‎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...

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

We present a finite temperature calculation of the transverse spin-diffusion coefficient, D⊥, in a dilute degenerate Fermi gas in the presence of a small external magnetic field, H. While the longitudinal diffusion coefficient displays the conventional low-temperature Fermi-liquid behavior, D‖ ∝ T−2, the corresponding results for D⊥ show three separate regimes: (a) D⊥ ∼ H−2 for T ≪ H; (b) D⊥ ∼ ...

Let H be a bipartite graph and let Gn be the Mycielski graph with χ(G) = n, n ≥ 4. Then the chromatic number of the strong product of Gn by H is at most 2n− 2. We use this result to show that there exist strong products of graphs in which a projection of a retract onto a factor is not a retract of the factor. We also show that in the Cartesian product of graphs G and H, any triangles of G trans...

Pd−Au bimetallic catalysts have shown promising performance in numerous reactions that involve hydrogen. Fundamental studies of hydrogen interactions with Pd−Au surfaces could provide useful insights into the reaction mechanisms over Pd−Au catalysts, which may, in turn, guide future catalyst design. In this study, the interactions of hydrogen (i.e., adsorption, absorption, diffusion, and desorp...

In this paper, we introduce two concepts of weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in Banach spaces. Then we obtain some results of the solutions existence for a system of vector variational-like inequalities with weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in reflexive...

A one-sided ideal of a ring has the insertion of factors property (or simply, IFP) if implies r for . We say a one-sided ideal of has the weakly IFP if for each , implies , for some non-negative integer . We give some examples of ideals which have the weakly IFP but have not the IFP. Connections between ideals of which have the IFP and related ideals of some ring extensions a...

Let M be an arbitrary structure. We say that an M -formula φ(x) defines a stable set in M if every formula φ(x)∧α(x, y) is stable. We prove: If G is an M -definable group and every definable stable subset of G has U-rank at most n (the same n for all sets) then G has a maximal connected stable normal subgroup H such that G/H is purely unstable. The assumptions holds for example when the structu...

Two Ag(I) ions, deprotonated 1-methyl-thymine (1MT-H)(-) and 1,3-dideaza-adenine (DDA), self-assemble in methanolic solution to a cationic [(Ag)2(1MT-H)(DDA)](+) complex as identified by electrospray ionization mass spectrometry. Assignment of vibrational bands and identification of the silver coordination pattern arise from comparison of one- and two-color Infrared Multiple Photon Dissociation...