This complements the work of [2] on the construction of scales of minimal complexity on sets of reals in K(R). Theorem 0.1 was proved there under the stronger hypothesis that all sets definable over M are determined, although without the capturing hypothesis. (See [2, Theorem 4.14].) Unfortunately, this is more determinacy than would be available as an induction hypothesis in a core model induc...

Starting from a logic which speciies how to make deductions from a set of sentences (a ``at theory'), a way to generalise this to a partially ordered bag of sentences (a `structured theory') is given. The partial order is used to resolve connicts. If occurs below then is accepted only insofar as it does not connict with. We start with a language L, a set of interpretations M and a satisfaction ...

We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator S : X ⇒ X∗ by Sse, the smallest enlargement belonging to a certain class of enlargements associated to S. Moreover, we prove the weak∗ closedness of the set ShS (ε1, x)+ThT (ε2, x) under a weak generalized interior regularity condition.

and Applied Analysis 3 2. Results Solutions to 1.1 subject to conditions 1.2 are meant in the following weak sense. Definition 2.1. A function u ∈ Lmloc Q ∩ L p loc Q is called a weak solution to 1.1 if ∫ Q |u|φ dP ∫ S u 0, t2;x φ 0, t2;x dP2 ∫ S u t1, 0;x φ t1, 0;x dP1 − ∫

In the title compound, C(18)H(17)FO(2)S, the 3-fluoro-phenyl ring makes a dihedral angle of 78.60 (5)° with the mean plane of the benzofuran fragment. In the crystal, mol-ecules are linked by weak inter-molecular C-H⋯O hydrogen bonds and weak inter-molecular C-S⋯π [3.490 (2) Å] inter-actions.

In the title mol-ecule, C(19)H(22)N(4)O(2)S, the two benzene rings form a dihedral angle of 9.16 (13)°. In the crystal, pairs of weak inter-molecular C-H⋯S hydrogen bonds link the mol-ecules into centrosymmetric dimers, which are further linked through weak C-H⋯O inter-actions into sheets parallel to (012).

An improved stabilized multilevel Monte Carlo (MLMC) method is introduced for stiff stochastic differential equations in the mean square sense. Using S-ROCK2 with weak order 2 on the finest time grid and S-ROCK1 (weak order 1) on the other levels reduces the bias while preserving all the stability features of the stabilized MLMC approach. Numerical experiments illustrate the theoretical findings.

here‎, ‎we aim to develop a new algorithm for solving a multiobjective linear programming problem‎. ‎the algorithm is to obtain a solution which approximately meets the decision maker's preferences‎. ‎it is proved that the proposed algorithm always converges to a weak efficient solution and at times converges to an efficient solution‎. ‎numerical examples and a simulation study are used to...

in this paper we define weak $f$-contractions on a‎ ‎metric space into itself by extending $f$-contractions‎ ‎introduced by d‎. ‎wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎some relationships between weak‎ ‎$f$-contractions and $fi$-contractions are highlighted‎. ‎we also ‎give some application...

We show that the class of weak equivalences of a combinatorial model category can be detected by an accessible functor into simplicial sets. The purpose of this short note is to prove the following result that was conjectured by J.H. Smith in [[2],p. 460]. 0.1. Theorem. For every combinatorial model categoryM, there is an accessible functor F :M→ SSet that detects the weak equivalences, i.e., a...