Differential Transform Method for Solving the Two-dimensional Fredholm Integral Equations

In this paper, we develop the Differential Transform (DT) method in a new scheme to solve the two-dimensional Fredholm integral equations (2D-FIEs) of the second kind. The differential transform method is a procedure to obtain the coefficients of the Taylor expansion of the solution of differential and integral equations. So, one can obtain the Taylor expansion of the solution of arbitrary order and hence the solution of the given equation can be obtained with required accuracy. Here, we first give some basic definitions and properties about DT from references, and then we prove some theorems to extend the DT method for solving the 2D-FIEs. Then by using the DT, the 2D-FIE is converted to a system of linear algebraic equations whose unknowns are the coefficients of the Taylor expansion of the solution. Solving the system gives us an approximate solution. Finally, we give some examples to show the accuracy and efficiency of the presented method

Differential Transform Method for Solving the Two-dimensional Fredholm Integral Equations

Abstract In this paper, we develop the Differential Transform (DT) method in a new scheme to solve the two-dimensional Fredholm integral equations (2D-FIEs) of the second kind. The differential transform method is a procedure to obtain the coefficients of the Taylor expansion of the solution of differential and integral equations. So, one can obtain the Taylor expansion of the solution of arbitrary order and hence the solution of the given equation can be obtained with required accuracy. Here, we first give some basic definitions and properties about DT from references, and then we prove some theorems to extend the DT method for solving the 2D-FIEs. Then by using the DT, the 2D-FIE is converted to a system of linear algebraic equations whose unknowns are the coefficients of the Taylor expansion of the solution. Solving the system gives us an approximate solution. Finally, we give some examples to show the accuracy and efficiency of the presented method

A novel mutation in SEPN1 causing rigid spine muscular dystrophy 1: A Case report

Abstract Background Muscular dystrophies are a clinically and genetically heterogeneous group of disorders characterized by variable degrees of progressive muscle degeneration and weakness. There is a wide variability in the age of onset, symptoms and rate of progression in subtypes of these disorders. Herein, we present the results of our study conducted to identify the pathogenic genetic variation involved in our patient affected by rigid spine muscular dystrophy. Case presentation A 14-year-old boy, product of a first-cousin marriage, was enrolled in our study with failure to thrive, fatigue, muscular dystrophy, generalized muscular atrophy, kyphoscoliosis, and flexion contracture of the knees and elbows. Whole-exome sequencing (WES) was carried out on the DNA of the patient to investigate all coding regions and uncovered a novel, homozygous missense mutation in SEPN1 gene (c. 1379 C > T, p.Ser460Phe). This mutation has not been reported before in different public variant databases and also our database (BayanGene), so it is classified as a variation of unknown significance (VUS). Subsequently, it was confirmed that the novel variation was homozygous in our patient and heterozygous in his parents. Different bioinformatics tools showed the damaging effects of the variant on protein. Multiple sequence alignment using BLASTP on ExPASy and WebLogo, revealed the conservation of the mutated residue. Conclusion We reported a novel homozygous mutation in SEPN1 gene that expands our understanding of rigid spine muscular dystrophy. Although bioinformatics analyses of results were in favor of the pathogenicity of the mutation, functional studies are needed to establish the pathogenicity of the variant

Boron Isotope Effect on the Thermal Conductivity of Boron Arsenide Single Crystals

© 2019 Elsevier Ltd Boron arsenide (BAs) with a zinc blende structure has recently been discovered to exhibit unusual and ultrahigh thermal conductivity (κ), providing a new outlook for research on BAs and other high thermal conductivity materials. Technology for BAs crystal growth has been continuously improving; however, the influence of boron isotopes, pure or mixed, on the thermal conductivity in BAs is still not completely clear. Here we report detailed studies on the growth of single crystals of BAs with different isotopic ratios and demonstrate that the κ of isotopically pure BAs is at least 10% higher than that of BAs grown from natural B. Raman spectroscopy characterization shows differences in scattering among various BAs samples. The presented results will be helpful in guiding further studies on the influence of isotopes on optimizing κ in BAs

System for recycling wastewater resulting form the washing and rinsing proces sof a dishwasher, expecially for reuse in said process and for irrigation of plants, and process for the use of said system

A system for recycling waste water form the washing and rinsing process of a dishwasher is described, said dishwasher having at least one washing cycle and at least one rinsing cycle, the system comprising: a plant irrigation system; a first reservoir, adapted to receive and contain liquid drained from the dishwasher as a result of said washing and rinsing cycles; a second reservoir adapted to receive and contain a liquid; a first filter adapted to contain a liquid coming from said reservoir; a biological filter adapted to further filter the liquid coming from said first filter, said biological filter being adapted to transform an organic component of the liquid received from said first filter into an inorganic component comprising nutrition substances for said plants