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.

In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions. 

Quantitative real-time Polymerase Chain Reaction (RT-qPCR) has become a valuable molecular technique in biomedical research. The selection of suitable endogenous reference genes is necessary for normalization of target gene expression in RT-qPCR experiments. The aim of this study was to determine the suitability of each 18S rRNA and ACTB as internal control genes for normalization of RT-qPCR data in some human cell lines transfected with small interfering RNA (siRNA). Four cancer cell lines including MCF-7, T47D, MDA-MB-231 and Hela cells along with HEK293 representing an embryonic cell line were depleted of E2F6 using siRNA specific for E2F6 compared to negative control cells, which were transfected with siRNA not specific for any gene. Us

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1^st and 2^nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

Scheduling Timetables for courses in the big departments in the universities is a very hard problem and is often be solved by many previous works although results are partially optimal. This work implements the principle of an evolutionary algorithm by using genetic theories to solve the timetabling problem to get a random and full optimal timetable with the ability to generate a multi-solution timetable for each stage in the collage. The major idea is to generate course timetables automatically while discovering the area of constraints to get an optimal and flexible schedule with no redundancy through the change of a viable course timetable. The main contribution in this work is indicated by increasing the flexibility of generating opti