This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.  

This research deals with a shrinking method concernes with the principal components similar to that one which used in the multiple regression “Least Absolute Shrinkage and Selection: LASS”. The goal here is to make an uncorrelated linear combinations from only a subset of explanatory variables that may have a multicollinearity problem instead taking the whole number say, (K) of them. This shrinkage will force some coefficients to equal zero, after making some restriction on them by some "tuning parameter" say, (t) which balances the bias and variance amount from side, and doesn't exceed the acceptable percent explained variance of these components. This had been shown by MSE criterion in the regression case and the percent explained v

This research is trying to study the Intellectual political structures of the Open Society according to British Thinker –with Austrian origin- Karl Popper (1902-1994). In First Axe we dealt with the context of Open and Closed society in the Popper's thought. While in the Second Axe we studied the Utopian and graduated Engineering. Finally in the third Axe  for the Rationalism, Freedom, Individualism, and the Democracy of Equality. 

The present study analyzes the effect of couple stress fluid (CSF) with the activity of connected inclined magnetic field (IMF) of a non-uniform channel (NUC) through a porous medium (PM), taking into account the sliding speed effect on channel walls and the effect of nonlinear particle size, applying long wavelength and low Reynolds count estimates. The mathematical expressions of axial velocity, stream function, mechanical effect and increase in pressure have been analytically determined. The effect of the physical parameter is included in the present model in the computational results. The results of this algorithm have been presented in chart form by applying the mathematical program.

The marine collagens are biocompatible and biodegradable materials that are considered as a biomimetic approach for tissue regeneration. This study evaluated the effect of daily consumption of marine collagen supplement drink on enamel white spot lesions (WSLs), comparing the results against Regenerate system and Sylc air abrasion methods. Fifty human enamel slabs were allocated into five groups (n = 10 per group): non-treated (sound); non-treated (WSLs, 8% methylcellulose gel with 0.1 M lactic acid (pH 4.6) at 37 °C for 21 days); and three treated surfaces with marine collagen; Regenerate system; and Sylc air abrasion. The treatment lasted for 28 days followed by four weeks’ storage in artificial saliva (pH = 7.0, 37 °C). Evalu