The Kerr black holes possess a photon region with prograde and retrograde orbits radii, respectively, $M\leq r_p^-\leq 3M$ $3M\leq r_p^+\leq 4M$, thereby always cast closed ring or shadow silhouette for $a\leq M$. For $a>M$, it is no-horizon spacetime (naked singularity) wherein spiral into the central singularity, produce an arc-like dark spot at center. We compare holes' structure those produ...

In the discussion of A-solvable groups, the question arises if a torsion-free abelian group A of finite rank is flat as a module over its endomorphism ring if every A-generated subgroup of a torsion-free A-solvable group is A-solvable. This paper gives a negative answer by constructing a torsion-free group of rank 3 for which all A-generated torsion-free groups are A-solvable, although A is not...

A rectangular-waveguide output UTC-PD module integrating a HEMT power amplifier has been developed for operation in the 125-GHz band. The fabricated module exhibits maximum output power of more than 14 dBm with nearly flat frequency dependence in the 115-135GHz range. A 10-Gbit/s error-free wireless transmission at 125GHz with a minimum sensitivity of −34 dBm for a bit-error-rate of 10−12 is al...

In this paper we study some properties of GC -projective, injective and flat modules, where C is a semidualizing module and we discuss some connections between GC -projective, injective and flat modules , and we consider these properties under change of rings such that completions of rings, Morita equivalences and the localizations.

This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437–445 and J. Algebra Appl., 8 (2009), 219–227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n, m)-strongly Gorenstein projective ((n, m)-SG-projective for short) for integers n ≥ 1 and m ≥ 0. We are mainly interested in studyi...

Let k be a commutative ring, H a faithfully flat Hopf algebra with bijective antipode, A a k-flat right H-comodule algebra. We investigate when a relative Hopf module is projective over the subring of coinvariants B = A , and we study the semisimplicity of the category of relative Hopf modules.

Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.

comIn the present study, CO2 removal from natural gas stream has been studied using a flat sheet membrane contactor. A three dimensional mathematical model is developed to describe the process. The model considers the transport of a gas mixture containing carbon dioxide and methane through a flat sheet membrane contactor module. The model is based on the non-wetted mode of operation, in which t...

Suppose R and S are local rings and (R,m) → (S,n) is a flat local homomorphism. Given a finitely generated S-module N , we say N is extended (from R) provided there is an R-module M such that S ⊗R M is isomorphic to N as an S-module. If such a module M exists, it is unique up to isomorphism (cf. [EGA, (2.5.8)], and it is necessarily finitely generated. The m-adic completion R → R̂ and the Hensel...