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Differential properties of power functions

2010
*
International Journal of Information and Coding Theory
*

Some

doi:10.1504/ijicot.2010.032132
fatcat:2blr7vl26bccvcabutwiw6ts4e
*properties**of**power*permutations, that is, monomials bijective mappings on F 2 n , are investigated. ... In particular, the*differential*spectrum*of*these*functions*is shown to be*of*great interest for estimating their resistance to some variants*of**differential*cryptanalysis. ... Section 2 recalls some definitions and*properties*related to the resistance*of*a*function*to*differential*attacks. ...##
###
Differential properties of power functions

2010
*
2010 IEEE International Symposium on Information Theory
*

Some

doi:10.1109/isit.2010.5513437
dblp:conf/isit/BlondeauCC10
fatcat:ikrd5wgzxjbhfiepofx5ot35v4
*properties**of**power*permutations, that is, monomials bijective mappings on F 2 n , are investigated. ... In particular, the*differential*spectrum*of*these*functions*is shown to be*of*great interest for estimating their resistance to some variants*of**differential*cryptanalysis. ... Section 2 recalls some definitions and*properties*related to the resistance*of*a*function*to*differential*attacks. ...##
###
Properties of powers of functions satisfying second-order linear differential equations with applications to statistics
[article]

2014
*
arXiv
*
pre-print

We derive

arXiv:1405.4451v1
fatcat:6x5lwe2wdjf7locx6ezqwf7g5u
*properties**of**powers**of*a*function*satisfying a second-order linear*differential*equation. ... In particular we prove that the n-th*power**of*the*function*satisfies an (n+1)-th order*differential*equation and give a simple method for obtaining the*differential*equation. ... Koutschan for computation*of*(16) . ...##
###
ON ONE METHOD OF CORRELATION AND SPECTRUM ESTIMATION DEVELOPMENT

2006
*
Aviation
*

*differential*

*properties*. ... The article deals with a non‐linear method

*of*correlation

*function*and spectrum

*power*density estimation for which analogies

*of*A. Shuster's periodic diagrams have been used. ... As it is know the very

*properties*

*of*these signals determine both the character

*of*the decrease

*of*

*power*spectrum density

*of*signals and

*differential*characteristics

*of*the correlation

*function*[4, 6, ...

##
###
Page 40 of Mathematical Reviews Vol. , Issue 89A
[page]

1989
*
Mathematical Reviews
*

Noether

*property*for equations*of*the first kind with*power*kernels. 32. Equations with*power*-logarithmic kernels and a variable limit*of*integration. 33. ... The main*properties**of*fractional integrals and deriva- tives. 6. The representability*of**functions*by fractional integrals*of**functions*belonging to L,. 7. ...##
###
Page 4627 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

Using an example, he shows that the existence

*of*a Lyapunov*function*for equation (1) is insufficient for satisfying the A-*property*. ... Krasovskii introduced the so-called A-*property**of*trajectories and established its equivalence to the existence*of*a Lyapunov*function*admitting an infinitesi- mal upper limit and with a derivative*of*...##
###
Page 392 of American Sociological Review Vol. 18, Issue 4
[page]

1953
*
American Sociological Review
*

This is to say, it cannot yet be demonstrated that it is unavoidable that

*differential*pres- tige and esteem shall accrue to positions which command*differential*rewards in*power*and*property*. ... If such dif- ferential*power*and*property*are viewed by all as commensurate with the*differential*responsibilities, and if they are culturally defined as resources and not as rewards, then, no*differentials*...##
###
Comments on "The Minkowski's space–time is consistent with differential geometry of fractional order" [Phys. Lett. A 363 (2007) 5–11]

2015
*
Physics Letters A
*

We also prove that the usual Leibniz rule with α = 1 cannot hold for sets

doi:10.1016/j.physleta.2015.02.005
fatcat:76mke56pnvd6zlqjp6ruwrbgv4
*of**differentiable*and non-*differentiable**functions*. ... We prove that Eq. (3.6) for fractional-order derivative*of**power**function*and the usual Leibniz rule (3.7) , which are based relations*of*the considered paper, cannot hold together for fractional derivatives ... Then these*functions*are α-*differentiable*. In addition, Eq. (1) (see Eq. (3.6)*of*[1] ) means that fractional derivatives*of**power**functions*exist. Step 3. ...##
###
The Foundations of the Elliptic Functions

1920
*
Rendiconti del circolo matematico di Palermo
*

o (o) The

doi:10.1007/bf03014597
fatcat:etzigjp2jfhwndfu3cednvqrka
*properties**of*the Elliptic*functions*may be then derived directly from those*of*the Theta-*functions*. ... The Theta-*functions*being elemental in the whole theory, it is more scientific to establish their*properties*without making use*of*the*properties**of*the elementary elliptic*functions*sn, cn and dn. ... the analogous*properties**of*the*functions*just mentioned. ...##
###
On a Leibnitz-type fractional derivative
[article]

2017
*
arXiv
*
pre-print

Based on the definition

arXiv:1202.2714v3
fatcat:qs3lboibjzb2pk2qehy2mrfemu
*of*\alpha-derivative the operations*of*analysis and*differential*geometry are studied It was recently proved, that this variant*of*introduction*of*the derivative leads to a new ... scaling*of*the common Leibniz derivative, but not to a alternative type*of*derivation. ... In accordance with the theory*of*analytic continuation*of*complex variable*function*all*properties**of*a*function*analytic in some point are defined by its*power*expansion in this point [ 17 ] . ...##
###
Viscoelastic Properties of Differentiating Blood Cells Are Fate- and Function-Dependent

2012
*
PLoS ONE
*

Although cellular mechanical

doi:10.1371/journal.pone.0045237
pmid:23028868
pmcid:PMC3459925
fatcat:jir7b36ovnfs3jjutwzwltbmq4
*properties*are known to alter during stem cell*differentiation*, understanding*of*the*functional*relevance*of*such alterations is incomplete. ... Our results indicate that the material*properties**of*cells define their*function*, can be used as a cell*differentiation*marker and could serve as target for novel therapies. ... Acknowledgments We are grateful to Donald and Ada Olins for providing the HL60/S4 cells and for sharing their expertise in induced*differentiation**of*these cells. ...##
###
Free-Space Optical channel turbulence analysis based on lognormal distribution and stochastic differential equation

2018
*
JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES
*

To examine the resemblance between numerical and theoretical analysis, two

doi:10.26782/jmcms.2018.12.00002
fatcat:zxkrvtqgwjerxovqmnsg7r36zi
*properties**of*free-space optical channel is considered including the probability density*function*and auto-covariance*property*... This paper provide a model that can analyze the influence*of*inevitable turbulence effect on a free-space channel which is based on the stochastic*differential*equation to synthesis lognormal distributed ... III.a Probability Density*Function*Statistics The probability density*function**of*gain samples is the most important*property**of*free-space optical channel. ...##
###
Some Extensions of Pincherle's Polynomials

1920
*
Proceedings of the Edinburgh Mathematical Society
*

The polynomials which satisfy linear

doi:10.1017/s0013091500035756
fatcat:hm2cdsy43ffhdiaw3zgl2it5yy
*differential*equations*of*the second order and*of*the hypergeometric type have been the object*of*extensive work, and very few*properties**of*them remain now hidden; ... To show what can be done in these ways, I shall briefly give the definition and principal*properties**of*some polynomials analogous to Pineheile's and*of*some allied*functions*. I. ... The polynomials which satisfy linear*differential*equations*of*the second order and*of*the hypergeometric type have been the object*of*extensive work, and very few*properties**of*them remain now hidden; ...##
###
The Use of an Existence Theorem in Developing the Properties of the Sine and Cosine

1923
*
The American mathematical monthly
*

We shall now develop some

doi:10.2307/2298915
fatcat:6kparzki3fcz7dux6c64fon5n4
*of*the*properties**of*these*functions*, ultimately to be identified with the sine and cosine, on the basis*of*this definition. TuHeorEM I. U?+ V?= 1. By hypothesis U” + n? ... The*power**of*the method which is here developed attaches to the fact that the theorem just quoted assures us*of*the uniqueness as well as the existence*of*the two*functions*U and V which we shall choose ...##
###
Page 507 of Automation and Remote Control Vol. 25, Issue 4
[page]

1964
*
Automation and Remote Control
*

*of*invariance, rigid technical requirements with regard to its dy- namic

*properties*must be imposed on the transfer

*function*

*of*the amplifier with the slide valve, It is desirable that the transfer

*function*...

*of*this unit should be described by the relation W = a'(p)/4,(p)=Ky over its available operating frequency band, This will substantially improve the dynamic

*properties*

*of*a hydraulic

*power*servo drive ...

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