In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

Background: Generally, genetic disorders are a leading cause of spontaneous abortion, neonatal death, increased morbidity and mortality in children and adults as well. They a significant health care and psychosocial burden for the patient, the family, the healthcare system and the community as a whole. Chromosomal abnormalities occur much more frequently than is generally appreciated. It is estimated that approximately 1 of 200 newborn infants had some form of chromosomal abnormality. The figure is much higher in fetuses that do not survive to term. It is estimated that in 50% of first trimester abortions, the fetus has a chromosomal abnormality. Aim of the study: This study aims to shed some light on the results of chromosomal studies per

The -mixing of  - transition in Er 168 populated in Er)n,n(Er 168168  reaction is calculated in the present work by using a2- ratio method. This method has used in previou studies [4, 5, 6, 7] in case that the second transition is pure or for that transition which can be considered as pure only, but in one work we applied this method for two cases, in the first one for pure transition and in the 2nd one for non pure transitions. We take into accunt the experimental a2- coefficient for p revious works and -values for one transition only [1]. The results obtained are, in general, in agood agreement within associated errors, with those reported previously [1], the discrepancies that occur are due to inaccuracies existing

The - M ultiple mixing ratios of -transitions from levels of 56Fe populated in 56 56 Fe n n Fe ( , )  reactions are calculated by using const. S.T.M. This method has been used in other works [3,7] but with pure transition or with transitions that can be considered as pure transitions، in our work we used This method for mixed  - transitions in addition to pure  - transitions. The experimental angular distribution coefficients a2 was used from previous works [1] in order to calculet - values. It is clear from the results that the - values are in good agreement or consistent, within associated errors, with those reported previously [1]. The discrepancies that occur are due to inaccuracies existing in the expe

A mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc

Conditional logistic regression is often used to study the relationship between event outcomes and specific prognostic factors in order to application of logistic regression and utilizing its predictive capabilities into environmental studies. This research seeks to demonstrate a novel approach of implementing conditional logistic regression in environmental research through inference methods predicated on longitudinal data. Thus, statistical analysis of longitudinal data requires methods that can properly take into account the interdependence within-subjects for the response measurements. If this correlation ignored then inferences such as statistical tests and confidence intervals can be invalid largely.

Background: Cystinosis is a rare autosomal recessive lysosomal storage disease with high morbidity and mortality. It is caused by mutations in the CTNS gene that encodes the cystine transporter, cystinosin, which leads to lysosomal cystine accumulation. It is the major cause of inherited Fanconi syndrome, and should be suspected in young children with failure to thrive and signs of renal proximal tubular damage. The diagnosis can be missed in infants, because not all signs of renal Fanconi syndrome are present during the first months of life. Elevated white blood cell cystine content is the cornerstone of the diagnosis. Since chitotriosidase (CHIT1 or chitinase-1) is mainly produced by activated macrophages both in normal and inflammator

Water quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their performance is evaluated usin