ly, a combination is equivalent to partitioning a set into two disjoint subsets, one containing k objects and the other containing the n−k remaining elements. In general, the set S = {1, 2, . . . , n} can be partitioned into r disjoint subsets. Let n1, n2, . . . , nr be nonnegative integers such that r ∑

This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the development of homotopy probability theory, allowing the principles of deri...

there are many places in our lives which we can’t imagine ourselves without them. each of these places makes some parts of “i/me” or “self”; the entity which is called “personal identity” by psychologists. in this regard, the concept of “place identity” explains physical aspects of personal identity; those aspects which are made through experiencing physical environment (places). also based on ...

Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...

one of the main agreements among classical and contemporary sociologists is putting emphasis on the role and place of utilizing forms of capital in reconsidering identity limits and expansion of collective belongings. this article is based on conceptual framework (jenekins and bourdieu) and tries to study empirically the theory of the relationship between the amount of economic capital as well ...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper Re], we start with probability distributions on the space of the innnite Young tableaux. Then we calculate the probability that the entry of a random tableau at a given box equals n = 1; 2; : : :. Summing these probabilities over n and equa...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...