Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

This paper presents the matrix completion problem for image denoising. Three problems based on matrix norm are performing: Spectral norm minimization problem (SNP), Nuclear norm minimization problem (NNP), and Weighted nuclear norm minimization problem (WNNP). In general, images representing by a matrix this matrix contains the information of the image, some information is irrelevant or unfavorable, so to overcome this unwanted information in the image matrix, information completion is used to comperes the matrix and remove this unwanted information. The unwanted information is handled by defining {0,1}-operator under some threshold. Applying this operator on a given ma

Praise be to God, and may blessings and peace be upon our master and Prophet Muhammad and those who follow him, and may God be pleased with him

Taha is my guardian and whoever follows their path until the Day of Judgment. And after... The book (The Treasure in the Ten Recitations), written by Abu Muhammad Abdullah bin Abd al-Wasiti, who died in the year 710 AH, is considered one of the important books in recitations: because it included the universal custom that it contained in the books Al-Taysir by Al-Dani and Al-Irshad by Al-Falanisi, as the first of them was specialized.

Satisfy the second with the ten readings

May God bless my time, through His grace and generosity, to achieve this treasure and to publish it

An annular two-phase, steady and unsteady, flow model in which a conductingfluid flow under the action of magnetic field is concavely. Two models arepresented, in the model one; the magnetic field is perpendicular to the long side ofthe channel, while in the model two is perpendicular to the short side. Also, westudy, to some extent the single-phase liquid flow.It is found that the motion and heat transfer equations are controlled by differentdimensionless parameters namely, Reynolds, Hartmann, Prandtl, and Poiseuilleparameters. The Laplace transform technique is used to solve each of the motion andheat transfer equations. The effects of each of dimensionless parameters upon thevelocity and heat transfer is analyzed.A comprehensive study fo

Firstly, in this study, a brief updated description and applications of different solar collectors used in renewable energy systems for supplying electric and thermal energy was presented. Secondly, an attempt was made to utilize tilting orientation of solar collector for maximizing collector energy with time in respect to horizontal orientation. For energy calculation, global solar radiation was used since they are directly related.  For that purpose, field measurements of half-hourly radiation on two flat panels of tilting and horizontal orientations were carried out throughout 8-month period under local climate of Baghdad. Then, energy gain and radiation level averages were calculated based on the field radiation

Acinetobacter baumannii ability to form biofilm makes it to be opportunistic pathogen causing of nosocomial infections and to be good survivor in adverse environmental conditions including medical devices and hospital environments. Six isolates of A. baumannii were isolated from drinking water and tested to investigate biofilm formation capacity on three different type of abiotic surface, also several factors were examined such as hydrophobicity, PH and temperature. All A. baumannii isolates displayed a positive biofilm on congored aga test CRA (pigmented colonies with black color) and Christensen's test (adhesive layer of stained material to the inside surface of the tube).The obtained data of microbial adhesion to hydrocarbons assay (MATH

Correct grading of apple slices can help ensure quality and improve the marketability of the final product, which can impact the overall development of the apple slice industry post-harvest. The study intends to employ the convolutional neural network (CNN) architectures of ResNet-18 and DenseNet-201 and classical machine learning (ML) classifiers such as Wide Neural Networks (WNN), Naïve Bayes (NB), and two kernels of support vector machines (SVM) to classify apple slices into different hardness classes based on their RGB values. Our research data showed that the DenseNet-201 features classified by the SVM-Cubic kernel had the highest accuracy and lowest standard deviation (SD) among all the methods we tested, at 89.51 %  1.66 %. This

In this paper, an approximate solution of nonlinear two points boundary variational problem is presented. Boubaker polynomials have been utilized to reduce these problems into quadratic programming problem. The convergence of this polynomial has been verified; also different numerical examples were given to show the applicability and validity of this method.