The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

Community detection is useful for better understanding the structure of complex networks. It aids in the extraction of the required information from such networks and has a vital role in different fields that range from healthcare to regional geography, economics, human interactions, and mobility. The method for detecting the structure of communities involves the partitioning of complex networks into groups of nodes, with extensive connections within community and sparse connections with other communities. In the literature, two main measures, namely the Modularity (Q) and Normalized Mutual Information (NMI) have been used for evaluating the validation and quality of the detected community structures. Although many optimization algo

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The methods of the Principal Components and Partial Least Squares can be regard very important methods  in the regression analysis, whe

Semiconductor quantum dots (QDs) have attracted tremendous attentions for their unique characteristics for solid-state lighting and thin-film display applications. A simple chemical method was used to synthesis quantum dots (QDs) of zinc sulfide (ZnS) with low cost. The XRD) shows cubic phase of the prepared ZnS with an average particles size of (3-29) nm. In UV-Vis. spectra observed a large blue shift over 38 nm. The band gaps energy (Eg) was 3.8 eV and 3.37eV from the absorption and photoluminescence (PL) respectively which larger than the Eg for bulk. QDs-LED hybrid devices were fabricated using ITO/ PEDOT: PSS/ Poly-TPD/ ZnS-QDs/ with different electron transport layers and cathode of LiF/Al layers. The EL spectrum reveals a bro

            The research is dealing with the absorption and fluorescence spectra for the hybrid of  an Epoxy Resin doped with organic dye Rhodamine (R6G) of different concentrations (5*10^-6, 5*10^-5, 1*10^-5, 1*10^-4, 5*10^-4) Mol/ℓ at room temperature. The Quantum efficiency Q_fm, the rate of fluorescence emission K_fm (s^-1), the non-radiative lifetime τ_fm (s), fluorescence lifetime τ_f and the Stokes shift were calculated. Also the energy gap (Eg) for each dye concentration was evaluated. The results showed that the maximum quantum effi

This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

Ensuring security, integrity, and reliability of the election process consider as the main challenges in the electronic voting system. This paper describes the e-voting system by integrating the biometric authentication, advanced encryption, and watermarking techniques towards meeting such challenges. The system employs the fingerprint authentication by utilizing the Scale-Invariant Feature Transform (SIFT) for verifying the identity of the voter to ensure genuineness and non-repudiation of the service. The vote will be encrypted with the AES-GCM technique to be employed in securing the voting process, thus ensuring both data privacy and integrity. Hybrid Blind Watermarking employs the technique of Discrete Wavelet Transform (DWT) a