A complexified adjoint representations of the complexification Lie algebras associated with the special orthogonal group SO(3) and special linear group SL(2,₵)  have been obtained. A new representation of their tensor product is naturally arisen and computed in details.

This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica^®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving

The present study was conducted to induce mutations by UV- light in Trichoderma harzianum for tolerance of Bavistin fungicides which are commonly used to control soil born phytopathogens. The mycelium growth of T. harzianum T1, T2 was inhibited completely by 30 μg (a.i.) /ml PDA of Bavistin. Two isolates of Trichoderma harzianum T1 and T2 conidia suspensions 104 conidia / ml were irradiated by UV lights at 254, 320, 365nm wavelength for 10, 20, 40, 80, 160 min using UV dark room cabinet and spectrophotometer and cultured on PDA media containing 50, 60, 75, 100, and 150 μg (a.i) / ml Bavistin. A thirty one unstable mutants tolerant to Bavistin were obtained after irradiation the T. harzianum T1, T2 conidia suspension 104 conidia / ml by

     Getting knowledge from raw data has delivered beneficial information in several domains. The prevalent utilizing of social media produced extraordinary quantities of social information. Simply, social media delivers an available podium for employers for sharing information. Data Mining has ability to present applicable designs that can be useful for employers, commercial, and customers. Data of social media are strident, massive, formless, and dynamic in the natural case, so modern encounters grow. Investigation methods of data mining utilized via social networks is the purpose of the study, accepting investigation plans on the basis of criteria, and by selecting a number of papers to serve as the foundation for this arti

In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

Rhythm is considered one of the creative concepts in the recent architectural thought; it has emerged clearly as a mean of creating the highest levels of creativity in architecture, especially in contemporary architectural movements. The importance of rhythm has  emerged, especially, when the architecture , its beginnings concentrated on the principle of the links with poetic structures. Many architectural studies deal with concept of rhythm in architecture with different ways various according to the trend of each study, this show the importance of studying the concept of rhythm in the architectural field in general. This study try to focus on the utilization of rhythm as creative system in architecture of heritage and contemporary

Research summary

Muslim scholars have established fundamental rules for deriving rulings to be a methodology for every mujtahid who wants to extract rulings from his reliable sources, and one of the most prominent fundamental rules on which many rulings are built is the permissible and the many rulings related to it.

Leaving what is permissible on its own terms sometimes causes embarrassment and distress in some cases, so we need something that restricts it. In our Islamic law, many legal rulings are embodied in which the restriction of what is permissible is in the public interest, or to relieve embarrassment in public.

Because of the importance of this fundamentalist rule, and the difference in some

Resistance to aminoglycosids is a great problem to therapeutics. Aminoglycoside acetyltransferase producing Pseudomonas aeruginosa have been reported to be important cause of nosocomial infections. The purpose of this study was to determine the occurrence of aminoglycoside acetyltransferase. A total of 200 clinical and environmental samples were collected over period of five months. The P. aeruginosa isolates were confirm their identification, antibiotic susceptibility profile according to vitek2 compact system. The isolates were subjected to polymerase chain reaction (PCR) assays with specific primers for aac (6')-I, aac (6')-Ib, aac (3')-I . Only 32 (16.%) P. aeruginosa isolates were recovered from the samples. in present investigation

Experts of Psychology and education emphasized that childhood is one of the most important stages in the formation of human personality, and the most influential in his public life, especially the stage in which he lives within his family, which must provide him with the requirements of healthy growth of physical, emotional, moral and social. Emotional-social connection of the child to his family, is especially important in determining the characteristics of his social character, in accordance with the norms and values ​​prevailing in society. This requires the child to be cared for and cared for, and to deal with him in a healthy social manner. So as to achieve positive growth and harmony in the process of social control in internal

The aim of this paper is to prove some results for equivalence of moduli of smoothnes in approximation theory , we used a"non uniform" modulus of smoothness and the weighted Ditzian –Totik moduli of smoothness in by spline functions ,several results are obtained .For example , it shown that ,for any the inequality , is satisfied ,finally, similar result for chebyshev partition and weighted Ditzian –Totik moduli of smoothness are also obtained.