Circular Orbits in Stationary Axisymmetric Spacetimes

Several types of characteristics of spatially circular timelike trajectories in stationary axisymmetric spacetimes are related in a simple and covariant manner. The relations allow us to establish straightforward links between different phenomena often studied on circular orbits: mechanics of a single test particle, precession of gyroscopes with respect to important vectors defined along the orbit, geometrical parameters (curvatures) of the trajectory provided by the Frenet-Serret formalism, and geometrical properties (vorticity and shear) of the whole circular congruence.     

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l _??(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel?CLegendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system??s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et?al. (SIAM J. Optim. 20, 1504?C1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system??s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.     

Controlled Markov processes on the infinite planning horizon: Weighted and overtaking cost criteria

Stochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, we study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several recent results by Feinberg and Shwartz, and by Krass et al. In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; our approach is based on qualitative properties of the optimality equation for problems with an average cost criterion.Research partially supported by the Engineering Foundation under grant RI-A-93-10, in part by the National Science Foundation under grant NSF-INT 9201430, and in part by a grant from the AT&T Foundation.Research partially supported by the Air Force Office of Scientific Research under Grant F49620-92-J-0045, and in part by the National Science Foundation under Grant CDR-8803012.     

Analytical Study of Raw Materials of Zinc Oxide Used for Enamels on Industrial Ceramics: Quantitative Analysis of Zinc,Lead, and Sulfur in These Samples by X‐ray Fluorescence and Flame Atomic Absorption Spectrometry

An analytical study is carried out to optimize X‐ray fluorescence (XRF) and flame atomic absorption spectrometry (FAAS) quantitative analysis of Zn, Pb, and S in ZnO samples commonly used to obtain industrial ceramic enamels. Pb and S in the raw materials often contaminate ZnO and are very detrimental in industrial applications. Thus, very accurate analytical determination of these elements in ceramic samples is extremely important. First of all, a mineralogical study by X‐ray diffraction (XRD) on the different components in these raw materials and the materials produced during the firing process is performed in order to establish the mineral forms in a reference sample for analysis by XRF spectrometry. The working conditions are optimized for XRF multielemental analysis, using the sample in the form of pellets, due to high loss on ignition (LOI) values. The preparation of suitable standards and working conditions for FAAS analysis have also been optimized. The content of these elements was determined by FAAS for the reference sample and several samples for industrial use, and the results were compared with those obtained by XRF. Comparison of the results obtained from XRF and FAAS analysis of Pb and Zn show more accurate values for FAAS. For ZnO, an accuracy of 0.11% with ±0.1% precision by FAAS and 0.46% accuracy with ±0.2% precision by XRF are found. For PbO, 1.06% accuracy and ±0.06% precision using FAAS and 5.6% accuracy and ±0.35% precision by XRF were found. For SO₃ determined only by XRF, accuracy was 4.76% with ±0.25% precision. These values are highly satisfactory given that these two elements are only found in small proportions.     

High-Temperature dispersion zones in cross-linked natural rubber

The complex dielectric constant of natural rubber samples cross-linked by sulfur and dicumyl peroxide has been measured over a frequency range from 1.5 to 3.0 × 10⁵ cps by the bridge method and from 3.0 to 1.0 × 10⁴ cps by the relaxation method. Two dispersion peaks were detected which lay in the measured frequency range at temperatures above the main dispersion zone. Temperature and cross-link density-dependent shift of these peaks were studied and compared with the results obtained by Ferry et al. from complex compliance measurements performed on analogous systems.     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

X‐ray absorption study of the local structure at the NiO/oxide interfaces

This work reports an X‐ray absorption near‐edge structure (XANES) spectroscopy study at the Ni K‐edge in the early stages of growth of NiO on non‐ordered SiO₂, Al₂O₃ and MgO thin films substrates. Two different coverages of NiO on the substrates have been studied. The analysis of the XANES region shows that for high coverages (80 Eq‐ML) the spectra are similar to that of bulk NiO, being identical for all substrates. In contrast, for low coverages (1 Eq‐ML) the spectra differ from that of large coverages indicating that the local order around Ni is limited to the first two coordination shells. In addition, the results also suggest the formation of cross‐linking bonds Ni—O—M (M = Si, Al, Mg) at the interface.     

Pressure-induced structural transformations,orbital order and antiferromagnetism in La<Subscript>0.75</Subscript>Ca<Subscript>0.25</Subscript>MnO<Subscript>3</Subscript>

High pressure evolution of structural, vibrational and magnetic properties of La_0.75Ca_0.25MnO₃ was studied by means of X-ray diffraction and Raman spectroscopy up to 39 GPa, and neutron diffraction up to 7.5 GPa. The stability of different magnetic ground states, orbital configurations and structural modifications were investigated by LDA + U electronic structure calculations. A change of octahedral tilts corresponding to the transformation of orthorhombic crystal structure from the Pnma symmetry to the Immaone occurs above P ~ 6 GPa. At the same time, the evolution of the orthorhombic lattice distortion evidences an appearance of the e _g d _{x² ? z²} orbital polarization at high pressures. The magnetic order in La_0.75Ca_0.25MnO₃ undergoes a continuous transition from the ferromagnetic 3D metallic (FM) ground state to the A-type antiferromagnetic (AFM) state of assumedly 2D pseudo-metallic character under pressure, that starts at about 1 GPa and extends possibly to 20–30 GPa.     

The diameter of random regular graphs

We give asymptotic upper and lower bounds for the diameter of almost everyr-regular graph onn vertices (n → ∞).