Functions with slowly-growing area and harmonic majorants

Letf be a function holomorphic inU={|z|<1}, and letA(R,f) be the area off(U)∩{|w|<R}, not counting multiplicities. IfA(R,f)=O(R ^γ) asR→∞ for a γ, 0≦γ<2, then the subharmonic function exp |f| ^p has a harmonic majorant inU for eachp, 0<p<2−γ. If 0≦γ<1 further, thene ^f is of Hardy classH ^p for eachp, 0<p<∞.     

Effects of substrate microstructure on the magnetic anisotropy of sputtered cobalt alloy film

The magnetic properties and crystalline structure of Co alloy film deposited on a regularly corrugated substrate have been studied. Microscopic grooves are lithographically fabricated on InP substrates. In-plane anisotropy energy is 4–5×10⁴J/m³. The magnetic anisotropy is affected by the crystallographic orientation and the microscopic shape of the corrugated Co alloy film.     

Buffer-gas pressure broadening for the (3 0(0) 1)III <-- (0 0 0) band of CO2 measured with continuous-wave cavity ring-down spectroscopy

Buffer-gas pressure broadening for the (3 0(0) 1)(III)<--(0 0 0) band of CO(2) in the 1600 nm region was investigated with continuous wave cavity ring-down spectroscopy within the temperature range 263-326 K. The measured absorption profiles were analyzed with Voigt functions. Pressure broadening coefficient, gamma(gas), and the temperature dependent parameter (broadening exponent), n, were determined for a variety of buffer gases: N(2), O(2), He, Ne, Ar, Kr and Xe. gamma(air) values estimated subsequently are 0.096(2) for R(0), 0.085(5) for P(8), 0.075(2) for P(16), 0.070(4) for P(26), and 0.069(2) for P(38) in units of cm(-1) atm(-1), where numbers in parentheses are one standard deviation in units of the last digits quoted. n(air) values are 0.77(4) for R(0), and 0.73(11) for P(8).     

Shape and topology optimization based on the phase field method and sensitivity analysis

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.     

Carrier-concentration dependence of the pseudogap ground state of superconducting Bi₂Sr(₂-x)La(x)CuO(₆+δ) revealed by ⁶³,⁶⁵Cu-nuclear magnetic resonance in very high magnetic fields

We report the results of the Knight shift by ?3,??Cu-NMR measurements on single-layered copper-oxide Bi?Sr(?-x)La(x)CuO(?+δ) conducted under very high magnetic fields up to 44 T. The magnetic field suppresses superconductivity completely, and the pseudogap ground state is revealed. The ?3Cu-NMR Knight shift shows that there remains a finite density of states at the Fermi level in the zero-temperature limit, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual density of states in the pseudogap ground state decreases with decreasing doping (increasing x) but remains quite large even at the vicinity of the magnetically ordered phase of x ≥ 0.8, which suggests that the density of states plunges to zero upon approaching the Mott insulating phase.     

A note on the uniqueness and the non-degeneracy of positive radial solutions for semilinear elliptic problems and its application

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may have sublinear growth.As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified Schr¨odinger equations.     

The elliptic Apostol–Dedekind sums generate odd Dedekind symbols with Laurent polynomial reciprocity laws

Dedekind symbols are generalizations of the classical Dedekind sums (symbols). There is a natural isomorphism between the space of Dedekind symbols with Laurent polynomial reciprocity laws and the space of modular forms. We will define a new elliptic analogue of the Apostol–Dedekind sums. Then we will show that the newly defined sums generate all odd Dedekind symbols with Laurent polynomial reciprocity laws. Our construction is based on Machide’s result (J Number Theory 128:1060–1073, 2008) on his elliptic Dedekind–Rademacher sums. As an application of our results, we discover Eisenstein series identities which generalize certain formulas by Ramanujan (Collected Papers of Srinivasa Ramanujan, pp. 136–162. AMS Chelsea Publishing, Providence, 2000), van der Pol (Indag Math 13:261–271, 272–284, 1951), Rankin (Proc R Soc Edinburgh Sect A 76:107–117, 1976) and Skoruppa (J Number Theory 43:68–73, 1993).     

Sequential pericyclic reaction of ene-diallenes: an efficient approach to the steroid skeleton

[reaction: see text] The one-pot construction of polycyclic aromatic systems from acyclic ene-bis(propargyl alcohols) was achieved through a tandem dual [2,3]-sigmatropic rearrangement/6pi-electrocyclic reaction/intramolecular [4 + 2] cycloaddition sequence. A steroidal compound was conveniently synthesized using the present method.     

Simultaneous measurements of indoor radon and thoron and inhalation dose assessment in Douala City,Cameroon

ABSTRACT

Radon, thoron and associated progeny measurements have been carried out in 71 dwellings of Douala city, Cameroon. The radon–thoron discriminative detectors (RADUET) were used to estimate the radon and thoron concentration, while thoron progeny monitors measured equilibrium equivalent thoron concentration (EETC). Radon, thoron and thoron progeny concentrations vary from 31?±?1 to 436?±?12 Bq?m^–3, 4?±?7 to 246?±?5 Bq?m^–3, and 1.5?±?0.9 to 13.1?±?9.4 Bq?m^–3. The mean value of the equilibrium factor for thoron is estimated at 0.11?±?0.16. The annual effective dose due to exposure to indoor radon and progeny ranges from 0.6 to 9?mSv?a^–1 with an average value of 2.6?±?0.1?mSv?a^–1. The effective dose due to the exposure to thoron and progeny vary from 0.3 to 2.9?mSv?a^–1 with an average value of 1.0?±?0.4?mSv?a^–1. The contribution of thoron and its progeny to the total inhalation dose ranges from 7 to 60?% with an average value of 26?%; thus their contributions should not be neglected in the inhalation dose assessment.