bidual renormings of banach spaces abstract given a separable banach space x with no isomorphic copies of l 1 and a separable subspace y of its bidual we provide a sufficient condition on y to ensure that x admits an equivalent norm such that the restriction to y of the corresponding bidual norm is midpoint locally uniformly rotund this result applies to the separable subspaces of the bidual of a banach space with a shrinking unconditional schauder basis and to the bidual of the james space

symmetry relations in exactly soluble models symmetry relations such as the star triangle or the inverse relation are very useful in determining the partition function of two dimensional exactly soluble models a common construction of the three dimensional equivalents of these symmetry relations is presented they are used to derive in a geometric way applying simultaneously to different kinds of spin models the consequent global properties i e the commutativity of the transfer matrices and the inverse functional equations on the transfer matrix and the partition function the usefulness of the inverse relation is illustrated by an application to the three dimensional ising model

three dimensional integrable models and associated tangle invariants in this paper we show that the boltzmann weights of the three dimensional baxter bazhanov model give representations of the braid group if some suitable spectral limits are taken in the trigonometric case we classify all possible spectral limits which produce braid group representations furthermore we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones

characterizing the statistical properties of mutual information in mimo channels we consider gaussian multiple input multiple output mimo frequency selective spatially correlated fading channels assuming that the channel is unknown at the transmitter and perfectly known at the receiver for gaussian codebooks using results from multivariate statistics we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal to noise ratio snr we show that our bound is tighter than previously reported analytical lower bounds and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity based on a closed form approximation of the variance of mutual information in correlated flat fading mimo channels we provide insights into the multiplexing diversity tradeoff for gaussian code books furthermore for a given total number of antennas we consider the problem of finding the optimal ergodic capacity maximizing number of transmit and receive antennas and we reveal the snr dependent nature of the maximization strategy finally we present numerical results and comparisons between our capacity bounds and previously reported bounds

gruenhage compacta and strictly convex dual norms abstract we prove that if k is a gruenhage compact space then c k admits an equivalent strictly convex dual norm as a corollary we show that if x is a banach space and x span k where k is a gruenhage compact in the w topology and is equivalent to a coarser w lower semicontinuous norm on x then x admits an equivalent strictly convex dual norm we give a partial converse to the first result by showing that if is a tree then c 0 admits an equivalent strictly convex dual norm if and only if is a gruenhage space finally we present some stability properties satisfied by gruenhage spaces in particular gruenhage spaces are stable under perfect images

strictly convex norms and topology we introduce a new topological property called and the corresponding class of topological spaces which includes spaces with g diagonals and gruenhage spaces using we characterize those banach spaces which admit equivalent strictly convex norms and give an internal topological characterization of those scattered compact spaces k for which the dual banach space c k admits an equivalent strictly convex dual norm we establish some relationships between and other topological concepts and the position of several well known examples in this context for instance we show that c k admits an equivalent strictly convex dual norm where k is kunen s compact s space also under additional axioms we provide examples of compact scattered non gruenhage spaces of cardinality 1 having

on a classical renorming construction of v klee we further develop a classical geometric construction of v klee and show typically that if x is a nonreflexive banach space with separable dual then x admits an equivalent norm which is frechet differentiable locally uniformly rotund its dual norm is uniformly g teaux differentiable the weak and the norm topologies coincide on the sphere of x and yet is not rotund this proves a stronger form of a conjecture of v klee

continuous functions on totally ordered spaces that are compact in their order topologies abstract the totally ordered spaces that are compact and connected in their order topologies are characterized as images of lexicographic cubes the banach space of continuous functions on the lexicographic product of compact totally ordered spaces whose spaces of continuous functions have locally uniformly convex norms has an equivalent locally uniformly convex norm if and only if the product is countable the banach space of continuous functions on a compact totally ordered space always has an equivalent kadec norm those compact totally ordered spaces for which the banach space of continuous functions has an equivalent locally uniformly convex norm are characterized in terms of the bounded decreasing interval functions that can be defined on the intervals of the totally ordered spaces some examples are discussed in detail

topological properties of banach spaces weakly compact sets in banach spaces are fragmentable we introduce the weaker notion of the a fragmentability of a subset of a banach space a notion that has a far wider range of applicability we prove that all weakly cech analytic subsets of a banach space are a fragmented this implies that all banach spaces having kadec norms are a fragmented however l is not fragmented

the fixed point property for mappings admitting a center abstract we introduce a class of nonlinear continuous mappings in banach spaces which allow us to characterize the banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping later on we give an application to the existence of zeroes for certain kinds of accretive operators

identification of non linear systems using multi scale ridges and skeletons of the wavelet transform abstract a new procedure of non linear system identification is presented the procedure employs the slowly varying time dependent amplitude and phase functions of the impulse response of the system these instantaneous characteristics are obtained from the ridges and skeletons of the wavelet transform the ridge extraction procedure uses the modulus of the transform and involves a combinatorial optimization algorithm based on simulated annealing the method is illustrated using two simple simulated examples it is shown that the procedure can be used for multi degree of freedom systems due to the frequency localization property of the continuous grossman morlet wavelets

information flow and nontrivial collective behavior in chaotic coupled map lattices this work quantitatively demonstrates a nontrivial collective behavior which depends on the coupling strength in chaotic coupled map lattices using the interdependence measure emerging from a local unit the amount of information flow which flows from the instantaneous mean field to a local map has been investigated using the time delayed mutual information interestingly the collective system s behavior is found to be associated with the amount of information flow as mentioned above both methods can effectively display the nontrivial collective behavior and the amount of information flow

a topological characterization of dual strict convexity in asplund spaces abstract let x be an asplund space we show that the existence of an equivalent norm on x having a strictly convex dual norm is equivalent to the dual unit sphere s x equivalently x possessing a non linear topological property called which was introduced by j orihuela s troyanski and the author

efimov spaces and the separable quotient problem for spaces cp k abstract the classic rosenthal lacey theorem asserts that the banach space c k of continuous real valued maps on an infinite compact space k has a quotient isomorphic to c or l 2 more recently kakol and saxon 20 proved that the space c p k endowed with the pointwise topology has an infinite dimensional separable quotient algebra iff k has an infinite countable closed subset hence c p n lacks infinite dimensional separable quotient algebras this motivates the following question does c p k admit an infinite dimensional separable quotient shortly sq for any infinite compact space k particularly does c p n admit sq our main theorem implies that c p k has sq for any compact space k containing a copy of n consequently this result reduces problem to the case when k is an efimov space i e k is an infinite compact space that contains neither a non trivial convergent sequence nor a copy of n although it is unknown if efimov spaces exist in zfc we show making use of some result of r de la vega 2008 under that for some efimov space k the space c p k has sq some applications of the main result are provided

on zamolodchikov s solution of the tetrahedron equations the tetrahedron equations arise in field theory as the condition for thes matrix in 2 1 dimensions to be factorizable and in statistical mechanics as the condition that the transfer matrices of three dimensional models commute zamolodchikov has proposed what appear from numerical evidence and special cases to be non trivial particular solutions of these equations but has not fully verified them here it is proved that they are indeed solutions

weak sequential properties of johnson lindenstrauss spaces abstract a banach space x is said to have efremov s property e if every element of the weak closure of a convex bounded set c x is the weak limit of a sequence in c by assuming the continuum hypothesis we prove that there exist maximal almost disjoint families of infinite subsets of n for which the corresponding johnson lindenstrauss spaces enjoy resp fail property e this is related to a gap in plichko 2015 12 and allows to answer consistently questions of plichko and yost

alur dual renormings of banach spaces we give a covering type characterization for the class of dual banach spaces with an equivalent alur dual norm

zn n 1 generalization of the chiral potts model we show that ther matrix which intertwines twon by nn 1 state cyclicl operators related with a generalization ofuq sl n algebra can be considered as a boltzmann weight of four spin box for a lattice model with two spin interaction just as ther matrix of the checkerboard chiral potts model the rapidity variables lie on the algebraic curve of the genusg n2 n 1 n 1 n n 1 defined by 2n 3 independent moduli this curve is a natural generalization of the curve which appeared in the chiral potts model factorization properties of thel operator and its connection to the sos models are also discussed

generalized chiral potts models and minimal cyclic representations of u_q widehat mathfrak g mathfrak l n c finite dimensional cyclic representations of the quantized universal enveloping algebra u q g exist only when the deformation parameter q is a root of unity q n 1 in such representations the n th power of each chevalley generator acts as a non zero scalar these values of e i n f i n and t i n are part of a continuous family of parameters upon which the cyclic representations depend

sensitivity analysis of an auto correlation function based damage index and its application in structural damage detection abstract structural damage detection using time domain vibration responses has advantages such as simplicity in calculation and no requirement of a finite element model which attracts more and more researchers in recent years in present paper a new approach to detect the damage based on the auto correlation function is proposed the maximum values of the auto correlation function of the vibration response signals from different measurement points are formulated as a vector called auto correlation function at maximum point value vector amv for short the relative change of the normalized amv before and after damage is used as the damage index to locate the damage sensitivity analysis of the normalized amv with respect to the local stiffness shows that the normalized amv has a sharp change around the local stiffness change location which means the normalized amv is a good indicator to detect the damage even when the damage is very small stiffness reduction detection of a 12 story frame structure is provided to illustrate the validity effectiveness and the anti noise ability of the proposed method comparison of the normalized amv and the other correlation function based damage detection method shows the normalized amv has a better detectability

smoothing of bump functions abstract let x be a separable banach space with a schauder basis admitting a continuous bump which depends locally on finitely many coordinates then x admits also a c smooth bump which depends locally on finitely many coordinates

star triangle relation for a three dimensional model the solvablesl n chiral potts model can be interpreted as a three dimensional lattice model with local interactions to within a minor modification of the boundary conditions it is an ising type model on the body centered cubic lattice with two and three spin interactions the corresponding local boltzmann weights obey a number of simple relations including a restricted star triangle relation which is a modified version of the well known star triangle relation appearing in two dimensional models we show that these relations lead to remarkable symmetry properties of the boltzmann weight function of an elementary cube of the lattice related to the spatial symmetry group of the cubic lattice these symmetry properties allow one to prove the commutativity of the row to row transfer matrices bypassing the tetrahedron relation the partition function per site for the infinite lattice is calculated exactly

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

on binormality in non separable banach spaces we study binormality a separation property of the norm and weak topologies of a banach space we show that every banach space which belongs to a p class is binormal we also show that the asplundness of a banach space is equivalent to a related separation property of its dual space

on trees and dual rotund norms abstract we give a necessary and sufficient condition for the existence of an equivalent dual rotund norm on c 0 l 1 where is a tree the condition is expressed succinctly in terms of the embeddability of into a particular totally ordered set and compares very well with the analogous situation for local uniform rotundity this resolves an open problem from haydon s work in asplund spaces trees and renorming theory

polyhedral norms on non separable banach spaces abstract we prove the existence of equivalent polyhedral norms on a number of classes of non separable spaces the majority of which being of the form c k in particular we obtain a complete characterization of those trees t such that c 0 t admits an equivalent polyhedral norm

testing for nonlinearity using redundancies quantitative and qualitative aspects abstract a method for testing nonlinearity in time series is described based on information theoretic functionals redundancies linear and nonlinear forms of which allow either qualitative or after incorporating the surrogate data technique quantitative evaluation of dynamical properties of scrutinized data an interplay of quantitative and qualitative testing on both the linear and nonlinear levels is analyzed and robustness of this combined approach against spurious nonlinearity detection is demonstrated evaluation of redundancies and redundancy based statistics as functions of time lag and embedding dimension can further enhance insight into dynamics of a system under study

on weakly locally uniformly rotund banach spaces abstract we show that every normed space e with a weakly locally uniformly rotund norm has an equivalent locally uniformly rotund norm after obtaining a discrete network of the unit sphere s e for the weak topology we deduce that the space e must have a countable cover by sets of small local diameter which in turn implies the renorming conclusion this solves a question posed by deville godefroy haydon and zizler for a weakly uniformly rotund norm we prove that the unit sphere is always metrizable for the weak topology despite the fact that it may not have the kadec property moreover banach spaces having a countable cover by sets of small local diameter coincide with the descriptive banach spaces studied by hansell so we present here some new characterizations of them

extension operators and twisted sums of c0 and c k spaces abstract we investigate the following problem posed by cabello sanchez castillo kalton and yost let k be a nonmetrizable compact space does there exist a nontrivial twisted sum of c 0 and c k i e does there exist a banach space x containing a non complemented copy y of c 0 such that the quotient space x y is isomorphic to c k using additional set theoretic assumptions we give the first examples of compact spaces k providing a negative answer to this question we show that under martin s axiom and the negation of the continuum hypothesis if either k is the cantor cube 2 1 or k is a separable scattered compact space of height 3 and weight 1 then every twisted sum of c 0 and c k is trivial we also construct nontrivial twisted sums of c 0 and c k for k belonging to several classes of compacta our main tool is an investigation of pairs of compact spaces k l which do not admit an extension operator c k c l

weak locally uniformly rotund norms and descriptive compact spaces we prove that a dual banach space x has an equivalent w lur norm if and only if the weak topology has a isolated network we give sufficient conditions for the existence of equivalent norms with various kinds of differentiability

knot invariants associated with a particular n continuous limit of the baxter bazhanov model first we briefly recall the definition of the three dimensional baxter bazhanov lattice model the spins of this model are elements ofzn and ther matrix is associated to the algebrauqsl n ifq is a primitiventh root of unity then we construct a particularn limit of the model in which it is meaningful to interpret the spins as elements ofr and which gives the free gaussian boson model finally we study special limits of the rapidity variables in which we obtain braid group representations and we show that forn odd the associated knot invariants are given by the inverse of products of alexander polynomials evaluated at certain roots of unity

generalized chiral potts models and minimal cyclic representations of u_q widehat germ g germ l n bf c we present for odd n a construction of the n 1 state generalization of the chiral potts model proposed recently by bazhanov et al the yang baxter equation is proved

networks for the weak topology of banach and frechet spaces abstract we start the systematic study of frechet spaces which are spaces in the weak topology a topological space x is an 0 space or an space if x has a countable k network or a locally finite k network respectively we are motivated by the following result of corson 1966 if the space c c x of continuous real valued functions on a tychonoff space x endowed with the compact open topology is a banach space then c c x endowed with the weak topology is an 0 space if and only if x is countable we extend corson s result as follows if the space e c c x is a frechet lcs then e endowed with its weak topology e e is an space if and only if e e e is an 0 space if and only if x is countable we obtain a necessary and some sufficient conditions on a frechet lcs to be an space in the weak topology we prove that a reflexive frechet lcs e in the weak topology e e is an space if and only if e e e is an 0 space if and only if e is separable we show however that the nonseparable banach space l 1 r with the weak topology is an space

tetrahedron equations and the relativistic s matrix of straight strings in 2 1 dimensions the quantums matrix theory of straight strings infinite one dimensional objects like straight domain walls in 2 1 dimensions is considered thes matrix is supposed to be purely elastic and factorized the tetrahedron equations which are the factorization conditions are investigated for the special two colour model the relativistic three strings matrix which apparently satisfies this tetrahedron equation is proposed

locally uniformly convex norms in banach spaces and their duals abstract it is shown that a banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex

sequential normal compactness versus topological normal compactness in variational analysis abstract we study relationships between two normal compactness properties of sets in banach spaces that play an essential role in many aspects of variational analysis and its applications particularly in calculus rules for generalized differentiation necessary optimality and suboptimality conditions for optimization problems etc both properties automatically hold in finite dimensional spaces and reveal principal features of the infinite dimensional variational theory similar formulations of these properties involve the weak convergence of sequences and nets respectively containing generalized normal cones in duals to banach spaces we prove that these properties agree for a large class of banach spaces that include weakly compactly generated spaces we also show that they are always different in banach spaces whose unit dual ball is not weak sequentially compact moreover the sequential and topological normal compactness properties may not coincide even in non separable asplund spaces that admit an equivalent c smooth norm

oscillations complex spatiotemporal behavior and information transport in networks of excitatory and inhibitory neurons various types of spatiotemporal behavior are described for two dimensional networks of excitatory and inhibitory neurons with time delayed interactions it is described how the network behaves as several structural parameters are varied such as the number of neurons the connectivity and the values of synaptic weights a transition from spatially uniform oscillations to spatiotemporal chaos via intermittentlike behavior is observed the properties of spatiotemporally chaotic solutions are investigated by evaluating the largest positive lyapunov exponent and the loss of correlation with distance finally properties of information transport are evaluated during uniform oscillations and spatiotemporal chaos it is shown that the diffusion coefficient increases significantly in the spatiotemporal phase similar to the increase of transport coefficients at the onset of fluid turbulence it is proposed that such a property should be seen in other media such as chemical turbulence or networks of oscillators the possibility of measuring information transport from appropriate experiments is also discussed

differentiability of lipschitz functions on banach spaces abstract the main result of this note says that if the norm of a banach space e is differentiable frechet gateaux or in some intermediate sense away from the origin then every locally lipschitz function defined on an open subset g of e is differentiable in the same sense at every point of some subset of g dense in g as the main corollary we prove that every lipschitz function on an asplund space is frechet differentiable on a dense set moreover in all these results the mean value theorem for the points of differentiability which is equivalent to the possibility of computing the clarke subdifferential from the points of differentiability is shown to hold

damage identification of nonlinear structural systems the present investigation develops methods for the identie cation of highly localized structural damages in nonlinear structures the damage is dee ned as either a reduction of stiffness or a change of restoring force characteristics from linear undamaged state to weak nonlinear damaged state one method for identifying both the location and type of damages is the location vector method lvm the other method is for quantifying the damage the lvm requires only the modal data from the e rst few fundamental modes the second method is based on fast fourier transform fft and the least squares method under the assumptions that the location of the damages can be identie ed and their responses can be measured by testing without loss of generality the methods are illustrated by a e ve degree of freedom dufe ng s nonlinear system measurement data are simulated in the time domain and in the frequency domain by using the runge kutta method and fft respectively the robustness and effectiveness of the methods are examined by using a simulated output time history contaminated by a 5 white noise which represents more realistic levels of measurement errors

a method for detecting damage induced nonlinearities in structures using information theory abstract in this work a new approach is presented for detecting the presence of damage induced nonlinearities in structures from measurements of structural dynamics two different information theoretic it measures the time delayed mutual information and the time delayed transfer entropy are used to provide a probabilistic measure of the coupling between structural components these measures may be used to capture both linear and nonlinear relationships among time series data the formula for both quantities is derived for a linear five degree of freedom system subject to gaussian excitation an algorithm is then described for computing the it metrics from time series data and results are shown to agree with theory we then show that as the coupling between the structure s components changes from linear to nonlinear the information flow can be used to indicate the degree of nonlinearity deviations from a linear model are quantified statistically by generating surrogate data sets that by construction possess only linear second order correlations we then apply the proposed algorithms to both the original data and the surrogates differences in the results are shown to be proportional to the degree of nonlinearity this result is shown to be independent of global changes in stiffness and is therefore unaffected by certain models of environmental variability furthermore the method provides an absolute measure of nonlinearity and therefore does not require a baseline data set for making comparisons this approach is discussed in the context of structural health monitoring where damage is often associated with structural nonlinearity

study on an auto correlation function based damage index sensitivity analysis and structural damage detection abstract the damage index based on the auto correlation function to detect the damage of the structure under white noise excitation is studied in detail in this paper the maximum values of the auto correlation function of the vibration response signals displacement velocity and acceleration from different measurement points of the structure are collected and formulated as a vector called auto correlation function at maximum point value vector amv which is expressed as a weighted combination of the hadamard product of two mode shapes amv is normalized by its root mean square value so that the influence of the excitation can be eliminated sensitivity analysis for the different parts of the normalized amv shows that the sensitivity of the normalized amv to the local stiffness is dependent most on the sensitivity of the hadamard product of the two lower order mode shapes to the local stiffness which has a sudden change of the value around the local stiffness change position the sensitivity of the normalized amv has the similar shape and same trend that shows it is a very good damage indicator even for the very small damage the relative change of the normalized amv before and after damage occurs in the structure is adopted as the damage index to show the damage location several examples of the stiffness reduction detection of a 12 story shear frame structure are utilized to validate the results in sensitivity analysis illustrate the effectiveness and anti noise ability of the amv based damage detection method and compare the effect of the response type on the detectability of the normalized amv

normality and modulability indices part ii convex cones in hilbert spaces this paper proposes and compares several ways of measuring the degree of normality of a convex cone contained in a normed space the dual concept of modulability is also considered other notions like solidity and sharpness are also analyzed from a quantitative point of view

a smooth variational principle with applications to hamilton jacobi equations in infinite dimensions abstract we prove that if x is a banach space which admits a smooth lipschitzian bump function then for every lower semicontinuous bounded below function there exists a lipschitzian smooth function g on x such that f g attains its strong minimum on x thus extending a result of borwein and preiss we then show how the above result can be used to obtain existence and uniqueness results of viscosity solutions of hamilton jacobi equations in infinite dimensional banach spaces a without assuming the radon nikodym property

some remarks on smooth renormings of banach spaces abstract we prove that in every separable banach space x with a schauder basis and a c k smooth norm it is possible to approximate uniformly on bounded sets every equivalent norm with a c k smooth one in a way that the approximation is improving as fast as we wish on the elements depending only on the tail of the schauder basis our result solves a problem from the recent monograph of guirao montesinos and zizler

three dimensional vertex model in statistical mechanics from baxter bazhanov model we find that the boltzmann weight of the three dimensional baxter bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube and the wu kadanoff wegner duality between the cube and vertex type tetrahedron equations is obtained explicitly for the baxter bazhanov model then a three dimensional vertex model is obtained by considering the symmetry property of the weight function which corresponds to the three dimensional baxter bazhanov model the vertex type weight function is parametrized as the dihedral angles between the rapidity planes connected with the cube we write down the symmetry relations of the weight functions under the actions of the symmetry groupg of the cube the six angles with a constraint condition appearing in the tetrahedron equation can be regarded as the six spectra connected with the six spaces in which the vertextype tetrahedron equation is defined

on banach spaces whose norm open sets are fσ sets in the weak topology we investigate non separable banach spaces whose norm open sets are countable unions of sets closed in the weak topology and a narrower class of banach spaces with a network for the norm topology which is discrete in the weak topology in particular we answer a question of arhangel skii exhibiting various examples of non separable function spaces c k with a discrete network for the pointwise topology and consistently we answer some questions of edgar and oncina concerning borel structures and kadec renormings in banach spaces

information transfer in continuous processes we discuss a recently proposed quantity called transfer entropy which uses time series data to measure the amount of information transferred from one process to another in order to understand its foundation merits and limitations we review some aspects of information theoretic functionals while for symbol sequences these measures have an intuitive interpretation their application to continuous state processes and in particular their estimation from finite data sets is problematic for mutual information finite length scale estimates converge from below and can thus be used to reject the assumption that the observed processes are independent however mutual information does not provide any directional information conversely transfer entropy does resolve the directionality of information exchange but no similar monotonic convergence seems to hold thus only in the case of zero transfer entropy in one direction we can reliably infer an asymmetry of the information exchange

continuous functions on compact totally ordered spaces abstract the banach space c k of continuous functions on k with its pointwise topology is shown to be fragmented by pointwise closed sets when k is a compact totally ordered set when k is a dendron and when k is a compact hausdorff space with a closed crossfree subbase for its topology in some special instances c k will have an equivalent locally uniformly convex norm

improved surrogate data for nonlinearity tests current tests for nonlinearity compare a time series to the null hypothesis of a gaussian linear stochastic process for this restricted null assumption random surrogates can be constructed which are constrained by the linear properties of the data we propose a more general null hypothesis allowing for nonlinear rescalings of a gaussian linear process we show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity an iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution

average locally uniform rotundity and a class of nonlinear maps abstract we consider some topological characterizations of dual banach spaces that admit an equivalent dual average locally uniformly rotund norm and provide a criterion for such renorming which involves the class of slicely continuous maps

convex sets which are intersections of closed balls in this paper we aim to investigate different questions concerning the stability of the set m of all intersections of closed balls in a normed space we are mainly concerned with i the stability of m under the closure of the vector sums ii the stability under the addition of balls we prove that i and ii are different properties which have strong connections with the geometry of the space they have interest both in finite and infinite dimension in the former case there is a link with linear programming theory we also study two more stability properties related to the well known binary intersection property mazur sets and mazur spaces are introduced as a natural family satisfying i we prove that every two dimensional normed space is a mazur space a result which distinguishes dimension d 2 from dimension d 3 we also discuss the connections between mazur spaces and porosity

uniformly gâteaux smooth approximations on c0 γ abstract every lipschitz mapping from c 0 into a banach space y can be uniformly approximated by lipschitz mappings that are simultaneously uniformly g teaux smooth and c frechet smooth

new solvable lattice models in three dimensions in this paper we establish a remarkable connection between two seemingly unrelated topics in the area of solvable lattice models the first is the zamolodchikov model which is the only nontrivial model on a three dimen sional lattice so far solved the second is the chiral potts model on the square lattice and its generalization associated with theu q sl n algebra which is of current interest due to its connections with high genus algebraic curves and with representations of quantum groups at roots of unity we show that this last sl n generalized chiral potts model can be interpreted as a model on a threedimensional simple cubic lattice consisting ofn square lattice layers with ann valued n 2 spin at each site further in then 2 case this three dimen sional model reduces after a modification of the boundary conditions to the zamolodchikov model we mentioned above

hilbert generated spaces we classify several classes of the subspaces of banach spaces x for which there is a bounded linear operator from a hilbert space onto a dense subset in x dually we provide optimal affine homeomorphisms from weak star dual unit balls onto weakly compact sets in hilbert spaces or in c0 spaces in their weak topology the existence of such embeddings is characterized by the existence of certain uniformly g teaux smooth norms

on weakly countably determined banach spaces for a topological space x let ci x denote the banach space of all bounded functions x r such that for every e 0 the set x x f x e is closed and discrete in x endowed with the supremum norm the main theorem is the following let l be a weakly countably determined subset of a banach space then there exist a subset e of the baire space e a compact space k and a bounded linear one to one operator t c l ci e x k that is pointwise to pointwise continuous in the case where l is weakly analytic e can be replaced by e this theorem is connected with the basic result of amir lindenstrauss on wcg banach spaces and has corresponding consequences such as the representation of gulko resp ta lagrand compact spaces as pointwise compact subsets of ci e x k resp ci e x k a compact space f is called gulko or talagrand compact if c o is wcd or a weakly k analytic banach space the characterization of wcd resp weakly k analytic banach spaces e using one to one operators from e into ci e x k resp ci e x k and the existence of equivalent good norms on e and e simultaneously

sailing over three problems of koszmider abstract we discuss three problems of koszmider on the structure of the spaces of continuous functions on the stone compact k a generated by an almost disjoint family a of infinite subsets of we present a solution to two problems and develop previous results of marciszewski and pol answering the third one we will show in particular that assuming martin s axiom the space c k a is uniquely determined up to isomorphism by the cardinality of a whenever a c while there are 2 c nonisomorphic spaces c k a with a c we also investigate koszmider s problems in the context of the class of separable rosenthal compacta and indicate the meaning of our results in the language of twisted sums of c 0 and some c k spaces

twisted sums of c0 and c k spaces a solution to the ccky problem abstract we consider the class of banach spaces y for which c 0 admits a nontrivial twisted sum with y we present a characterization of such spaces y in terms of properties of the w e a k topology on y we prove that under the continuum hypothesis c 0 has a nontrivial twisted sum with every space of the form y c k where k is compact and not metrizable this gives a consistent affirmative solution to a problem posed by cabello castillo kalton and yost