Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.    In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all.

      In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

In recent years, data centre (DC) networks have improved their rapid exchanging abilities. Software-defined networking (SDN) is presented to alternate the impression of conventional networks by segregating the control plane from the SDN data plane. The SDN presented overcomes the limitations of traditional DC networks caused by the rapidly incrementing amounts of apps, websites, data storage needs, etc. Software-defined networking data centres (SDN-DC), based on the open-flow (OF) protocol, are used to achieve superior behaviour for executing traffic load-balancing (LB) jobs. The LB function divides the traffic-flow demands between the end devices to avoid links congestion. In short, SDN is proposed to manage more operative configur

In the present work, the nuclear shell model with Hartree–Fock (HF) calculations have been used to investigate the nuclear structure of ²⁴Mg nucleus. Particularly, elastic and inelastic electron scattering form factors and transition probabilities have been calculated for low-lying positive and negative states. The sd and sdpf shell model spaces have been used to calculate the one-body density matrix elements (OBDM) for positive and negative parity states respectively. Skyrme-Hartree-Fock (SHF) with different parameterizations has been tested with shell model calculation as a single particle potential for reproducing the experimental data along with a harmonic oscillator (HO) and Woods-Saxo

Although the concept of difference is as old as the foundational concept of similarity, the modern (and contemporary) understanding of difference as a working notion that not only differentiates, but also approximates conflicting elements in an all encompassing system owes a great deal to the German philosopher Georg Wilhelm Friedrich Hegel (1770-1831). An idealist to the backbone, Hegel bequeathed to modern philosophy the postulation that the identity of an individual rests not in itself but in the relationship that individual‟s identity entertains with other members of society. In his classic Phenomenology of Spirit, Hegel explains how humans come to consciousness (pivotal concept in Idealism) through a strenuous, albeit apparently i

In the present work, a program for calculating the coefficients of the Aplanatic Cassegrain Telescope (ACT) system, free from the effects of spherical and coma aberrations, were constructed. In addition, the two-mirrors of the optical system, as aspherical surfaces, were adopted. This means, that the two-equations of the mirrors are assumed to be polynomial function of five even terms only. The numerical method, least-squares curve fitting method to calculate the two-mirror coefficients system, was adopted. For choosing the values and ratios that give the best results, Rayleigh Criterion (Rayleigh Limit), for purpose of comparison and preference, was adopted.