the inclusion problem for mixed norm spaces given two mixed norm lebesgue spaces on an n fold product of arbitrary finite measure spaces when is one contained in the other if so what is the norm of the inclusion map these questions are answered completely for a large range of lebesgue indices and all measure spaces when the measure spaces are atomless both questions are settled for all indices when the measure spaces are not purely atomic the first question is settled for all indices some complete and some partial results are given in the remaining cases but a wide variety of behaviour is observed in particular the norm problem for purely atomic measure spaces is seen to be intractable for certain ranges of the lebesgue indices it is equivalent to an optimization problem that includes a known np hard problem as a special case

comment on jamming at zero temperature and zero applied stress the epitome of disorder phys rev e 68 011306 2003 claim that a special point j of a jamming phase diagram in density temperature stress space is related to random close packing of hard spheres and that it represents for their suggested definitions of jammed and random the recently introduced maximally random jammed state we point out several difficulties with their definitions and question some of their claims furthermore we discuss the connections between their algorithm and other hard sphere packing algorithms in the literature

a decomposition theorem for polymeasures we prove that every countably additive polymeasure can be decomposed in a unique way as the sum of a discrete polymeasure plus a continuous polymeasure this generalizes a previous result of saeki

bohr inequalities for free holomorphic functions on polyballs abstract multivariable operator theory is used to provide bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball b n n n 1 n k n k which is a noncommutative analogue of the scalar polyball c n 1 1 c n k 1 the bohr radius k m h b n resp k h b n associated with the multi homogeneous resp homogeneous power series expansions of the free holomorphic functions are the main objects of study in this paper we extend a theorem of bombieri and bourgain for the disc d z c z 1 to the polyball and obtain the estimations 1 3 k k m h b n 2 log k k if k 1 extending boas khavinson result for the scalar polydisc d k with respect to the homogeneous power series expansion we prove that k h b n 1 3 extending the classical result and obtain analogues of caratheodory fejer and egervary szasz inequalities for free holomorphic functions with operator coefficients and positive real parts on the polyball these results are used to provide multivariable analogues of landau s inequality and bohr s inequality when the norm is replaced by the numerical radius of an operator when specialized to the regular polydisc d k which corresponds to the case n 1 n k 1 we obtain new results concerning bohr landau fejer and harnack inequalities for operator valued holomorphic functions and k pluriharmonic functions on the scalar polydisc d k the results of the paper can be used to obtain bohr type inequalities for the noncommutative ball algebra a n the hardy algebra f n and the c algebra c s generated by the universal model s of the polyball b n

there exist multilinear bohnenblust hille constants cn n 1 with limn cn 1 cn 0 abstract the n linear bohnenblust hille inequality asserts that there is a constant c n 1 such that the l 2 n n 1 norm of u e i 1 e i n i 1 i n 1 n is bounded above by c n times the supremum norm of u for any n linear form u c n c n c and n n the same holds for real scalars we prove what we call fundamental lemma which brings new information on the optimal constants k n n 1 for both real and complex scalars for instance k n 1 k n 0 87 n 0 473 for infinitely many n s for complex scalars we give a formula of surprisingly low growth in which e and the famous euler mascheroni constant appear k n 1 4 1 e 2 1 2 j 1 n 1 j log 2 e 2 1 2 1 n 2 we study the interplay between the kahane salem zygmund and the bohnenblust hille polynomial and multilinear inequalities and provide estimates for bohnenblust hille type inequality constants for any exponent q 2 n n 1

a subexponential vector valued bohnenblust hille type inequality abstract bayart pellegrino and seoane recently proved that the polynomial bohnenblust hille inequality for complex scalars is subexponential we show that a vector valued polynomial bohnenblust hille inequality on complex banach lattices is also subexponential for some special cases our main result recovers the best known constants of the classical polynomial inequality provided in 4

on the real polynomial bohnenblust hille inequality abstract it was recently proved by f bayart and the fourth and fifth authors that the complex polynomial bohnenblust hille inequality is subexponential here we show that for real scalars this no longer holds moreover we show among other results that if d r m stands for the real bohnenblust hille constant for m homogeneous polynomials then lim sup m d r m 1 m 2 a quite surprising result having in mind that the exact value of the bohnenblust hille constants is still a mystery

generalization of a theorem of bohr for bases in spaces of holomorphic functions of several complex variables abstract in the first part we generalize the classical result of bohr by proving that an analogous phenomenon occurs whenever d is an open domain in c m or more generally a complex manifold and n n 0 is a basis in the space of holomorphic functions h d such that 0 1 and n z0 0 n 1 for some z0 d namely then there exists a neighborhood u of the point z0 such that whenever a holomorphic function on d has modulus less than 1 the sum of the suprema in u of the moduli of the terms of its expansion is less than 1 too in the second part we consider some natural hilbert spaces of analytic functions and derive necessary and sufficient conditions for the occurrence of bohr s phenomenon in this setting

the bohr radius of the n dimensional polydisk is equivalent to sqrt frac log n n we show that the bohr radius of the polydisk mathbb d n behaves asymptotically as sqrt log n n our argument is based on a new interpolative approach to the bohnenblust hille inequalities which allows us to prove that the polynomial bohnenblust hille inequality is subexponential

volterra operators on hardy spaces of dirichlet series for a dirichlet series symbol g s n 1bnn s the associated volterra operator tg acting on a dirichlet series f s n 1ann s is defined by the integral f sf w g w dw we show that tg is a bounded operator on the hardy space hp of dirichlet series with 0 0 whenever tg is bounded in particular such g belong to hp for every p we relate the boundedness of tg to several other bmo type spaces bmoa in half planes the dual of h1 and the space of symbols of bounded hankel forms moreover we study symbols whose coefficients enjoy a multiplicative structure and obtain coefficient estimates for m homogeneous symbols as well as for general symbols finally we consider the action of tg on reproducing kernels for appropriate sequences of subspaces of h2 our proofs employ function and operator theoretic techniques in one and several variables a variety of number theoretic arguments are used throughout the paper in our study of special classes of symbols g

a tensor norm preserving unconditionality for lp spaces we show that for each n n there is an n tensor norm a in the sense of grothendieck with the surprising property that the tensor product y 1 y n has local unconditional structure for each choice of n arbitrary cp j spaces yj in fact a is the tensor norm associated to the ideal of multiple 1 summing n linear forms on banach spaces

sharp bohr type inequality abstract this article is devoted to the sharp improvement of the classical bohr inequality for bounded analytic functions defined on the unit disk we also prove two other sharp versions of the bohr inequality by replacing the constant term by the absolute of the function and the square of the absolute of the function respectively

factorization of absolutely continuous polynomials abstract in this paper we study the ideal of dominated p continuous polynomials that extend the nowadays well known ideal of p dominated polynomials to the more general setting of the interpolated ideals of polynomials we give the polynomial version of pietsch s factorization theorem for this new ideal although based on botelho et al in press 16 our factorization theorem requires new techniques inspired in the theory of banach lattices

improving the closed formula for subpolynomial constants in the multilinear bohnenblust hille inequalities abstract for k r or c the bohnenblust hille inequality asserts that there exists a sequence of scalars c k m m 1 such that i 1 i m 1 n u e i 1 e i m 2 m m 1 m 1 2 m c k m sup z 1 z m d n tu z 1 z m for all m linear forms u k n k n k and every positive integer n where e i i 1 n denotes the canonical basis of k n and d n represents the open unit polydisc in k n very recently 2012 it was shown that there exist constants c k m m 1 with subpolynomial growth satisfying this inequality however these constants were obtained via a complicated recursive formula we improve the best known closed non recursive approximation for these constants

new upper bounds for the constants in the bohnenblust hille inequality a classical inequality due to bohnenblust and hille states that for every positive integer m there is a constant c m 0 so that sigma n i1 im 1 vertical bar u e i1 e im vertical bar 2m m 1 m 1 2m c where c m m m 1 2m 2 m 1 2 the value of c m was improved to c m 2 m 1 2 by s kaijser and more recently h queffelec and a defant and p sevilla peris remarked that c m 2 root pi m 1 also works the bohnenblust hille inequality also holds for real banach spaces with the constants c m 2 m 1 2 in this note we show that a recent new proof of the bohnenblust hille inequality due to defant popa and schwarting provides in fact quite better estimates for c m for all values of m is an element of n in particular we will also show that for real scalars if m is even with 2 m 24 then c r m 2 1 2 c r m 2 we will mainly work on a paper by defant popa and schwarting giving some remarks about their work and explaining how to numerically improve the previously mentioned constants

bohr s phenomenon for functions on the boolean cube abstract we study the asymptotic decay of the fourier spectrum of real functions f 1 1 n r in the spirit of bohr s phenomenon from complex analysis every such function admits a canonical representation through its fourier walsh expansion f x s 1 n f s x s where x s k s x k given a class f of functions on the boolean cube 1 1 n the boolean radius of f is defined to be the largest 0 such that s f s s f for every f f we give the precise asymptotic behavior of the boolean radius of several natural subclasses of functions on finite boolean cubes as e g the class of all real functions on 1 1 n the subclass made of all homogeneous functions or certain threshold functions compared with the classical complex situation subtle differences as well as striking parallels occur

a new multilinear insight on littlewood s 4 3 inequality abstract we unify littlewood s classical 4 3 inequality a forerunner of grothendieck s inequality together with its m linear extension due to bohnenblust and hille which originally settled bohr s absolute convergence problem for dirichlet series with a scale of inequalties of bennett and carl in l p spaces which are of fundamental importance in the theory of eigenvalue distribution of power compact operators as an application we give estimates for the monomial coefficients of homogeneous l p valued polynomials on c 0

isometries between spaces of multiple dirichlet series abstract in this paper we study spaces of multiple dirichlet series and their properties we set the ground of the theory of multiple dirichlet series and define the spaces h c k k n of convergent and bounded multiple dirichlet series on c k we give a representation for these banach spaces and prove that they are all isometrically isomorphic independently of the dimension the analogous result for a c k k n which are the spaces of multiple dirichlet series that are convergent on c k and define uniformly continuous functions is obtained

a note on the polynomial bohnenblust hille inequality abstract recently in a paper published in the annals of mathematics it was shown that the bohnenblust hille inequality for complex homogeneous polynomials is hypercontractive however and to the best of our knowledge there is no result providing nontrivial lower bounds for the optimal constants for n homogeneous polynomials n 2 in this short note we provide lower bounds for these famous constants

the asymptotic growth of the constants in the bohnenblust hille inequality is optimal the search of sharp estimates for the constants in the bohnenblust hille inequality besides its challenging nature has quite important applications in different fields of mathematics and physics for homogeneous polynomials it was recently shown that the bohnenblust hille inequality for complex scalars is hypercontractive this result interesting by itself has found direct striking applications in the solution of several important problems for multilinear mappings precise information on the asymptotic behavior of the constants of the bohnenblust hille inequality is of particular importance for applications in quantum information theory and multipartite bell inequalities in this paper using elementary tools we prove a quite surprising result the asymptotic growth of the constants in the multilinear bohnenblust hille inequality is optimal besides its intrinsic mathematical interest and potential applications to different areas the mathematical importance of this result also lies in the fact that all previous estimates and related results for the last 80 years such as for instance the multilinear version of the famous grothendieck theorem for absolutely summing operators always present constants c m s growing at an exponential rate of certain power of m

multipliers of dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables let mathscr h infty be the set of all ordinary dirichlet series d sum n a n n s representing bounded holomorphic functions on the right half plane a completely multiplicative sequence b n of complex numbers is said to be an ell 1 multiplier for mathscr h infty whenever sum n a n b n infty for every d in mathscr h infty we study the problem of describing such sequences b n in terms of the asymptotic decay of the subsequence b p j where p j denotes the jth prime number given a completely multiplicative sequence b b n we prove among other results b is an ell 1 multiplier for mathscr h infty provided b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 1 and conversely if b is an ell 1 multiplier for mathscr h infty then b p j 1 for all j and overline lim n frac 1 log n sum j 1 n b p j 2 le 1 here b stands for the decreasing rearrangement of b following an ingenious idea of harald bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk mathbb d infty the open unit ball of ell infty for which every bounded and holomorphic function f on mathbb d infty has an absolutely convergent monomial series expansion sum alpha frac partial alpha f 0 alpha z alpha moreover we study analogous problems in hardy spaces of dirichlet series and hardy spaces of functions on the infinite dimensional polytorus mathbb t infty

unconditional basis and gordon lewis constants for spaces of polynomials abstract no infinite dimensional banach space x is known which has the property that for m 2 the banach space of all continuous m homogeneous polynomials on x has an unconditional basis following a program originally initiated by gordon and lewis we study unconditionality in spaces of m homogeneous polynomials and symmetric tensor products of order m in banach spaces we show that for each banach space x which has a dual with an unconditional basis x i the approximable nuclear m homogeneous polynomials on x have an unconditional basis if and only if the monomial basis with respect to x i is unconditional moreover we determine an asymptotically correct estimate for the unconditional basis constant of all m homogeneous polynomials on l n p and use this result to narrow down considerably the list of natural candidates x with the above property

bohr radius for subordinating families of analytic functions and bounded harmonic mappings abstract the class consisting of analytic functions f in the unit disk satisfying f z f z 2 f subordinated to some function h is considered the bohr radius for this class is obtained when h is respectively convex or starlike the bohr radius for analytic functions mapping the unit disk into a concave wedge domain as well as for bounded harmonic mappings are also established

ecmdd evidential c medoids clustering with multiple prototypes in this work a new prototype based clustering method named evidential c medoids ecmdd which belongs to the family of medoid based clustering for proximity data is proposed as an extension of fuzzy c medoids fcmdd on the theoretical framework of belief functions in the application of fcmdd and original ecmdd a single medoid prototype which is supposed to belong to the object set is utilized to represent one class for the sake of clarity this kind of ecmdd using a single medoid is denoted by secmdd in real clustering applications using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance in order to address this problem a variation of ecmdd using multiple weighted medoids denoted by wecmdd is presented unlike secmdd in wecmdd objects in each cluster carry various weights describing their degree of representativeness for that class this mechanism enables each class to be represented by more than one object experimental results in synthetic and real data sets clearly demonstrate the superiority of secmdd and wecmdd moreover the clustering results by wecmdd can provide richer information for the inner structure of the detected classes with the help of prototype weights

on the bohnenblust hille inequality and a variant of littlewoodʼs 4 3 inequality the search for sharp constants for inequalities of the type littlewood s 4 3 and bohnenblust hille has lately shown unexpected applications in many fields such as analytic number theory quantum information theory or in results on n dimensional bohr radii recent estimates obtained for the multilinear bohnenblust hille inequality for real scalars have been used as a crucial tool by a montanaro in order to solve problems in quantum xor games here among other results we obtain new upper bounds for the bohnenblust hille constants for complex scalars for bilinear forms we provide optimal constants of variants of littlewood s 4 3 inequality for real scalars when the exponent 4 3 is replaced by any r 4 3 we also prove that the optimal constants in real case are always strictly greater than those from the complex case

fuzzy k means clustering algorithms for interval valued data based on adaptive quadratic distances this paper presents partitioning fuzzy k means clustering models for interval valued data based on suitable adaptive quadratic distances these models furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion that measures the fit between the fuzzy clusters and their representatives these adaptive quadratic distances change at each algorithm iteration and can be either the same for all clusters or different from one cluster to another moreover additional interpretation tools for individual fuzzy clusters of interval valued data suitable to these fuzzy clustering models are also presented experiments with some interval valued data sets demonstrate the usefulness of these fuzzy clustering models and the merit of the individual fuzzy cluster interpretation tools

volume estimates in spaces of homogeneous polynomials given m we derive upper and lower estimates for the volume of the unit ball of the banach space mathcal p m e n all m homogeneous polynomials defined on the nth section e n of a symmetric banach sequence space e with constants depending on m only we apply this result to obtain asymptotically correct orders of various important invariants of mathcal p m e n from local banach space theory as e g volume ratios cotype and type 2 constants projection constants or banach mazur distances

from the statistics of data to the statistics of knowledge symbolic data analysis increasingly datasets are so large they must be summarized in some fashion so that the resulting summary dataset is of a more manageable size while still retaining as much knowledge inherent to the entire dataset as possible one consequence of this situation is that the data may no longer be formatted as single values such as is the case for classical data but rather may be represented by lists intervals distributions and the like these summarized data are examples of symbolic data this article looks at the concept of symbolic data in general and then attempts to review the methods currently available to analyze such data it quickly becomes clear that the range of methodologies available draws analogies with developments before 1900 that formed a foundation for the inferential statistics of the 1900s methods largely limited to small by comparison datasets and classical data formats the scarcity of available methodologies for symbolic data also becomes clear and so draws attention to an enor

nerf c means non euclidean relational fuzzy clustering abstract the relational fuzzy c means rfcm algorithm can be used to cluster a set of n objects described by pair wise dissimilarity values if and only if there exist n points in r n 1 whose squared euclidean distances precisely match the given dissimilarity data this strong restriction on the dissimilarity data renders rfcm inapplicable to most relational clustering problems this paper substantially improves rfcm by generalizing it to the case of arbitrary symmetric dissimilarity data the generalization is obtained using a computationally efficient modification of the existing algorithm that is equivalent to applying a spreading transformation to the dissimilarity data while the method given applies specifically to dissimilarity data a simple transformation can be used to convert similarity relations into dissimilarity data so the method is applicable to any numerical relational data that are positive reflexive or anti reflexive and symmetric numerical examples illustrate and compare the present approach to problems that can be studied with alternatives such as the linkage algorithms

the bohnenblust hille inequality for homogeneous polynomials is hypercontractive the bohnenblust hille inequality says that the 2m m 1 norm of the coefcients of an m homogeneous polynomial p on c n is bounded by kpk1 times a constant independent of n wherekk 1 denotes the supremum norm on the polydisc d n the main result of this paper is that this inequality is hypercontractive i e the constant can be taken to be c m for some c 1 combining this improved version of the bohnenblust hille inequality with other results we obtain the following the bohr radius for the polydisc d n behaves asymptotically as p logn n modulo a factor bounded away from 0 and innity

convergence of dirichlet polynomials in banach spaces both authors were supported by the mec project mtm2008 03211 the second author was partially supported by grants pr2007 0384 mec and upv paid 00 07

bohr radii of vector valued holomorphic functions abstract motivated by the scalar case we study bohr radii of the n dimensional polydisc d n for holomorphic functions defined on d n with values in banach spaces

on the fourier spectrum of functions on boolean cubes let f be a real valued function of degree d defined on the n dimensional boolean cube pm 1 n and f x sum s subset 1 ldots n widehat f s prod k in s x k its fourier walsh expansion the main result states that there is an absolute constant c 0 such that the ell 2d d 1 sum of the fourier coefficients of f pm 1 n longrightarrow 1 1 is bounded by c sqrt d log d it was recently proved that a similar result holds for complex valued polynomials on the n dimensional polytorus mathbb t n but that in contrast to this a replacement of the n dimensional torus mathbb t n by the n dimensional cube 1 1 n leads to a substantially weaker estimate this in the boolean case forces us to invent novel techniques which differ from the ones used in the complex or real case we indicate how our result is linked with several questions in quantum information theory

reply to comment on jamming at zero temperature and zero applied stress the epitome of disorder we answer the questions raised by donev torquato stillinger and connelly dtsc in their preceding comment on jamming at zero temperature and zero applied stress the epitome of disorder phys rev e 70 043301 2004 we emphasize that we follow a fundamentally different approach than they have done to reinterpret random close packing in terms of the maximally random jammed framework we define the maximally random jammed packing fraction to be where the largest number of initial states chosen completely randomly have relaxed final states at the jamming threshold in the thermodynamic limit thus we focus on an ensemble of states at the jamming threshold while dtsc are interested in determining the amount of order and degree of jamming for a particular configuration we also argue that soft particle systems are as clean as those using hard spheres for studying jammed packings and point out the benefits of using soft potentials

clustering and aggregation of relational data with applications to image database categorization in this paper we introduce a new algorithm for clustering and aggregating relational data card we assume that data is available in a relational form where we only have information about the degrees to which pairs of objects in the data set are related moreover we assume that the relational information is represented by multiple dissimilarity matrices these matrices could have been generated using different sensors features or mappings card is designed to aggregate pairwise distances from multiple relational matrices partition the data into clusters and learn a relevance weight for each matrix in each cluster simultaneously the cluster dependent relevance weights offer two advantages first they guide the clustering process to partition the data set into more meaningful clusters second they can be used in subsequent steps of a learning system to improve its learning behavior the performance of the proposed algorithm is illustrated by using it to categorize a collection of 500 color images we represent the pairwise image dissimilarities by six different relational matrices that encode color texture and structure information

pair correlation function characteristics of nearly jammed disordered and ordered hard sphere packings we study the approach to jamming in hard sphere packings and in particular the pair correlation function g2srd around contact both theoretically and computationally our computational data unambiguously separate the narrowing d function contribution to g2 due to emerging interparticle contacts from the background contribution due to near contacts the data also show with unprecedented accuracy that disordered hard sphere packings are strictly isostatic i e the number of exact contacts in the jamming limit is exactly equal to the number of degrees of freedom once rattlers are removed for such isostatic packings we derive a theoretical connection between the probability distribution of interparticle forces pfsfd which we measure computationally and the contact contribution to g2 we verify this relation for computationally generated isostatic packings that are representative of the maximally random jammed state we clearly observe a maximum in pf and a nonzero probability of zero force shedding light on long standing questions in the granular media literature we computationally observe an unusual power law divergence in the near contact contribution to g2 persistent even in the jamming limit with exponent 0 4 clearly distinguishable from previously proposed inversesquare root divergence additionally we present high quality numerical data on the two discontinuities in the split second peak of g2 and use a shared neighbor analysis of the graph representing the contact network to study the local particle clusters responsible for the peculiar features finally we present the computational data on the contact contribution to g2 for vacancy diluted fcc crystal packings and also investigate partially crystallized packings along the transition from maximally disordered to fully ordered packings we find that the contact network remains isostatic even when ordering is present unlike previous studies we find that ordering has a significant impact on the shape of pf for small forces

relational partitioning fuzzy clustering algorithms based on multiple dissimilarity matrices this paper introduces fuzzy clustering algorithms that can partition objects taking into account simultaneously their relational descriptions given by multiple dissimilarity matrices the aim is to obtain a collaborative role of the different dissimilarity matrices to get a final consensus partition these matrices can be obtained using different sets of variables and dissimilarity functions these algorithms are designed to furnish a partition and a prototype for each fuzzy cluster as well as to learn a relevance weight for each dissimilarity matrix by optimizing an adequacy criterion that measures the fit between the fuzzy clusters and their representatives these relevance weights change at each algorithm iteration and can either be the same for all fuzzy clusters or different from one fuzzy cluster to another experiments with real valued data sets from the uci machine learning repository as well as with interval valued and histogram valued data sets show the usefulness of the proposed fuzzy clustering algorithms

type and cotype of musielak orlicz sequence spaces let n be a musielak orlicz function and l the musielak orlicz sequence space generated by it is shown that satisfies condition qiff is equivalent to aq concave function n it is also proved thatl is of cotypeq typep if and only if satisfies condition q 2and pconditions respectively as applications we obtain characterization of the type and cotype of various sequence spaces nakano weighted orlicz and orlicz sequence spaces furthermore a relation betweenq concavity p convexity lowerq estimate upperp estimate and cotype type of l is given

equivalent norms in polynomial spaces and applications abstract in this paper equivalence constants between various polynomial norms are calculated as an application we also obtain sharp values of the hardy littlewood constants for 2 homogeneous polynomials on l p 2 spaces 2 p we also provide lower estimates for the hardy littlewood constants for polynomials of higher degrees