The Solution Of Nonhomogen Abstract Cauchy Problem by Semigroup Theory of Linear Operator

Abstract

<jats:p>&lt;div style="text-align: justify;"&gt;In this article we will investigate how to solve nonhomogen degenerate Cauchy problem via theory of semigroup of linear operator. The problem is formulated in Hilbert space which can be written as direct sum of subset Ker M and Ran M*. By certain assumptions the problem can be reduced to nondegenerate Cauchy problem. And then by composition between invers of operator M and the nondegenerate problem we can transform it to canonic problem, which is easier to solve than the original problem. By taking assumption that the operator A is infinitesimal generator of semigroup, the canonic problem has a unique solution. This allow to define special operator which map the solution of canonic problem to original problem. ©2016 JNSMR UIN Walisongo. All rights reserved.&lt;/div&gt;</jats:p>

Application and Deconstruction of Visual Communication in Art Design Based on Linear Operator Theory

“…Compare the mapping figures between the visual communication of art design based on the color scale mapping algorithm and the traditional visual communication of art design. When performing the tone-level mapping algorithm, the image needs to be linearly transformed, and the optimal figure mapping solution (r i ′ , k i ′ ) is obtained by formula (7). By comparing the visual communication effects of the two visual communication methods in different figure scenarios, the comparison results of the two ways of visual communication of art design are shown in Figure 4.…”

“…e video presentation of visual communication of art design is the main way of new mediatization of visual communication. Compare the mapping video between the visual communication of artistic design based on the gradation mapping algorithm and the traditional visual communication of artistic design, and obtain the optimal video mapping solution (r i ′ , k i ′ ) under the chromatic mapping algorithm through the mapping transformation of formula (7). Compare the visual communication effects of different visual communication methods of video scenes.…”

“…Among them, the research of Murean and Murean showed that the linear operator theory can optimize the image quality of visual communication and make the visual communication of art design more effective [6]. Hariyanto applied the semigroup algorithm in the linear operator theory to the visual communication of art design, which improved the problem of unclear image quality in visual communication [7]. Altmann and Zimmer utilized the boundary control of linear operators to improve the image quality of visual communication, which make visual communication more effective [8].…”