18. We find several interesting properties in the logarithm conformal mappings after introducing two dual logarithm terms with one linear term. We plot virtual space and physical space of both mappings to present their geometry. With two kissing mirrored Maxwell's fish-eye lenses applied in the ...
of surface plasmon polaritons; Pendry and Luo et al.27,28 proposed an analytical solution for interactions at the nanometer scale, which can be used to analyzed accurately the nonlocality in 3D plasmonic systems; Kraft et al.29 calculated analytically the electromagnetic properties of an spheroid. ...
All these algorithms are based on the discrete logarithm problem. We will introduce two algorithms which can be used to calculate discrete logarithms in finite fields. We will see, that the running time of these algorithms is high for large groups (or groups with special properties) and ...
(x). Allofthesefollowfromthecorrespondingidentitiesforln. Actions... (1)Wecancalculateln(x)forgivenxbyusingtheusualmethodsofestimatingthevaluesofintegrals, appliedtothefunction1/x.Wecanalsousetheknownpropertiesoflogarithms,aswellasapprox- imatelnvaluesforsomespecificxvalues,toestimatelnxtoareasonable...
{ }increasesatleastasrapidlyasageometricprogressionwhosecommonratioisbiggerthan1.Lacunaryseriesexhibitmanyofthepropertiesofpartialsumsofindependentrandomvariables.Inthemodernprobabilitytheor,lacunaryseriesarecalled'weaklydependent'randomvariables.Keywordsandphrases:lawoftheiteratedlogarithm,lacunaryseries,normalnumbers,...
௧,ೞሻmod ൌ ݎ௦ ܭݕଷሺ,௧,ೞሻmod Next section discusses the security properties that satisfy the needs of proxy signature with revocation and we show how the two hard problems will make our system more secure based on these properties....
opening the opportunity for the hider to use a polynomialfwith nice algebraic properties that accelerate the NFS algorithm. The so-called Murphy-\alphavalue [37, Sect. 3.2] has a measurable influence on the probability of the norms to be smooth. A norm ofsbits is expected to have a smoothn...
1;kx<1(-1)k+1(1-kx)n-1n,allx>0.kReceivedAugust27,1979;revisedAugust5,1980.'ThisresearchwassponsoredinpartbyNationalResearchCouncilofCanadaGrantNo.A3456.AMS1980subjectclassifications.Primary60F15.Keywordsandphrases.Lawoftheiteratedlogarithm,orderstatistics,spacings,stronglaws,almostsureconvergence....
samples,itsdependencesolelyonelementarylawsofproba-bility,andtheeasewithwhichallkindsoffamiliesandpedigreesmaybecombined"(1).Itisconservativewhenthesamplesize*isfixed(2),butitminimizesthenumberofobservationsrequiredforsignificanceinthesequentialtest(3).InlargesampletheoryitgivesX2,itprovidesaBayesiansolutionwhenthat...