A Parabolic Approach to Martin Boundaries for Elliptic Equations in Skew Product Form

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin compactifications and Martin kernels for a wide class of elliptic equations in skew product form by exploiting parabolic Martin kernels for associated parabolic equations.     

Martin Boundaries of Elliptic Skew Products, Semismall Perturbations, and Fundamental Solutions of Parabolic Equations

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations.     

SO+(A2Π-X2Πr) emission produced from a dissociative charge-transfer reaction of He+ with SO2 at thermal energy

The extensive bands observed from the helium afterglow reaction of SO₂ in the 250–540 nm region are assigned to the new SO⁺(A²Π-X²Π_r) system produced from the He⁺/SO₂ dissociative charge-transfer reaction at thermal energy. They had been erroneously interpreted as the SO⁺₂ (C?-X?) system produced from He(2³S)/SO₂ Penning ionization. The spectroscopic constants for the SO⁺A²Π) and SO⁺(X²Π_r) states were determined.     

Conjugate and cut loci of a two-sphere of revolution with application to optimal control

The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control.     

On height isotopy classes of embeddings in the plane of a Morse function of a circle

Let \(\mathrm{SM}_{2n}(S^1,\mathbb {R})\) be a set of stable Morse functions of an oriented circle such that the number of singular points is \(2n\in \mathbb {N}\) and the order of singular values satisfies the particular condition. For an orthogonal projection \(\pi :\mathbb {R}^2\rightarrow \mathbb {R}\), let \({\tilde{f}}_0\) and \({\tilde{f}}_1:S^1\rightarrow \mathbb {R}^2\) be embedding lifts of f. If there is an ambient isotopy \(\tilde{\varphi }_t:\mathbb {R}^2\rightarrow \mathbb {R}^2\) \((t\in [0,1])\) such that \({\pi \circ \tilde{\varphi }}_t(y_1,y_2)=y_1\) and \(\tilde{\varphi }_1\circ {\tilde{f}}_0={\tilde{f}}_1\), we say that \({\tilde{f}}_0\) and \({\tilde{f}}_1\) are height isotopic. We define a function \(I:\mathrm{SM}_{2n}(S^1,\mathbb {R})\rightarrow \mathbb {N}\) as follows: I(f) is the number of height isotopy classes of embeddings such that each rotation number is one. In this paper, we determine the maximal value of the function I equals the n-th Baxter number and the minimal value equals \(2^{n-1}\).     

Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M_∂D×[0,T)), where M_∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D).     

Adsorption and dissociation of water on LaB6(100) investigated by surface vibrational spectroscopy

The chemisorption of water (H₂O and D₂O) on a LaB₆(100) surface was studied with reflection absorption infrared spectroscopy (RAIRS) and high resolution electron energy loss spectroscopy (HREELS). The clean surface was exposed to H₂O and D₂O at temperatures from 90 K to room temperature, and spectra were acquired after heating to temperatures as high as 1200 K. It was found that water molecularly adsorbs on the surface at 90 K as a monomer at low coverages and as amorphous solid water at higher coverages. Water adsorbs dissociatively at room temperature to produce surface hydroxyl species as indicated by OH/OD stretch peaks at 3676/2701 cm^?1. Room temperature adsorption also reveals low frequency loss features in HREEL spectra near 300 cm^?1 that are quite similar to results obtained following the dissociative adsorption of O₂. In the latter case, the loss features were attributed to the LaO stretch of O atoms bridge-bonded between two La atoms. In the case of dissociative adsorption of H₂O, the low frequency loss features could be due to either the LaO vibrations of adsorbed O or of adsorbed OH.     

Luminescence study of self-trapped excitons in CdMoO4

Luminescence properties of CdMoO₄ crystals have been investigated in a wide temperature range of T=5–300 K. The luminescence-excitation spectra are examined by using synchrotron radiation as a light source. A broad structureless emission band appears with a maximum at nearly 550 nm when excited with photons in the fundamental absorption region (<350 nm) at T=5 K. This luminescence is ascribed to a radiative transition from the triplet state of a self-trapped exciton (STE) located on a (MoO₄)^2? complex anion. Time-resolved luminescence spectra are also measured under the excitation with 266 nm light from a Nd:YAG laser. It is confirmed that triplet luminescence consists of three emission bands with different decay times. Such composite nature is explained in terms of a Jahn–Teller splitting of the triplet STE state. The triplet luminescence at 550 nm is found to be greatly polarized in the direction along the crystallographic c axis at low temperatures, but change the degree of polarization from positive to negative at T>180 K. This remarkable polarization is accounted for by introducing further symmetry lowering of tetrahedral (MoO₄)^2? ions due to a uniaxial crystal field, in addition to the Jahn–Teller distortion. Furthermore, weak luminescence from a singlet state locating above the triplet state is time-resolved just after the pulse excitation, with a polarization parallel to the c axis. The excited sublevels of STEs responsible for CdMoO₄ luminescence are assigned on the basis of these experimental results and a group-theoretical consideration.     

Electrical control of the direction of spin accumulation

We are able to continuously change the direction of polarization of spin accumulation in a nonmagnetic metal by varying the currents injected by two ferromagnetic spin injectors. From measurements made at a distance from the injection area, we find a cosvarphi variation of the spin signal. This confirms that the angle of polarization of the nonlocal spin polarization with respect to the magnetization of the fixed spin detector is continuously varied as we change the injection currents. We give an explanation for the origin of this simple cosvarphi variation of the spin signal.