Entropy formula of Pesin type for noninvertible random dynamical systems

In this paper we consider random dynamical systems (abbreviated henceforth as RDS's) generated by compositions of random endomorphisms (maybe noninvertible and with singularities) of class of a compact manifold. Entropy formula of Pesin type is proved for such RDS's under some absolute continuity conditions on the associated invariant measures. Received October 17, 1997; in final form January 5, 1998     

XAS and XMCD studies of amorphous FeCo-based ribbons

This paper reports x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) studies at Fe L_3,2 and Co L_3,2-edges to investigate the electronic structure of (Fe_100 ? xCo_x)₇₈Si₉Nb₃B₉Cu₁ (0 < x < 95) alloys. The influence of controlled Co addition on electronic structural and magnetic properties of (Fe_100 ? xCo_x)₇₈Si₉Nb₃B₉Cu₁ (x = 0, 20, 40, and 60) alloys has been investigated and it has been observed that Co exists as Co²⁺/Co³⁺, while Fe exists as a mixture of Fe⁰ (metallic) and Fe²⁺. The XMCD studies confirm these results and reveal that Co-ions are responsible for the room temperature ferromagnetism (RTFM) in the system, while at Fe L_3,2-edge it shows a diamagnetic behavior.     

Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities

We prove a general duality result showing that a Brascamp–Lieb type inequality is equivalent to an inequality expressing subadditivity of the entropy, with a complete correspondence of best constants and cases of equality. This opens a new approach to the proof of Brascamp–Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving a general inequality expressing the subadditivity property of the entropy on ${\mathbb {R}^n}We prove a general duality result showing that a Brascamp–Lieb type inequality is equivalent to an inequality expressing subadditivity of the entropy, with a complete correspondence of best constants and cases of equality. This opens a new approach to the proof of Brascamp–Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving a general inequality expressing the subadditivity property of the entropy on \mathbb Rⁿ{\mathbb {R}^n}, and fully determining the cases of equality. As a consequence of the duality mentioned above, we obtain a simple new proof of the classical Brascamp–Lieb inequality, and also a fully explicit determination of all of the cases of equality. We also deduce several other consequences of the general subadditivity inequality, including a generalization of Hadamard’s inequality for determinants. Finally, we also prove a second duality theorem relating superadditivity of the Fisher information and a sharp convolution type inequality for the fundamental eigenvalues of Schr?dinger operators. Though we focus mainly on the case of random variables in \mathbb Rⁿ{\mathbb {R}^n} in this paper, we discuss extensions to other settings as well.     

Origin invariant approaches to the calculation of two-photon circular dichroism

The origin dependence of the expression of two-photon circular dichroism in the length formulation employed by the authors in a recent computational study [B. Jansik et al., Chem. Phys. Lett. 414, 461 (2005)] is discussed in detail, and some inherently origin invariant alternative formulations are introduced. Extensive computational tests on a small reference chiral system, namely, a chiral form of H(2)O(2), are performed at the density functional theory (DFT)/B3LYP level of theory with large diffuse correlation consistent basis sets. The results indicate that the velocity formulation originally proposed by Tinoco, Jr. [J. Chem. Phys. 62, 1006 (1975)] provides the most convenient approach for an origin invariant calculation of two-photon circular dichroism.     

Combined density functional/polarizable continuum model study of magnetochiral birefringence: can theory and experiment be brought to agreement?

The magnetic-field-induced axial birefringence (magnetochirality) of five closed-shell chiral molecules (three substituted oxiranes, carvone, and limonene) is studied at the density functional theory level using Becke's 3-parameter Lee-Yang-Parr functional and frequency-dependent quadratic response theory. The influence of the environment and the conformational distribution on the property is also studied. The environment effects are described by the polarizable continuum model in its integral-equation formulation. The effect of the conformational distribution is investigated by performing calculations on several conformers-for carvone and limonene-followed by Boltzmann averaging. The calculated values for the magnetochiral birefringence are compared to previous ab initio results and experimental data where available. The refined model presented here brings the ab initio values closer to experiment. Still, disagreements remain in some cases and it appears difficult to resolve these discrepancies.     

On binding energy of trions in bulk materials

We study the negatively $T^{?}$ and positively $T^{+}$ charged trions in bulk materials in the effective mass approximation within the framework of a potential model. The binding energies of trions in various semiconductors are calculated by employing Faddeev equation in configuration space. Results of calculations of the binding energies for $T^{?}$ are consistent with previous computational studies and are in reasonable agreement with experimental measurements, while the $T^{+}$ is unbound for all considered cases. The mechanism of formation of the binding energy of trions is analyzed by comparing contributions of a mass-polarization term related to kinetic energy operators and a term related to the Coulomb repulsion of identical particles.     

Laser induced mixing in multilayered Ti/Ta thin film structures

The possibility of interlayer mixing in a Ti/Ta multilayer system, induced by laser irradiation, was the main purpose of these experiments. Ti/Ta multilayer system, consisting of ten alternating Ti and Ta thin films and covered by slightly thicker Ti layer, was deposited on Si (100) wafers to a total thickness of 205 nm. Laser irradiation was performed in air by picoseconds Nd:YAG laser pulses in defocused regime with fluences of 0.057 and 0.11 J cm^?2. Laser beam was scanned over the 5?×?5 mm surface area with different steps along y-axes. Structural and compositional characterisation was done by auger electron spectroscopy, X-ray photoelectron spectroscopy, atomic force microscopy, and scanning electron microscopy. Laser processing at lower fluence caused only oxidation of the top Ti layer, despite of the number of applied laser pulses. Interlayer mixing was not observed. Application of laser pulses at fluence of 0.11 J cm^?2 caused partial and/or complete ablation of deposited layers. In partially ablated regions considerable mixing between Ti and Ta films was registered.     

Mathieu and Heun Solutions to the Wheeler–De Witt Equation for Hyperbolic Universes

For the spatially open Friedmann–Robertson–Walker (FRW) Universe with stiff matter and radiation as non-interacting matter sources, the scale function coming from the integration of the Friedmann equation is expressed in terms of elliptic integrals. For a negative cosmological constant, we identify the allowed ranges for the model’s parameters. Within the quantum analysis, the Wheeler–De Witt (WDW) equation turns into a modified Morse equation whose solutions are Mathieu and Heun functions.     

Benzil Photoperoxidations in Polymer Films and Crosslinking by the Resultant Benzoyl Peroxides in Polystyrene and Other Polymers

Benzil (BZ) can be converted almost quantitatively to benzoyl peroxide (BP) in aerated polymer films upon irradiation at >400 nm (i.e., the long-wavelength edge of the n→π* absorption band of BZ, where BP does not absorb). Here, we summarize results for the photoperoxidation of BZ structures with molecular oxygen, principally in glassy polymer matrices. Some of the polymers are doped directly with BZ or its derivatives, and others, contain covalently attached BZ pendant groups from which BP groups are derived. While the decomposition of low-molecular-weight BP doped into polymer films (such as those of polystyrene (PS)) results in a net decrease in polymer molecular weight, thermal decomposition of pendant BP groups is an efficient method for chain crosslinking. Crosslinking of PS films doped with a molecule containing two covalently linked BZ or BP groups proceeds in a similar fashion. Free radicals from the covalently attached BP allow grafting of new monomers, as well. Additionally, the use of radiation filtered through masks has been used to create patterns of polymers on solid surfaces. Crosslinking of photodegradable poly(phenyl vinyl ketone) with BP structures obtained by photoperoxidation of BZ structures for the preparation of photodegradable polymer networks is described as well. In sum, the use of BZ and BP and their derivatives offers simple and convenient routes for modifying polymer chains and, especially, for crosslinking them. Specific applications of each use and process are provided. Although applications with PS are featured here, the methodologies described are amenable to a wide variety of other polymers.