bentea and tu{a}rnu{a}uceanu~(an. c{s}tiinc{t}. univ. al. i.cuza iac{s}, ser. nouv{a}, mat., {bf 54(1)} (2008), 209-220)proposed the following problem: find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$q_8times mathbb{z}_n$ where $q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. in this paper weconsider more general grou...

0

the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhoo...

Twisted Alexander invariants have been defined for any knot and linear representation of its group π. The invariants are generalized for any periodic representation of the commutator subgroup π. Properties of the new twisted invariants are given. Under suitable hypotheses, reciprocality and bounds on the moduli of zeros are obtained. A topological interpretation of the Mahler measure of the inv...

The main result of this note, Theorem 2, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant under the action of the infinite unitary group and that admits welldefined projections onto the quotient space of “corners” of finite size, must be finite. A similar result, Theorem 1, is also established for unitarily invariant measures on the space of all i...

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf’s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown’s theorem for locally smooth G-manifolds where G is a finite group.

The H. Ooguri, A. Strominger and C. Vafa conjecture ZBH = |Ztop| is extended for the topological strings on generalized CY manifolds. It is argued that the classical black hole entropy is given by the generalized Hitchin functional, which defines by critical points a generalized complex structure on X. This geometry differs from an ordinary geometry if b1(X) 6= 0. In a critical point the genera...