Integrability and algebraic structure of the quantum Calogero-Moser model

For the quantum Calogero-Moser model, we present the following two results. First, it has a set of conserved operators which are involutive. This proves the integrability of the model. Second, the Lax operator gives a list of new operators (boost operators). The conserved operators and the boost operators constitute the U(1)-current algebra.     

Factors and factorizations of graphs—a survey

A degree factor of a graph is either an r-factor (regular of degree r) or an [m, n]-factor (with each degree between m and n). In a component factor, each component is a prescribed graph. Both kinds of factors are surveyed, and also corresponding factorizations.     

FLUORESCENCE QUENCHING OF 5,10,15,20-TETRA(p-TOLYL)PORPHINE and ITS ZINC COMPLEX BY QUINONES. CHARGE-TRANSFER INTERACTION and TRANSIENT EFFECT

The fluorescent states of tetratolylporphyrin and its zinc complex in acetone were quenched by various kinds of quinones. The transient effect for the collisional quenching caused the upward deviation of the plots of the inversed fluorescence intensities of the porphyrins vs the quinone concentrations. A charge-transfer interaction between the porphyrins in the singlet excited states and the quinones was suggested from the dependence of the quenching rate constants on the electron affinities of the quinones.     

Casimir energy of a scalar field with a space-dependent mass distribution

The Casimir energy is evaluated for a free scalar field that has a mass term m²(x₁), depending on one space coordinate x₁. The formalism for evaluating the Casimir energy is developed for the case of m²(x₁) finite everywhere in d-dimensional space-time. The case with $\text{m}{}^2\text{(x}{}_1\text{) = m}{}_0{}^2\text{θ(}\text{1}\text{2}\text{L}\text{-|x}{}_1\text{|) + m}{}_{\mathrm{\infty }}{}^2\text{θ (|x}{}_1\text{| -}\text{1}\text{2}\text{L}$) is explicity evaaluated for any value of 1197 1568 V m₀ and m_∞ without any approximation. The result consists of valume energy terms, a surface term, and a non-leading term. Most of the UV divergences are in the volume energy terms and renormalize the coupling constants of the underlying theory. The surface energy term is finite for d ? 4 and divergent for d ? 5 due to the boundaries being sharp. A closed finite expression is obtained for the non-leading term. Our results are shown to reproduce the known Casimir energies for the limiting cases, 1197 15 m₀ → ∞ andm_∞ → ∞.     

Effects of pair creation on the expansion of vacuum bubbles

The real-time behavior of true-vacuum bubbles nucleated in the false-vacuum background is studied in a λ?⁴ theory. Classically, the bubble expansion rate has been known to approach the velocity of light asymptotically. A quantum effect, creation of Higgs and fermion pairs, is studied by a semiclassical method, and is shown to lead to a slower expansion rate. Within the thin-wall approximation, several possible asymptotic behaviors are examined. A solution that behaves like the classical one but with different coefficients is shown to be stable. The first-order corrections to the coefficients are calculated approximately. The created Higgs pairs are found to remain inside the bubble and carry an energy of approximately 10^?3 λ of the energy released from the false vacuum. The fermions that are massless in the false vacuum go out of the bubble and have energy ～10^?3g², where g is the Yukawa coupling constant. It is shown that the resulting asymptotic state is Lorentz invariant.     

A sufficient condition for a bipartite graph to have a k-factor

P. Katerinis obtained a sufficient condition for the existence of a 2-factor in a bipartite graph, in the spirit of Hall's theorem. We show a sufficient condition for the existence of a k-factor in a bipartite graph, as a generalization of Katerinis's theorem and Hall's theorem.     

Uphill transport of uranium across a liquid membrane

A liquid membrane was prepared by entrapping tributyl phosphate (TBP) in a cellulose triacetate (TAC) membrane matrix. The membrane was used to separate two aqueous solutions, one acidic and the other alkaline, which were saturated with TBP to prevent its loss from the membrane. Uphill transport of uranium was achieved with the TBP liquid membrane. Both solutions containing TBP were stirred magnetically. When the initial concentration of uranium in the two solutions was 3.5 mM, more than 50% of the uranium contained in the acidic solution was transported to the alkaline solution across the liquid membrane within 5 h. A transport mechanism is described in which the membrane-bound TBP acts as a mobile carrier for uranium.     

Pressure control of diastereodifferentiating [2 + 2] photocycloaddition of (E)-stilbene to chiral fumarate upon direct and charge-transfer excitation

The geometry (donor-acceptor distance) and association constant of the ground-state CT complex were considerably affected by applied pressure, thus enhancing the reaction rate and the adduct yield particularly upon CT excitation, but the diastereoselectivity did not show any substantial change at elevated pressures in both excitation modes.     

Prediction of peptide conformation using a scale-transformed entropy sampling algorithm

An algorithm for predicting the lowest energy structure of a peptide has been developed. High-energy barriers on an energy surface can be easily overcome by logarithmically transforming the energy space. For efficient optimizations, the energy space is searched using a scale-transformed entropy sampling method, and conformations specific to a primary structure of the peptide are sampled with large weights. The efficiency of the present method is demonstrated by calculations on cholecystokinin octapeptide (CCK-8).     

A new artificial cyclase for polyprenoids: enantioselective total synthesis of (-)-chromazonarol, (+)-8-epi-puupehedione, and (-)-11'-deoxytaondiol methyl ether

This paper describes a new artificial cyclase, optically pure 3-o-fluorobenzyloxy-2-hydroxy-2'-(p-methoxybemzyl)-1,1'-binaphthyl.SnCl4, which is effective for the enantioselective cyclization of 2-(polyprenyl)phenol derivatives to afford polycyclic terpenoids bearing a chroman skeleton such as (-)-chromazonarol, (+)-8-epi-puupehedione, a key synthetic intermediate of (+)-wiedendiol, and (-)-11'-deoxytaondiol methyl ether.