The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

The asymmetric unit of the title compound, C(19)H(21)NOS, contains two mol-ecules, which form dimers via pairs of weak C-H⋯O hydrogen bonds.

In this article we will present some problems that have weak symmetries. In contrast to a proper symmetry, a weak symmetry acts only on a subset of the variables and preserves the feasibility state only with respect to a subset of the constraints. Therefore, breaking weak symmetries with standard techniques would lead to a loss of solutions. This article presents also a modelling technique whic...

In this paper, we classify all generalized quadrangles weakly embedded of degree 2 in projective space. More exactly, given a (possibly infinite) generalized quadrangle Γ = (P,L, I ) and a map π from P (respectively L) to the set of points (respectively lines) of a projective space PG(V ), V a vector space over some skew field (not necessarily finite-dimensional), such that: (i) π is injective ...

The asymmetric unit of the title compound, C(18)H(29)NO(3), contains two independent mol-ecules. The benzene ring and the mean plane of the alkyl unit form dihedral angles of 83.69 (12) and 77.14 (11)° in the two mol-ecules. In the crystal structure, weak C-H⋯O hydrogen bonds link mol-ecules into double-layer ribbons extending in [110].

The title compound, C(39)H(33)N(9)S(3), features a mesitylene unit substituted with three thio-ether arms. The distances from the center of mesitylene unit to the N atoms of the three pyridine rings in the arms are 10.05 (1), 9.94 (3) and 8.79 (3) Å. The crystal structure shows weak intra-molecular C-H⋯N hydrogen bonds.

We discuss the axioms for vertex algebras and their modules, using formal calculus. Following certain standard treatments, we take the Jacobi identity as our main axiom and we recall weak commutativity and weak associativity. We derive a third, companion property that we call “weak skew-associativity.” This third property in some sense completes an S3-symmetry of the axioms, which is related to...

Solving well-structured problems often requires using considerable related concepts which are usually scattered and introduced throughout different learning units of a subject. In addition, poor learning of related concepts of preceding units may block the learning of subsequent units, and eventually leads to the inability to solve wellstructured problems of a subject. Thus, this work proposes ...

We extend the Larson–Sweedler theorem [10] to weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We show that the category of modules over a weak Hopf algebra is autonomous monoidal with semisimple unit and invertible modules. We also reveal the connection of invertible modules to left and right grouplik...