A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

This research aim to exploring the positive psychological capital concept (PsyCap) which drawn from positive psychology and applying it at workplace. PsyCap emerged as extending for recent another types of capital, such as human capital and social capital. It has been defined as “an individual’s positive psychological state of development". The PsyCap consist of four core constructs (self- efficacy, optimism, hope, and resilience). Each of the four components has considerable theorizing and researching that can contribute to developing an integrative theoretical foundation for PsyCap. But their combined motivational effects will be broader and more impactful than any one of t

Steel–concrete–steel (SCS) structural systems have economic and structural advantages over traditional reinforced concrete; thus, they have been widely used. The performance of concrete made from recycled rubber aggregate from scrap tires has been evaluated since the early 1990s. The use of rubberized concrete in structural construction remains necessary because of its high impact resistance, increases ductility, and produces a lightweight concrete; therefore, it adds such important properties to SCS members. In this research, the use of different concrete core materials in SCS was examined. Twelve SCS specimens were subjected to push-out monotonic loading for inspecting their mechanical performance. One specimen was constructed from co

    In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

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The goal of this work is demonstrating, through the gradient observation of a   of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of  ( -system) was developed based on finite time  ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypo

In this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.

     In this work, new di-acid monomers 4, 4’-di-carboxillic-2”-chloro-4”- nitro triphenylamine (Di-CO2H-1), 4, 4’- di-carboxylic -2”,4”,6”-trichloro-triphenylamine (Di-CO2H-2) were synthesized by reaction of p-cyanobenzofluride with two aromatic amines (2-chloro 4-nitro aniline and 2,4,6-trichloro aniline by aromatic nucleophilc substitution method to produce two di cyano intermediates compounds 4, 4’-Dicyano-2”-chloro-4”- nitro triphenylamine (Di-CN1) and 4, 4’-dicyano-2”,4”,6”-trichloro-triphenylamine (Di-CN2) which form final di-carboxylic monomers after alkaline hydrolysis. Finally, these monomers react with two different arom