In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.

This paper concentrates on employing the -difference equations approach to prove another generating function, extended generating function, Rogers formula and Mehler’s formula for the polynomials , as well as thegenerating functions of Srivastava-Agarwal type. Furthermore, we establish links between the homogeneous -difference equations and transformation formulas.

      The present study discusses the semantic characteristics of the Russian newspapers journalistic headlines (The Russian newspaper "Komsomolskaya Pravda" as Example"). The study traces the characteristics of the Russian newspaper headlines, its relevance to grammar, syntax, lexical items and style. These characteristics in Russian will be investigated and compared to their Arabic correspondents in the process of translation. The study also specifies the meanings and the functions of the newspaper headlines in the light of modern linguistics stressing the grammatical, lexical and stylistic aspects of headlines translation from Russian into Arabic.

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      Today, the world is living in a time of epidemic diseases that spread unnaturally and infect and kill millions of people worldwide. The COVID-19 virus, which is one of the most well-known epidemic diseases currently spreading, has killed more than six million people as of May 2022. The World Health Organization (WHO) declared the 2019 coronavirus disease (COVID-19) after an outbreak of SARS-CoV-2 infection. COVID-19 is a severe and potentially fatal respiratory disease caused by the SARS-CoV-2 virus, which was first noticed at the end of 2019 in Wuhan city. Artificial intelligence plays a meaningful role in analyzing medical images and giving accurate results that serve healthcare workers, especially X-ray images, which are co

       D-mannose sugar was used to prepare [benzoic acid 6-formyl-2,2-dimethyl-tetrahydrofuro[3,4-d][1,3]dioxol-4-yl ester] (compound A). The condensation reaction of folic acid with (compound A) resulted in the formation of new ligand [L]. These compounds were characterized by elemental analysis CHN, atomic absorption A.A, (FT-I.R.), (U.V.-Vis), TLC, E.S. mass (for electrospray), molar conductance, and melting point. The new tetradentate ligand [L], reacted with two moles of some selected metal ions and two moles of (2-aminophenol), (metal : ligand : 2-aminophenol) at reflux in water medium to give a series of  new complexes of the general formula K2[M2(L)(HA)2]  where M= Co(II), Ni(II), Cu(II) an

The purpose of this research is to prepare new vanillic acid derivatives with 1,2,4-triazole-3-thiol heterocyclic ring and evaluate their antimicrobial activity in a preliminary assessment. A multistep synthesis was established for the preparation of new vanillic acid-triazole conjugates. The intermediate of 4-(4-amino-5-mercapto-4H-1,2,4-triazol-3-yl)-2-methoxyphenol (4) reacts with different heterocyclic aldehydes (thiophene-2-carboxaldehyde, pyrrole-2-carboxaldehyde, thiophene-3-carboxaldehyde, and furfural ) in ethanol containing few drops of acetic acid yielded the corresponding 4-(4-(substituted amino)-5-mercapto-4H-1,2,4-1triazol-3-yl)-2-methoxy phenol derivatives (5-8). These compounds were characterized spectroscopically by

In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters l , θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes

      A series of 1,3-diarylprop-2-en-1-one oximes (7-12) were synthesized via reaction of 1,3-diarylprop-2-en-1-one (1-6) with NH₂OH. HCl in dry pyridine. In order to produce the required products (13-18) as anti-isomers, these products (7–12) were then treated with acetic anhydride in dry pyridine. Different substitutes are maintained, resulting in the separation of different products in different yields The recently produced esters are thought to be useful as building blocks for the synthesis of substituted pyridines and many other nitrogen-holding complexes, which are elaborate structures in medicinal chemistry and present in a variety of pharmaceutical medications. The synthesized products were characteriz

The shape for even-even (54Xe 118≤ A ≤ 140 and 82Pb 204 ≤ A ≤ 210 ) nuclei have been studied and investigated through the deformation parameters and δ , these deformation parameters were calculated by two different methods. The first one is nucleus quadrupole deformation parameter β2 from reduced transition probability B(E2)↑ for 0+→2+1 transitions and the second is nucleus quadrupole deformation parameters δ from quadrupole moment Qo.The relationship between two deformation parameters ( , ) and neutrons magic number (N=82 & 126) was studied through plotting the deformation parameters ( , ) as a function of neutrons number , from this relationship we can see very cleary that the deformation of nucleus decreased when th