systems with fuzzy matrices abstract this paper investigates the first order linear fuzzy differential dynamical systems with fuzzy matrices we use a complex number representation of the level sets of the fuzzy system and obtain the solution by employing such representation it is applicable to practical computations and has also some implications for the theory of fuzzy differential equations we then present some properties of the 2 dimensional dynamical systems and their phase portraits some examples are considered to show the richness of the theory and we can clearly see that new behaviors appear we finally present some conclusions and new directions for further research in the area of fuzzy dynamical systems

coupling subduction and induction transformations for group representations the basis of a representation space of any group may be chosen according to its decomposition into representations of the group and a subgroup chain coupling recoupling subduction and resubduction factors are each shown to arise as a result of schur s lemmas and a particular group subgroup structure when induction and mackey s subgroup theorem are considered new transformation factors occur those of induction and reinduction key properties of these factors are given together with their relationship with double coset matrix elements

subeigenvectors and supereigenvectors of fuzzy matrices abstract a fuzzy algebra is a triple b where b is a nonempty bounded linearly ordered set and a b max a b a b min a b for a b b a vector x is said to be a eigenvector of a square matrix a if a x x for some b the aim of the paper is to solve subeigenproblem and supereigenproblem for some b that is to find a solution x of a x x and a x x x is called subeigenvector and supereigenvector respectively the problems are related to and motivated by the similar problems of tropical linear algebra in this paper the properties of subeigenvectors and supereigenvectors are described and the values associated with subeigenvectors and supereigenvectors are characterized as a consequence efficient algorithms for checking all equivalent conditions are introduced

the diffusion drift equation on comb like structure from the generalized scheme of random walks on the comb like structure one can obtain the fractional fokker planck equation in the domain of fractal time evolution with critical exponent 0 1 the operator method for the moments associated with the density p x t is used to solve the obtained equation it is shown that due to fingers diffusion has an anomalous character the first two moments increase sub linearly in time

the character table for the corepresentations of magnetic groups a square character table is shown to exist for all finite magnetic groups the table possesses row and column orthogonality properties similar to the character table for linear groups

transport properties on a random comb we study the random walk of a particle in a random comb structure both in the presence of a biasing field and an the field free case we show that the mean field treatment of the quenched disorder can be exactly mapped on to a continuous time random walk ctrw on the backbone of the comb with a definite waiting time density we find an exact expression for this central quantity the green function for the ctrw is then obtained its first and second moments determine the drift and diffusion at all times we show that the drift velocity v vanishes asymptotically for power law and stretched exponential distributions of branch lengths on the comb whatever be the biasing field strength for an exponential branch length distribution v is a nonmonotonic function of the bias increasing initially to a maximum and then decreasing to zero at a critical value in the field free case anomalous diffusion occurs for a range of power law distributions of the branch length the corresponding exponent for the mean square displacement is obtained as is the asymptotic form of the positional probability distribution for the random walk we show that normal diffusion occurs whenever the mean branch length is finite and present a simple formula for the effective diffusion constant these results are extended to regular nonrandom combs as well the physical reason for anomalous drift or diffusion is traced to the properties of the distribution of a first passage time on a finite chain that controls the effective waiting time density of the ctrw

simultaneity and reality of u n and su n 3jm and 6j symbols a simple proof is given of the simultaneous existence of a real set of 3jm and 6j symbols for the unitary groups u n and su n including the case of mixed tensor representations we observe that simultaneity is incompatible with the conventional permutation symmetries for u n with n 3 the relevance of these results to the schur weyl duality of u n with the symmetric groups sl is discussed

propagators of random walks on comb lattices of arbitrary dimension we study diffusion on comb lattices of arbitrary dimension relying on the loopless structure of these lattices and using first passage properties we obtain exact and explicit formulae for the laplace transforms of the propagators associated to nearest neighbour random walks in both cases where either the first or the last point of the random walk is on the backbone of the lattice and where the two extremities are arbitrarily chosen as an application we compute the mean square displacement of a random walker on a comb of arbitrary dimension we also propose an alternative and consistent approach of the problem using a master equation description and obtain simple and generic expressions of the propagators this method is more general and is extended to study the propagators of random walks on more complex comb like structures in particular we study the case of a two dimensional comb lattice with teeth of finite length

diffusion on random comblike structures field induced trapping effects an analytic study of diffusion in random comblike structures in which field induced trapping effects enter into play is presented in order to mimic at best a percolation cluster above pc the distribution of the lengths of the branches is taken as exponential the branches act as traps of efficiency growing with the applied bias the asymptotic behaviour at large time of the probability of presence of the particle at its initial site and on the backbone and of its position and dispersion are computed in an exact manner as a result when the field exceeds a certain critical value anomalous behaviours emerge characterized by exponents depending continuously on the field

an algorithm for addressing the real interval eigenvalue problem in this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices such matrices could be used to model real life problems where data sets suffer from bounded variations such as uncertainties e g tolerances on parameters measurement errors or to study problems for given states the algorithm that we propose is a subdivision algorithm that exploits sophisticated techniques from interval analysis the quality of the computed approximation and the running time of the algorithm depend on a given input accuracy we also present an efficient c implementation and illustrate its efficiency on various data sets in most of the cases we manage to compute efficiently the exact boundary points limited by floating point representation

single level constraint interval arithmetic in the present paper we propose a variant of constraint interval arithmetic that operates with a single parameter level in each interval operand of an expression this results in a computationally simple interval arithmetic that has several desirable properties not shared in general by interval operations previously defined in the literature the actualization and usefulness of this approach to fuzzy interval arithmetic is accomplished via alpha levels the evaluation of arithmetic expressions using the proposed single level constrained arithmetic is discussed in detail and we extend this theory to the fuzzy context

symmetry classification and exact solutions of the one dimensional fokker planck equation with arbitrary coefficients of drift and diffusion symmetry properties of the one dimensional fokker planck equations with arbitrary coefficients of drift and diffusion are investigated it is proved that the group symmetry of these equations can be one two four or six parametric and corresponding criteria are obtained the changes of the variables reducing fokker planck equations to the heat equation and schrodinger equation with certain potentials are determined using the substructure of the invariance algebra of the rayleigh process equation we obtain the differential invariants and construct some classes of the exact solutions of this equation

the auxiliary group approach to the reduction of kronecker products bijective mappings of matrix representations are used to derive generating relations for clebsch gordon coefficients and to reduce the multiplicity problem

interval linear systems as a necessary step in fuzzy linear systems this article clarifies what it means to solve a system of fuzzy linear equations relying on the fact that they are a direct extension of interval linear systems of equations already studied in a specific interval mathematics literature we highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals each of which based on a generalization of scalar equality to intervals each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals we also consider the smallest multidimensional intervals containing the solution sets we propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals this unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies

generalized hukuhara differentiability of interval valued functions and interval differential equations abstract in the present paper we use a recently proposed generalization of the hukuhara difference for compact convex sets to introduce and study a generalization of the hukuhara differentiability to the case of interval valued functions we also consider several possible definitions for the derivative of an interval valued function recently proposed in the literature and we study connections between them and their properties using these concepts we study interval differential equations local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ode systems several examples are also shown

quantum oscillations in mesoscopic rings and anomalous diffusion we consider the weak localization correction to the conductance of a ring connected to a network we analyse the harmonics content of the al tshuler aronov spivak aas oscillations and we show that the presence of wires connected to the ring is responsible for a behaviour different from the one predicted by aas the physical origin of this behaviour is the anomalous diffusion of brownian trajectories around the ring due to the diffusion in the wires we show that this problem is related to the anomalous diffusion along the skeleton of a comb we study in detail the winding properties of brownian curves around a ring connected to an arbitrary network our analysis is based on the spectral determinant and on the introduction of an effective perimeter probing the different time scales a general expression of this length is derived for arbitrary networks more specifically we consider the case of a ring connected to wires to a square network and to a bethe lattice

additional symmetry of clebsch gordan coefficients for corepresentations the concept of associated representations is generalised for the case of corepresentations symmetry relations for the clebsch gordan coefficients based on the association of corepresentations are derived this additional symmetry not only reduces the volume of the calculations and the tables of coupling coefficients but it also improves the correlation between the coefficients a simple method for obtaining the clebsch gordan coefficients for odd under space inversion basis functions is proposed

speeding up evolutionary search by small fitness fluctuations we consider a fixed size population that undergoes an evolutionary adaptation in the weak mutation rate limit which we model as a biased langevin process in the genotype space we show analytically and numerically that if the fitness landscape has a small highly epistatic rough and time varying component then the population genotype exhibits a high effective diffusion in the genotype space and is able to escape local fitness minima with a large probability we argue that our principal finding that even very small time dependent fluctuations of fitness can substantially speed up evolution is valid for a wide class of models

analytical solutions for diffusion on fractal objects a generalization of the euclidean diffusion equation is proposed for diffusion on fractals on the basis of a scaling argument a renormalization group theory for the green s function and numerical tests conjectures on the applicability to natural fractals such as porous media are presented

generating relations for reducing matrices iv subduced representations a subduced representation da gb is a co representation of the group gb obtained by restricting the co representation da of a supergroup ga to the elements of gb a systematic and efficient method for calculating the matrices needed for the decomposition of da gb into irreducible constituents is discussed in this paper where the auxiliary group approach developed previously j math phys 27 37 2236 1986 28 1947 1987 is adopted to the present problem

transport and fluctuation dissipation relations in asymptotic and preasymptotic diffusion across channels with variable section we study the asymptotic and preasymptotic diffusive properties of brownian particles in channels whose section varies periodically in space the effective diffusion coefficient d mathrm eff is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries considering even cases of steep variations of the channel boundaries moreover we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known fick jacobs approximation building an effective one dimensional equation for the longitudinal diffusion we obtain an approximation for the effective diffusion coefficient such a result goes beyond a perturbation approach and it is in good agreement with the actual values obtained by the numerical simulations we discuss also the preasymptotic diffusion which is observed up to a crossover time whose value in the presence of strong spatial variation of the channel cross section can be very large in addition we show how the einstein s relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes

exact results and self averaging properties for random random walks on a one dimensional infinite lattice we present new exact results for a one dimensional asymmetric disordered hopping model the lattice is taken infinite from the start and we do not resort to the periodization scheme used by derrida an explicit resummation allows for the calculation of the velocityv and the diffusion constantd which are found to coincide with those given by derrida and for demonstrating thatv is indeed a self averaging quantity the same property is established ford in the limiting case of a directed walk