In this paper, we study Cotton solitons on certain three-dimensional almost contact metric manifolds. We are particularly interested in the potential vector field which is collinear with one of the elements of the fundamental basis. Finally, we give an open question.
In continuation of the study of semi-Menger and nearly Menger properties in a topological space, we discuss some characterizations of semi-Menger and nearly Menger spaces, and derive the relation of these spaces to other well-known spaces. Further, we prove that a weakly Hausdorff semi-Menger $P$-space is extremally disconnected.
In this paper, we first study the relationships among the classes of cosilting modules, finitely cosilting modules, and finitely cotilting modules. We also investigate the relationship between the classes of finitely cosilting bimodules and cotilting triples. Finally, assume that $_ST_R$ is a finitely cosilting $S-R$-bimodule. We give the upper bounds for the homological dimensions of the rings $R$ and $S$. In particular, whenever $R$ is a right Noetherian ring and $S$ is a left Noetherian ring, $(S, T,R)$ forms a cotilting triple and if the global dimension of $R$ or $S$ is finite, then $|\mathsf{gl.dim}(R) - \mathsf{gl.dim}(S)| \leq 1$.
We confirm the validity of a conjecture of Besse in the class of compact, regular, locally homogeneous contact metric manifolds, and show that such a manifold $M$ must be isometric to the standard sphere $\mathbb S^{2n+1}$, provided that the scalar curvature equals $2n(2n+1)$, where $\mathrm{dim}(M)=2n+1$, and the Riemannian metric associated with the contact form satisfies the critical point equation for the total scalar curvature functional.
Let p be a positive real number. We determine the best constants of two types of discrete lp Sobolev inequalities on a complete graph KN. The discrete lp Sobolev inequality shows that the maximum ofju & eth;i & THORN;jp is estimated from above by constant multiples of the potential energy for vector u 1/4 t & eth;u & eth;0 & THORN;, ... , u & eth;N - 1 & THORN;& THORN; A CN. The potential energy is the lp norm of u with damping coefficient a. In addition, we also have the best constant of the discrete lp Sobolev inequality in the case of a 1/4 0.
