Gravitational energy in quadratic-curvature gravities

We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Lambda-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.     

Hereditary and Formally Smooth Coalgebras

We define formally smooth coalgebras and we study their relation with hereditary coalgebras. The main result of the paper establishes that a coalgebra with separable coradical is hereditary if and only if it is formally smooth if and only if it is the cotensor coalgebra , where C₀ is the coradical of C and N is a certain (C₀,C₀)–bicomodule. Presented by A. Verschoren Mathematics Subject Classifications (2000) primary: 16W30; secondary: 18G20. D. Ştefan: This author thanks the members of the Algebra Department of the University of Granada for their warm hospitality. He is especially grateful to Pascual Jara for the kind invitation to visit University of Granada. This research was partially supported by CERES, Contract 4-147.     

Nuclear level densities below 40 MeV excitation energy in the mass regionA ≃ 50

Consistent pre-equilibrium emission and statistical model calculations of fast neutron induced reaction cross sections are used to validate nuclear level densities for excitation energies up to 40 MeV in the mass regionA ?50. A “composed” level density approach has been employed by using the back-shifted Fermi gas model for excitation energies lower than 12 MeV and a realistic analytical formula for higher excitations. In the transition region from the BSFG model range to that of full applicability of the realistic formula, an interpolation between the predictions of the two models is adopted. The interpolation rule, suggested by microscopic level density calculations, has been validated through the comparison of the calculated and experimental cross sections.     

2S autoionizing states of lithium

The energy positions and the wavefunctions of ²S autoionizing states of the neutral lithium atom have been calculated using the derivative method with a Hylleraas-type basis set. Computed energies are in good agreement with experiment and with other theoretical results.     

The crystal and molecular structure of (−)—Crinine (C16H17NO3)

(–)—Crinine, C₁₆H₁₇NO₃, is an alkaloid extracted from the bulbs of Pancratium maritimum L. (Amaryllidaceae). The compound crystallizes in the space group P2₁2₁2₁ with cell dimensions a = 6.040(1), b = 12.382(1), c = 17.861(2) Å, with Z = 4. The molecule has five rings and an OH group. The N-containing, five-membered ring and the D ring have envelope conformations. The A and B rings have distorted chair and half-chair conformations, respectively.     

Irreducible representations of infinite-dimensional Lie algebras

Some results concerning the operatorially irreducible, topologically irreducible, operatorially and topologically irreducible representations of a class of infinite-dimensional Lie algebras by bounded operators in a complex Banach space are obtained.     

Effect of ultrasound on the dissolution kinetics of phosphate rock in HNO3

Ultrasound is known to enhance solid/liquid reactions. This paper deals with the investigation of the dissolution of phosphate rock in nitric acid, in the absence and presence of ultrasound. The reaction is first-order with respect to H⁺ and activation energy equal to 16 kJ/mol in both cases. The effect of ultrasound is on the pre-exponential factor A. An empirical relation is given, which relates rate constant to ultrasound power.     

Statistically D-bounded sequences in probabilistic normed spaces

In this study, the concept of a statistically D-bounded sequence in a probabilistic normed (PN) space endowed with the strong topology is introduced and its basic properties are investigated. It is shown that a strongly statistically convergent sequence and a strong statistically Cauchy sequence are statistically D-bounded under certain conditions. A sequence which goes far away from the limit point infinitely many times and presents random deviations in a PN space may be handled with the tools of strong statistical convergence and statistical D-boundedness.