A SIMPLE NUMBER THEORETIC PROBLEM II

Abstract. In this note, we shall consider a number theoretic problem finitely determined

LARGE DEVIATIONS BOUNDS FOR A POLLING SYSTEM WITH MARKOVIAN ON/OFF SOURCES AND BERNOULLI SERVICE SCHEDULE

Abstract. In this paper we consider a large deviations problem for a discrete-time polling system consisting of two-parallel queues and a single server. The arrival process of each queue is a superposition of traffic streams generated by a number of mutually independent and identical Markovian on/off sources, and the single server serves the two queues according to the so-called Bernoulli service schedule. Using the large deviations techniques, we derive the upper and lower bounds of the probability that the queue length of each queue exceeds a certain level (i.e., the buffer overflow probability). These results have important implications for traffic management of high-speed communication networks such as call admission control and bandwidth allocation

DENSE C-EMBEDDED SUBSPACES OF PRODUCTS

Abstract. Throughout this paper the spaces X i are assumed Tychonoff, (X I )κ denotes X I := Π i∈I X i with the κ-box topology (so (X I )ω = X I ), and Σ λ (p) := {x ∈ X I : |{i ∈ I : Milton Ulmer proved in 1970/1973 that in a product of first-countable spaces, each Σ-product is C-embedded. The authors generalize this theorem in several ways. Theorem. Let κ be a regular cardinal. If q ∈ (X I )κ\Σ κ + (p) and each q i is a In the same works, Ulmer constructed an example showing that a Σ-product in a product of spaces of countable pseudocharacter need not be C-embedded. Again the authors modify and extend his work, this time as follows. Theorem. For every κ ≥ ω there are a set {X i : i ∈ I} of Tychonoff spaces with |I| = κ, q ∈ X I and f ∈ C(X I \{q}, {0, 1}) such that no continuous function from X I to [0, 1] extends f . One may arrange further that |X i | = κ for every i ∈ I, and either (i) there is i 0 ∈ I such that ψ(X i 0 ) = ω and for i 0 = i ∈ I the space X i is the one-point compactification of a discrete space with cardinality κ; or (ii) the spaces X i are pairwise homeomorphic, with ψ(X i ) = ω, and: either (a) all but one point in each X i is isolated, or (b) each X i is dense-in-itself

ON IDEALS AND UPPER SETS IN BE-ALGEBRAS

Abstract. In this paper, the idea of ideals of BE-algebras is introduced and several descriptions of ideals are given in terms of upper sets A(u, v) = {z ∈ X|u * (v * z) = 0} for transitive and for self distributive BE-algebras (X; * , 1) of type (2, 0)

ERG RELATION ON HYPER K-ALGEBRAS

Abstract. In this manuscript at first by considering the notion of equivalence, regular and good, (ERG), relations on a hyper K-algebra H, we characterize it on a hyper Kalgebra H in which H is an (H-absorbing hyper K-ideal)-decomposable. Then we investigate the quotient hyper K-algebra related to an ERG relation on H. Moreover we show that the Theorem 4.1 and Corollary 4.3 o

INTUITIONISTIC FUZZY d-ALGEBRAS

Abstract. The intuitionistic fuzzification of a d-algbera is considered, and related results are investigated. The notion of equivalence relations on the family of all intuitionistic fuzzy d-algebras of a d-algebra is introduced, and then some properties are discussed. The concept of intuitionistic fuzzy topological d-algebras is introduced, and some related results are obtained

THE DISCRETE WALSH-TYPE TRANSFORM FOR INFINITE SEQUENCES

Abstract. We introduce a set of Walsh-type functions on positive integers and give the inversion formula by using these functions for an infinite sequence of complex numbers whose series converges absolutely. Discrete orthogonal transforms apply to finite sequences. In this paper we introduce a special transform for infinite sequences and give the inversion formula. For this purpose we modify the generalized Walsh functions constructed by Chrestenson Let q ≥ 2 be a fixed integer. We define a set of functions, for j, k ≥ 1, by where [x] is the greatest integer ≤ x. Lemma 1 Let x denote the least integer Here we write A(m, n) = t − 1 : m q t−1 − n q t−1 ≡ 0 (mod q) 2000 Mathematics Subject Classification. 11A25, 42C10

WEAK CONVERGENCE THEOREMS FOR FINDING COMMON ELEMENTS OF FINITE SETS IN BANACH SPACES

Abstract. In this paper, we deal with the problem for finding a common element of finite sets in a Banach space. We first prove that an operator given by a convex combination of sunny generalized nonexpansive retractions in a Banach space is asymptotically regular. Using this result, we obtain a weak convergence theorem which is connected with the problem of image recovery. Further, using another weak convergence theorem, we prove a weak convergence theorem of Mann's type for finding a common element of finite sets in a Banach space

ON THE CARDINALITY OF HOMOGENEOUS COMPACTA OF COUNTABLE TIGHTNESS

Abstract. We prove that every homogeneous compacta of countable tightness and d(X)≤2 ℵo , is first countable. A relevant conjecture is raised by Arhangel'skiĩ, conjecture 1.17 in [1], see also van Mill [11], which says: every homogeneous compacta of countable tightness is first countable

MULTIWAVELET NEURAL NETWORK PREPROCESSING OF IRREGULARLY SAMPLED DATA

Abstract. Multiwavelets are briefly reviewed and preprocessing and postprocessing for such wavelets are introduced. Least squares curve fitting of irregularly sampled data is achieved by means of unshifted and shifted multiscaling functions. This preprocessing procedure combined with multiwavelet neural networks for data-adaptive curve fitting is shown to perform well in the case of high resolution. In the case of low resolution it is more accurate than numerical integration and cheaper than matrix inversion