Solution of the Schr\"odinger Equation for Quantum Dot Lattices with Coulomb Interaction between the Dots

The Schr\"odinger equation for quantum dot lattices with non-cubic, non-Bravais lattices built up from elliptical dots is investigated. The Coulomb interaction between the dots is considered in dipole approximation. Then only the center of mass (c.m.) coordinates of different dots couple with each other. This c.m. subsystem can be solved exactly and provides magneto- phonon like collective excitations. The inter-dot interaction is involved only through a single interaction parameter. The relative coordinates of individual dots form decoupled subsystems giving rise to intra-dot excitations. As an example, the latter are calculated exactly for two-electron dots. Emphasis is layed on qualitative effects like: i) Influence of the magnetic field on the lattice instability due to inter-dot interaction, ii) Closing of the gap between the lower and the upper c.m. mode at B=0 for elliptical dots due to dot interaction, and iii) Kinks in the single dot excitation energies (versus magnetic field) due to change of ground state angular momentum. It is shown that for obtaining striking qualitative effects one should go beyond simple cubic lattices with spherical dots. We also prove a more general version of the Kohn Theorem for quantum dot lattices. It is shown that for observing effects of electron- electron interaction between the dots in FIR spectra (breaking Kohn's Theorem) one has to consider dot lattices with at least two dot species with different confinement tensors.Comment: 11 figures included as ps-file

Manufacture of Two-layers and Double-sided Iron Castings with Differential Structure and Properties

The paper proposes a new method of production of bilayer and double-sided castings with differentiated structure and properties using the technology of in-mold modification of the initial melt, smelted in a single melting furnace, which ensures formation of hard wear-resistant white iron as the working layer, and formation of ductile shock-resistant cast iron with nodular graphite as the core or the mounting part. Numerous laboratory studies confirm the feasibility of the proposed method and provide conditions ensuring differentiation of structure and properties in local parts or layers of castings. The prospects of the method for manufacturing a wide range of industrial castings are indicated

Povidone-iodine in wound healing and prevention of wound infections

The wound infections caused by bacteria and fungi are a significant problem in healthcare. Therefore, an effective treatment and prevention seems to be essential. Povidone-iodine is one of the commercial antimicrobial agents used for skin disinfection, in surgery and for local anti-infective treatment. The broad activity spectrum of this compound includes numerous species of Gram-positive and Gram-negative bacteria, mycobacteria, fungi, protozoa and viruses. Povidone-iodine is recommended for acute wounds as well as lacerations, bruises and deep wounds due to its good tissue penetration. DOI: http://dx.doi.org/10.5281/zenodo.395822

Sharp Upper Bounds for Fractional Moments of the Riemann Zeta Function

We establish sharp upper bounds for the 2kth moment of the Riemann zeta function on the critical line, for all real 0 ⩽ k ⩽ 2⁠. This improves on earlier work of Ramachandra, Heath-Brown and Bettin–Chandee–Radziwiłł

Asymptotic Analysis of SU-MIMO Channels With Transmitter Noise and Mismatched Joint Decoding

Hardware impairments in radio-frequency components of a wireless system cause unavoidable distortions to transmission that are not captured by the conventional linear channel model. In this paper, a 'binoisy' single-user multiple-input multiple-output (SU-MIMO) relation is considered where the additional distortions are modeled via an additive noise term at the transmit side. Through this extended SU-MIMO channel model, the effects of transceiver hardware impairments on the achievable rate of multi-antenna point-to-point systems are studied. Channel input distributions encompassing practical discrete modulation schemes, such as, QAM and PSK, as well as Gaussian signaling are covered. In addition, the impact of mismatched detection and decoding when the receiver has insufficient information about the non-idealities is investigated. The numerical results show that for realistic system parameters, the effects of transmit-side noise and mismatched decoding become significant only at high modulation orders.Comment: 16 pages, 7 figure

Origin of Magic Angular Momentum in a Quantum Dot under Strong Magnetic Field

This paper investigates origin of the extra stability associated with particular values (magic numbers) of the total angular momentum of electrons in a quantum dot under strong magnetic field. The ground-state energy, distribution functions of density and angular momentum, and pair correlation function are calculated in the strong field limit by numerical diagonalization of the system containing up to seven electrons. It is shown that the composite fermion picture explains the small magic numbers well, while a simple geometrical picture does better as the magic number increases. Combination of these two pictures leads to identification of all the magic numbers. Relation of the magic-number states to the Wigner crystal and the fractional quantum Hall state is discussed.Comment: 12 pages, 9 Postscript figures, uses jpsj.st

Counting arithmetic formulas

An arithmetic formula is an expression involving only the constant 1, and the binary operations of addition and multiplication, with multiplication by 1 not allowed. We obtain an asymptotic formula for the number of arithmetic formulas evaluating to as goes to infinity, solving a conjecture of E.K. Gnang and D. Zeilberger. We give also an asymptotic formula for the number of arithmetic formulas evaluating to and using exactly multiplications. Finally we analyze three specific encodings for producing arithmetic formulas. For almost all integers , we compare the lengths of the arithmetic formulas for that each encoding produces with the length of the shortest formula for (which we estimate from below). We briefly discuss the time-space tradeoff offered by each

Bunches of misfit dislocations on the onset of relaxation of Si0.4_{0.4}Ge0.6_{0.6}/Si(001) epitaxial films revealed by high-resolution x-ray diffraction

The experimental x-ray diffraction patterns of a Si$_{0.4}$Ge$_{0.6}$/Si(001) epitaxial film with a low density of misfit dislocations are modeled by the Monte Carlo method. It is shown that an inhomogeneous distribution of 60$^\circ$ dislocations with dislocations arranged in bunches is needed to explain the experiment correctly. As a result of the dislocation bunching, the positions of the x-ray diffraction peaks do not correspond to the average dislocation density but reveal less than a half of the actual relaxation

Counting arithmetic formulas

Anarithmeticformulaisanexpressioninvolvingonlytheconstant1, and the binary operations of addition and multiplication, withmultiplicationby1notallowed.Weobtainanasymptoticformulaforthenumberofarithmeticformulasevaluatingtonasngoestoinfinity, solving a conjecture of E.K. Gnang and D. Zeilberger. Wegivealsoanasymptoticformulaforthenumberofarithmeticfor-mulas evaluating tonand using exactlykmultiplications. Finallyweanalyzethreespecificencodingsforproducingarithmeticfor-mulas. For almost all integersn, we compare the lengths of thearithmetic formulas fornthat each encoding produces with thelength of the shortest formula forn(which we estimate from be-low).Webrieflydiscussthetime-spacetradeoffofferedbyeac