‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

In this paper the notion of a quadratic automaton transformation is defined and studied. The automata considered transform infinite input sequences of elements from a finite commutative ring with identity to infinite output sequences. Results extending the linear automaton transformation theory of 4. Nerode are derived and two distinct approaches to machine realization arise depending upon whet...

This article introduces a novel Monte Carlo type algorithm, which we call the Metropolized Forward Chaining (MFC) algorithm, to find a stable model of a general propositional logic program P if P has a stable model or to find a maximal subprogram P ′ of P and stable model M ′ of P ′ if P does not have a stable model. Our algorithm combines the forward chaining algorithm of Marek, Nerode, and Re...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

Let A be a recursive structure, and let ψ be a recursive infinitary Π2 sentence involving a new relation symbol. The main result of the paper gives syntactical conditions which are necessary and sufficient for every recursive copy of A to have a recursive expansion to a model of ψ, provided A satisfies certain decidability conditions. The decidability conditions involve a notion of rank. The ma...

For a givenweighted finite automaton over a strong bimonoid we construct its reducedNerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics.We show that the reducedNerode automaton is even smaller than theNerode automaton, which was previously used in determinization related to this semantics. We determine ne...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...