Enhancing the Performance of Multi-parameter Patient Monitors by Homogeneous Kernel Maps

2016 ◽  
pp. 1-7
Author(s):  
S. Premanand ◽  
S. Sugunavathy
Keyword(s):  
Homogeneous Kernel

scholarly journals On a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xingshou Huang ◽  
Bicheng Yang
Keyword(s):  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Real Analysis ◽  
Homogeneous Kernel ◽  
Hilbert’S Inequality ◽  
The Best Possible Constant ◽  
Hilbert Type ◽  
Weight Coefficients

AbstractBy the use of the weight coefficients, the idea of introduced parameters and the technique of real analysis, a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of the more accurate Hardy–Hilbert’s inequality. An equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered.

On the Spectrum of the Bergman-Hilbert Matrix II

1990 ◽  
Vol 33 (1) ◽  
pp. 60-64 ◽  
Author(s):  
Chandler Davis ◽  
Pratibha Ghatage
Keyword(s):  
Spectral Density ◽  
Mellin Transform ◽  
Homogeneous Kernel ◽  
Homogeneous Part ◽  
Infinite Matrices ◽  
Hilbert Matrix ◽  
Class Of Matrices

AbstractWe study a class of matrices (introduced by T. Kato) with principal homogeneous part, and use Mellin transform of the homogeneous kernel to determine spectral density of the positive infinite matrices.

scholarly journals A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 342 ◽  
Author(s):  
Bicheng Yang ◽  
Shanhe Wu ◽  
Aizhen Wang
Keyword(s):  
Type Inequality ◽  
Homogeneous Kernel ◽  
Hilbert Type

We establish a new inequality of Hilbert-type containing positive homogeneous kernel ( min { m , n } ) λ and derive its equivalent forms. Based on the obtained Hilbert-type inequality, we discuss its equivalent forms and give the operator expressions in some particular cases.

scholarly journals Infinite linear systems with homogeneous kernel of degree –1

1965 ◽  
Vol 5 (2) ◽  
pp. 129-168
Author(s):  
T. M. Cherry
Keyword(s):  
Continuous Function ◽  
Linear Systems ◽  
Algebraic Function ◽  
Additional Restriction ◽  
Main Concern ◽  
Homogeneous Kernel ◽  
Infinite Linear Systems ◽  
Image Position ◽  
Infinite Linear

The main concern of this paper is with the solution of infinite linear systems in which the kernel k is a continuous function of real positive variables m, n which is homogeneous with degree –1, so that If k is a rational algebraic function it is supposed further that the continuity extends up to the axes m = 0, n > 0 and n = 0, m > 0; the possibly additional restriction when k is not rational is discussed in § 1,2.

Optimal Reduced-Set Vectors for Support Vector Machines with a Quadratic Kernel

2004 ◽  
Vol 16 (9) ◽  
pp. 1769-1777 ◽  
Author(s):  
Thorsten Thies ◽  
Frank Weber
Keyword(s):  
Support Vector Machine ◽  
Support Vector Machines ◽  
Discriminant Function ◽  
Explicit Solution ◽  
Computational Cost ◽  
One Dimension ◽  
Support Vector ◽  
Homogeneous Kernel ◽  
Vector Machines

To reduce computational cost, the discriminant function of a support vector machine (SVM) should be represented using as few vectors as possible. This problem has been tackled in different ways. In this article, we develop an explicit solution in the case of a general quadratic kernel k(x, x′) = (C + Dx⊺x′)2. For a given number of vectors, this solution provides the best possible approximation and can even recover the discriminant function if the number of used vectors is large enough. The key idea is to express the inhomogeneous kernel as a homogeneous kernel on a space having one dimension more than the original one and to follow the approach of Burges (1996).

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