Commonly-preserved radial convolution is a prominent characteristic of the mammalian cerebral cortex. Endeavors from multiple disciplines have been devoted for decades to explore the causes for this enigmatic structure. However, the underlying mechanisms that lead to consistent cortical convolution patterns still remain poorly understood. In this work, inspired by prior studies, we propose and ...

We present a monotonic convolution for planar regions A and B bounded by line and circular arc segments. The Minkowski sum equals the union of the cells with positive crossing numbers in the arrangement of the convolution, as is the case for the kinetic convolution. The monotonic crossing number is bounded by the kinetic crossing number, and also by the maximum number of intersecting pairs of m...

plates and shells are the significant structural components for many engineering and industrial applications. in this study, free vibration analysis of annular plates is investigated. for this, two different numerical methods such as differential quadrature and discrete singular convolution methods have been performed for numerical simulations. frequency values have been obtained via these two ...

2. Arithmetic functions 19 2.1. Arithmetic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2. Multiplicative functions . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3. The Dirichlet convolution . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4. Examples of Dirichlet convolutions . . . . . . . . . . . . . . . . . . . 34 2.5. Möbius inversion . . . . . . . . . ....

A criterion for the solvability of systems of nonhomogeneous convolution equations in convex domains on the complex plane is obtained in terms of lower estimates for the characteristic functions of the convolution equations at their noncommon zeros. §

The symmetric-convolution multiplication (SCM) property of discrete trigonometric transforms (DTTs) based on unitary transform matrices is developed. Then as the reciprocity of this property, the novel multiplication symmetric-convolution (MSC) property of discrete trigonometric transforms, is developed.

We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

Conjecture: Let Γ be a discrete group, f ∈ L(Γ) and Tf : L (Γ) → L(Γ) be the right convolution by f . Then if Tf is injective, it is surjective as well. We prove the conjecture for the class of sofic groups. AMS Subject Classification: 43A20

On this Technical era the excessive velocity and low area of VLSI chip are veryvery crucial elements. Each day quantity of transistors and different active and passive elements are drastically developing on a VLSI chip. All of the processors of the gadgets adders and multipliers are playing an essential position. An adder is a pleasing element for the designing of fast multiplier. Ultimately he...

Modern texts continue to cite Broca's 1861 study of a single patient, Tan, as the first definitive localization of a cerebral function, specifically, articulate speech. We describe the development of Broca's theory from his initial support in 1861 for Bouillaud's view that speech is localized in both frontal lobes to his description in 1865 of a center for articulate speech in the third left fr...