We completely characterize extreme contractions between two-dimensional strictly convex and smooth real Banach spaces, perhaps for the very first time. In order to obtain desired characterization, we introduce notions of (weakly) compatible point pair (CPP) μ-compatible (μ-CPP) in geometry spaces. As a concrete application our abstract results, describe all rank one L(ℓ42,ℓ42) L(ℓ42,H), where H...

In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are ...

‎this paper presents two main results that the singular values of the hadamard product of normal matrices $a_i$ are weakly log-majorized by the singular values of the hadamard product of $|a_{i}|$ and the singular values of the sum of normal matrices $a_i$ are weakly log-majorized by the singular values of the sum of $|a_{i}|$‎. ‎some applications to these inequalities are also given‎. ‎in addi...

in the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎we also define the concept of weakly related mappings on an ordered space‎. ‎moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

Let (Q.,l,ß) be a probability space, X a Banach space, and L (fi, X) the Banach space of Bochner integrable functions f: Í2 —> X . Let W = {/ € Ll(p, X) : for a.e. w in Í2, ||/(w)|| < 1} . In this paper we characterize the rwc (relatively weakly compact) subsets of L (ß, X). The main results are as follows: Theorem A. A subset H of W is rwc iff given any sequence (/„) in H there exists a sequen...

Denote by nA the sum of n copies of a Boolean algebra A. We prove that, for any countable Boolean algebra A, nA at mA with m > n implies nA a (n + \)A. In [2], W. Hanf constructed a Boolean algebra H isomorphic to the direct product H X H X H but not to H X H. This result of Hanf was strengthened by J. Ketonen in [4]: there exists even a countable Boolean algebra with this property. In [1], P. ...

Sidorenko’s conjecture states that the number of copies a bipartite graph H in G is asymptotically minimised when quasirandom graph. A notorious example where this remains open = K5,5C10. It was even unknown whether possesses strictly stronger, weakly norming property.We take step towards understanding K5,5C10 by proving it not norming. More generally, we show ‘twisted’ blow-ups cycles, which i...

In the present study, commonly used weakly compressible lattice Boltzmann method and Guo incompressible lattice Boltzmann method have been used to simulate fluid flow in a stirred tank. For this purpose a 3D Parallel code has been developed in the framework of the lattice Boltzmann method. This program has been used for simulation of flow at different geometries such as 2D channel fluid flow an...