Formulation of N- and ν-representable density functional theory. V. Exchange-only self-consistent field

The concept of a self-consistent field is developed within the version of density functional theory based on local-scaling transformations. It is shown that in this context there arise two types of consistency: one relating to the charge-consistency within an orbit and another to “orbit jumping.” The latter is analyzed in terms of one-particle equations. The connection with other methods is discussed. © 1992 John Wiley & Sons, Inc.     

Regularity and other properties of absolutely continuous invariant measures for the quadratic family

In the current paper we study in more detail some properties of the absolutely continuous invariant measures constructed in the course of the proof of Jakobson's Theorem. In particular, we show that the density of the invariant measure is continuous at Misiurewicz points. From this we deduce that the Lyapunov exponent is also continuous at these points (our considerations apply just to the parameters constructed in the proof of Jakobson's Theorem). Other properties, like the positivity of the Lyapunov exponent, uniqueness of the absolutely continuous invariant measure and exactness of the corresponding dynamical system, are also proved.This paper was written during the author's stay at the IAS while supported by NSF grant DMS-860 1978     

Nucleophilic addition to acetylenes in superbasic catalytic systems: XV. Vinylation of 2-hydroxymethylfuran

2-Hydroxymethylfuran reacted with acetylene in superbasic catalytic systems MOH-DMSO (M = Na, K) under mild temperature conditions (75–85°C, 1–2 h), yielding 80% of 2-vinyloxymethylfuran. The product, as well as acetaldehyde acetals derived therefrom, turned out to be promising as modifiers for electrolyte in lithium-sulfur rechargeable batteries.     

A New Strong Laplacian on Differential Forms

We construct a strong Laplacian D ^* D by using the third operator in the basis {d,d ^*,D} of the space of natural first-order operators acting on the differential forms of a Riemannian manifold (M,g). We study the properties of the Laplacian D ^* D and obtain Weitzenbock's formula relating the three strong Laplacians dd ^*, d ^* d, and D ^* D to the curvature of the manifold (M,g).     

2,12‐Dichloro‐10,20‐diphenyl‐5,7,15,17‐tetrahydro‐6H,16H‐dibenzo[d,l][1,9,2,6,10,14]dioxotetraazacyclohexadecine‐6,16‐dione dioxane solvate as a potential macrocyclic hexadentate ligand

The macrocyclic title compound crystallizes as a dioxane solvate, C₃₀H₂₂Cl₂N₄O₄·C₄H₈O₂, with two independent formula units in the unit cell. The observed syn conformation is controlled by both intramolecular N—H...O hydrogen bonds and intermolecular C—H...π interactions. The relative macrocyclic inner bore is estimated to be 4.19 Å. In the crystal structure, molecules form dimers via intermolecular C—H...π interactions, and these dimers are, in turn, linked to form columns along the a axis by intermolecular C—H...O hydrogen bonds. Both X‐ray diffraction analysis and density functional theory (DFT) calculations reveal that the macrocycle possesses very high flexibility. This property, as well as the presence of six donor atoms accessible for coordination, makes the title macrocycle a very promising ligand for complexation with the majority of transition metals.     

Experimental investigation of highly excited states of the 5,6He and 5,6Li nuclei in the (6Li, 7Be) and (6Li, 7Li) one-nucleon pickup reactions

The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions on ⁶Li and ⁷Li nuclei were investigated in the angular interval 0°–20° in the laboratory system at a ⁶Li energy of 93 MeV. In addition to low-lying states of the ^5,6He and ^5,6Li nuclei, broad structures were observed near the t(³He)+d and t(³He)+t thresholds at the excitation energies of 16.75 (3/2⁺) and ～20 MeV (for ⁵He), 16.66 (3/2⁺) and ～20 MeV (⁵Li), 14.0 and 25 MeV (⁶He), and ～20 MeV (⁶Li). The angular distributions measured in the ⁷Li(⁶Li, ⁷Be)⁶He reaction for transitions to the ground state (0⁺) and excited states at E _x=1.8 MeV (2⁺) and 14.0 MeV of the ⁶He nucleus were analyzed by the finite-range distorted-wave method assuming the 1p-and 1s-proton pickup mechanism. The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions were shown to proceed predominantly through the one-step pickup mechanism, and the broad structures observed at high excitation energies are considered as quasimolecular states of the t(³He)+d and t(³He)+t types.     

Generalized characters of the symmetric group

Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diagS(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand pair (S(n)×S(n−1),diagS(n−1)). Zonal spherical functions of this Gelfand pair form an orthogonal basis in a larger space of functions on S(n), namely in the space of functions invariant with respect to conjugations by S(n−1). We refer to these zonal spherical functions as normalized generalized characters of S(n). The main discovery of the present paper is that these generalized characters can be computed on the same level as the irreducible characters of the symmetric group. The paper gives a Murnaghan-Nakayama type rule, a Frobenius type formula, and an analogue of the determinantal formula for the generalized characters of S(n).     

Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

In this paper the nonlinear wave equation $$u_u - u_{xx} + v(x)u(x,t) + \varepsilon u^3 (x,t) = 0$$ is studied. It is shown that for a large class of potentials,v(x), one can use KAM methods to construct periodic and quasi-periodic solutions (in time) for this equation.     

Statistical mechanics of probabilistic cellular automata

We investigate the behavior of discrete-time probabilistic cellular automata (PCA), which are Markov processes on spin configurations on ad-dimensional lattice, from a rigorous statistical mechanics point of view. In particular, we exploit, whenever possible, the correspondence between stationary measures on the space-time histories of PCAs on ^d and translation-invariant Gibbs states for a related Hamiltonian on ( ^d+1). This leads to a simple large-deviation formula for the space-time histories of the PCA and a proof that in a high-temperature regime the stationary states of the PCA are Gibbsian. We also obtain results about entropy, fluctuations, and correlation inequalities, and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high-noise regime. We discuss phase transitions in the low-noise (or low-temperature) regime and review Toom's proof of nonergodicity of a certain class of PCAs.