Low-energy resonances in photodissociation of CH+

Close coupling calculations for the photodissociation cross sections of CH⁺+hv → C⁺(²P) + H(²S) exhibit near threshold peaks not ascribable only to quasi-bound levels in the A ¹Π potential. Our calculations demonstrate the importance of non-adiabatic transitions and thereby suggest the necessity to revise earlier predictions of the rate of radiative association of C⁺ with H.     

A Liouville-type Theorem for Schrödinger Operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P ₁, such that a nonzero subsolution of a symmetric nonnegative operator P ₀ is a ground state. Particularly, if P _j : = ?Δ + V _j , for j = 0,1, are two nonnegative Schrödinger operators defined on \(\Omega\subseteq \mathbb{R}^d\) such that P ₁ is critical in Ω with a ground state φ, the function \(\psi\nleq 0\) is a subsolution of the equation P ₀ u = 0 in Ω and satisfies \(\psi_+\leq C\varphi\) in Ω, then P ₀ is critical in Ω and \(\psi\) is its ground state. In particular, \(\psi\) is (up to a multiplicative constant) the unique positive supersolution of the equation P ₀ u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds.     

A scale-dependent equation for solute transport in porous media

The governing equation describing solute transport in porous media is reformulated using standard volume averaging techniques. The alternative formulation is based on a modified definition of the deviation, which allows for variation of macroscopic velocity across the REV. The new equation contains additional scale-dependent terms which are functions of the size of the averaging volume (REV). This result indicates that the scale-dependent nature of the dispersion phenomenon is inherent even at the scale of the REV.     

A modified Weiszfeld algorithm for the Fermat-Weber location problem

This paper gives a new, simple, monotonically convergent, algorithm for the Fermat-Weber location problem, with extensions covering more general cost functions. Received: September 1999 / Accepted: January 2001?Published online April 12, 2001     

Kitungolides A, B, and C, new diterpenes from a soft coral of a new genus

Three novel compounds, designated kitungolides A (1), B (2), and C (3), were isolated from a soft coral of a new genus collected at Kitungamwe, Kenya. The three new compounds are of a unique heterotricyclic skeleton. The structures and relative stereochemistry of the compounds were elucidated by interpretation of MS, COSY, HMQC, HMBC, and NOESY experiments. [structure: see text]     

Callynormine A, a new marine cyclic peptide of a novel class

[structure: see text] A novel cyclic peptide, callynormine A, was isolated from the Kenyan marine sponge Callyspongia abnormis and its structure elucidated by interpretation of its NMR data and X-ray diffraction analysis. Callynormine A represents a new class of heterodetic cyclic peptides (designated endiamino peptides) possessing an alpha-amido-beta-aminoacrylamide cyclization functionality.     

Novel electronic transitions within excited doublets of dimers

We consider the electronic transition between the split components of the excited electronic doublet of a dimer species when the monomer species have permanent dipole moments. We show that the transition moment is given in terms of the permanent dipole moments of the ground and excited states of the monomers. Extension to ionic dimers and transitions between exciton bands in molecular crystals are suggested.     

Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity

The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the structure theory of totally disconnected groups are established along the way and are of independent interest. Other ideas in the argument motivate a sweeping conjecture, presented in the last section of the paper, which naturally unifies in an adelic setting deep results and fundamental conjectures in the rigidity theory of arithmetic groups.