paracompactness in l topological spaces in this paper a certain fuzzy paracompactness is presented by means of the concept of locally finite family of l fuzzy sets the concept of locally finite family can be used to characterize fuzzy countable compactness this fuzzy paracompactness is a natural generalization of lowen fuzzy compactness a fuzzy countably compact l set is fuzzy paracompact if and only if it is fuzzy compact a topological space x j is paracompact if and only if its induced space x j is fuzzy paracompact when ms l the fuzzy enhanced real line r l is fuzzy paracompact the product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact a fuzzy strongly t2 paracompact space is strongly s regular and strongly ws normal moreover a strongly s regular lindelof space is fuzzy paracompact

induced i l fuzzy topological spaces abstract in this paper we introduce the notion of induced i l fuzzy topological spaces by using the i l valued lower semicontinuous mappings and investigate some of their basic properties in particular we give a necessary and sufficient condition for an i l fuzzy topological space to be induced and prove that this kind of induced space preserves the cartesian product and the n compactness as well

discrete dynamical systems in l topological spaces in this paper we investigate iteration of zadeh image operators and their discrete dynamical systems in l topological spaces some basic concepts such as limit set invariant set periodic point nonwandering point and recurrent point are discussed in weakly induced topological spaces we also study topological mixing topological transitivity and minimality for such dynamical systems while comparing with those corresponding ones in crisp spaces

compactness in l fuzzy topological spaces abstract a good definition of compactness in an l fuzzy topological space was introduced by warner and mclean 1993 in this paper we give an extension of this notion to arbitrary l fuzzy subsets and study its properties

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

a new definition of fuzzy compactness in this paper a new definition of fuzzy compactness is presented in l topological spaces when l is a complete demorgan algebra this definition does not rely on the structure of the basis lattice l and no distributivity in l is required the intersection of a fuzzy compact l set and a closed l set is fuzzy compact the continuous image of a fuzzy compact l set is fuzzy compact if the set of all prime elements of l is order generating then the alexander subbase theorem is true when l is a completely distributive demorgan algebra it is equivalent to lowen s fuzzy compactness and in this case its many characterizations are presented by means of open l sets and closed l sets

reflections on value regions limit regions and truncation errors for continued fractions for continued fractionsk a n 1 the concept of limit region is discussed and its use for obtaining modified truncation error estimates is illustrated on examples a certain strategy for numerical computation of limit regions is presented and illustrated on examples

a new fuzzy compactness defined by fuzzy nets compactness is one of the most important notions in topology and is thoroughly investigated in general topology but it seems that the research about this notion in the area of fuzzy topology is not so effective as in general topology in fact it would seem that there was not even a good definition of compactness in this area until recently indeed soon after the famous article written by zadeh 8 was published chang 1 introduced the notion of fuzzy topological spaces and at the same time a certain fuzzy compactness was given from then on a series of different notions of fuzzy compactness have been discussed 2 3 71 and in 5 they were compared in detail but it seems unsatisfactory that all these fuzzy compactness ideas are defined for the whole fuzzy topological space but not for an arbitrary fuzzy subset therefore they are far from the crisp compactness for example it is impossible to discuss the hereditary property with respect to closed subsets of fuzzy compactness in 1977 pu and liu introduced the notion of fuzzy nets and a new concept of so called q neighborhood was given which could reflect the features of neighborhood structure in fuzzy topological spaces and by this new neighborhood structure the moore smith convergence theory was established spendidly 6 it furnishes us a basic tool to investigate the fuzzy compactness in a more general way to investigate the compactness of arbitrary fuzzy subsets in this paper a new fuzzy compactness defined by fuzzy nets we shall call it n compactness is given but we introduce the notion of r neighborhood see section 2 instead of qneighborhood to establish the moore smith convergence theory for it is perhaps more convennient to use n compactness possesses the following properties 1 n compactness is defined for arbitrary fuzzy subsets 2 for n compactness the hereditary property with respect to closed subsets holds 3 n compactness is a good extension 5 4 the continuous images of ncompact sets are n compact 5 for n compactness the tychonoff product theorem holds 6 if an n compact fuzzy topological space is t2 6 then it will satisfy a stronger separation axiom which will be called t4 in this paper 1 0022 247x 83 3 00

a new approach to fuzzy topological spaces and various fuzzy topological notions defined by nets n fuzzy spaces introduced by the authors are further investigated various fuzzy topological motions such as fuzzy local compactness functions with closed fuzzy graph fuzzy subcontinuity inverse fuzzy subcontinuity etc are studied in the light of n i these notions are found to be more coherent in n i than in the chang s category

introduction to convex optimization in financial markets convexity arises naturally in financial risk management in risk preferences concerning random cash flows convexity corresponds to the fundamental diversification principle convexity is a basic property also of budget constraints both in classical linear models as well as in more realistic models with transaction costs and constraints moreover modern securities markets are based on trading protocols that result in convex trading costs the first part of this paper gives an introduction to certain basic concepts and principles of financial risk management in simple optimization terms the second part reviews some convex optimization techniques used in mathematical and numerical analysis of financial optimization problems

a convergence question inspired by stieltjes and by value sets in continued fraction theory abstract let v be a subset of the complex plane c let fn n 1 be a sequence of self mappings of v i e fn v v the question is then under what conditions will the sequence fn w f1 f2 fn w n 1 2 3 of composite maps converge to a constant function in v in this paper we give a survey of some of the answers and open problems connected with this question such answers have applications in dynamical systems schur analysis continued fractions and other similar structures like infinite exponentials infinite radicals

general convergence of continued fractions on introduit la notion de convergence generale des fractions continues qu on compare a celles de convergence ordinaire et de convergence forte on etablit quelques unes de ses proprietes

continued fractions with applications i introductory examples ii more basics iii convergence criteria iv continued fractions and three term recurrence relations v correspondence of continued fractions vi hypergeometric functions vii moments and orthogonality viii pade approximants ix some applications in number theory x zero free regions xi digital filters and continued fractions xii applications to some differential equations appendix some continued fraction expansions references index

minimal hausdorff l fuzzy topological spaces abstract in this paper the author introduced the concept of minimal hausdorff l fuzzy topological spaces investigated basic properties of it by means of fuzzy ideals and fuzzy nets and compared it with the concepts of compactness and h closedness

compositions of analytic functions of the form f n z f n 1 f n z f n z f z abstract frequently in applications a function is iterated in order to determine its fixed point which represents the solution of some problem in the variation of iteration presented in this paper fixed points serve a different purpose the sequence f n z is studied where f 1 z f 1 z and f n z f n 1 f n z with f n f many infinite arithmetic expansions exhibit this form and the fixed point of f may be used as a modifying factor z to influence the convergence behaviour of these expansions thus one employs rather than seeks the fixed point of the function f

paracompactness in fuzzy topological spaces abstract in this paper we introduce two kinds of fuzzy paracompactnesses which are defined on general fuzzy subsets each of them is a good extension of crisp paracompactness they are all hereditary with respect to closed subsets and take n compactness and some other compactnesses in fuzzy topological spaces as special cases of them furthermore in a class of spaces so called weakly induced spaces which connects crisp spaces with fuzzy spaces both a fuzzy regular lindeloff property and a fuzzy pseudo metric property imply these two kinds of paracompactnesses

countable compactness in generalized l topological spaces in this paper the generalized countable l compact sets and generalized lindelof sets are introduced in generalized l topological spaces based on the notion of generalized l compactness they are described by cover form and finite intersection property they are preserved under generalized l continuous mapping inherited for l closed subsets and finitely additive and an l subset is generalized l compact if and only if it is generalized lindelof and generalized

stochastic equilibria in von neumann gale dynamical systems this paper examines a class of random dynamical systems related to the classical von neumann and gale models of economic dynamics such systems are defined in terms of multivalued operators in spaces of random vectors possessing certain properties of convexity and homogeneity we establish a general existence theorem for equilibrium which holds under conditions analogous to the standard deterministic ones our results answer questions that remained open for more than three decades

log optimal and rapid paths in von neumann gale dynamical systems abstract von neumann gale dynamical systems are defined in terms of multivalued operators in spaces of random vectors possessing certain properties of convexity and homogeneity a central role in the theory of such systems is played by a special class of paths trajectories called rapid they grow over each time period t 1 t in a sense faster than others the paper establishes existence and characterization theorems for such paths showing in particular that any trajectory maximizing a logarithmic functional over a finite time horizon is rapid the proof of this result is based on the methods of convex analysis in spaces of measurable functions the study is motivated by the applications of the theory of von neumann gale dynamical systems to the modeling of capital growth in financial markets with friction

o convergence of fuzzy nets and its applications abstract in this paper an o convergence theory of fuzzy nets is built in l topological spaces by means of neighborhoods of fuzzy points it has many nice properties it can be used to characterize the closed set open set t 2 separation axiom and fuzzy compactness

compositions of contractions we prove that if d is a simply connected open domain in the complex plane c e is a closed subset of d and fn n 1 are functions analytic in d such that fn d e for all n then the compositions fn z f1of2o ofn z for n 1 2 3 converge uniformly in d to a constant function some generalizations are also presented

convex duality in stochastic optimization and mathematical finance this paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration the framework unifies many well known duality frameworks from operations research and mathematical finance the unification allows the extension of some useful techniques from these two fields to a much wider class of problems in particular combining certain finite dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance we are able to close the duality gap in some situations where traditional topological arguments fail

convex duality in optimal investment under illiquidity we study the problem of optimal investment by embedding it in the general conjugate duality framework of convex analysis this allows for various extensions to classical models of liquid markets in particular we obtain a dual representation for the optimum value function in the presence of portfolio constraints and nonlinear trading costs that are encountered e g in modern limit order markets the optimization problem is parameterized by a sequence of financial claims such a parameterization is essential in markets without a numeraire asset when pricing swap contracts and other financial products with multiple payout dates in the special case of perfectly liquid markets or markets with proportional transaction costs we recover well known dual expressions in terms of martingale measures

stochastic programs without duality gaps this paper studies dynamic stochastic optimization problems parameterized by a random variable such problems arise in many applications in operations research and mathematical finance we give sufficient conditions for the existence of solutions and the absence of a duality gap our proof uses extended dynamic programming equations whose validity is established under new relaxed conditions that generalize certain no arbitrage conditions from mathematical finance

on some gross misunderstandings about the theory of topological molecular lattices abstract some gross misunderstandings have arisen since the theory of topological molecular lattices briefly tmls was presented wang 1989 1992 certain scholars think that there is a correspondence between tmls and classical spaces and they could obtain the results in the theory of tmls hence fuzzy topology by simply translating the corresponding results in classical topology the aim of this paper is to clear out such misunderstandings