Black holes on the plane drawn by a Wiener process

Summary We say that the discD(v8jgpl2j2v153u5/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">)v8jgpl2j2v153u5/xxlarge8834.gif" alt="sub" align="MIDDLE" BORDER="0">R ², of radius v8jgpl2j2v153u5/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">, located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzv8jgpl2j2v153u5/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0">D(v8jgpl2j2v153u5/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">) there exists a 0v8jgpl2j2v153u5/xxlarge8806.gif" alt="lE" align="MIDDLE" BORDER="0">tv8jgpl2j2v153u5/xxlarge8806.gif" alt="lE" align="MIDDLE" BORDER="0">T such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those v8jgpl2j2v153u5/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">'s (v8jgpl2j2v153u5/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">v8jgpl2j2v153u5/xxlarge8807.gif" alt="gE" align="MIDDLE" BORDER="0">0) is studied for which,D(v8jgpl2j2v153u5/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">) isp-covered inT.     

Morphology,surface roughness,electron inelastic and quasielastic scattering in elastic peak electron spectroscopy of polymers

In elastic peak electron spectroscopy (EPES), the nearest vicinity of elastic peak in the low kinetic energy region reflects electron inelastic and quasielastic processes. Incident electrons produce surface excitations, inducing surface plasmons, with the corresponding loss peaks separated by 1–20 eV energy from the elastic peak. In this work, X‐ray photoelectron spectroscopy (XPS) and helium pycnometry are applied for determining surface atomic composition and bulk density, whereas atomic force microscopy (AFM) is applied for determining surface morphology and roughness. The component due to electron recoil on hydrogen atoms can be observed in EPES spectra for selected primary electron energies. Simulations of EPES predict a larger contribution of the hydrogen component than observed experimentally, where hydrogen deficiency is observed. Elastic peak intensity is influenced more strongly by surface morphology (roughness and porosity) than by surface excitations and quasielastic scattering of electrons by hydrogen atoms. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of impact-excited HeI states by applying magnetic and electric depolarization techniques

The magnetic depolarization of the impact radiation at λ(4¹ D?2¹ P)=492 nm and λ(3¹ D?2¹ P) = 668 nm as well as the splitting of the magnetic depolarisation signals in electric fields were investigated for 10–25 keV H ₂ ⁺ (D ₂ ⁺ )-He collisions (only 492 nm line) and for 5-22.5 keV He-He collisions (both lines). The results are compared with analogous measurements for He⁺- He and Ne⁺ - He collisions and the dynamics of the excitation process are qualitatively discussed. In particular, we emphasize the importance of inertia for the evolution of the electron cloud during the final phase of the collision process.     

Complexes of Mn(II), Co(II), Ni(II), Cu(II) and Zn(II) with 4-chloro-2-methoxybenzoic acid anion

The complexes of 4-chloro-2-methoxybenzoic acid anion with Mn²⁺, Co²⁺, Ni²⁺, Cu²⁺ and Zn²⁺ were obtained as polycrystalline solids with general formula M(C₈H₆ClO₃)₂·nH₂O and colours typical for M(II) ions (Mn – slightly pink, Co – pink, Ni – slightly green, Cu – turquoise and Zn – white). The results of elemental, thermal and spectral analyses suggest that compounds of Mn(II), Cu(II) and Zn(II) are tetrahydrates whereas those of Co(II) and Ni(II) are pentahydrates. The carboxylate groups in these complexes are monodentate. The hydrates of 4-chloro-2-methoxybenzoates of Mn(II), Co(II), Ni(II), Cu(II) and Zn(II) heated in air to 1273 K are dehydrated in one step in the range of 323–411 K and form anhydrous salts which next in the range of 433–1212 K are decomposed to the following oxides: Mn₃O₄, CoO, NiO and ZnO. The final products of decomposition of Cu(II) complex are CuO and Cu. The solubility value in water at 293 K for all complexes is in the order of 10^–3 mol dm^–3. The plots of χ_M vs. temperature of 4-chloro-2-methoxybenzoates of Mn(II), Co(II), Ni(II) and Cu(II) follow the Curie–Weiss law. The magnetic moment values of Mn²⁺, Co²⁺, Ni²⁺ and Cu²⁺ ions in these complexes were determined in the range of 76−303 K and they change from: 5.88–6.04 μ_B for Mn(C₈H₆ClO₃)₂·4H₂O, 3.96–4.75 μ_B for Co(C₈H₆ClO₃)₂·5H₂O, 2.32–3.02 μ_B for Ni(C₈H₆ClO₃)₂·5H₂O and 1.77–1.94 μ_B for Cu(C₈H₆ClO₃)₂·4H₂O.     

Linear low density polyethylene: Microstructure and sealing properties correlation

The microstructures of four commercial linear low density polyethylenes (LLDPE) were evaluated and correlated with their sealing properties. Atomic Force Microscopy (AFM), Temperature Rising Elution Fractionation (TREF), Differential Scanning Calorimetry (DSC) and Crystallization Analysis Fractionation (CRYSTAF) experiments revealed that the comonomer distribution is one of the main factors that influence the sealing properties. The superior sealing performance showed by metallocene LLDPE samples in comparison to Ziegler-Natta LLDPE samples can be attributed to their well balanced chemical composition distribution.