In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.

Abstract. We present a closed-form, computable expression for the expected number of times any transition event occurs during the transient phase of a reducible Markov chain. Examples of events include time to absorption, number of visits to a state, traversals of a particular transition, loops from a state to itself, and arrivals to a state from a particular subset of states. We give an analog...

In J. T. Wilson’s doctoral dissertation, the author takes up the subject of free meets, that is, subsets S of a frame L whose meet V S is preserved by a designated class of frame homomorphisms out of L. Wilson proves that all subsets of L have free meets if and only if the dual frame law holds in L and the assembly NL is a boolean frame. In this paper it is shown that a frame L has free meets w...

Let be a compact orientable surface with genus g and n boundary components ∂1, . . . , ∂n. Let b = (b1, . . . , bn) ∈ [−2, 2]n. Then the mapping class group Mod( ) acts on the relative SU(2)-character varietyXb := Homb(π , SU(2))/SU, comprising conjugacy classes of representations ρ with tr(ρ(∂i)) = bi. This action preserves a symplectic structure on the open dense smooth submanifold of Homb(π ...

This work proposes an alternative approach to the so-called lattice of embedded subsets, which is included in the product of the subset and partition lattices of a finite set, and whose elements are pairs consisting of a subset and a partition where the former is a block of the latter. The lattice structure proposed in a recent contribution relies on ad-hoc definitions of both the join operator...

We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or abili...

If given n ∈ N and Γ, a multiplicatively closed subset of Zn, then the set HΓ = {n ∈ Z : x ∈ N : x + nZ ∈ Γ} ∪ {1} is a multiplicative submonoid of N0 known as a congruence monoid. Much work has been done to characterize the factorial (every element has unique factorization) and half-factorial (lengths of irreducible factorizations of an element remain constant) properties of such objects. Our ...

We prove that for every M,N ∈ N, if τ is a Borel, finite, absolutely friendly measure supported on a compact subset K of R , then K ∩ BA(M,N) is a winning set in Schmidt’s game sense played on K, where BA(M,N) is the set of badly approximable M × N matrices. As an immediate consequence we have the following application. If K is the attractor of an irreducible finite family of contracting simila...

In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.

Let Σ be a compact orientable surface with genus g and n boundary components ∂1, . . . , ∂n. Let b = (b1, . . . , bn) ∈ [−2, 2]. Then the mapping class groupMod(Σ) acts on the relative SU(2)-character variety Xb := Homb(π, SU(2))/SU(2), comprising conjugacy classes of representations ρ with tr(ρ(∂i)) = bi. This action preserves a symplectic structure on the open dense smooth submanifold of Homb...