Results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Λ. It is shown that all curvature invariants containing derivatives of Weyl tensor vanish if a type-III spacetime admits a non-expanding and non-twisting null geodesic congruence. A non-vanishing curvature invariant containing first derivatives of Weyl tensor is found in th...

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the Lq,p-cohomology of these manifolds. Some applications to vanishing and non vanishing results in Lq,pcohomology are given.

In this article we study deformations of a holomorphic foliation with a generic non-rational first integral in the complex plane. We consider two vanishing cycles in a regular fiber of the first integral with a non-zero self intersection and with vanishing paths which intersect each other only at their start points. It is proved that if the deformed holonomies of such vanishing cycles commute t...

We discuss results from lattice calculations for a few observables that are sensitive to different length scales in the high temperature phase of QCD and can give insight into its non-perturbative structure. We compare lattice results with perturbative calculations at high temperature obtained for vanishing and non-vanishing quark chemical potential.

This paper explores the interplay between the Frobenius functor and Serre’s vanishing conjecture over a Noetherian local ring R of prime characteristic p. We show that the Frobenius functor induces a diagonalizable map on certain Q-vector spaces, which are tensor products of Q with quotients of Grothendieck groups. This allows us to decompose an element (representing a bounded complex of finite...

Key properties of multimedia traac are characterized by the great diversity of correlation and burstiness. Construct the multimedia traac by heterogeneous 2-state Markov chains as in 1] 2]. Here we allow each 2-state MC to be deened on diierent transition intervals, representing the diversity of peak access rate from individual sources. Upon time renormalization, the queue is modeled by a multi...

We propose a modification of the partial wave approach to deal with relativistic quantum scattering bosonic and fermionic particles in class models concerning gravitating cosmic string spacetimes. These spacetimes are characterized by Minkowski line element at center vortex, non-vanishing curvature finite distance from but conical structure far core. find correction expansion phase shift. Conse...

In this paper we study the vanishing and non-vanishing of generalized local cohomology and generalized local homology. In particular for a Noetherian local ring (R,m) and two non-zero finitely generated R-modules M and N , it is shown that H m (M,N) 6= 0.

The vanishing and exploding gradient problems are well-studied obstacles that make it difficult for recurrent neural networks to learn long-term time dependencies. We propose a reparameterization of standard recurrent neural networks to update linear transformations in a provably norm-preserving way through Givens rotations. Additionally, we use the absolute value function as an element-wise no...