On boundedness of square means for the logarithms of Blaschke products

We establish conditions for boundedness of square means of the logarithms of Blaschke products. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 255–259, February, 1999.     

The structural features of Cu1−xPbx liquid alloys

Structure of Cu_1−xPb_x (x=0, 0.025, 0.05, 0.075, 0.1, 0.125) molten alloys has been studied by means of X-ray diffraction method. Structural parameters obtained from structure factors (SF) and radial distribution functions were analyzed. Partial structure factors were calculated by using Reverse Monte-Carlo method. It is shown that tendency to preferred interaction of atoms of the same kind grows with increasing of lead content.     

Transition Metal Centered Trigonal Prisms as Building Units in Various Rare Earth–Transition Metal-Indides

Summary. The rare earth–transition metal-indides GdPdIn, ErPdIn, YbPdIn, YPtIn, TmPtIn, Dy₄Pd₁₀In₂₁, PrPt₂In₂, and Tb₂Pt₇In₁₆ were prepared by arc-melting of the elements or by induction melting of the elements in sealed tantalum tubes in a water-cooled sample chamber of a high-frequency furnace. Single crystals of Dy₄Pd₁₀In₂₁ and Tb₂Pt₇In₁₆ were grown through special annealing procedures. The indides were investigated via X-ray powder diffraction and all structures were refined from X-ray single crystal diffractometer data: ZrNiAl type, , a = 767.8(3), c = 390.7(2) pm, wR2 = 0.0722, 356 F² values for GdPdIn; a = 766.7(3), c = 376.7(1) pm, wR2 = 0.0433, 348 F² values for ErPdIn; a = 757.2(2), c = 393.59(8) pm, wR2 = 0.0388, 434 F² values for YbPdIn; a = 758.2(2), c = 384.95(8) pm, wR2 = 0.0643, 353 F² values for YPtIn; and a = 753.4(1), c = 376.71(4) pm, wR2 = 0.0844, 310 F² values for TmPtIn, with 14 variable parameters per refinement. Dy₄Pd₁₀In₂₁ crystallizes with the monoclinic Ho₄Ni₁₀Ga₂₁ structure: C2/m, a = 2284.5(8), b = 441.0(2), c = 1931.4(7) pm, β = 132.74(2)°, wR2 = 0.0419, 1690 F² values, 112 variable parameters. PrPt₂In₂ adopts the CePt₂In₂ type: P2₁/m, a = 1013.2(3), b = 447.2(3), c = 1019.5(3) pm, β = 116.69(2)°, wR2 = 0.0607, 1259 F² values, 63 variable parameters. Tb₂Pt₇In₁₆ is the second representative of the orthorhombic Dy₂Pt₇In₁₆ type: Cmmm, a = 1211.6(2), b = 1997.1(4), c = 440.52(9) pm, wR2 = 0.0787, 1341 F² values, 45 variable parameters. The common structural motif of the four different structure types are transition metal centered trigonal prisms formed by the rare earth metal and indium atoms. These prisms are condensed via common corners or via In–In bonds. The crystal chemistry of the four different structure types is discussed.     

Acoustically driven charge separation in semiconductor heterostructures sensed by optical spectroscopy techniques

We demonstrate a method of using a two-layer sandwich structure, which includes a LiNbO₃ plate and a semiconductor heterostructure to create an inhomogeneous stress and piezoelectric harmonic potential in the semiconductor. Both the GaAs/AlGaAs quantum well (QW) structures and SiGe/Si heterostructures are attempted, working with and without using a piezoelectric field in the semiconductor layer. The standing-wave fields generated in the semiconductor and the electron and hole distributions driven by the piezoelectric field are computed by finite element method (FEM) techniques. It is experimentally shown that, in a GaAs/Al_xGa_1-x As asymmetric double quantum well structure, the resonance enhancement of the narrower QW photoluminescence band is observed, which may be explained by the resonant charge transfer between the wider and narrower QWs. It is also shown that the piezoelectric fields quench the pure LO-phonon lines in the Raman spectra, whereas the coupled LO-phonon-plasmon mode strengthens. Experimental results indicate that the charge separation occurs in the plane of the QWs due to the piezoelectric fields. The recombination of carriers in the SiGe/Si heterostructures can be effectively enhanced by the presence of ultrasonic stress, displaying features consistent with varying electrical activity at dislocations.     

Raman properties of silicon nanoparticles

The Raman spectra of silicon nanoparticles in the size range between d=3.5– have been studied experimentally. Scattering processes up to second order are being observed. The experimental results are analyzed in the framework of the phonon confinement model. While this model describes qualitatively the observations for first-order scattering processes, it is not applicable for scattering processes of higher order. From the analysis of second-order scattering, we determine a redshift of the TO phonon at the X and L points.     

Unbounded Representations of q-Deformation of Cuntz Algebra

We study a deformation of the Cuntz–Toeplitz C ^*-algebra determined by the relations ${a_i^*a_i=1+q a_ia_i^*,\, a_i^*a_j=0}$ . We define its well-behaved unbounded *-representations and classify all irreducible ones up to unitary equivalence.     

Influence of Freezing and Low Molecular Weight Cryoprotectants on Microsomal Membrane Structure: A Study by Multiparametric Fluorescent Probe

The influence of low molecular weight cryoprotectants (CPs) such as glycerol (GL), 1,2-propanediol (PD) and dimethylsulfoxide (DMSO) on the structure of rat liver microsomal membranes on the stages of equilibration and upon freezing up to −196°C was studied using a multiparametric fluorescent probe of flavonol nature. It was estimated that the studied CPs have individual concentration ranges defining low amplitude of their action on biomembranes. An exceeding of these ranges strongly increases the violation of membrane native structure already at the stage of incubation with CPs, strengthening it during the freezing procedure. According to the perturbation effect on microsomal membranes the studied CPs can be arranged in a sequence: DMSO > PD > GL.     

Syntheses and Structures of RE4Pt10In21 (RE = La–Nd)

The isotypic indides RE₄Pt₁₀In₂₁ (RE = La, Ce, Pr, Nd) were prepared by melting mixtures of the elements in an arc‐furnace under an argon atmosphere. Single crystals were synthesized in tantalum ampoules using special temperature modes. The four samples were studied by powder and single crystal X‐ray diffraction: Ho₄Ni₁₀Ga₂₁ type, C2/m, a = 2305.8(2), b = 451.27(4), c = 1944.9(2) pm, β = 133.18(7)°, wR2 = 0.045, 2817 F² values, 107 variables for La₄Pt₁₀In₂₁, a = 2301.0(2), b = 448.76(4), c = 1941.6(2) pm, β = 133.050(8)°, wR2 = 0.056, 3099 F² values, 107 variables for Ce₄Pt₁₀In₂₁, a = 2297.4(2), b = 447.4(4), c = 1939.7(2) pm, β = 132.95(1)°, wR2 = 0.059, 3107 F² values, 107 variables for Pr₄Pt₁₀In₂₁, and a = 2294.7(4), b = 446.1(1), c = 1938.7(3) pm, β = 132.883(9)°, wR2 = 0.067, 2775 F² values, 107 variables for Nd₄Pt₁₀In₂₁. The 8j In2 positions of all structures have been refined with a split model. The In1 sites of the lanthanum and the cerium compound show small defects, leading to the refined composition La₄Pt₁₀In_20.966(6) and Ce₄Pt₁₀In_20.909(6) for the investigated crystals. The same position shows Pt/In mixing in the praseodymium and neodymium compound leading to the refined compositions Pr₄Pt_10.084(9)In_20.916(9) and Nd₄Pt_10.050(9)In_20.950(9). All platinum atoms have a tricapped trigonal prismatic coordination by rare‐earth metal and indium atoms. The shortest interatomic distances occur for Pt–In followed by In–In. Together, the platinum and indium atoms build up three‐dimensional [Pt₁₀In₂₁] networks in which the rare earth atoms fill distorted pentagonal tubes. The crystal chemistry of RE₄Pt₁₀In₂₁ is discussed and compared with the RE₄Pd₁₀In₂₁ indides and isotypic gallides.     

Novel two-band ratiometric fluorescence probes with different location and orientation in phospholipid membranes

3-hydroxyflavone (3-HF) derivatives are very attractive fluorescence sensors due to their ability to respond to small changes in their microenvironment via a dramatic alteration of the relative intensities of their two well-separated emission bands. We developed fluorescence probes with locations at different depths and orientations of 3-HF moiety in the phospholipid bilayer, which determine their fluorescence behavior. While the spectral shifts of the probes correlate with their binding site polarity, the intensity ratio is a complex parameter that is also sensitive to the local hydration. We demonstrate that even the deeply located probes sense this hydration effect, which can be modulated by the charge of the lipid heads and is anisotropic with respect to the bilayer plane. Thus the two-band ratiometric fluorescence probes can provide multiparametric information on the properties of lipid membranes at different depths.