Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...

In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset subject to forbidden r+ s configurations, where r+s = 4. Generalizing previous work on weak discrepancy in [5, 12, 13], the notion of fractional weak discrepancy wdF (P ) of a poset P = (V,≺) was introduced in [7] as the minimum nonnegative k for which there exists a function f : V → R ...

The weak order on the symmetric group naturally extends to a lattice on all integer binary relations. We first show that the subposet of this weak order induced by integer posets defines as well a lattice. We then study the subposets of this weak order induced by specific families of integer posets corresponding to the elements, the intervals, and the faces of the permutahedron, the associahedr...

and Applied Analysis 3 x0, y0 ∈ L StrD F, S resp., x0, y0 ∈ LW MinD F, S , if there exists a neighborhood U of x0 in X such that y0 ∈ StrD F U ∩ S ( resp., y0 ∈ W minD F U ∩ S ) , that is, ∀x ∈ S∩U, F x − y0 ∩ −D\{0} ∅ resp. ∀x ∈ S∩U, F x − y0 ∩ − intD ∅. 2.4 We will say that x0, y0 is a global strict global weak minimizers when U X. The set of all global strict minimizers resp., weak minimizer...

In the title triazole compound, C(10)H(12)N(4)OS, the triazole ring is essentially planar [maximum deviation = 0.009 (1) Å] and forms a dihedral angle of 5.78 (4)° with the benzene ring. In the crystal structure, mol-ecules are linked into dimers by centrosymmetric N-H⋯S inter-actions. These dimers are linked into two-mol-ecule-wide tapes by N-H⋯N and S⋯S [3.2634 (3) Å] inter-actions. In additi...

A hard-core disordered boson system is mapped onto a quantum spin 1/2 XYmodel with transverse random fields. It is then generalized to a system of spins with an arbitrary magnitude S and studied through a 1/S expansion. The first order 1/S expansion corresponds to a spin-wave theory. The effect of weak disorder is studied perturbatively within such a first order 1/S scheme. We compute the reduc...

In the title compound, C(15)H(12)N(4)OS, the dihedral angle between the nine-membered indolin-2-one ring system and the phenyl ring is 2.72 (7)°. Intra-molecular cyclic N-H⋯O and C-H⋯S hydrogen-bonding inter-actions [graph set S(6)] are present, as are weak N-H⋯N inter-actions [graph set S(5)]. In the crystal, mol-ecules form centrosymmetric cyclic dimers through pairs of N-H⋯O hydrogen bonds [...

One of the r e c u r r e n t d r e a m s in e l e m e n t a r y p a r t i c l e s phys ics i s that of a poss ib le fundamenta l synthes is between e l e c t r o m a g n e t i s m and weak in te rac t ions [1]. The idea has i t s or ig in in the fol lowing shared c h a r a c t e r i s t i c s : 1) Both f o r c e s affect equal ly a l l f o r m s of m a t t e r leptons as wel l as hadrons. 2) Bo...

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties. 1. Introduction. Let S be a semitopological semigroup, let ᐄ be...