This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.

Maximum values of one particle radial electronic density distribution has been calculated by using Hartree-Fock (HF)wave function with data published by[A. Sarsa et al. Atomic Data and Nuclear Data Tables 88 (2004) 163–202] for K and L shells for some Be-like ions. The Results confirm that there is a linear behavior restricted the increasing of maximum points of one particle radial electronic density distribution for K and L shells throughout some Be-like ions. This linear behavior can be described by using the nth term formula of arithmetic sequence, that can be used to calculate the maximum radial electronic density distribution for any ion within Be like ions for Z<20.

Based on analyzing the properties of Bernstein polynomials, the extended orthonormal Bernstein polynomials, defined on the interval [0, 1] for n=7 is achieved. Another method for computing operational matrices of derivative and integration D_b and R_(n+1)^B respectively is presented. Also the result of the proposed method is compared with true answers to show the convergence and advantages of the new method.

Orthogonal polynomials and their moments have significant role in image processing and computer vision field. One of the polynomials is discrete Hahn polynomials (DHaPs), which are used for compression, and feature extraction. However, when the moment order becomes high, they suffer from numerical instability. This paper proposes a fast approach for computing the high orders DHaPs. This work takes advantage of the multithread for the calculation of Hahn polynomials coefficients. To take advantage of the available processing capabilities, independent calculations are divided among threads. The research provides a distribution method to achieve a more balanced processing burden among the threads. The proposed methods are tested for va

Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes app

In the analysis of multiple linear regression, the problem of multicollinearity and auto-correlation drew the attention of many researchers, and given the appearance of these two problems together and their bad effect on the estimation, some of the researchers found new methods to address these two problems together at the same time. In this research a comparison for the performance of the Principal Components Two Parameter estimator (PCTP) and The (r-k) class estimator and the r-(k,d) class estimator by conducting a simulation study and through the results and under the mean square error (MSE) criterion to find the best way to address the two problems together. The results showed that the r-(k,d) class estimator is the best esti

Derivatives of Schiff-bases possess a great importance in pharmaceutical chemistry. They can be used for synthesizing different types of bioactive compounds. In this paper, derivatives of new Schiff bases have been synthesized from several serial steps. The acid (I) was synthesized from the reaction of dichloroethanoic acid with 2 moles of p-aminoacetanilide. New acid (I) converted to its ester (II) via the reaction of (I) with dimethyl sulphate in the present of anhydrous of sodium carbonate and dry acetone. Acid hydrazide (III) has been synthesized by adding 80% of hydrazine hydrate  to the new ester using ethanol as a solvent. The last step included the preparation of new Schiff-bases (IV-VIII) by the reaction of acid hydrazide with

Derivatives of Schiff-bases possess a great importance in pharmaceutical chemistry. They can be used for synthesizing different types of bioactive compounds. In this paper, derivatives of new Schiff bases have been synthesized from several serial steps. The acid (I) was synthesized from the reaction of dichloroethanoic acid with 2 moles of p-aminoacetanilide. New acid (I) converted to its ester (II) via the reaction of (I) with dimethyl sulphate in the present of anhydrous of sodium carbonate and dry acetone. Acid hydrazide (III) has been synthesized by adding 80% of hydrazine hydrate  to the new ester using ethanol as a solvent. The last step included the preparation of new Schiff-bases (IV-VIII) by the reaction of acid hydrazide with app