Let $\epsilon>0$ and let $q$ be a prime going to infinity. We prove that with high probability given $x,y$ in the projective plane over finite field $F_q$ there exists $\gamma$ $SL_3(Z)$, coordinates bounded by $q^{1/3+\epsilon}$, whose projection $SL_{3}(F_q)$ sends $x$ $y$. The exponent $1/3$ is optimal result rank generalization of Sarnak's strong approximation theorem for $SL_2(Z)$.

A family of sets $${\cal F}$$ is said to satisfy the (p, q) property if among any p in some q have a non-empty intersection. Hadwiger and Debrunner (1957) conjectured that for ≥ d + 1 there exists minimum integer c = HDd(p, q), such finite convex ℝd satisfies can be pierced by at most points. In celebrated result from 1992, Alon Kleitman proved conjecture. However, obtaining sharp bounds on kno...

Estimation of distribution algorithm for optimization of neural networks for intrusion detection system p. 9 Neural network implementation in reprogrammable FPGA devices-an example for MLP p. 19 A new approach for finding an optimal solution and regularization by learning dynamic momentum p. 29 Domain dynamics in optimization tasks p. 37 Nonlinear function learning by the normalized radial basi...

George Klir and Bo Yuan named after Lotfi Zadeh the implication p→q=max(1−p,min(p,q)) (also Early implication). In a series of papers, author introduced two intuitionistic fuzzy forms Zadeh’s studied their basic properties. present paper, new (third) form is proposed some its properties are studied.

We study the optical absorption, especially the (far-) infrared absorption by phonons, of semiconducting and metallic nanospheres. In the nanoscopic sphere, phonons as well as states of electronic excitations are quantized by confinement. It is also known that in the nanoscopic geometry, the confined electron-phonon interaction has a different form from the usual one in the bulk. First, we anal...

This article concerns the existence of multiple non-radial positive solutions L<sup>2</sup>-constrained problem $$\displaylines{-\Delta{u}-Q(\varepsilon x)|u|^{p-2}u=\lambda{u},\quad \text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=1,}$$ where \(Q(x)\) is a radially symmetric function, ε>0 small parameter, \(N\geq 2\), and \(p \in (2, 2+4/N)\) assumed to be m...

Let $\mathfrak{j}$ and $\mathfrak{j}^{'}$ be the Cartan subalgebras of complex semi-simple Lie algebras $\mathfrak{g}$ $\mathfrak{g}^{'}$, $\mathfrak{j}^{*}$ $(\mathfrak{j}^{'})^{*}$ their duals, $\mathfrak{j}^{\vee}$ $(\mathfrak{j}^{'})^{\vee}$ biduals respectively. We consider $B(.,.)$, restriction to Killing form $\mathfrak{g}^{'}$. In this work, using kernel $K$ reproducing subalgebra an op...

In this research, the relationship between P-wave velocity (Vp) and Electrical Resistivity (ER) parameters with rock mass quality indices is investigated; parameters such as rock mass quality classification (Q) and modified system for sedimentary rocks, known as Qsrm. For making predictive models, about 1200 data-sets extracted from sections drilled in Seymareh and Karun 2 Dam Sites (SDS and KD...

in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...

The definition of a D-admissible fuzzy subset for an operator domain D on a group G is modified to obtain new kinds of (∈,∈ ∨q)-fuzzy subgroups such as an (∈,∈ ∨q)-fuzzy normal subgroup, an (∈,∈ ∨q)-fuzzy characteristic subgroup, an (∈,∈ ∨q)fuzzy fully invariant subgroup which are invariant under D. As results, some of the fundamental properties of such (∈,∈ ∨q)−fuzzy subgroups are obtained.