on adjunctions between lim sl top and sl lim abstract consider l 1 be a commutative strictly two sided quantale with the underlying lattice l being meet continuous two adjunctions one is between limit spaces and stratified l limit spaces and the other is between stratified l limit spaces and stratified l topological spaces are established the first adjunction can be viewed as an extension of lowen s adjunction between the category of topological spaces and stratified 0 1 topological spaces the second is an extension of an adjunction between limit spaces and stratified l topological spaces established in u hohle and t kubiak hohle kubiak semigroup forum 2007

on l m fuzzy convergence spaces this paper presents a definition of l m fuzzy convergence spaces it is shown that the category l m fc of l m fuzzy convergence spaces which embeds the category l m ftop of l m fuzzy topological spaces as a reflective subcategory is a cartesian closed topological category further it is proved that the category of topological pretopological l m fuzzy convergence spaces is isomorphic to the category of topological l m fuzzy quasi coincident neighborhood spaces moreover the relations among l m fuzzy convergence spaces pretopological l m fuzzy convergence spaces and topological l m fuzzy convergence spaces are investigated in the categorical sense

on stratified l convergence spaces in the classical theory of convergence spaces fischer s diagonal axiom ensures that a generalized convergence space is topological in this note we present a lattice valued fischer diagonal axiom and show that this axiom leads to the conclusion that a stratified l convergence space is l topological

partial quasi metrics in this article we introduce and investigate the concept of a partial quasi metric and some of its applications we show that many important constructions studied in matthews s theory of partial metrics can still be used successfully in this more general setting in particular we consider the bicompletion of the quasi metric space that is associated with a partial quasi metric space and study its applications in groups and bck algebras

some corollaries of the correspondence between partial metrics and multivalued equalities multivalued equalities originally arose in the context of the theory of sheaves while partial metrics originally arose in the context of the theory of domains for denotational semantics it turns out that multivalued equalities and partial metrics are closely related one can either consider them equivalent up to the choice of dual notation or one can formally capture the duality between logical and metric viewpoints by explicitly requiring logical values and distances to be represented by dual structures not only does this allow the transfer of the ideas and results between these two fields but the most interesting situations are those of interplay between logical and metric considerations the computational understanding of partial metrics as upper bounds and of multivalued equalities as lower bounds is discussed together with the lower bound counterparts to partial metrics and the corresponding upper bound counterparts to multivalued equalities it is shown that separated pre sheaves of sets and functions over complete heyting algebras can be understood as the pre sheaves of ultrametrics valued in the corresponding brouwerian algebras and non expansive maps of those ultrametrics it is proposed that the natural logical counterparts for partial metrics valued in non negative reals are multivalued equalities valued in the quantale of non positive reals the issue of canonical partial metrics on higher order and reflexive scott domains is revisited the intuition behind strong triangularity vickers form the computational version of strong triangularity and weighted quasi metrics are discussed in the context of quantaloid enrichment

lattice valued convergence spaces and regularity we define a regularity axiom for lattice valued convergence spaces where the lattice is a complete heyting algebra to this end we generalize the characterization of regularity by a dual form of a diagonal condition we show that our axiom ensures that a regular t1 space is separated and that regularity is preserved under initial constructions further we present an extension theorem for a continuous mapping from a subspace to a regular space a characterization in the restricted case that the lattice is a complete boolean algebra in terms of the closure of an l filter is given

analysis of tbzn resistivity temperature derivative above the curie point using singular fitting equations new analyses were carried out of previously published tbzn resistivity temperature derivative data just above the curie temperature tc fitting was accomplished using a weighted nonlinear least squares program genls which allows one to take proper account of errors present in both the independent and the dependent variables the utility of fitting with equations of either logarithmic or power law form involving a critical exponent both with a pole at the curie point was investigated in detail fitting results were uncertain for the four parameter power law choice but with one parameter fixed led to estimates of tc of 199 61 0 02 k and of of 0 16 0 01 the latter value is rather far removed from the value of 0 104 which is expected for a three dimensional n 1 ising model and from the value of 0 014 for a three dimensional n 2 xy model by contrast fitting with a three parameter logarithmic law corresponding to a three dimensional n 2 xy model led to estimated standard deviations of all three free parameters much smaller than the corresponding ones of the four parameter power law fit and to a tc estimate of 199 56 0 03k the present results thus indicate the presence of marked xy or even ising anisotropy quadrupolar effects seem irrelevant

continuity spaces reconciling domains and metric spaces abstract we use continuity spaces a common refinement of posets and metric spaces to develop a general theory of semantic domains which includes metric spaces and domains of cpo s as special cases and provides the appropriate tools for producing new examples which may be suitable for modeling language constructs that occur in concurrent and probabilistic programming our proposal for a general notion of semantic domain is a symmetrically compact continuity space where is a value quantale we show that the category of symmetrically compact continuity spaces with continuous maps has many of the key properties required of a category of domains and that it captures in a natural way the traditional examples in general the category will not be cartesian closed however powerdomains do exist and by adapting a construction of suenderhauf to continuity spaces we show that they define a computational monad in the sense of moggi

precise m k zipf diagram analysis of mathematical and financial time series when m 6 k 2 for studying short range time correlations in nancial signals we have envisaged to combine the zipf method and the i variability diagrams vd as useful tools the 2 vd describes the local curvature short range correlations we have resulted into ranking the 2 vd data according to their frequency of occurrence after having tested the ideas and estimated the error bars on a brownian motion signal we have examined two stocks i e sgp and oxhp closing price and volume of transaction long series a precise m k zipf diagram analysis when m 6 k 2 has been shown to lead to a non immediate information on the signal behavior even taking into account error bars the set of curvatures translated into words indicates a brownian motion like set for the closing price local curvature of such signals over a 6 day span moreover it has been shown that the conjecture about a simple relationship between the hurst exponent h and the exponent of zipf plots does not seem to be substantiated here c 1999 elsevier science b v all rights reserved

toward a phase diagram for stocks abstract a display of the tentatively basic parameters of stocks i e the daily closing price and the daily transaction volume is presented eliminating the time variable between them the phase diagram looks like a triangular region similar to the two phase region of traffic diagrams the data is taken for two companies sgp and oxhp which present different long range correlations in the closing price value as examined by the linearly detrended fluctuation analysis dfa statistical method substructures are observed in the phase diagram as due to changes in management policy e g stock splits

on many valued stratified l fuzzy convergence spaces based on complete residuated lattices the relations between stratified l fuzzy convergence spaces and enriched l fuzzy topological spaces are studied it is shown that as a reflective subcategory the category of enriched l fuzzy topological spaces can embedded in the category of stratified l fuzzy convergence spaces also the specialization l preorder of stratified l fuzzy convergence spaces is investigated

the order theoretic duality and relations between partial metrics and local equalities for a gl monoid l hohle introduced l valued sets to formalize the mathematical theory of identity and existence in monoidal logic for the purpose of analyzing deadlock situations in data flow networks the notion of partial metric space was proposed by matthews later on a lattice theoretic generalization of pseudo partial metric spaces extending the range of pseudo partial metrics to a value lattice v were studied under the name of v pseudo pmetric spaces referring to a gl monoid l and a dual gl monoid v we show that l valued sets are order theoretically dual to v pseudopmetric spaces and apply this duality to the representation of v pseudopmetric spaces and the determination of their various categorical properties in addition to this the present paper provides not only some new results about the representation of l valued sets and their categories but also some non trivial categorical connections between l valued sets and v pseudopmetric spaces

the n zipf analysis of financial data series and biased data series the zipf analysis of n words in random sequences and financial data series like the stock prices of a company has been performed the bias as well as the resulting staircase structure of the zipf plots are taken into account in the subsequent analysis it is found that correlations for the sign of the fluctuations as well as for the amplitude of the fluctuations can be found in financial time series the relevance of the n zipf analysis to financial sequences is underlined to be only weakly predictive for a binary transformation level but could be more interesting for higher translation levels

a common framework for lattice valued uniform spaces and probabilistic uniform limit spaces we study a category of lattice valued uniform convergence spaces where the lattice is enriched by two algebraic operations this general setting allows us to view the category of lattice valued uniform spaces as a reflective subcategory of our category and the category of probabilistic uniform limit spaces as a coreflective subcategory

equilibrium and dynamic methods when comparing an english text and its esperanto translation abstract a comparison of two english texts written by lewis carroll one alice in wonderland also translated into esperanto the other through the looking glass are discussed in order to observe whether natural and artificial languages significantly differ from each other one dimensional time series like signals are constructed using only word frequencies fts or word lengths lts the data is studied through i a zipf method for sorting out correlations in the fts and ii a grassberger procaccia gp technique based method for finding correlations in lts the methods correspond to an equilibrium and a dynamic approach respectively to human texts features there are quantitative statistical differences between the original english text and its esperanto translation but the qualitative differences are very minutes however different power laws are observed with characteristic exponents for the ranking properties and the phase space attractor dimensionality the zipf exponent can take values much less than unity 0 50 or 0 30 depending on how a sentence is defined this variety in exponents can be conjectured to be an intrinsic measure of the book style or purpose rather than the language or author vocabulary richness since a similar exponent is obtained whatever the text moreover the attractor dimension r is a simple function of the so called phase space dimension n i e r n with 0 79 such an exponent could also be conjectured to be a measure of the author style versatility here well preserved in the translation

low order variability diagrams for short range correlation evidence in financial data bgl usd exchange rate dow jones industrial average gold ounce price a method to sort out short range correlations and decorrelations in financial data is tested on three typical sets the bulgarian lev usa dollar bgl usd exchange rate the dow jones industrial average the gold ounce price the method makes use of the so called variability diagram technique three toys are used as models in order to understand features our findings indicate that some predictability can be found at short range time intervals c 1999 elsevier science b v all rights reserved

zipf s law is not a consequence of the central limit theorem it has been observed that the rank statistics of string frequencies of many symbolic systems e g word frequencies of natural languages follows zipf s law in good approximation we show that contrary to claims in the literature zipf s law cannot be realized by the central limit theorem s the observation that a log normal distribution of string frequencies yields an approximately zipf like rank statistics is actually misleading indeed zipf s law for the rank statistics is strictly equivalent to a power law distribution of frequencies there are two natural ways to perform the infinite size limit for the vocabulary the first one is the method of choice in the literature it makes the upper word length bound tend to infinity and leads in the case of a multistate bernoulli process via a central limit theorem to a log normal frequency distribution an alternative and for text samples actually better realizable way is to make the lower frequency bound tend to zero this limit procedure leads to a power law distribution and hence to zipf s law char22 at least for bernoulli processes and to a very good approximation for natural languages where it passes the ensuremath chi 2 test for the bernoulli case we will give a heuristic proof

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

a non commutative and non idempotent theory of quantale sets in fuzzy set theory non idempotency arises when the conjunction is interpreted by arbitrary t norms there are many instances in mathematics where set theory ought to be non commutative and or non idempotent the purpose of this paper is to combine both ideas and to present a theory of non commutative and non idempotent quantale sets among other things standard concepts like fuzzy preorders and fuzzy equivalence relations will be exhibited as special cases more specifically the category q set is investigated where q is an arbitrary involutive quantale objects quantale sets are pairs consisting of a set and a q valued equality with a suitable symmetry axiom three important properties of q set are shown it is complete cocomplete and has the epi extremal mono factorization property its subcategory s q set of separated quantale sets is reflective in q set and shares the same fundamental properties with q set in particular s q set is also a complete and cocomplete epi extremal mono category the objects of the category q set are interesting categories in their own right two categorical frameworks for objects of q set are exhibited first it is shown that q valued equalities arise from q valued preorders with self adjoint extents by symmetrization which leaves q valued equalities invariant here sets with quantale preorders are shown to be b categories with base b being a specific quantaloid the second approach is based on involutive quantaloids a combination of two well known things quantaloids and ordered categories with involution in this context quantale sets are precisely symmetric b categories w r t appropriately chosen quantaloid b with involution further the cauchy completion preserves the symmetry axiom for a large class of involutive quantales which include quantic frames our non commutative generalization of frames and all left continuous t norms there exist at least two monads on q set the singleton monad and quasi singleton monad which are of special interest for fuzzy set theory the kleisli category associated with the singleton monad is the non commutative and non idempotent analogue of higgs topos while the eilenberg moore category of the quasi singleton monad permits the internalization of lukasiewicz negation as truth arrow finally an application of quantale sets to c algebras is given and the change of base is treated

monoidal closedness of the category of stratified l semiuniform convergence spaces abstract for an integral commutative unital quantale l we show that there exists a tensor product between stratified l semiuniform convergence spaces and with respect to this tensor product that the category of stratified l semiuniform convergence spaces and uniformly continuous maps is a symmetric monoidal category as a result we obtain the monoidal closedness of the category of stratified l semiuniform convergence spaces and uniformly continuous maps

strategy for investments from zipf law s abstract we have applied the zipf method to extract the exponent for seven financial indices dax ftse djia nasdaq sp hang seng and nikkei 225 after having translated the signals into a text based on two letters we follow considerations based on the signal hurst exponent and the notion of a time dependent zipf law and exponent in order to implement two simple investment strategies for such indices we show the time dependence of the returns