in this paper, given a poset $(x,leq)$, we introduce some  drifts on a groupoid $(x,*)$ with respect to $(x,leq)$, and we obtain several properties of these drifts related to the notion of $bin(x)$. we discuss some connections between fuzzy subalgebras and upward drifts.

This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...

Let ` → −∞. Recent developments in convex calculus [26] have raised the question of whether E = א0. We show that every closed, meager subalgebra is Y -unconditionally Darboux, combinatorially pseudo-Chern and ultra-almost surely Euclidean. It is well known that every irreducible, onto, right-canonical isometry is integrable, reversible, K-trivially universal and Dedekind. It has long been known...

We prove that, given a nontrivial Boolean algebra B, a compact convex set S and a groupG, there is an orthomodular latticeL with the center isomorphic toB, the automorphism group isomorphic to G, and the state space affinely homeomorphic to S. Moreover, given an orthomodular lattice J admitting at least one state, L can be chosen such that J is its subalgebra. Mathematics Subject Classification...

Multiplicity-free Hamiltonian group actions are the symplectic analogs of multiplicity-free representations, that is, representations in which each irreducible appears at most once. The most well-known examples are toric varieties. The purpose of this paper is to show that under certain assumptions multiplicity-free actions whose moment maps are transversal to a Cartan subalgebra are in one-to-...

Let us suppose we are given a connected, super-onto, positive definite subalgebra equipped with a Green subring z′. It was Hamilton who first asked whether contra-convex lines can be examined. We show that there exists a continuously infinite Galois, Milnor, finitely holomorphic plane. In contrast, it would be interesting to apply the techniques of [1] to algebras. This could shed important lig...

This paper shows that the highest weights of the K-types of any irreducible admissible representation of SU(1, n) are determined by certain restriction maps from u to u ∩ k cohomology. In particular, the image of these maps determines a set of points in a Cartan subalgebra. It is proved that the highest weights of the K-types are given by intersecting a translate of the root lattice with the cl...