We compare the cohomology ring of flag variety ${\\mathcal{F}\\ell}n$ and Chow Gelfand–Zetlin toric $X{\\operatorname{GZ}}$.We show that $H^(\\mathcal{F}{\\ell}\_n, \\mathbb{Q})$ is Poincaré duality quotient subalgebra $A^(X\_{\\operatorname{GZ}}, generated by degree $1$ elements. compute these algebras for $n=3$ see that, in general, this does not have duality.

In one mode of opera t ion o f an electron ring accelerator (ERA), at the end o f compress ion rings are slowly moved th rough the radia l in tegra l be ta t ron resonance Qr = 1. A l though the coherent radial oscillation frequency of the ring as a whole remains below unity, the oscillation frequencies o f individual electron are ( incoherent ly) caused to pass t h rough the resonance because ...

A ring with identity is said to be clean if every element can be written as a sum of a unit and an idempotent. The study of clean rings has been at the forefront of ring theory over the past decade. The theory of partially-ordered groups has a nice and long history and since there are several ways of relating a ring to a (unital) partially-ordered group it became apparent that there ought to be...

$!!!!$ in this paper, the notion of fuzzy $!$ krasner $!(m, n)$-hyperrings($!f^{(m, n)}!$-hyperrings) by using the notion of$f^m$-hyperoperations and $f^n$-operations is introduced and somerelated properties are investigated. in this regards,relationships between krasner $f^{(m, n)}$-hyperrings and krasner$(m, n)$-hyperrings are considered. we shall prove that everykrasner $f^{(m, n)}$-hyperrin...

The asymmetric unit of the title compound, C(14)H(7)Cl(3)F(2)N(2)O(2), contains two unique molecules. The 2,3,5-trichloro-phenyl ring is almost coplanar with the urea group in both molecules, whereas the 2,6-difluoro-phenyl ring is twisted from the urea plane by 54.83 (10)° in one molecule and 60.58 (10)° in the other. An intra-molecular N-H-O hydrogen bond stabilizes the mol-ecular conformatio...

‎Let $f:Arightarrow B$ and $g:A rightarrow C$ be two ring homomorphisms and let $J$ and $J^{'}$ be two ideals of $B$ and $C$‎, ‎respectively‎, ‎such that $f^{-1}(J)=g^{-1}(J^{'})$‎. ‎The bi-amalgamation of $A$ with $(B,C)$ along $(J,J^{'})$ with respect of $(f,g)$ is the subring of $Btimes C$ given by‎ ‎$Abowtie^{f,g}(J,J^{'})={(f(a)+j,g(a)+j^{'})‎/ ‎a in A‎, ‎(j,j^{'}) in Jtimes J^{'}}.$‎ ‎In ...

In this work we report structural and computational studies of favipiravir, which is now used as a drug for COVID-19 treatment. The molecule completely flat stabilized by an intramolecular O–H···O hydrogen bond, yielding six-membered pseudo-aromatic ring. aromaticity index ring was found to be 0.748, while the same indix pyrazine in favipiravir 0.954. crystal packing mainly constructed through ...

Method of secure evaluation of polynomial y = F(x1, ..., xk) over some rings on untrusted computer is proposed. Two models of untrusted computer are considered: passive and active. In passive model untrusted computer correctly computes polynomial F and tries to know secret input (x1, ..., xk) and output y. In active model untrusted computer tries to know input and output and tries to change cor...

This study focuses on the employment effects of military spending versus alternative domestic spending priorities, in particular investments in clean energy, health care and education. We first present some simple alternative spending scenarios, namely devoting $1 billion to the military versus the same amount of money spent on clean energy, health care, and education, as well as for tax cuts w...