Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) S(\rho_C)\geq 0$ for any tripartite $\rho_{ABC}$, fact is equivalent to strong subadditivity entropy. We prove an operator inequality, which, upon taking expectation value with respect state reduces weak inequality. Generalizations this inequality one invo...

For small involutive and integral quantaloids Q it is shown that covariant presheaves on symmetric Q-categories are equivalent to certain subalgebras of a speci c monad on the category of symmetric Q-categories. This construction is related to a weakening of the subobject classi er axiom which does not require the classi cation of all subalgebras, but only guarantees that classi able subalgebra...

In a graph G = (V,E) a vertex is said to dominate itself and all its neighbours. A weak dominating set is a set S ⊆ V where for every vertex u not in S there is a vertex v of S adjacent to u with dG(v) 6 dG(u) . A restrained dominating set is a set S ⊆ V where every vertex in V − S is adjacent to a vertex in S as well as another vertex in V − S . The weak domination number γw(G) (resp. restrain...

one of the thinkers¨ demands for governments is to take due care of the social rights of citizens thus far. no doubt, imam `ali (a.s.), as a muslim ruler, concentrated on maintaining man¨s rights both in theory and in practice. this article refers to the relationship between the right and the duty from imam ali¨s viewpoint, studies the foundations of man¨s rights and duties and discusses imam a...

A study has been made of the transmural fluxes of benzoic, phenylacetic, and pentanoic acids, benzylamine, hexylamine, and D-amphetamine across rat jejunum incubated in vitro. The M to S fluxes of the weak acids were greater than their corresponding S to M fluxes, and the S to M fluxes of the weak bases were larger than their M to S fluxes. These patterns of asymmetric movements were observed w...

In the title mol-ecule, C(10)H(16)O(3)S(4), a short intra-molecular S⋯O(=C) distance [2.726 (2) Å] indicates the presence of a nonbonding attractive inter-action. In the crystal, mol-ecules are linked into centrosymmetric dimers via weak inter-molecular C-H⋯O and S⋯S [3.405 (3) Å] inter-actions. These dimers are linked by further weak C-H⋯O inter-actions into columns along the a axis.

The title mol-ecule, C(13)H(17)ClN(2)O(3)S, shows an anti and syn disposition of the butanoyl and 2,5-dimethoxyphenyl groups with respect to the thione and is stabilized by intra-molecular N-H⋯O and weak C-H⋯S hydrogen bonds. In the crystal, inter-molecular N-H⋯S hydrogen bonds link the mol-ecules into centrosymmetric dimers. The crystal structure is stabilized by weak C-H⋯O and C-H⋯S contacts.

It is shown that S-N-S weak links with an heavy-fermion metal as the weak link (N) can be useful thermosensors. This property is due to the large thermopower of heavy-fermion metals which is of the order 10−6 V/K. The longitudinal sound can also generate voltage oscillation due to the large Grüneisen parameter, Ωhf ∼ 10 2, in heavy-fermions. Similar effects are expected with other Kondo systems...