Let $K$ be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber are non-zero. As a consequence, fill gap in paper of first author, and homomorphism $Diff(K)\to \pi_0 Diff(K)$ does not split. One proof uses result Franke on stable cohomology arithmetic groups strengthens work Borel, may independent i...

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

in this paper, we derive the exact analytical expressions for the shannon entropy of generalized orderstatistics from pareto-type and related distributions.

Patras, Reutenauer (J. Algebr. Comb. 16:301–314, 2002) describe a subalgebra A of the Malvenuto-Reutenauer algebra P . Their paper contains several characteristic properties of this subalgebra. In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra. In this paper we establish a slightly generalized v...

A relational structure is homomorphism-homogeneous if any homomorphism between its finite substructures extends to an endomorphism of the structure in question. In this note, we characterise all permutations on a finite set enjoying this property. To accomplish this, we switch from the more traditional view of a permutation as a set endowed with two linear orders to a different representation b...

Twisted Alexander invariant is defined for a finitely presentable group G and a representation of G and a surjective homomorphism of G to a free abelian group. In this talk, we introduce some examples and some properties of the twisted Alexander invariant. Moreover, as an application, we consider a partial order on the set of prime knots. Let K be a knot and G(K) the knot group. For two prime k...

A generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and basis form in terms of Malliavin derivative on a projective Fock scale, and their uniform continuity and QS differentiability with respect to the inductive limit convergence is proved. A new form of QS calculus based on an inductive ⋆–algebraic structure in an indefinite spac...

In the early eighties, A. Huhn proved that if D, E are finite distributive lattices and ψ : D → E is a {0}-preserving join-embedding, then there are finite lattices K, L and there is a lattice homomorphism φ : K → L such that ConK (the congruence lattice of K) is isomorphic to D, ConL (the congruence lattice of L) is isomorphic to E, and the natural induced mapping extφ : ConK → ConL represents...

in this paper, we obtain  bayesian prediction intervals as well as bayes predictive estimatorsunder square error loss for generalized order statistics when the distribution of the underlying population belongs to a family which includes several important distributions.