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RELATIVE DEFECTS AND MULTIPLE COMMON ROOTS OF TWO MEROMORPHIC FUNCTIONS
HARINA P. WAGHAMORE,SUBHAS S.BHOOSNURMATH 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.2
In this paper, we consider two different meromorphic functions having com-mon roots and and some relations involving the relative defects.
SOME IDENTITIES ON THE q-BERNSTEIN POLYNOMIALS, q-STIRLING NUMBERS AND q-BERNOULLI NUMBERS
김태균,최종성,김영희 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.3
In this paper, we consider the q-Bernstein polynomials on Zp and investigate some interesting properties of q-Bernstein polynomials related to q-Stirling numbers and Carlitz’s type q-Bernoulli numbers.
Interactions in an art neural system
Trifon Trifonov,Kalin Georgiev,George Mengov 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.16 No.1
This work continues a series of papers about a neural network that incorporates adaptive resonance theory (ART) as a system of ordinary differential equations. The original, Exact ART, requires huge computational resources even for small-scale tasks. However, for technological applications it is necessary to devise more efficient computing algorithms. Here we propose simplifications of the original subsystem responsible for bottom-up and top-down data matching. In effect we formulate and solve a substitution problem that preserves only those features, which are essential for the overall system dynamics.
On one of Murthy-Ashbacher's conjectures related to Euler's totient function
K. T. Atanassov,M. V. Vassilev-Missana 장전수학회 2006 Proceedings of the Jangjeon mathematical society Vol.9 No.1
A. Murthy and C. Ashbacher formulated a lot of open problems and conjectures in the area of elementary number theory. One of them is: For every positive integer k there exists a number n such that n '(n) = k: In the paper it is shown that this conjecture is not valid. It is proved that the only values of k for which the Diophantine equation k:'(n) = n is valid, are k = 1; 2; 3, where ' is Euler's totient function.
Convergence of q-Meyer-König-Zeller-Durrmeyer operators
N. K. Govil,V. Gupta 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
In the present paper, we introduce a new type of q integrated Meyer-Konig-Zeller-Durrmeyer operators, obtain moments for the these operators and estimate the convergence of these integrated q-MKZD operators.
Generalized net model for parallel optimization of feed-forward neural network
K. T. Atanassov,S. Sotirov,A. Antonov 장전수학회 2007 Advanced Studies in Contemporary Mathematics Vol.15 No.1
The used generalized net wil give us a possibility for parallel optimization of fed-forward neural network based on assigned training pairs and time limits.
Unification of space-time-matter-energy
Sobczyk,Yarman 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.2
A complete description of space-time, matter and energy is given in terms of the conservation of energy-momentum in Einstein’s special the- ory of relativity. We derive explicit equations of motion for two falling bodies, based upon the principle that each body must subtract the mass- equivalent for any change in its kinetic energy that is incurred during the fall. In this theory, we …nd that there are no singularities and consequently no blackholes.
On the edge-balance index sets of B(n)
J. Lu,Y. Zheng,S. M. Lee 장전수학회 2009 Proceedings of the Jangjeon mathematical society Vol.12 No.1
Let G be a graph with vertex set V (G) and edge set E(G), and let Z₂ = {0, 1}. A labeling f of a graph G is said to be edge-friendly if |ef (0) - ef (1)| ≤ 1. A edge-friendly labeling f : E(G) → Z2 induces a partial vertex labeling f+ : V (G) ! Z₂ de¯ned by f+(x) = 0 if the number of edges incident on x is 0 more than 1. similarly, f+(x) = 1 if the number of edges incident on x is 1 more than 0. f+(x) is not defined if the number of edges incident on x is 1 equal to the number of edges labeled by 0. For i ∈Z₂, let vf (i) = v(i) = card{v ∈ V (G) : f+(v) = i} and ef (i) = e(i) = card{e ∈ E(G) : f(e) = i}. The edge-balance index set of the graph G, EBI(G), is defined as {|vf (0) - vf (1)| :the edge labeling f is edge-friendly}. Let G be a graph and u, v be two distinct vertices of G. We construct the graph Pn(G, {u, v}) as follows. The vertex set V (Pn(G, {u, v}) is the union of n - 1 copies of V (G). We denote the vertices u, v in the copy of V (G) by ui, vi. The edge set E(Pn(G, {u, v}) is the union of n - 1 copies of E(G) with vj and uj+1 identified for j = 1, 2,.., n - 2. We call Pn(G, {u, v}) the chain sum of (G, {u, v}) by Pn. For n > 3, We denote Pn(K₄ - e, {х,z}) by B(n - 1) and Pn(K₄- e, {u, v}) by H(n - 1). In this paper, the edge-balance index set, the perfect index set and the complete index set of B(n) are de¯ned, the perfect index sets of B(n)(n = 1, 2, ..., 3) are researched.
Existence of integral manifolds for impulsive integro-differential equations
Gani Tr. Stamov 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.1
In the paper the problem of existence of integral manifolds for impulsive integro-dierential equations is considered. The investigations are carried out by means ofpiecewise continuous functions which are analogues of Lyapunov’s functions.