An explicit formula for the monogenic Szegö kernel function on 3D spheroids

Author(s):  
S. Georgiev ◽  
J. Morais
Author(s):  
Xinyi Yuan ◽  
Shou-Wu Zhang ◽  
Wei Zhang

This chapter computes the derivative of the analytic kernel. It first decomposes the kernel function into a sum of infinitely many local terms indexed by places v of Fnonsplit in E. Each local term is a period integral of some kernel function. The chapter then considers the v-part for non-archimedean v. An explicit formula is given in the unramified case, and an approximation is presented in the ramified case assuming the Schwartz function is degenerate. An explicit result of the v-part for archimedean v is also introduced. The chapter proceeds by reviewing a general formula of holomorphic projection, and estimates the growth of the kernel function in order to apply the formula. It also computes the holomorphic projection of the analytic kernel function and concludes with a discussion of the holomorphic kernel function.


2009 ◽  
Vol 29 (6) ◽  
pp. 1680-1682
Author(s):  
Chang-tao CHEN ◽  
Qin ZHU ◽  
Sheng-yi ZHOU ◽  
Jia-ming ZHANG

Author(s):  
Renxiong Liu

Objective: Lithium-ion batteries are important components used in electric automobiles (EVs), fuel cell EVs and other hybrid EVs. Therefore, it is greatly important to discover its remaining useful life (RUL). Methods: In this paper, a battery RUL prediction approach using multiple kernel extreme learning machine (MKELM) is presented. The MKELM’s kernel keeps diversified by consisting multiple kernel functions including Gaussian kernel function, Polynomial kernel function and Sigmoid kernel function, and every kernel function’s weight and parameter are optimized through differential evolution (DE) algorithm. Results : Battery capacity data measured from NASA Ames Prognostics Center are used to demonstrate the prediction procedure of the proposed approach, and the MKELM is compared with other commonly used prediction methods in terms of absolute error, relative accuracy and mean square error. Conclusion: The prediction results prove that the MKELM approach can accurately predict the battery RUL. Furthermore, a compare experiment is executed to validate that the MKELM method is better than other prediction methods in terms of prediction accuracy.


Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 506
Author(s):  
Jorge Daniel Mello-Román ◽  
Adolfo Hernández ◽  
Julio César Mello-Román

Kernel partial least squares regression (KPLS) is a non-linear method for predicting one or more dependent variables from a set of predictors, which transforms the original datasets into a feature space where it is possible to generate a linear model and extract orthogonal factors also called components. A difficulty in implementing KPLS regression is determining the number of components and the kernel function parameters that maximize its performance. In this work, a method is proposed to improve the predictive ability of the KPLS regression by means of memetic algorithms. A metaheuristic tuning procedure is carried out to select the number of components and the kernel function parameters that maximize the cumulative predictive squared correlation coefficient, an overall indicator of the predictive ability of KPLS. The proposed methodology led to estimate optimal parameters of the KPLS regression for the improvement of its predictive ability.


2015 ◽  
Vol 93 (2) ◽  
pp. 186-193 ◽  
Author(s):  
MASANOBU KANEKO ◽  
MIKA SAKATA

We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.


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