| viXra.org > Functions and Analysis > 2302 |
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| viXra.org > Functions and Analysis > 2302 |
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[5] viXra:2302.0138 [pdf] submitted on 2023-02-27 01:42:00
Authors: Israel Julins Andersen Yañez
Comments: 19 Pages. (Correction made by viXra Admin)
This paper is about sequences. The author uses the new theorems to approximate better the values on the sequence, the bigger the number, the better the approximation.
Category: Functions and Analysis
[4] viXra:2302.0097 [pdf] submitted on 2023-02-20 21:28:10
Authors: Saburou Saitoh
Comments: 18 Pages.
The theory of reproducing kernels is very fundamental, beautiful and will have many applications in analysis, numerical analysis and data sciences. In this paper, some essential results in complex analysis derived from the theory of reproducing kernels will be introduced, simply.
Category: Functions and Analysis
[3] viXra:2302.0031 [pdf] submitted on 2023-02-08 17:28:44
Authors: Sing Kuang Tan
Comments: 8 Pages.
In this paper, I am going to propose a gradient descent algorithm using fixed point theorem. Fixed point theorem comes from topology mathematics. This gradient descent is able to converge at exponential rate, faster than Netwon method which converges at quadratic rate. Besides that, it does not need second order derivatives. The algorithm is simple and can be implemented using a few lines of equations. It can be used for training Relu deep learning network.
Category: Functions and Analysis
[2] viXra:2302.0019 [pdf] submitted on 2023-02-06 21:42:02
Authors: Saburou Saitoh
Comments: 17 Pages.
In this paper, we would like to refer to some deep results of the Green function of Q. Guan on the conjugate analytic Hardy $H_2$ norm and on the line of Oikawa-Sario's problems; Suita's conjecture, Saitoh's conjecture and Yamada's conjecture and to propose new related open problems. In particular, Q. Guan examined the deep properties of the inversion of the normal derivative of the Green function, the property of the level curve of the Green function and the magnitude of the logarithm capacity with his colleagues.
Category: Functions and Analysis
[1] viXra:2302.0017 [pdf] submitted on 2023-02-06 00:19:47
Authors: Boning Zhang, Eric B. Herbold, Richard A. Regueiro
Comments: 14 Pages.
Granular material is showing very often in geotechnical engineering, petroleum engineering, material science and physics. The packings of the granular material play a very important role in their mechanical behaviors, such as stress-strain response, stability, permeability and so on. Although packing is such an important research topic that its generation has been attracted lots of attentions for a long time in theoretical, experimental, and numerical aspects, packing of granular material is still a difficult and active research topic, especially the generation of random packing of non-spherical particles. To this end, we will generate packings of same particles with same shapes, numbers, and same size distribution using geometry method and dynamic method, separately. Specifically, we will extend one of Monte Carlo models for spheres to ellipsoids and poly-ellipsoids.
Category: Functions and Analysis
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