In this note, we show that cite[Corollary 3.2]{sad} is not always true. In fact, we characterize essential left $phi$-contractibility of the group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group $G$, $L^{2}(G)$ is always essentially left $phi$-contractible. We discuss the essential left $phi$-contractibility of some Fou...

Let X be a completely regular topological space, B(X) the Banach space of real-valued bounded continuous functions on X, with the usual norm ||&|| =supa?£x|&(#)| • A subset GCB(X) is called completely regular (c.r.) over X if given any closed subset KQ.X and point XoÇzX — K, there exists a ô £ G such that &(#o) = |NI a n ( i sup^^is: \b(x)\ <||&||. A topological space X is completely regular in...

We present a new criterion for the complex hyperbolicity of non-compact quotient X bounded symmetric domain. For each $$p \ge 1$$ , this gives precise condition under which subvarieties $$V \subset X$$ with $$\dim V p$$ are general type, and is p-measure hyperbolic. Then, we give several applications related to ball quotients, or Siegel moduli space principally polarized abelian varieties. In c...

We provide an abstract framework for a Logvinenko-Sereda type theorem, where the classical compactness assumption on support of Fourier transform is replaced by that functions under consideration belong to spectral subspace associated with finite energy interval some lower semibounded self-adjoint operator Euclidean $L^2$-space. Our result then provides bound $L^2$-norm such in terms their thic...

We prove that the topological statement: “Any compact covering mapping between two Borel sets is inductively perfect” is equivalent to the set-theoretical statement: “ ∀α ∈ ωω , א 1 < א1”. The starting point of this work is the following topological problem: Problem. Is any compact covering mapping between two Borel spaces inductively perfect? We recall that if f : X → Y is a continuous and ont...

A kind of Sr(2+) selective resin was applied as an absorption phase to extract Sr(2+) ion from an aqueous solution, and the amount of Sr(2+) was determined using inductively coupled plasma optical emission spectrometer. Factors, including absorption time, temperature, stirring rate, salt-out effect, desorption, and the pH of the aqueous solution, were investigated to optimize the absorption eff...

An efficient method was developed to encapsulate water insoluble organic particles of Sudan red III (SR) in aqueous suspensions by using a polymerizable cationic gemini surfactant, 1,3-bis(N,N-dimethyl-N-cetylammonium)-2-(propylacrylate dibromide) (AGC16). The AGC16 coated SR microcapsules (AGC16@SR) were prepared by absorption of AGC16 on the surface of SR, followed by in situ homopolymerizati...

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

Synchrotron radiation (SR) X-ray microbeam analyses revealed the detailed chemical nature of radioactive aerosol microparticles emitted during the Fukushima Daiichi Nuclear Power Plant (FDNPP) accident, resulting in better understanding of what occurred in the plant during the early stages of the accident. Three spherical microparticles (∼2 μm, diameter) containing radioactive Cs were found in ...

We present the experimental setup and first results of PTB’s transportable Sr clock. It consists of a physics package, several compact laser breadboards, and a transportable high finesse cavity for the clock laser. A comparison of the transportable system with our stationary optical lattice clock yields an instability of 2.2 × 10−15 √ s/τ for the transportable clock. The current fractional unce...