In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

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 research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

Throughout this paper we study the properties of the composition operator
C
p1  o
p2  o…o
pn  induced by the composition of finite numbers of special
automorphisms of U,
pi  (z)  i
i
p z
1 p z


Such that pi  U, i  1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.

Carbon dioxide geo-sequestration (CGS) into sediments in the form of (gas) hydrates is one proposed method for reducing anthropogenic carbon dioxide emissions to the atmosphere and, thus reducing global warming and climate change. However, there is a serious lack of understanding of how such CO2 hydrate forms and exists in sediments. We thus imaged CO2 hydrate distribution in sandstone, and investigated the hydrate morphology and cluster characteristics via x-ray micro-computed tomography in 3D in-situ. A substantial amount of gas hydrate (∼17% saturation) was observed, and the stochastically distributed hydrate clusters followed power-law relations with respect to their size distributions and surface area-volume relationships. The layer-

Background: The Streptococcus genus are the predominant bacteria in the mouth and the Streptococcus sanguinis is one of them which performing a primary function for expansion of dental biofilm. Gingival and periodontal disorders are caused by dental biofilm, today, there is a necessity to discover naturally presenting antibacterial compounds from herbs with less side effects as a substitutive to the commonly handled chlorohexidine. Thus, the purpose of this study was to assess the antibacterial activity of thymus vulgaris oil on Streptococcus sanguinis bacteria In vitro. Materials and Methods: Human supragingival plaque samples were taken from 10 subjects, then morphological and microscopical examination, bioch

Presents here in the results of comparison between the theoretical equation stated by Huang and Menq and laboratory model tests used to study the bearing capacity of square footing on geogrid-reinforced loose sand by performing model tests. The effects of several parameters were studied in order to study the general behavior of improving the soil by using the geogrid. These parameters include depth of first layer of reinforcement, vertical spacing of reinforcement layers, number of reinforcement layers and types of reinforcement layers The results show that the theoretical equation can be used to estimate the bearing capacity of loose sand.

The paper is concerned with, the behavior of the hydrostatic thrust bearings lubricated with liquid-solid lubricants using Einstein viscosity formula, and taking into account the centrifugal force resulting from high speed.  Also studied is the effect of the bearing dimensions on the pressure, flow rate, load capacity, shear stress, power consumption and stiffness.

The theoretical results show an increase in load capacity by (8.3%) in the presence of solid graphite particles with concentration of (16%) by weight as compared with pure oil, with increasing shear stress.  .

In general the performance of hydrostatic thrust bearings improve for load carrying capacity, volume flow rate,

Changing the Wine into Vinegar