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In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{*}} where q {\displaystyle q} is a prime, index calculus leads to a family of algorithms adapted to finite fields and to ...
A subgroup H of finite index in a group G (finite or infinite) always contains a normal subgroup N (of G), also of finite index. In fact, if H has index n, then the index of N will be some divisor of n! and a multiple of n; indeed, N can be taken to be the kernel of the natural homomorphism from G to the permutation group of the left (or right ...
Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.
Noteworthy examples of vacuum solutions, electrovacuum solutions, and so forth, are listed in specialized articles (see below). These solutions contain at most one contribution to the energy–momentum tensor, due to a specific kind of matter or field. However, there are some notable exact solutions which contain two or three contributions ...
A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by Maxwell is no longer included. The vector calculus formalism below, the work of Oliver Heaviside, [6] [7] has become standard.
However, both types of "law" may be considered instances of a scientific law in the field of statistics. What distinguishes an empirical statistical law from a formal statistical theorem is the way these patterns simply appear in natural distributions , without a prior theoretical reasoning about the data.
(Jury Trial-Morning Session)XIII - February 11, 2015 Pledger v. Janssen 1 IN THE COURT OF COMMON PLEAS OF PHILADELPHIA COUNTY FIRST JUDICIAL DISTRICT OF PENNSYLVANIA 2 CIVIL TRIAL
D.A. – D.B.A. – D.U.I. – D.W.I. – Damages – Damnation – Dangerous weapon – Data protection – Date rape – Daubert standard – Day in court – de bonis asportatis – de bonis non administratis – de facto – De facto corporation – de futuro – de integro – de jure – De jure corporation – de lege ferenda – de lege lata – de minimis – de novo – Deadlock ...