The title mol-ecule, C(16)H(14)N(2)O(4)S, adopts an L-shaped conformation, with the central C-S-N-C torsion angle being -69.1 (3)°. The two benzene rings form a dihedral angle of 89.94 (15)°. The mol-ecular conformation may be influenced by a weak intra-molecular C-H⋯O hydrogen bond which generates an S(6) ring motif. In the crystal, mol-ecules are linked by N-H⋯O and weak C-H⋯O hydrogen bonds,...

In the title mol-ecule, C23H22N2OS, the di-phenyl-acetyl and ethyl-benzene groups adopt a trans-cis conformation, respectively, with respect to the S atom across the (S=)C-N bonds. This conformation is stabilized by an intra-molecular N-H⋯O hydrogen bond and a weak C-H⋯S hydrogen bond. The ethyl-substituted benzene ring forms dihedral angles of 87.53 (15) and 73.94 (15)° with the phenyl rings. ...

Suppose that S is a space. There is an injective and a projective model structure for the resulting category of spaces with S-action, and both are easily derived. These model structures are special cases of model structures for presheaf-valued diagrams X defined on a fixed presheaf of categories E which is enriched in simplicial sets. Varying the parameter category object E (or parameter space ...

We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three commuting complemented closure operators, i.e., that of diagonal-free 3-dimensional cylindric algebras (Df3’s). Equivalently, set theory can be formulated in pr...

We derive the generating functional of |∆S| = 1, 2 hadronic weak interactions at one loop for a generic number of flavours and its counterpart in the quenched approximation. A systematic analysis of the ultraviolet divergences in the full theory (with and without a singlet dynamical field) and in the quenched case is performed. We show that the quenched chiral logarithms in the presence of weak...

A flow is homotopy continuous if it is indefinitely divisible up to S-homotopy. The full subcategory of cofibrant homotopy continuous flows has nice features. Not only it is big enough to contain all dihomotopy types, but also a morphism between them is a weak dihomotopy equivalence if and only if it is invertible up to dihomotopy. Thus, the category of cofibrant homotopy continuous flows provi...

We show that models for screening of nuclear reactions in the Sun can be tested by means of helioseismology. As well known, solar models using the weak screening factors are in agreement with data. We find that the solar model calculated with the anti screening factors of Tsytovitch is not consistent with helioseismology, both for the sound speed profile and for the depth of the convective enve...

(Generalized) Riemann Hypothesis (that all non-trivial zeros of the (Dirichlet L-function) zeta function have real part one-half) is arguably the most important unsolved problem in contemporary mathematics due to its deep relation to the fundamental building blocks of the integers, the primes. The proof of the Riemann hypothesis will immediately verify a slew of dependent theorems ([BRW], [SA])...