Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

Structural and physical properties of Mg3−xZnxSb2 (x=0-1.34)

The Mg_3−xZn_xSb₂ phases with x=0-1.34 were prepared by direct reactions of the elements in tantalum tubes. According to the X-ray single crystal and powder diffraction, the Mg_3−xZn_xSb₂ phases crystallize in the same P3¯m1 space group as the parent Mg₃Sb₂ phase. The Mg_3−xZn_xSb₂ structure is different from the other substituted structures of Mg₃Sb₂, such as (Ca, Sr, Ba) Mg₂Sb₂ or Mg_5.23Sm_0.77Sb₄, in a way that in Mg_3−xZn_xSb₂ the Mg atoms on the tetrahedral sites are replaced, while in the other structures Mg on the octahedral sites is replaced. Thermoelectric performance for the two members of the series, Mg₃Sb₂ and Mg_2.36Zn_0.64Sb₂, was evaluated from low to room temperatures through resistivity, Seebeck coefficient and thermal conductivity measurements. In contrast to Mg₃Sb₂ which is a semiconductor, Mg_2.36Zn_0.64Sb₂ is metallic and exhibits an 18-times larger dimensionless figure-of-merit, ZT, at room temperature. However, thermoelectric performance of Mg_2.36Zn_0.64Sb₂ is still poor and it is mostly due to its large electrical resistivity.     

Plasma-Assisted ALD of Highly Conductive HfNx: On the Effect of Energetic Ions on Film Microstructure

Plasma Chemistry and Plasma Processing - In this work, we report on the atomic layer deposition (ALD) of HfNx thin films by employing CpHf(NMe2)3 as the Hf(IV) precursor and Ar–H2 plasma in...     

Thin Film Flow of a Second Grade Fluid over a Stretching/Shrinking Sheet with Variable Temperature-Dependent Viscosity

Effects of variable viscosity on the flow and heat transfer in a thin film on a horizontal porous stretching sheet are analyzed. The steady boundary layer equations for momentum and thermal energy are simplified by using similarity transformations. The resulted and coupled nonlinear differential equations are solved by Homotopy analysis method. The results are presented graphically to interpret various physical parameters appearing in the problem.     

Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi2Se3

We report a Rashba spin splitting of a two-dimensional electron gas in the topological insulator Bi(2)Se(3) from angle-resolved photoemission spectroscopy. We further demonstrate its electrostatic control, and show that spin splittings can be achieved which are at least an order-of-magnitude larger than in other semiconductors. Together these results show promise for the miniaturization of spintronic devices to the nanoscale and their operation at room temperature.     

Mathematical modeling of the stress state of a transverse plastic layer in a round rod

We construct mathematical models of plastic deformations of a continuous round rod containing a transverse (less strong) inhomogeneous layer under an axial load. We thoroughly study the local strengthening of such layers by involving the base material of the rod in the plastic deformation process. We obtain explicit formulas for the critical stress states in the layer and the critical axial load on the rod.     

P-Al/NaX结构和酸碱性位调控对甲苯甲醇侧链烷基化性能影响

采用水热法原位合成了P-Al/NaX催化剂,然后通过浸渍NaOH对其进行酸碱性调控,并探究了它在甲苯甲醇侧链烷基化反应中的催化性能。结合X射线衍射（XRD）、X射线光电子能谱（XPS）、N₂吸附-脱附等表征及催化活性数据发现,原位负载P、Al后,合成的磷铝硅酸盐（Na₁₃Al₂₄Si₁₃P₁₁O₉₆·H₂O）结构展现出较好的甲苯甲醇侧链烷基催化活性;随着NaOH负载量的增加,乙苯和苯乙烯的选择性呈先上升后下降的趋势,当负载质量分数为9%的NaOH时,苯乙烯选择性为45.84%,乙苯和苯乙烯的收率之和达到63.08%。这可能是由于NaOH的负载有利于催化剂表面碱性的提高和酸性的降低,而高的强碱性位和弱酸性位数量有利于甲苯甲醇侧链烷基化反应的进行。     

Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide

The propagation of electromagnetic surface waves along a radially inhomogeneous dielectric waveguide is investigated. The problem is formulated in terms of differential equations to be satisfied by the radially dependent parts of the electromagnetic field vectors. The dielectric waveguide is assumed to consist of a homogeneous cladding of infinite extent and a radially inhomogeneous core of higher permittivity. Numerical solutions of the differential equations in the core are obtained by two different methods, viz. by direct numerical integration and by substitution of an appropriate power series expansion. In the cladding the field is expressed in terms of modified Bessel functions. Imposing the boundary conditions at the interface of core and cladding, an equation for the unknown propagation coefficient is obtained. From this equation the propagation coefficients for the lower order modes are computed numerically. Numerical results are presented for some permittivity profiles of practical interest in single-mode transmission along optical fibres.Nomenclature a radius of the core - a _q vector coefficient in the power series expansion off() - A _i constants - A square matrix - b _q coefficient in the power series expansion of _r() - B square matrix - C square matrix - c _n unknown constant - d _n unknown constant - D() fundamental matrix - E,E _r,,z electric field vector and components - E,e _r,,z radially dependent parts ofe _r,,z - f solution vector - G _q square matrix - H,H _r,,z magnetic field vector and components - h _r,,z radially dependent parts ofE _r,,z - h reduced wavenumber - i radial mode number - j imaginary unit - k _0,m wave number - K _n modified Bessel function of the second kind and order n - n azimuthal mode number - t time - U normalized propagation constant - Z _m plane wave impedance of the cladding - r, , z cylindrical co-ordinates - p, q, s integers - propagation coefficient - increment - _0,m,r permittivity - normalized radiusr - ₀ wavelength in free space - ₀ permeability - angular frequency - d _r, differentiation with respect tor, Engineering and Professor H. J. Frankena of the Physics Department for their valuable discussions.     

The stress state of a plastic layer with a variable yield strength under a flat deformation

We study the stress state of a plastic layer with a variable yield strength in a strip under a flat deformation with a tensile load. We approximately calculate the first integrals of the system of plastic equilibrium equations, obtain an analog of the first Hencky theorem, and solve the conjugation problem for stresses on the contact boundary.     

Influence of tungsten doping concentration on the electronic and optical properties of anatase TiO2

The structural, electronic and optical properties of tungsten-doped TiO₂ have been investigated using density functional theory with plane wave basis sets and ultrasoft pseuodopotential. Substitutional W doping at Ti sites create W 5d states just below the conduction band minimum while interstitial W doping gives isolated W 5d states in the middle of forbidden region. Averaged bond lengths show that W doping at Ti sites produce minimum structural distortion as compared to the interstitial W-doped TiO₂. Substitutional W-doped TiO₂ has better visible light absorption compared to interstitial W-doped TiO₂ and has stable configuration which provide reasonable explanation for the experimental findings. Tungsten doping in TiO₂ with different doping concentrations is investigated as an enabling concept for enhancing the visible light absorption. Optical properties show that optimal W doping concentration would improve the visible light absorption. 2.08% W doping concentration gives strong visible and ultraviolet light absorption among all doped models found consistent with experiments.