We completely determine those natural numbers $n$ for which the full matrix ring $M_n(F_2)$ and triangular $T_n(F_2)$ over two elements field $F_2$ are either n-torsion clean or almost clean, respectively. These results somewhat address settle a question, recently posed by Danchev-Matczuk in Contemp. Math. (2019) as well they supply more precise aspect nil-cleanness property of $n\times n$ all ...

Let R be a commutative ring with multiplicative identity and C coassociative counital R-coalgebra the α-condition. A clean comodules defined based on cleanness rings modules. C-comodule M is comodule if endomorphism of clean. over itself i.e., as For an idempotent e ∈ R, there are relations between eRe R. It’s motivated us to investigate this condition for coalgebra. any C, we can construct ⇀C↼...

The lowest eigenenergies of few, strongly interacting electrons in a one–dimensional ring are studied in presence of an impurity barrier. The persistent current I , periodic in an Aharonov–Bohm flux penetrating the ring, is strongly influenced by the electron spin. The impurity does not remove discontinuities in I at zero temperature. The total electron spin of the ground state oscillates with ...

Air exhibiting very low concentrations of light-scattering aerosol particles is occasionally observed even in industrialized regions. Evidence is presented that this very clean air results from highly efficient removal of aerosol particles coupled to the removal of water in precipitation.

We analyze the crossover from an hc /e periodicity of the persistent current in flux-threaded clean metallic rings toward an hc /2e-flux periodicity of the supercurrent upon entering the superconducting state. On the basis of a model calculation for a one-dimensional ring we identify the underlying mechanism, which balances the hc /e versus the hc /2e periodic components of the current density....

The Cox construction presents a toric variety as quotient of affine space by torus. category coherent sheaves on the corresponding stack thus has an evident description invariants in modules over polynomial ring. Here we give mirror to this description, and particular, clean new proof symmetry for smooth stacks.

the present paper deals with the results of the foresight analysis concerning the development of energy technologies in upper silesia. twelve experts representing science, industry and independent authoritieswere involved in these investigations. upper silesia is a specific region in poland, characterized by coal energy technologies. as 9 result of steep and swot analyses several scenarios of e...

Racket’s syntax parameters support the hygienic implementation of syntactic forms that would otherwise introduce implicit identifiers unhygienically.

We show that an ambiguity in setting the primitives of the matching with contracts model by Hatfield and Milgrom (2005) has serious implications for the model. Of the two ways to clear the ambiguity, the first (and what we consider more “clean”) remedy renders several of the results of the paper invalid in the absence of an additional irrelevance of removed contracts condition implicitly assume...