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Principal Solutions of Difference Equations

American Journal of Mathematics, 1947
One of the central problems in the theory of difference equations is that of eradicating, as far as possible, the arbitrary elements in the manifold of solutions.2 In brief, a difference equation has so many solutions, (in those cases where the complete manifold has been determined, involving one or more arbitrary periodic functions), that the property
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ON FUNDAMENTAL SOLUTIONS OF OPERATORS OF PRINCIPAL AND NONPRINCIPAL TYPES

Acta Mathematica Scientia, 1981
This paper deals with the construction of fundamental solutions for some special classes of partial differential operators with simple and multiple characteristics. To do this, an analytic continuation with respect to the dual variable \(\xi\) is done and the construction of a parametrix for classical elliptic equations is applied.
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Accuracy of suboptimal solutions to kernel principal component analysis

Computational Optimization and Applications, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giorgio Gnecco, Marcello Sanguineti
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An efficient solution to the informed principal problem

Journal of Economic Theory, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Dilemmas and solutions regarding principal evaluation

Peabody Journal of Education, 1990
School reform embraced the American psyche in the 1980s, and waves of initiatives emerged to revitalize and improve a system perceived as not meeting the country's needs (Murphy, 1990; Plank & Ginsberg, 1990). Today, ideas such as school choice, for-profit schools, site-based management, participatory decision-making, teacher empowerment, school ...
Rick Ginsberg, Tom Thompson
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PROPAGATION OF SINGULARITIES FOR SOLUTIONS OF AN EQUATION OF PRINCIPAL TYPE

Mathematics of the USSR-Sbornik, 1983
Translation from Mat. Sb., Nov. Ser. 118(160), No.4, 523-534 (Russian) (1982; Zbl 0516.35084).
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On the Behavior of Principal Fundamental Solutions of Elliptic Equations

SIAM Journal on Mathematical Analysis, 1975
Fundamental solutions which decay exponentially at $\infty $ together with their first derivatives are called principal fundamental solutions. Such solutions of elliptic equations in $R^m $, $m \geqq 2$, play an important role in the study of pseudo-parabolic equations in $R^m \times R$. We establish the behavior as $| {x - y} | \to \infty $ and as $| {
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Localized principal components of natural images-an analytic solution

Network: Computation in Neural Systems, 1994
Summary: The structure of receptive fields in the visual cortex is believed to be shaped by unsupervised learning. A simple variant of unsupervised learning is the extraction of principal components. We derive analytically the form of the principal components of natural images.
Liu, Yong, Shouval, Harel
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Principal and Vice Principal Selection Model Based on the Opinions of Principals and Teachers: Problems and Solution

2021
The research aims to discuss the regulation of selecting and assigning managers/ principals to educational institutions affiliated to the Ministry of National Education, which was published in the Official Paper on February 5th 2021. With the research, the current situation regarding the method of selecting and assigning managers/principals to ...
DEMİRER, Mustafa, ERGEZEN, Mehmet Duran
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Exact motion planning solution for principally kinematic systems

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011
In this paper, we take a rather new approach to solving the motion planning problem for principally kinematic systems, that is, systems whose dynamics is completely specified by the right number of nonholonomic constraints. Given a planar curve in the Special Euclidean group, we analytically solve for the base variables that locomote the principally ...
Elie A. Shammas   +1 more
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