Congruences


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Congruences

 

morphological adaptations in different individuals of the same species that foster closer functional ties and ensure the integrity of the species.

Congruences arise in individuals of different generations (for example, in mammals, between the extraembryonic membranes of the embryo and the uterine mucosa), different sexes (for example, in insects, the mutual adaptation of the copulative apparatus of male and female), the same sex (for example, in male ruminants, the “tournament” horns, which prevent the males from killing one another in battles for the female), and colonial forms, which have different functions and different structures (for example, in hydroids, the gastrozooids and dactylozooids).

References in periodicals archive ?
Inspired by the work of Ramanujan on the standard partition function p(n), Chan [4] asked whether there are any other congruence properties of the following form: [c.
Key words: Modular Arithmetic, Congruence, Divisibility, b-adic expension.
It is the smallest congruence containing both ~ and [approximately equal to];
Some single-country longitudinal studies have tried to explain opinion-policy congruence using variables that do vary in the medium run, like the party in power or the size of the majority in parliament.
Waldherr, On certain explicit congruences for mock theta functions, Proc.
Since we are interested in first order Congruences, we may need that the congruence B splits in some components.
Thus it becomes interesting to find solutions of congruences of the type Equation through Numerical Analysis as this is the generalization of the above case in a sense that if Equation is substituted in last equation then all of the results for finding the inverse of numbers modulo prime powers are produced.
q-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher.
Let C(S) be the set of all congruences on S and let A[sigma] be the set {a [member of] S| ([there exists]x [member of] A) (a, x) [member of] [sigma]} for any [sigma] [member of] C(S).
There's nothing about the definition of partitions that gives an easy explanation for why the three Ramanujan congruences exist" These congruences forge a link between two ways of expressing numbers--as sums and as products.
The motivation for the definition of shards arises from the study of lattice congruences of the weak order, and will be discussed in Section 5.
Nothing in the definition of partitions hinted that such relationships, called congruences, should exist or that the prime numbers 5, 7, and 11 should play a special role.