Hyperspaces of Normed Linear Spaces with the Attouch–Wets Topology

Let Cld _AW (X) be the hyperspace of nonempty closed subsets of a normed linear space X with the Attouch–Wets topology. It is shown that the space Cld _AW (X) and its various subspaces are AR's. Moreover, if X is an infinite-dimensional Banach space with weight w(X) then Cld _AW (X) is homeomorphic to a Hilbert space with weight 2 ^w(X).     

Origin of visible-light-driven photocatalysis: A comparative study on N/F-doped and N-F-codoped TiO2 powders by means of experimental characterizations and theoretical calculations

An overall comparative study was carried out on N-doped, F-doped, and N-F-codoped TiO₂ powders (NTO, FTO, NFTO) synthesized by spray pyrolysis in order to elucidate the origin of their visible-light-driven photocatalysis. The comparisons in their experimentally obtained characteristics were based on the analysis of XPS, UV-Vis, PL, NH₃-TPD and ESR spectra. The comparisons in their theoretically predicted properties were based on the analysis of the calculated electronic structures. As the results, N-doping into TiO₂ resulted in not only the improvement in visible-light absorption but also the creation of surface oxygen vacancies. F-doping produced several beneficial effects including the creation of surface oxygen vacancies, the enhancement of surface acidity and the increase of Ti³⁺ ions. Doped N atoms formed a localized energy state above the valence band of TiO₂, whereas doped F atoms themselves had no influence on the band structure. The photocatalytic tests indicated that the NFTO demonstrated the highest visible-light activity for decompositions of both acetaldehyde and trichloroethylene. This high activity was ascribed to a synergetic consequence of several beneficial effects induced by the N-F-codoping.     

FORMATION OF SINGLE AND DOUBLE STRAND BREAKS IN DNA ULTRAVIOLET IRRADIATED AT HIGH INTENSITY

The induction of single-strand breaks (SSB) by two quantum processes in DNA is well established. We now report that biphotonic processes result in double-strand breaks (DSB) as well. pUC19 and bacteriophage M13 RF DNA were irradiated using an excimer laser (248 nm) at intensities of 10(7), 10(9), 10(10) and 10(11) W/m2 and doses up to 30 kJ/m2. The proportion of DNA as supercoil, open circular, linear and short fragments was determined by gel electrophoresis. Linear molecules were noted at fluences where supercoiled DNA was still present. The random occurrence of independent SSB in proximity to each other on opposite strands (producing linear DNA) implies introduction of numerous SSB per molecule in the sample. If so, supercoiled DNA that has sustained no SSB should not be observed. A model accounting for the amounts of supercoiled, open circular, linear and shorter fragments of DNA due to SSB, DSB and Scissions (opposition of two independently occurring SSB producing an apparent DSB) was developed, our experimental data and those of others were fit to the model, and quantum yields determined for SSB and DSB formation at each intensity. Results showed that high intensity laser radiation caused an increase in the quantum yields for both SSB and DSB formation. The mechanism of DSB formation is unknown, and may be due to simultaneous cleavage of both strands in one biphotonic event or the biased introduction of an SSB opposite a preexisting SSB, requiring two biphotonic events.     

Jordan-Wigner Approach to Dynamic Correlations in 2D Spin-1/2 Models

We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevance of the fermionic picture for interpreting the neutron scattering measurements in the two-dimensional frustrated quantum magnet Cs₂CuCl₄.     

Instability of the finite‐difference split‐step method applied to the nonlinear Schrödinger equation. I. standing soliton

We consider numerical instability that can be observed in simulations of solitons of the nonlinear Schrödinger equation (NLS) by a split‐step method (SSM) where the linear part of the evolution is solved by a finite‐difference discretization. The von Neumann analysis predicts that this method is unconditionally stable on the background of a constant‐amplitude plane wave. However, simulations show that the method can become unstable on the background of a soliton. We present an analysis explaining this instability. Both this analysis and the features and threshold of the instability are substantially different from those of the Fourier SSM, which computes the linear part of the NLS by a spectral discretization. For example, the modes responsible for the numerical instability are not similar to plane waves, as for the Fourier SSM or, more generally, in the von Neumann analysis. Instead, they are localized at the sides of the soliton. This also makes them different from “physical” (as opposed to numerical) unstable modes of nonlinear waves, which (the modes) are localized around the “core” of a solitary wave. Moreover, the instability threshold for thefinite‐difference split‐step method is considerably relaxed compared with that for the Fourier split‐step. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1002–1023, 2016     

Division and <Emphasis Type="Italic">k</Emphasis>-th root theorems for <Emphasis Type="Italic">Q</Emphasis>-manifolds

We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z _∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f: K → X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X ² and X × [0, 1] are Q-manifolds as well. We construct a countable family χ of spaces with DDP and cd-AP such that no space X ∈ χ is homeomorphic to the Hilbert cube Q whereas the product X × Y of any different spaces X, Y ∈ χ is homeomorphic to Q. We also show that no uncountable family χ with such properties exists. This work was supported by the Slovenian-Ukrainian (Grant No. SLO-UKR 04-06/07)     

Large free sets in powers of universal algebras

We prove that for each universal algebra ${(A, \mathcal{A})}$ of cardinality ${|A| \geq 2}$ and infinite set X of cardinality ${|X| \geq | \mathcal{A}|}$ , the X-th power ${(A^{X}, \mathcal{A}^{X})}$ of the algebra ${(A, \mathcal{A})}$ contains a free subset ${\mathcal{F} \subset A^{X}}$ of cardinality ${|\mathcal{F}| = 2^{|X|}}$ . This generalizes the classical Fichtenholtz–Kantorovitch–Hausdorff result on the existence of an independent family ${\mathcal{I} \subset \mathcal{P}(X)}$ of cardinality ${|\mathcal{I}| = |\mathcal{P}(X)|}$ in the Boolean algebra ${\mathcal{P}(X)}$ of subsets of an infinite set X.     

Band mixing in 49Cr and 47V: Importance of a correct treatment of hole excitations and the J2 term

Band mixing calculations treating correctly the $\text{j}{}^2$ term and hole excitations have been undertaken on the cross-conjugate pair ⁴⁷V, ⁴⁹Cr. It is found that such a treatment gives rise to appreciable differences from the usual band mixing calculations of nuclei in the lf-2p shell. The results are in good agreement with the experimental level schemes.     

On the Continuity of Inversion in Countably Compact Inverse Topological Semigroups

Let S be a countably compact Hausdorff space endowed with a continuous semigroup operation turning S into an inverse semigroup. It is shown that the inversion inv : x x^-1 in S is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, (3) the semigroup S is Clifford, topologically periodic and the square S × S is regular and countably compact. These results are close to the best possible since there is an example of a quasi-regular sequentially compact commutative inverse topological semigroup with discontinuous inversion.     

Effect of Two Different UVA Doses on the Rabbit Cornea and Lens

The aim of the present paper was to examine the irradiation effect of two doses of UVA rays (365 nm) on the rabbit cornea and lens. Corneas of anesthetized adult albino rabbits were irradiated with UVA rays for 5 days (daily dose 1.01 J cm⁻² in one group of rabbits and daily dose 2.02 J cm⁻² in the second group of animals). The third day after the last irradiation, the rabbits were killed, and their eyes were employed for spectrophotometrical, biochemical and immunohistochemical investigations. Normal eyes served as controls. Absorption spectra of the whole corneal centers were recorded over the UV–VIS (visible) spectral range. Levels of antioxidant and prooxidant enzymes, nitric oxide synthases and nitric oxide (indirectly measured as nitrate concentration) were investigated in the cornea. Malondialdehyde, a byproduct of lipid peroxidation, was examined in the cornea and lens. The results show that the staining for endothelial nitric oxide synthase was more pronounced in corneas irradiated with the higher UVA dose. Otherwise, UVA rays at either dose did not significantly change corneal light absorption properties and did not cause statistically significant metabolic changes in the cornea or lens. In conclusion, UVA rays at the employed doses did not evoke harmful effects in the cornea or lens.