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Matrix Derivation of Multiple Correlation

The Journal of Experimental Education, 1965
IN MANY textbooks on statistics for students in the behavioral sciences, a rather full discussion can be found of the type of problem situation and as sumptions involved in multiple correlation. How ever, their authors usually then present without derivation the "normal equations" and finally dis cuss computational techniques for solving these ...
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Multiplicative (generalized)-derivation in semiprime rings

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2015
Let \(R\) be a semiprime ring. A mapping \(F:R\to R\) is a multiplicative generalized-derivation associated with a mapping \(d:R\to R\) if \(F(xy)=F(x)y+xd(y)\) for all \(x,y\in R\). In this article, many identities involving multiplicative generalized-derivations \(F\) and \(G\) of a semiprime ring \(R\) with associated mappings \(g\) and \(d ...
Tiwari, S. K., Sharma, R. K., Dhara, B.
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On semiprime rings with multiplicative (generalized)-derivations

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2015
The author in this paper emphasizes \(R\) to be an associative semiprime ring with center \(Z(R)\) and a map \(F\colon R\to R\) is called a multiplicative (generalized)-derivation if \(F(xy)=F(x)y+xd(y)\) is fulfilled for all \(x,y\in R\), where \(d\colon R\to R\) is any map (not necessarily a derivation nor additive).
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On a multiplicative inequaluty for derived functions

Analysis Mathematica, 1989
The author considers the space \(L_ \infty\) of all essentially bounded functions on \([0,1]\) and introduces a subspace \(H^{r,s}\). This subspace consists of all functions with essentially bounded derivatives of order at most \(r\) and with a Lipschitz condition in \(L_ \infty\) for the highest order derivatives involving a logarithmic factor to the ...
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Derivation of Rational Expressions with Multiplicity

2002
This paper introduces a generalization of the partial derivatives of rational expressions, due to Antimirov, to rational expressions with multiplicity. We define the derivation of a rational expression with multiplicity in such a way that the result is a polynomial of expressions.
Sylvain Lombardy, Jacques Sakarovitch
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment

Ca-A Cancer Journal for Clinicians, 2022
Jun J Mao,, Msce   +2 more
exaly  

The Lie Derivative and Interior Multiplication

2020
This chapter reviews two operations on differential forms, the Lie derivative and interior multiplication. These are necessary to the definition of invariant forms, horizontal forms, and basic forms in the construction of the Cartan model. The chapter then looks at the Lie derivative of a vector field and of a differential form. The Lie derivative of a
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Deriving Multiple “Object” Constructions

2018
Tonia Bleam, Norbert Hornstein
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