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Differential properties of power functions

Celine Blondeau, Anne Canteaut, Pascale Charpin
2010 International Journal of Information and Coding Theory  
Some 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.  ... 
doi:10.1504/ijicot.2010.032132 fatcat:2blr7vl26bccvcabutwiw6ts4e

Differential properties of power functions

Celine Blondeau, Anne Canteaut, Pascale Charpin
2010 2010 IEEE International Symposium on Information Theory  
Some 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.  ... 
doi:10.1109/isit.2010.5513437 dblp:conf/isit/BlondeauCC10 fatcat:ikrd5wgzxjbhfiepofx5ot35v4

Properties of powers of functions satisfying second-order linear differential equations with applications to statistics [article]

Naoki Marumo and Toshinori Oaku and Akimichi Takemura
2014 arXiv   pre-print
We derive 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) .  ... 
arXiv:1405.4451v1 fatcat:6x5lwe2wdjf7locx6ezqwf7g5u

ON ONE METHOD OF CORRELATION AND SPECTRUM ESTIMATION DEVELOPMENT

Volodymyr Denisiuk, Oleg Denisiuk
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,  ... 
doi:10.3846/16487788.2006.9635923 fatcat:7glcvziwtrclhpr2vdwpjxmbxe

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]

Vasily E. Tarasov
2015 Physics Letters A  
We also prove that the usual Leibniz rule with α = 1 cannot hold for sets 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.  ... 
doi:10.1016/j.physleta.2015.02.005 fatcat:76mke56pnvd6zlqjp6ruwrbgv4

The Foundations of the Elliptic Functions

Harris Hancock
1920 Rendiconti del circolo matematico di Palermo  
o (o) The 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.  ... 
doi:10.1007/bf03014597 fatcat:etzigjp2jfhwndfu3cednvqrka

On a Leibnitz-type fractional derivative [article]

V. V. Kobelev
2017 arXiv   pre-print
Based on the definition 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 ] .  ... 
arXiv:1202.2714v3 fatcat:qs3lboibjzb2pk2qehy2mrfemu

Viscoelastic Properties of Differentiating Blood Cells Are Fate- and Function-Dependent

Andrew E. Ekpenyong, Graeme Whyte, Kevin Chalut, Stefano Pagliara, Franziska Lautenschläger, Christine Fiddler, Stephan Paschke, Ulrich F. Keyser, Edwin R. Chilvers, Jochen Guck, Wilbur Lam
2012 PLoS ONE  
Although cellular mechanical 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.  ... 
doi:10.1371/journal.pone.0045237 pmid:23028868 pmcid:PMC3459925 fatcat:jir7b36ovnfs3jjutwzwltbmq4

Free-Space Optical channel turbulence analysis based on lognormal distribution and stochastic differential equation

TayyabaGul Tareen
2018 JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES  
To examine the resemblance between numerical and theoretical analysis, two 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.  ... 
doi:10.26782/jmcms.2018.12.00002 fatcat:zxkrvtqgwjerxovqmnsg7r36zi

Some Extensions of Pincherle's Polynomials

Pierre Humbert
1920 Proceedings of the Edinburgh Mathematical Society  
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;  ...  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;  ... 
doi:10.1017/s0013091500035756 fatcat:hm2cdsy43ffhdiaw3zgl2it5yy

The Use of an Existence Theorem in Developing the Properties of the Sine and Cosine

H. T. Davis
1923 The American mathematical monthly  
We shall now develop some 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  ... 
doi:10.2307/2298915 fatcat:6kparzki3fcz7dux6c64fon5n4

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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