critical phenomena and universal exponents in statistical physics on dyson s hierarchical model on etudie le comportement des etats de gibbs a la temperature critique ou a proximite on etudie en details le modele hierarchique de dyson et on presente les plus importants resultats

on some advanced type inequalities for sugeno integral and t s evaluators in this paper strengthened versions of the minkowski chebyshev jensen and holder inequalities for sugeno integral and t s evaluators are given as an application some equivalent forms and some particular results have been established

general chebyshev type inequalities for universal integral a new inequality for the universal integral on abstract spaces is obtained in a rather general form as two corollaries minkowski s and chebyshev s type inequalities for the universal integral are obtained the main results of this paper generalize some previous results obtained for special fuzzy integrals e g choquet and sugeno integrals furthermore related inequalities for seminormed integral are obtained

some isometric embedding and rigidity results for riemannian manifolds in this note we announce some new results concerning rigidity and isometric embeddings of riemannian manifolds a special case of the main result states that a general mn unk rn r r n 1 n 2 2 is uniquely determined up to finitely many constants by its induced ds2

low temperature properties of the hierarchical classical vector model we obtain low temperature properties of the classical vector model in a hierarchical formulation in three or more dimensions we consider the lattice model in a zero or non zero magnetic field where the single site spin variable r v has a density proportional to e lambda phi 2 1 2 for large using renormalization group methods we obtain a convergent expansion for the free energy with zero magnetic field for non zero fields a shift formula is used to obtain the effective action generated by the renormalization group transformation rgt to obtain the pure state zero field free energy and spontaneous magnetization we take the thermodynamic limit together with the zero field limit at a specified rate the spontaneous magnetization m is calculated is non zero and the pure state free energy coincides as expected with the zero field free energy also the sequence of zero field actions does not have a limit but we show that the sequence of actions generated from the original action shifted bym does the limiting action corresponds to a non canonical gaussian fixed point of the rgt

discrete bipolar universal integrals the concept of universal integral recently proposed generalizes the choquet shilkret and sugeno integrals those integrals admit a discrete bipolar formulation useful in those situations where the underlying scale is bipolar in this paper we propose the concept of discrete bipolar universal integral in order to provide a common framework for bipolar discrete integrals including as special cases the discrete choquet shilkret and sugeno bipolar integrals moreover we provide two different axiomatic characterizations of the proposed discrete bipolar universal integral

the linearized system for isometric embeddings and its characteristic variety abstract in this paper we prove a conjecture of bryant griffiths and yang concerning the characteristic variety for the determined isometric embedding system in particular we show that the characteristic variety is not smooth for any dimension greater than 4 this is accomplished by introducing a smaller yet equivalent linearized system in an appropriate way which facilitates analysis of the characteristic variety

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

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

generalizations of the chebyshev type inequality for choquet like expectation this paper proves generalizations of the chebyshev type inequality for choquet like expectation some previous results are obtained as corollaries

euclidean gibbs measures on loop lattices existence and a priori estimates we present a new method to prove existence and uniform a priori estimates for euclidean gibbs measures corresponding to quantum anharmonic crystals it is based first on the alternative characterization of gibbs measures in terms of their logarithmic derivatives through integration by parts formulas and second on the choice of appropriate lyapunov functionals

a hierarchical model of quantum anharmonic oscillators critical point convergence a hierarchical model of interacting quantum particles performing anharmonic oscillations is studied in the euclidean approach in which the local gibbs states are constructed as measures on infinite dimensional spaces the local states restricted to the subalgebra generated by fluctuations of displacements of particles are in the center of the study they are described by means of the corresponding temperature green matsubara functions the result of the paper is a theorem which describes the critical point convergence of such matsubara functions in the thermodynamic limit

multi and multi polar capacities aggregation of inputs from different categories generalizes both unipolar standard and bipolar aggregation this aggregation covers two main cases of multi polar and non monotone aggregation inputs from different categories can be found in classification methods multi criteria decision making game theory and political and sociological sciences two main concepts related to aggregation on the unit interval are capacities and aggregation on grid points boolean functions in this paper multi and multi polar capacities that extend bi and bipolar capacities are introduced the position of these capacities is clarified by means of the connection between boolean crisp functions capacities aggregation and concepts from other domains of science which are shown for the unipolar the bipolar and the multi polar case the connection between multi and multi polar capacities and the concept of games with n players and r alternatives is described

mass generations in two dimensional hierarchical heisenberg model of migdal kadanoff type finiteness of correlation length in the 2d heisenberg model is established within the migdal kadanoff approximate renormalization recursion formulas

the symmetric sugeno integral we propose an extension of the sugeno integral for negative numbers in the spirit of the symmetric extension of choquet integral also called sipos integral our framework is purely ordinal since the sugeno integral has its interest when the underlying structure is ordinal we begin by defining negative numbers on a linearly ordered set and we endow this new structure with a suitable algebra very close to the ring of real numbers in a second step we introduce the mobius transform on this new structure lastly we define the symmetric sugeno integral and show its similarity with the symmetric choquet integral

on the large distance behavior of correlations for a hierarchical n component classical vector model in three dimensions we consider the correlation functions for a hierarchical n component classical vector model in three dimensions for n we find explicitly the eigenvalues and global eigenfunctions of the linearized renormalization group transformation in a very direct way this yields the correlation functions for the n model in particular we check that the two point function has canonical decay

discrete bipolar pseudo integrals abstract in the authors paper strboja et al 2016 42 the notion of the bipolar pseudo integral has been introduced this paper extends investigations related to this new type of bipolar integrals defined with respect to decomposable bi capacities we consider the main properties of the discrete bipolar pseudo integral a characterization theorem for the discrete bipolar pseudo integral is proven monotone convergence theorems and the fatou type lemma for the discrete bipolar pseudo integral are considered in order to illustrate obtained results many interesting examples are provided

bipolar fuzzy integrals in decision analysis and especially in multiple criteria decision analysis several non additive integrals have been introduced in the last 60 years these include the choquet integral the shilkret integral and the sugeno integral among others recently a bipolar choquet integral was proposed for cases in which the underlying scale is bipolar in this paper we propose a bipolar shilkret integral and a bipolar sugeno integral moreover we provide an axiomatic characterization of all three bipolar fuzzy integrals

convergence theorems for monotone measures in classical measure theory there are a number of convergence theorems such as the egorov the riesz and the lusin theorem among others we consider monotone measures i e monotone set functions vanishing in the empty set and defined on a measurable space and discuss how and to which extent classical convergence theorems can be carried over to this more general case

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

renormalization of dyson s hierarchical vector valued φ 4 model at low temperatures we investigate dyson s hierarchical vector valued 4 model at low temperatures the case 2 c sqrt 2 is considered the pure phase is constructed and the existence of its large scale limit is proved the limit is gaussian but an unusual normalization has to be chosen in the direction of the spontaneous magnetization one has to divide by the square root of the volume but in the orthogonal direction one has to divide by a different power of the volume for all low temperatures

on the relation between classical and quantum critical systems we consider critical asymptotically hierarchical quantum models and show that the probability distribution of the appropriately scaled square of the total spin converges as the number of spins tends to infinity to the same function in the corresponding classical systems

a nonlinear dynamical system on the set of laguerre entire functions a nonlinear modification of the cauchy problem dtf t z dzf t z zd 2 zf t z t ir 0 z c 0 f 0 z g z l is considered the set l consists of laguerre entire functions which one obtains as a closure of the set of polynomials having real nonpositive zeros only in the topology of uniform convergence on compact subsets of c the modification means that the time half line ir is divided onto the intervals in n 1 n n in 0 and on each in the evolution is to be described by the above equation but at the endpoints the function f t z is changed f n z

lattice systems with a continuous symmetry iii low temperature asymptotic expansion for the plane rotator model we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

construction of non gaussian self similar random fields with hierarchical structure in the present work we construct non gaussian self similar random fields with hierarchical structure the construction is based on non gaussian solutions of the main nonlinear equation of the hierarchical models theory the existence of such solutions was proved originally by sinai and the author and later by another method by collet and eckmann next we establish the uniqueness of a gibbs state for the constructed self similar field finally for a class of hierarchical models we prove the convergence of renormalization transformations of a random field at the critical point to the self similar field

large field renormalization ii localization exponentiation and bounds for the r operation in this paper we conclude the discussion of the basic properties and bounds for ther operation this allows us to complete the proof of the ultraviolet stability of four dimensional pure gauge field theories as formulated in theorem 1

renormalization group approach to lattice gauge field theories ii cluster expansions the fluctuation field integral constructed in part i is represented by the exponentiated cluster expansion it is proved that the terms of the expansion satisfy the inductive assumptions this completes the construction of the sequence of effective actions in the small field approximation

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

lattice and continuum wavelets and the block renormalization group the authors obtain a resolution of the identity operator for functions on a lattice var epsilon z sup d which is derived from the block renormalization group the authors use eigenfunctions of the terms of the decomposition to form a basis for l sub 2 var epsilon z sup d and show how the basis is generated from lattice wavelets the lattice spacing var epsilon is taken to zero and continuum wavelets are obtained 12 refs

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

decomposable and k additive multi capacities and multi polar capacities extensions of several concepts for definition of capacities given by a small number of parameters in the unipolar and bipolar framework to the case of multi polar input spaces are studied the paper covers decomposable symmetric category symmetric additive reduced additive and k additive multi polar capacities and discusses its properties the multi polar mobius transform of multi polar capacities is introduced and its properties for coordinate wisely given additive and k additive multi polar capacities are described

a classical large n hierarchical vector model in three dimensions a nonzero fixed point and canonical decay of correlation functions we consider a hierarchical n component classical vector model on a three dimensional lattice z3 for large n the model differs from the usual one in that the kernel of the inverse laplace operator is nontranslational invariant but has matrix elements which are positive and exhibit the same falloff as the inverse laplacian in z3 we introduce a renormalization group transformation and for n corresponding to the leading order of the 1 n expansion we construct explicitly a nonzero fixed point for this transformation and also obtain some correlation functions the two point function has canonical decay for 1 n we obtain the fixed point and the two point function in the first 1 n approximation canonical decay is still verified in contrast to what is reported for the full model

lattice systems with a continuous symmetry we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

the random walk representation of classical spin systems and correlation inequalities ii the skeleton inequalities on utilise la representation marche aleatoire pour prouver les premieres d une nouvelle famille d inegalites de correlation pour des modeles reticules ferromagnetiques 4 ces inegalites etablissent que les sommes partielles finies du developpement en perturbation resomme du propagateur pour la fonction a 4 points forment un ensemble alterne de limites superieures et inferieures rigoureuses pour la fonction a 4 points exactes

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

the smallest semicopula based universal integrals ii in this paper we continue studying the smallest universal integral i s having s as the underlying semicopula we present convergence theorems for i s integral sequences including monotone almost everywhere almost uniform in measure and in mean converging sequences of measurable functions respectively it emerges that these convergences characterize the underlying measure properties such as null additivity monotone autocontinuity and autocontinuity we provide many examples and counter examples as well as a few interesting open problems

characteristics and existence of isometric embeddings soit m ds 2 une variete de riemann c a 3 dimensions et x 0 m un point tel que le tenseur d einstein 7b g x 0 n est pas l 2 ou l t x0 m alors il existe un plongement isometrique local c d un voisinage de x 0 dans e 6

on the critical behaviour of dyson s quantum hierarchical models we study the probability distribution of the appropriately scaled square of the total spin for critical asymptotically hierarchical quantum models and show that it converges as the number of spins tends to infinity to the same function related to the corresponding classical systems thus we exhibit explicitly a property of statistical mechanical systems which at the critical point does not depend whether one uses a classical or quantum mechanical description

the random walk representation of classical spin systems and correlation inequalities ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion by using a mixed spinrandom walk representation we present a unified approach to many recently established correlation inequalities as an application of these inequalities we obtain a simple proof of the mass gap for the 4 2 quantum field model we also establish new upper bounds on critical temperatures

asymmetric integral as a limit of generated choquet integrals based on absolutely monotone real set functions we introduce a generated choquet integral with respect to absolutely monotone and sign stable set functions another type of integrals defined with respect to such a set function is obtained as a limit of an appropriate sequence of generated choquet integrals

hierarchical ferromagnetic vector spin model possessing the lee yang property thermodynamic limit at the critical point and above the hierarchical ferromagneticn dimensional vector spin model as a sequence of probability measures onrn is considered the starting element of this sequence is chosen to belong to the lee yang class of measures that is defined in the paper and includes most known examples 4 measures gaussian measures and so on for this model we probe two thermodynamic limit theorems one of them is just the classical central limit theorem for weakly dependent random vectors it describes the convergence of classically normed sums of spins when temperature is sufficiently high the other theorem describes the convergence of more than normally normed sums that holds for some fixed temperature it corresponds to the strong dependence of spins which appears at the critical point of the model

a priori bounds for co dimension one isometric embeddings let x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i be a c 4 isometric embedding of a c4 metric g of nonnegative sectional curvature on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i into the euclidean space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i we prove a priori bounds for the trace of the second fundamental form h in terms of the scalar curvature r of g and the diameter d of the space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i g these estimates give a bound on the extrinsic geometry in terms of intrinsic quantities they generalize estimates originally obtained by weyl for the case n 2 and positive curvature and then by p guan and the first author for nonnegative curvature and n 2 using c 2 interior estimates of evans and krylov for concave fully nonlinear elliptic partial differential equations these bounds allow us to obtain the following convergence theorem for any 0 the set of metrics of nonnegative sectional curvature and scalar curvature bounded below by which are isometrically embedable in euclidean space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 06i is closed in the holder space c 4 0 suppose that g is a smooth metric of nonnegative sectional curvature and positive scalar curvature on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 07i which admits locally convex isometric embedding into inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 08i does inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 09i g then admit a smooth global isometric embedding x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 10i g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 11i

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

jensen type inequality for the bipolar pseudo integrals abstract the main purpose of this paper is to establish conditions under which the jensen type inequality for the discrete bipolar pseudo integral is valid besides we extend investigations of the properties of the bipolar pseudo integral the observations concern the discrete bipolar pseudo integrals based on the following three canonical cases of two binary symmetric operations in the first case they are generated by an odd strictly increasing and continuous function in the remaining two cases a symmetric addition is the symmetric maximum while in the second case the corresponding pseudo multiplication is a non idempotent operation and in the third case it is the symmetric minimum

pan operations structure abstract the structure of pan addition and pan multiplication of a commutative isotonic semiring r is analyzed we show that if v supremum then r is a g semiring i e a b g 1 g a g b and d a b g 1 g a g b conclusions for pan integrals with respect to a measure are shown

a unified approach to the monotone integral based premium principles under the cpt theory abstract we consider the relationship between different types of the monotone integral based premium principles as a common frame for the cpt premium principle and the mean premium principle the cpt like integral based premium principle is introduced and characterized the jensen type inequalities for the choquet integral and the cpt like premium principle on the class of non negative risks are proven we establish conditions under which the jensen steffensen type inequalities for the cpt premium principle and the cpt like premium principle hold for risks with finite range

ergodicity for the stochastic dynamics of quasi invariant measures with applications to gibbs states the convex set maof quasi invariant measures on a locally convex spaceewith given shift radon nikodym derivatives i e cocycles a atk k k0 t ris analyzed the extreme points of maare characterized and proved to be non empty a specification of lattice type is constructed so that macoincides with the set of the corresponding gibbs states as a consequence via a well known method due to dynkin and follmer a unique representation of an arbitrary element in main terms of extreme ones is derived furthermore the corresponding classical dirichlet forms e d e and their associated semigroups t t t 0onl2 e are discussed under a mild positivity condition it is shown that mais extreme if and only if e d e is irreducible or equivalently t t t 0is ergodic this implies time ergodicity of associated diffusions applications to gibbs states of classical and quantum lattice models as well as those occuring in euclidean quantum field theory are presented in particular it is proved that the stochastic quantization of a guerra rosen simon gibbs state on d r2 ininfinite volumewith polynomial interaction is ergodic if the gibbs state is extreme i e is a pure phase which solves a long standing open problem

signs of the ising model ursell functions it is proven that the ursell functionsu2k of the ising model have the conjectured signs 1 k 1u2k 0 the proof is based on aizenman s random current representation and combinatorics

renormalization group approach to lattice gauge field theories i generation of effective actions in a small field approximation and a coupling constant renormalization in four dimensions on etudie des theories de champs de jauge pures a 4 dimensions par l approche du groupe de renormalisation on se restreint a l approximation de champ petit dans cette region on construit une suite d actions effectives localisees par des developpements en amas dans des transformations de renormalisation a un pas

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics