The concept of -closedness, a kind of covering property for topological spaces, has already been studied with meticulous care from different angles and via different approaches. In this paper, we continue the said investigation in terms of a different concept viz. grills. The deliberations in the article include certain characterizations and a few necessary conditions for the -closedness of a space, the latter conditions are also shown to be equivalent to -closedness in a - almost regular space. All these and the associated discussions and results are done with grills as the prime supporting tool.

     A complex number  is called an extended eigenvalue for an operator  on a Hilbert space H if there exists a nonzero operator  such that: such  is called an extended eigenoperator corresponding to. The goal of this paper is to calculate extended eigenvalues and extended eigenoperators for the weighted unilateral (Forward   and Backward) shift operators. We also find an extended eigenvalues for weighted bilateral shift operator. Moreover, the closedness of extended eigenvalues for the weighted unilateral (Forward and Backward) shift operators under multiplication is proven.

The science of interpretation is considered one of the most important sciences due to its primacy and high status. Because knowledge is honored with the honor of its owner and related to it, and the science of interpretation is related to the Book of God, and from this importance emerges the importance of writing on a subject (from the terms of social organization in the Holy Qur’an); Because it deals with a matter that is considered a necessity in a place, and I called the research (from the terms of social organization in the Holy Qur’an - an analytical study), and the reason for choosing this topic was to clarify those terms and link them to our contemporary reality in order for them to be beacons of guidance and guidance for thos

In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given.  For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

The primary purpose of the present research was to study the effect of polyvinyl chloride (PVC) powder content on ultrasonic wave velocity in PVC/Epoxy composites. The second part is concerned with the relations of dynamic elastic moduli with the ultrasonic wave velocities, to determine how ultrasonic waves can affect them.
Experimental data have been obtained using the sonic viewer (model -5217 A) device to generate two types of waves, longitudinal waves of frequency 63 kHz and transverse waves of frequency 33 kHz and to measure the transit time required for those waves to travel through individual sample.
The experimental results have shown that the propagation of the ultrasonic velocity increases directly with PVC content in the

Some researchers are interested in using the flexible and applicable properties of quadratic functions as activation functions for FNNs. We study the essential approximation rate of any Lebesgue-integrable monotone function by a neural network of quadratic activation functions. The simultaneous degree of essential approximation is also studied. Both estimates are proved to be within the second order of modulus of smoothness.

   In this paper we obtain some statistical approximation results for a general class of maxproduct operators including the paused linear positive operators.

Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.