In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

‎    The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...

The classical absorption spectrum of visual purple (KSttgen and Abelsdorff, 1896) is the difference in photometric density (log Io/I) at different wave-lengths between a solution in its unbleached and its bleached condition. The reason for this procedure is that extracts of visual purple are not pure but contain other substances which may be colored. The resulting classical subtraction curve is...

Category Learning Atsushi Hashimoto and Haruo Hosoya Department of Computer Science The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan Abstract. Motivated by a neurophysiological experiment on prefrontal cortex, we study a scheme for learning abstract categories. An abstract category represents a set of vectors that are identical to each other modulo substitution, e.g., ’ABAB’, ’BABA’...

we consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmpxypxypxy++++2(,)(,)(,)nnmnmyqxyqxyqxy++&=++. for where and are homogeneous polynomials of degree i. inside this class of polynomial differential equation we consider a subclass of darboux integrable systems. moreover, under additional conditions we proved such darboux integrable systems can have at most 1 limit cycle.

in this paper, we introduce the new notion of strongly j-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly j-clean rings. we denotestrongly j-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-j-cleanrings. next, we investigate some properties of strongly g(x)-j-clean.