We prove that the theory of EXPTIME degrees with respect to polynomial time Turing and many-one re-ducibility is undecidable. To do so we use a coding method based on ideal lattices of Boolean algebras which was introduced in 7]. The method can be applied in fact to all hyper-polynomial time classes.

Dendritic macromolecules’ have attracted much attention as organic examples of well-defined nanostructures. These molecules are ideal model systems for studying how physical properties depend on molecular size and architecture. In this paper using a simple result, some GAP programs are prepared to compute Wiener and hyper Wiener indices of dendrimers.

We prove that the theory of EXPTIME degrees with respect to polynomial time Turing and many-one reducibility is undecidable. To do so we use a coding method based on ideal lattices of Boolean algebras which was introduced in [7]. The method can be applied in fact to all hyper-polynomial time classes.

In this paper, we selected three different CPU architectures for performance analysis: single-core, dualcore and hyper-threading CPU’s. Four kinds of operations are executed on these architectures. After analyzing all the data, we found that the single-core and dual-core act as usually expected: the execution times of combined operations are very close to the sum of that of compounding operatio...

Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show th...

Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can cons...

In this thesis we study the problems of distance approximation to monotonicity and distance approximation to convexity. Namely, we are interested in (randomized) sublinear algorithms that approximate the Hamming distance between a given function and the closest monotone/convex function. For the monotonicity property, we focus on functions over the d-dimensional hyper-cube, [n]d, with any finite...

We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Zp-extension of the CM field, where p is a prime of good, ordinary reduction for E. When the complex L-function of E vanishes to even order, Rubin’s proof of the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the p-power Selmer group over the anticyclotomic extension is a torsion Iwasa...

We study the Iwasawa theory of a CM elliptic curve E in the anticyclotomic Zp-extension of the CM field, where p is a prime of good, ordinary reduction for E. When the complex L-function of E vanishes to even order, Rubin’s proof the two variable main conjecture of Iwasawa theory implies that the Pontryagin dual of the p-power Selmer group over the anticyclotomic extension is a torsion Iwasawa ...