The Application of Fractal Transform and Entropy for Improving Fault Tolerance and Load Balancing in Grid Computing Environments

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.     

On Descartes’ rule for polynomials with two variations of signs

Lithuanian Mathematical Journal - For sequences of d + 1 signs + and ? beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence...     

Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras

In this paper, we study the tensor product structure of the category of finite dimensional modules over Drinfeld doubles of Taft Hopf algebras. Tensor product decomposition rules for all finite dimensional indecomposable modules are explicitly given.     

Convergence of Global and Bounded Solutions of Some Nonautonomous Second Order Evolution Equations with Nonlinear Dissipation

In this paper we study the asymptotic behavior of solutions of the following nonautonomous wave equation with nonlinear dissipation.

$\left\{\begin{array}{ll} u_{tt}+\vert u_{t}\vert^{\alpha}u_{t}-\Delta u +f(u)=g(t,x),\quad{\rm in}\,\mathbb{R}_{+}\times\Omega,\\ \qquad\qquad u(t,x)=0,\quad\, {\rm on}\,\mathbb{R}_{+}\times\partial\Omega,\end{array}\right.$

where f is an analytic function, α is a small positive real and g(t, ·) tends to 0 sufficiently fast in L ²(Ω) as t tends to ∞.

We also obtain a general convergence result and the rate of decay of solutions for a class of second order ODE containing as a special case

$\left\{\begin{array}{ll} \ddot{U}(t)+\Vert\dot{U}(t)\Vert^{\alpha}\dot{U}(t)+\nabla F(U(t))=g(t),\quad t \in \mathbb{R}_+,\\ \qquad U(0)=U_{0}\,\in \mathbb{R}^{N},\quad\dot{U}(0)=U_{1}\in \mathbb{R}^{N}. \end{array}\right.$

     

Theoretical and experimental investigations of complexation with BF3.Et2O effects on electronic structures,energies and photophysical properties of Anil and tetraphenyl (hydroxyl) imidazol

The novel compounds (E)‐2‐(((4‐hydroxyphenyl)imino)methyl)phenol, Tetraphenyl (hydroxyl) imidazole and their corresponding Boron difluoride complexes were synthesized and characterized by spectroscopic techniques. Density functional theory calculations at B3LYP‐D3/6–311++G (d, p) level of theory were performed for the geometric parameters. The MEP surface studies were used to understand the behavior of molecules in terms of charge transfer and to determine how these molecules interact. We used the GIAO and the B3LYP‐D3 with a 6–311++ G (d, p) basis set to simulate the (¹H‐NMR and ¹⁹F‐NMR) and the IR spectra, respectively. The corresponding calculated results are in good agreement with the experimental data. The stability of the molecule arising from hyperconjugation interaction and charge delocalization were analyzed using NBO analysis. FMOs revealed the occurrence of charge transfer within the molecule. The complexation using BF₃.Et₂O was also found to have remarkable effects on the electrochemical properties of the studied molecules, where (b) and (d) present lower chemical stability, higher reactivity and higher polarizability than (a) and (c), respectively. Moreover, the energy gap of (a) and (c) decreased after complexation using BF₃.Et₂O, indicating the reliability of the electrochemical evaluation of LUMO and HOMO energy levels. These values are the factors explaining the possible charge transfer interaction within the molecule. The absorption and emission spectra of the model compound were also simulated and compared to experimental observations in the DMF solvent. The results of DFT calculations supported the structural and spectroscopic data and confirmed the structure modification of frontier molecular orbitals for BF₂ complexes as well as tunable potentials and energy levels.     

Efficient and green syntheses of novel γ-aminophosphonate and phosphine oxide derivatives

Two synthetic protocols leading to novel γ-aminophosphonate and phosphine oxide derivatives, by reductive amination of γ-phosphonylketones, are reported. The first method involved a two-step procedure. Imine intermediates were first isolated from the p-toluenesulfonic acid-catalyzed reaction of primary amines with γ-ketophosphonates and phosphine oxides, then reduced with NaBH₄ in refluxing ethanol. The second method consists of a one-pot procedure which includes the condensation of γ-ketophosphonates and phosphine oxides with primary amines, in the presence of molecular sieves, followed by reduction with NaBH₄. These methods offer significant advantages over prior reports, such as efficiency, generality, and good yields. Furthermore, they are green protocols avoiding hazardous hydrides and solvents.     

Log-Polynomial Period Functions for Hecke Groups

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups.     

Impact of rough silicon buffer layer on electronic quality of GaAs grown on Si substrate

The electronic and the structural properties of n-GaAs layers grown on rough surface of silicon substrate by molecular beam epitaxy (MBE) has been investigated by photoluminescence (PL), time resolved photoluminescence (TRPL) and high resolution X-ray diffraction (HRXRD). The relationship between electronic and structural properties of the n-GaAs layer was checked, showing that the defect density is a strong cause for trapping the minority carriers. The impact of introducing intermediate rough silicon layer between silicon substrate and n-GaAs layer on the electronic properties was observed, showing that the structure grown on rough Si involves higher lifetime than those developed on flat silicon substrate. Such structure could be used for economic solar cells fabrication.     

Exact analytical solutions for shallow impurity states in symmetrical paraboloidal and hemiparaboloidal quantum dots

The problem of a shallow donor impurity located at the centre of a symmetrical paraboloidal quantum dot (SPQD) is solved exactly. The Schrödinger equation is separated in the paraboloidal coordinate system. Three different cases are discussed for the radial-like equations. For a bound donor, the energy is negative and the solutions are described by Whittaker functions. For a non-bound donor, the energy is positive and the solutions become coulomb wave functions. In the last case, the energy is equal to zero and the solutions reduce to Bessel functions. Using the boundary conditions at the dot surfaces, the variations of the donor kinetic and potential energies versus the size of the dot are obtained. The problem of a shallow donor impurity in a Hemiparaboloidal Quantum dot (HPQD) is also studied. It is shown that the wave functions of a HPQD are specific linear combinations of those of a SPQD.