the essential spectrum of schrodinger operators with asymptotically constant magnetic fields on the poincare upper half plane we study the essential spectrum of the magnetic schrodinger operators on the poincare upper half plane and establish a hyperbolic analog of iwatsuka s result j math kyoto univ 23 3 475 480 1983 on the stability of the essential spectrum under perturbations from constant magnetic fields

renormalization study of two dimensional convergent solutions of the porous medium equation in the focusing problem we study a solution of the porous medium equation ut d 1 u m whose initial distribution is positive in the exterior of a closed noncircular two dimensional region and zero inside we implement a numerical scheme that renormalizes the solution each time that the average size of the empty region reduces by a half the initial condition is a function with circular level sets distorted with a small sinusoidal perturbation of wave number k 3 we find that for nonlinearity exponents m smaller than a critical value which depends on k the solution tends to a self similar regime characterized by rounded polygonal interfaces and similarity exponents that depend on m and on the discrete rotational symmetry numberk f orm greater than the critical value the final form of the interface is circular 2000 elsevier science

renormalization group analysis of differential equations subject to slowly modulated perturbations abstract the application of renormalization group rg theory to the asymptotic analysis of differential equations is considered it is found that there is a class of small structural perturbations whose effects cannot be systematically treated using the gell mann low rg approach applied in this context guided by a reinterpretation of the calculational procedure employed in this approach whose motivation is provided by the unnecessarily complicated nature of its standard interpretation we formulate a generalized perturbative analysis and an rg approach which naturally and systematically treat equations subject to perturbations of this class this formulation of rg theory is demonstrated with a number of examples for which the gell mann low formulation fails to provide a systematic theoretical framework for one representative example it is found that the wilson rg formulation also fails the implications of this failure are discussed

brownian motion on the hyperbolic plane and selberg trace formula abstract we will show that the relation of the heat kernels for the schrodinger operators with uniform magnetic fields on the hyperbolic plane h 2 the maass laplacians and for the schrodinger operators with morse potentials on r is given by means of a one dimensional fourier transform in the framework of stochastic analysis where the brownian motion on h 2 plays an important role by using this relation we will give the explicit forms of the green functions as a typical related problem we will discuss the selberg trace formula the close relation of the trace formula with the corresponding classical mechanics will also be discussed

distributivity equation in the class of 2 uninorms this paper is mainly devoted to solving the functional equation of distributivity between aggregation operators with 2 neutral element our investigations are motivated by the couple of distributive logical connectives and their generalizations used in fuzzy set theory e g triangular norms conorms uninorms nullnorms and implications one of the recent generalizations covering both uninorms and nullnorms are 2 uninorms which form a class of commutative associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements in this work the distributivity of two binary operators from the class of 2 uninorms is considered in particular all possible solutions of the distributivity equation for the three defined subclasses of these operators depending on the position of its zero and neutral elements are characterized

pseudo arithmetical operations as a basis for the general measure and integration theory several generalizations of the classical measure and integration theory are based on some generalizations of the standard arithmetical operations the axiomatic approach to the pseudo arithmetical operations of pseudo addition and pseudo multiplication is discussed some of required properties strongly influence the structure of these operations and consequently the resulting measure and integral generalizations so e g the idempotency of the unit element u results to the idempotency of the pseudoaddition i e v sup several other properties of and and their consequences are discussed and illustrated by examples

determinants of laplacians the determinant of the laplacian on spinor fields on a riemann surface is evaluated in terms of the value of the selberg zeta function at the middle of the critical strip a key role in deriving this relation is played by the barnes double gamma function

optimal prediction with memory abstract optimal prediction methods estimate the solution of nonlinear time dependent problems when that solution is too complex to be fully resolved or when data are missing the initial conditions for the unresolved components of the solution are drawn from a probability distribution and their effect on a small set of variables that are actually computed is evaluated via statistical projection the formalism resembles the projection methods of irreversible statistical mechanics supplemented by the systematic use of conditional expectations and new methods of solution for an auxiliary equation the orthogonal dynamics equation needed to evaluate a non markovian memory term the result of the computations is close to the best possible estimate that can be obtained given the partial data we present the constructions in detail together with several useful variants provide simple examples and point out the relation to the fluctuation dissipation formulas of statistical physics

decomposable measures and nonlinear equations abstract using integrals based on decomposable measures with respect to a pseudo addition related to a semiring a b a b a unified method is given for solving some nonlinear differential ordinary and partial difference and optimization equations for that purpose important tools as pseudo superposition principle and pseudolaplace transform are used

numerical renormalization group calculations for similarity solutions and traveling waves we present a numerical implementation of the renormalization group rg for partial differential equations constructing similarity solutions and traveling waves we show that for a large class of well localized initial conditions successive iterations of an approximately defined discrete rg transformation in space and time will drive the system towards a fixed point this corresponds to a scale invariant solution such as a similarity or traveling wave solution which governs the long time asymptotic behavior we demonstrate that the numerical rg method is computationally very efficient

polyanalytic relativistic second bargmann transforms we construct coherent states through special superpositions of eigenstates of the relativistic isotonic oscillator in each superposition the coefficients are chosen to be l2 eigenfunctions of a weight maass laplacian on the poincare disk which are associated with the eigenvalue 4m 1 m m z 0 1 2 for each nonzero m the associated coherent states transform constitutes the m true polyanalytic extension of a relativistic version of the second bargmann transform whose integral kernel is expressed in terms of a special appel kampe de feriet s hypergeometric function the obtained results could be used to extend the known semi classical analysis of quantum dynamics of the relativistic isotonic oscillator

the distributive equations for idempotent uninorms and nullnorms the distributive equations only involving idempotent uninorms and nullnorms are investigated the following two cases are proved i as for a nullnorm with an idempotent uninorm having distributivity the necessary and sufficient conditions are given ii as for an idempotent uninorm with a nullnorm having distributivity the necessary and sufficient conditions are given also

on the distributivity of uninorms over nullnorms this paper investigates the functional equation of distributivity of uninorms over nullnorms we consider the case where the uninorm is continuous in 0 1 2 or is representable it has been proved that the absorbing element of the nullnorm is an idempotent element of the uninorm if the distributive equation holds and then combining the structures of the uninorm and the nullnorm we give the characterization of the pair of the functions of the uninorm and the nullnorm moreover when the nullnorm is continuous we obtain the sufficient and necessary conditions under which the distributive equation holds

analysis of wiener functionals malliavin calculus and its applications to heat kernels on donne un expose facilement accessible du calcul de malliavin du calcul differentiel de dimension infinie sur l espace de wiener

corrections to on distributive laws of uninorms over overlap and grouping functions the proof of the abovementioned paper case i of item 2 of proposition 9 is not suitable although the conclusion of proposition 9 is correct meanwhile the conditions of o satisfying o 1 e e or o6 in corollary 3 and g satisfying g 0 e e or g6 in corollary 7 are redundant so in this paper first we show the modification of the incorrect part of case i of the proof of item 2 of proposition 9 and express the statement of proposition 9 by a simpler way than before in addition the expression of the statements of propositions 10 19 and 20 is shown by a simpler way than before because they are related to proposition 9 second we remove the redundant conditions in corollaries 3 and 7

the focusing problem for the porous medium equation experiment simulation and analysis abstract the focusing problem involves the study of flows which are initially supported outside a compact empty region with the aim of describing how the flows eventually fill the empty region the work we describe has its origin in experimental studies of convergent gravity flows and in the global regularity theory of caffarelli vazquez and wolanski for the equivalent porous medium flow we give a comprehensive survey of the current state of the experiments numerical simulations and the analytic studies of this problem the numerical studies involve innovative renormalization techniques and supply raw material for the analysis

block spins for partial differential equations we investigate the use of renormalization group methods to solve partial differential equations pdes numerically our approach focuses on coarse graining the underlying continuum process as opposed to the conventional numerical analysis method of sampling it we calculate exactly the coarse grained or perfect laplacian operator and investigate the numerical effectiveness of the technique on a series of 1 1 dimensional pdes with varying levels of smoothness in the dynamics the diffusion equation the time dependent ginzburg landau equation the swift hohenberg equation and the damped kuramoto sivashinsky equation we find that the renormalization group is superior to conventional sampling based discretizations in representing faithfully the dynamics with a large grid spacing introducing no detectable lattice artifacts as long as there is a natural ultraviolet cutoff in the problem we discuss limitations and open problems of this approach

equation free modelling of evolving diseases coarse grained computations with individual based models we demonstrate how direct simulation of stochastic individualbased models can be combined with continuum numericalanalysis techniques to study the dynamics of evolving diseases sidestepping the necessity of obtaining explicit populationlevel models the approach analyses the unavailable in closed form coarse macroscopic equations estimating the necessary quantities through appropriately initialized short bursts of individualbased dynamic simulation we illustrate this approach by analysing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts building up from classical susceptibleinfectedrecovered and susceptibleinfectedrecoveredsusceptible models our example uses a onedimensional lattice for variant space and assumes a finite number of individuals macroscopic computational tasks enabled through this approach include stationarystate computation coarse projective integration parametric continuation and stability analysis

real space renormalization group approach to field evolution equations real space renormalization group approach to field evolution equations an operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations pde via real space renormalization group is introduced in which cell overlapping is the key concept applications to 1 1 dimensional pdes are presented for linear and quadratic equations that are first order in time

eigenvalue asymptotics for the schrodinger operators on the hyperbolic plane in this paper we consider the schrodinger operator hv 12 h v on the hyperbolic plane h z x y x r y 0 where h is the hyperbolic laplacian and v is a scalar potential on h it is proven that under an appropriate condition on v at infinity the number of eigenvalues of hv less than is asymptotically equal to the canonical volume of the quasi classically allowed region x y t h y2 2 2 2 v x y as our proof is based on the probabilistic methods and the standard tauberian argument as in the proof of theorem 10 5 in simon functional integration and quantum physics academic press new york 1979

enhancing multiclass classification in farc hd fuzzy classifier on the synergy between n dimensional overlap functions and decomposition strategies there are many real world classification problems involving multiple classes e g in bioinformatics computer vision or medicine these problems are generally more difficult than their binary counterparts in this scenario decomposition strategies usually improve the performance of classifiers hence in this paper we aim to improve the behavior of fuzzy association rule based classification model for high dimensional problems farc hd fuzzy classifier in multiclass classification problems using decomposition strategies and more specifically one versus one ovo and one versus all ova strategies however when these strategies are applied on farc hd a problem emerges due to the low confidence values provided by the fuzzy reasoning method this undesirable condition comes from the application of the product t norm when computing the matching and association degrees obtaining low values which are also dependent on the number of antecedents of the fuzzy rules as a result robust aggregation strategies in ovo such as the weighted voting obtain poor results with this fuzzy classifier in order to solve these problems we propose to adapt the inference system of farc hd replacing the product t norm with overlap functions to do so we define n dimensional overlap functions the usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in ovo and ova schemes furthermore we propose a new aggregation strategy for ovo to deal with the problem of the weighted voting derived from the inappropriate confidences provided by farc hd for this aggregation method the quality of our new approach is analyzed using 20 datasets and the conclusions are supported by a proper statistical analysis in order to check the usefulness of our proposal we carry out a comparison against some of the state of the art fuzzy classifiers experimental results show the competitiveness of our method

focusing of an elongated hole in porous medium flow abstract in the focusing problem we study solutions to the porous medium equation tu um whose initial distributions are positive in the exterior of a compact 2d region and zero inside we assume that the initial interface is elongated i e has an aspect ratio 1 and possesses reflectional symmetry with respect to both the x and y axes we implement a numerical scheme that adapts the numerical grid around the interface so as to maintain a high resolution as the interface shrinks to a point we find that as t tends to the focusing time t the interface becomes oval like with lengths of the major and minor axes o t t and o t t respectively thus the aspect ratio is o 1 t t by scaling and formal asymptotic arguments we derive an approximate solution which is valid for all m this approximation indicates that the numerically observed power law behavior for the major and minor axes is universal for all m 1

van melle s combining function in mycin is a representable uninorm an alternative proof abstract recently tsadiras and margaritis have shown that the function implemented in the expert system mycin for combining certainty factors is a uninorm in this paper we present a compact alternative to the given direct and lengthy proof based on the construction of representable uninorms by means of an additive generator consequently we show that van melle s combining function is a representable uninorm in fact it is a rescaled version of the representable uninorm on the unit interval constructed from the algebraic product and the probabilistic sum

renormalization group and singular perturbations multiple scales boundary layers and reductive perturbation theory perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis with numerous examples we illustrate its application to ordinary differential equation problems involving multiple scales boundary layers with technically difficult asymptotic matching and wkb analysis in contrast to conventional methods the renormalization group approach requires neither ad hoc assumptions about the structure of perturbation series nor the use of asymptotic matching our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally although the latter can be reproduced if desired by appropriate expansion of the renormalization group approximant we show that the renormalization group equation may be interpreted as an amplitude equation and from this point of view develop reductive perturbation theory for partial differential equations describing spatially extended systems near bifurcation points deriving both amplitude equations and the center manifold s1063651x 96 00506 5

unresolved computation and optimal predictions we present methods for predicting the solution of time dependent partial differential equations when that solution is so complex that it cannot be properly resolved numerically but when prior statistical information can be found the sparse numerical data are viewed as constraints on the solution and the gist of our proposal is a set of methods for advancing the constraints in time so that regression methods can be used to reconstruct the mean future for linear equations we offer general recipes for advancing the constraints the methods are generalized to certain classes of nonlinear problems and the conditions under which strongly nonlinear problems and partial statistical information can be handled are briefly discussed our methods are related to certain data acquisition schemes in oceanography and meteorology c 1999 john wiley sons inc

approximation of center manifolds on the renormalization group method the renormalization group rg method for differential equations is one of the perturbation methods for obtaining approximate solutions this article shows that the rg method is effectual for obtaining an approximate center manifold and an approximate flow on it when applied to equations having a center manifold

analysis of generalized negative binomial distributions attached to hyperbolic landau levels to each hyperbolic landau level of the poincare disc is attached a generalized negative binomial distribution in this paper we compute the moment generating function of this distribution and supply its atomic decomposition as a perturbation of the negative binomial distribution by a finitely supported measure using the mandel parameter we also discuss the nonclassical nature of the associated coherent states next we derive a levy khintchine type representation of its characteristic function when the latter does not vanish and deduce that it is quasi infinitely divisible except for the lowest hyperbolic landau level corresponding to the negative binomial distribution by considering the total variation of the obtained quasi levy measure we introduce a new infinitely divisible distribution for which we derive the characteristic function

self similar blowup solutions to an aggregation equation in r n we present numerical simulations of radially symmetric finite time blowup for the aggregation equation ut u k u where the kernel k x x the dynamics of the blowup exhibits self similar behavior in which zero mass concentrates at the core at the blowup time computations are performed in r n for n between 2 and 10 using a method based on characteristics in all cases studied the self similarity exhibits second kind anomalous scaling

characterization of hyperbolic landau states by coherent state transforms we deal with a family of generalized coherent states obtained by means of operators of an unitary irreducible representation of the group of affine transformations of the real line we prove that the ranges of the corresponding coherent state transforms coincide with spaces of bound states of the landau hamiltonian in the hyperbolic plane this provides us with a new characterization of hyperbolic landau states

completeness relations for maass laplacians and heat kernels on the super poincare upper half plane simple completeness relations are proposed for maass laplacians with the help of these completeness relations correct heat kernels of super maass laplacians are derived on the super poincare upper half plane

distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t conorm this paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms in particular the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict from the obtained results it is deduced that distributivity and conditional distributivity are equivalent moreover we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict

adaptive mesh computation of polycrystalline pattern formation using a renormalization group reduction of the phase field crystal model we implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field in microscopic material processes our numerical approach uses the systematic renormalization group formulation of a phase field crystal model of a pure material to provide the underlying equations for the complex amplitude of the atomic density field a quantity that is spatially uniform except near topological defects grain boundaries and other lattice imperfections our algorithm employs a hybrid formulation of the amplitude equations combining cartesian and polar decompositions of the complex amplitude we show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline grain growth in two dimensions

renormalization group analysis of nonlinear diffusion equations with time dependent coefficients and marginal perturbations in this paper we use a renormalization group rg method to study the long time asymptotics of nonlinear diffusion equations with time dependent diffusion coefficients and nonlinearities which are marginal or critical with respect to the rg operator these equations describe the time evolution of the average concentration of a passive scalar being advected by a random velocity field we prove that besides the expected diffusive behavior there is an extra logarithmic correction which is the imprint of the critical nonlinearity

random walks on three strand braids and on related hyperbolic groups we investigate the statistical properties of random walks on the simplest nontrivial braid group b3 and on related hyperbolic groups we provide a method using cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories the drift and the return probability the action of the groups under consideration in the hyperbolic plane is investigated and the distribution of a geometric invariant the hyperbolic distance is analysed it is shown that a random walk on b3 can be viewed as a magnetic random walk on the group psl 2

on some solutions of the distributivity equation abstract the aim of this paper is to present some interesting results on the distributivity equation for which several pairs of binary operations on 0 1 are considered moreover different methods to solve distributivity equations are used in this work

multi polar t conorms and uninorms abstract transformation of uninorms defined on the unit interval to the bipolar scale yields bipolar t conorms and transformation of nullnorms on the unit interval yields bipolar t norms we use this relation in the investigation of the structure of bipolar and multi polar t norms and t conorms we use the same transformation of the unit interval into the bipolar scale in order to obtain bipolar aggregation operators from ordinal sum t norms and t conorms the extensions of these special bipolar aggregation operators generalize both multi polar t norms and t conorms and therefore we call them multi polar uninorms several examples of multi polar t conorms and uninorms are also presented

renormalization group derivation of phase equations abstract phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method a general formula for phase diffusion coefficients is given under certain conditions

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

projective and coarse projective integration for problems with continuous symmetries temporal integration of equations possessing continuous symmetries e g systems with translational invariance associated with traveling solutions and scale invariance associated with self similar solutions in a co evolving frame i e a frame which is co traveling co collapsing or co exploding with the evolving solution leads to improved accuracy because of the smaller time derivative in the new spatial frame the slower time behavior permits the use of projective and coarse projective integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems respectively these methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries the ideas of projective integration in a co evolving frame are illustrated on the one dimensional translationally invariant nagumo partial differential equation pde a corresponding kinetic monte carlo model motivated from the nagumo kinetics is used to illustrate the coarse grained method a simple one dimensional diffusion problem is used to illustrate the scale invariant case the efficiency of projective integration in the co evolving frame for both the macroscopic diffusion pde and for a random walker particle based model is again demonstrated

diffusion in a one dimensional random medium and hyperbolic brownian motion classical diffusion in a random medium involves an exponential functional of brownian motion this functional also appears in the study of brownian diffusion on a riemann surface of constant negative curvature we analyse in detail this relationship and study various distributions using stochastic calculus and functional integration

multi self similar markov processes on ℝ n and their lamperti representations a classical result due to lamperti establishes a one to one correspondence between a class of strictly positive markov processes that are self similar and the class of one dimensional levy processes this correspondence is obtained by suitably time changing the exponential of the levy process in this paper we generalise lamperti s result to processes in n dimensions for the representation we obtain it is essential that the same time change be applied to all coordinates of the processes involved also for the statement of the main result we need the proper concept of self similarity in higher dimensions referred to as multi self similarity in the paper

horizontal lift of the brownian motion on the hyperbolic plane and the selberg trace formula by using an explicit representation for the horizontal lift of the brownian motion on the poincare upper half plane h2 we show an expression for the heat kernel for the de rham kodaira laplacian on h2 we apply the result to a study on the selberg trace formula

uninorms in fuzzy systems modeling abstract fuzzy systems modeling provides a framework in which input output relationships can be modeled by partitioning the input into fuzzy regions for which we can describe the output the fuzzy modeling inference process the procedure used to obtain the output of a fuzzy systems model for a given input is shown to involve an aggregation step in which the contributions of the different components of the fuzzy systems model are combined it is shown that the uninorm operator provides a general class of operators to implement this step the uninorm it is recalled is an operator that provides a generalization of the t norm and t conorm by allowing the identity element to be any value in the unit interval another step in the inference process is the determination of the contribution of each component of the model based on its relevancy to the current input the performance of this step requires the use of an operator related to the implication operator which we call a relevancy transformation ret operator it is shown that the form of this ret operator is dependent upon the identity value of the uninorm used in the aggregation step we provide some general formulations for this class of operators we show how the well known forms of fuzzy inference are special cases of our uninorm based approach

distributivity between semi t operators and mayor s aggregation operators the problem of distributivity was first posed over forty years ago and it has been investigated for families of certain operations such as t norms t conorms uninorms and nullnorms in this paper we investigate this topic further by focusing on mayor s aggregation operators and semi t operators which generalize the t operators by omitting commutativity the results that we obtain are complete and extend previous results concerning distributivity between mayor s aggregation operators and semi nullnorms

on determinants of laplacians on riemann surfaces determinants of laplacians on tensors and spinors of arbitrary weights on compact hyperbolic riemann surfaces are computed in terms of values of selberg zeta functions at half integer points

towards the evaluation of the relevant degrees of freedom in nonlinear partial differential equations we investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations the proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems we examine dynamical scaling characteristics in the short time and the long time evolution regime providing only a reduced number of degrees of freedom to the evolution process

asymptotics for nonlinear integral equations with a generalized heat kernel using renormalization group technique in this paper we employ the renormalization group method to study the long time asymptotics of solutions to a class of nonlinear integral equations with a generalized heat kernel the nonlinearities are classified and studied according to its role in the asymptotic behavior here we prove that the behavior in the limit as t goes to infinity remains unchanged when compared with the one in the linear case if the nonlinearities are the ones classified as irrelevant in the renormalization group sense