Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

Tour into the picture (TIP) proposed by Horry et al.[1] is a method for generating a sequence of walk-through images from a single reference picture (or image). By navigating a 3D scene model constructed from the picture, TIP produced convincing 3D effects. Assuming that the picture has one vanishing point, they proposed the scene modeling scheme called spidery mesh. However, this scheme has to...

Multipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing quadrupole moment, say, without specifying which coordinate system is used. (Except if this moment is the lowest non-vanishing one.) This result is demonstra...

Using first principles calculations we investigate the structural and electronic properties of interfaces between fluorographane and MoS2. Unsymmetrical functionalization of graphene with H and F results in an intrinsic dipole moment perpendicular to the plane of the buckled graphene skeleton. Depending on the orientation of this dipole moment, the electronic properties of a physically absorbed...

We introduce a new formalism to describe the polarization signal of galaxy clusters on the whole sky. We show that a sparsely sampled, half-sky map of the cluster polarization at z approximately 1 would allow us to better characterize the very large scale density fluctuations. While the horizon length is smaller in the past, two other competing effects significantly remove the contribution of t...

We study the 2k-th moment of central values family primitive cubic and quartic Dirichlet L-functions. establish sharp lower bounds for all real k≥1/2 unconditionally case under Lindelöf hypothesis case. also 0≤k<1/2 upper k≥0 both cases generalized Riemann (GRH). As an application our results, we quantitative non-vanishing results corresponding L-values.

In this article we introduce a family of valuative invariants defined in terms the p-th moment expected vanishing order. These lie between $$\alpha $$ and $$\delta -invariants. They vary continuously big cone semi-continuously families. Most importantly, they give sufficient conditions for K-stability Fano varieties, which generalizes -criterions literature. are also related to $$d_p$$ -geometr...

This paper conducts a research on the wavelet construction and application of image edge detection. Taking detection algorithm based modulus maxima as subject, this discusses problem dislocation phenomenon, threshold selection, multi-scale fusion evaluation criterion in algorithm, proposes an improved self-adaptive hierarchical information amount vanishing moment. From angle symmetry, filter co...

In this paper, we study a class of Finsler metrics with orthogonal invariance. We find an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence, we show that all orthogonally invariant Finsler metrics of almost vanishing H-curvature are of almost vanishing Ξ-curvature and corresponding one forms are exact, generalizing a result previously only known...