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[3] viXra:2407.0173 [pdf] submitted on 2024-07-29 11:45:57
Authors: Tai-Choon Yoon
Comments: 4 Pages.
Elliptic integral is an integral equation that appears in the process of calculating the length of an ellipse. It does not provide an exact solution, and the approximation equation for the solution is complicated. The arc length of an ellipse is given as l=aθE(k). And the entire arc length of an ellipse is l=2aπE(k).
Category: Algebra
[2] viXra:2407.0130 [pdf] submitted on 2024-07-21 13:13:42
Authors: Huanyin Chen
Comments: 18 Pages.
We present new necessary and sufficient conditionsunder which the sum of two generalized core-EP invertible elements in a Banach *-algebra has generalized core-EP inverse. As an application, the generalized core-EP invertibility for the matrices with generalized core-EP invertible entriesis investigated.
Category: Algebra
[1] viXra:2407.0037 [pdf] submitted on 2024-07-06 02:37:02
Authors: Huanyin Chen, Marjan Sheibani
Comments: 24 Pages.
In this paper, we introduce the generalized $w$-core inverse in a Banach *-algebra. We characterize this new generalized inverse by using the generalized weighted core decomposition and present the representations by the weighted g-Drazin inverse. The generalized $w$-core orders are investigated as well. These extend the weighted core inverse and pseudo core inverse for complex matrices and linear bounded operators to more general setting.
Category: Algebra
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