We define and study the symmetric version of differential torsion theories. We prove that the symmetric versions of some of the existing results on derivations on right modules of quotients hold for derivations on symmetric modules of quotients. In particular, we prove that the symmetric Lambek, Goldie and perfect torsion theories are differential. We also study conditions under which a derivat...

let $m_r$ be a non-zero‎ ‎module and ${mathcal f}‎: ‎sigma[m_r]times sigma[m_r]‎ ‎rightarrow$ mod-$bbb{z}$ a bifunctor‎. ‎the‎ ‎$mathcal{f}$-reversibility of $m$ is defined by ${mathcal‎ ‎f}(x,y)=0 rightarrow {mathcal f}(y,x)=0$ for all non-zero $x,y$‎ ‎in $sigma[m_r]$‎. ‎hom (resp‎. ‎rej)-reversibility of $m$ is‎ ‎characterized in different ways‎. ‎among other things‎, ‎it is shown‎ ‎th...

A new way of constructing (minimal) perfect hash functions is described. The technique considerably reduces the overhead associated with resolving buckets in two-level hashing schemes. Evaluating a hash function requires just one multiplication and a few additions apart from primitive bit operations. The number of accesses to memory is two, one of which is to a fixed location. This improves the...

We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...

In this paper, we give a criterion of the Gorenstein property Ehrhart ring stable set polytope an h-perfect graph: graph $G$ is if and only (1) sizes maximal cliques are constant (say $n$) (2) (a) $n=1$, (b) $n=2$ there no odd cycle without chord length at least 7 or (c) $n\geq 3$ 5.

We introduce graded $${\mathbb {E}}_{\infty }$$ -rings and modules over them, study their properties. construct projective schemes associated to connective {N}}$$ -graded in spectral algebraic geometry. Under some finiteness conditions, we show that the $$\infty $$ -category of almost perfect quasi-coherent sheaves a scheme $$\text { {Proj}}\,(A)$$ -ring A can be described terms $${{\mathbb {Z}...

Scale invariance refers to the maintenance of a constant ratio of developing organ size to body size. Although common, its underlying mechanisms remain poorly understood. Here, we examined scaling in engineered Escherichia coli that can form self-organized core-ring patterns in colonies. We found that the ring width exhibits perfect scale invariance to the colony size. Our analysis revealed a c...

The title compounds, C22H22N4 and C24H26N4O2 [alternative names: 2,6-dibenzyl-2,3,6,7-tetrahydro-1H,5H-dipyrrolo[3,4-b; 3',4'-e]pyrazine and 2,6-bis(4-methoxybenzyl)-2,3,6,7-tetrahydro-1H,5H-dipyrolo[3,4-b;3',4'-e]pyrazine], two 1,2,3,5,6,7-hexahydro-2,4,6,8-tetraaza-s-indacene derivatives, are both centrosymmetric and have similar S-shaped structures. In the former, there are two independent m...

An interacting quantum dot inserted in a mesoscopic ring is investigated. A variational ansatz is employed to describe the ground state of the system in the presence of the Aharonov-Bohm flux. It is shown that, for an even number of electrons with the energy level spacing smaller than the Kondo temperature, the persistent current has a value similar to that of a perfect ring with the same radiu...

Let M be a right module over a ring R. In this manuscript, we shall study on a special case of F-inverse split modules where F is a fully invariant submodule of M introduced in [12]. We say M is Z 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct summand of M for each endomorphism f of M. We prove that M is Z2(M)-inverse split if and only if M is a direct...