On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

Fluorescence Probes for Cyclodextrin Interiors

6-Propionyl-2-(dimethylamino)naphthalene (PRODAN) emits two fluorescence bands, at 510 and 435 run, when dissolved in -cyclodextrin (CD) aqueous solutions. The relative contributions of these two bands were found to depend on time and temperature. These emissions are attributed to the inclusion of PRODAN with the dimethylamino group toward the larger and smaller rims inside the -CD cavities, respectively. The first position corresponds to a slightly polar and slightly rigid environment, while the second corresponds to a hydrophobic and rigid environment relative to the aqueous polar bulk. In contrast, PRODAN in either -CD or -CD aqueous solutions emits a single fluorescence band at 525 and 510 nm, respectively. The emission of PRODAN in -CD is similar to that in water and indicates no inclusion at all. In -CD, only one kind of inclusion is possible with the dimethylamino group of PRODAN toward the larger rims of -cavities. These results are supported by fluorescence decay lifetime measurements and are consistent with our previous observations made for 4-dimethylaminobenzonitrile (DMABN) and 4-diethylaminobenzonitrile (DEABN) in - and -CD aqueous solutions [23,24]. Therefore the possibility of twisted intramolecular charge transfer (TICT) state formation in PRODAN in terms of environmental polarity and local free volume of CD cavities is discussed. These observations put PRODAN, DMABN, and other TICT compounds as fluorescence probes for CD interiors.     

Green Fluorescent Protein (GFP) as a Marker for Cell Viability After UV Irradiation

Generation of Chinese Hamster Ovary (CHO) cell lines stably expressing green fluorescent protein (GFP) was achieved using a plasmid vector that encoded the red-shifted pCX-xGFP under the control of a strong hybrid promoter composed of a CMV enhancer and a -actin/-globin gene promoter. Cotransfection of the promoter-less pSV2-Neo helper plasmid transmitting neomycin resistance was followed by selection with the antibiotic G418. Constitutive GFP expression could be visualized in living and fixed cells using fluorescence spectroscopy, fluorescence microscopy, and flow cytometry. DNA repair-proficient (AA8) and deficient (UV5) CHO strains were used for survival tests after UVC irradiation. Cells carrying the GFP construct (AA8-pGFP, UV5-pGFP) show the same response to UV irradiation (colony forming ability) as their nontransformed parental cell lines (AA8, UV5). Using GFP as a marker for cell viability, cells were harvested after certain postirradiation growth periods and the numbers of GFP expressing cells and fluorescence intensities were determined by FACS analysis. Generally, GFP fluorescence in irradiated cells is not seen when cell membranes are damaged (leak-out of the soluble GFP). Irradiated cells without membrane damage express GFP continuously (leading to a dose-dependent increase in GFP contents).     

Random surfaces with two-sided constraints: An application of the theory of dominant ground states

We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints _x m/2. The main result is that for ₀, where ₀ does not depend onm, the structure of thermodynamic phases in the model is determined by dominant ground states: for an evenm a Gibbs state is unique and for an oddm the number of space-periodic pure Gibbs states is two.     

Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

Hyperfine interactions in muonium-impurity complexes in silicon

The properties of paramagnetic complexes formed by muonium located near acceptor and donor impurities in silicon are calculated using the quantum chemical methods. The calculated data are compared to the experimentally observed characteristics of normal and anomalous muonium centers.     

On a ferromagnetic spin chain

The quotient (s-1)/(s) of Riemann zeta functions is shown to be the partition function of a ferromagnetic spin chain for inverse temperatures.     

Silver Fractal-Like Structures for Metal-Enhanced Fluorescence: Enhanced Fluorescence Intensities and Increased Probe Photostabilities

Substantial increases in fluorescence emission from fluorophore-protein–coated fractal-like silver structures have been observed. We review two methods for silver fractal structure preparation, which have been employed and studied. The first, a roughened silver electrode, typically yielded a 100-fold increase in fluorophore emission, and the second, silver fractal-like structures grown on glass between two silver electrodes, produced a 500-fold increase. In addition, significant increases in probe photostability were observed for probes coated on the silver fractal like structures. These results further serve to compliment our recent work on the effects of nobel metal particles with fluorophores, a relatively new phenomenon in fluorescence we have termed both metal-enhanced fluorescence [1] and radiative decay engineering [2,3]. These results are explained by the metallic surfaces modifying the radiative decay rate () of the fluorescent labels. We believe that this new silver-surface preparation, which results in ultrabright and photostable fluorophores, offers a new generic technology platform for increased fluorescence signal levels, with widespread potential applications to the analytical sciences, imaging, and medical diagnostics.     

Methodological imperfection and formalizations of scientific activity

Any mathematical formalization of scientific activity allows for imperfections in the methodology that is formalized. These can be of three types, dirty, rotten, and dammed. Restricting mathematical attention to those methods that cannot be construed to be imperfect drastically reduces the class of objects that must be analyzed, and relates all other objects to these more regular ones. Examples are drawn from empirical logic.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

The use of time-dependent projection operators in the derivation of master equations

In this paper we generalize our previous work on the use of time-dependent projection operators for the derivation of master equations for general systems. Previously we had generalized the usual time-independent projection operator approach to include time-dependent projection operators, in which the relevant part of the full density operator is considered to be the uncorrelated part of the full density operator. The irrelevant part of the density operator was then the part describing the correlations between the coupled systems. In the present work we present new time-dependent projections operators which have the property that some correlations between the interacting subsystems are placed in the relevant part of the distribution function and the remaining correlations are placed in the irrelevant part of the distribution function.     

The diffusion and non-radiative transfer of excitation energy in molecular crystals containing foreign molecules

A study is made of the non-radiative transfer and diffusion of excitation energy in molecular crystals containing foreign molecules and its influence on the luminescent properties of these crystals.

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On the ferromagnetism of thin films

In this paper the magnetic properties of ferromagnetic thin layers are studied by calculating the partition function for the magnetic system inKirkwood's approximation of the second order. The results obtained for the Curie temperature and the magnetization are in somewhat better agreement with the experiment than those obtained by Valenta.

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The author extends his thanks to the group of research workers who performed the numerical calculation of the Curie temperatures on the computer CIFA 1, as well as gratitude to Dr. l. Valenta for so kindly supplying information on the results of his investigations on the same subject.     

Resistivity exponent of two-dimensional lattice animals

We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L , is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

Kinetics of the Decay of Prolonged Luminescence of Disordered Chrysene under the Conditions of Nonequilibrium Transfer of Energy

We present the results obtained in investigation of the decay of the prolonged luminescence of disordered chrysene in a microsecond range. At the temperature of liquid nitrogen, a highly nonexponential decay of both phosphorescence and annihilation of delayed fluorescence is observed. The observed character of decay is due to relaxation of the energy of electronic excitation in a system of energydisordered centers, when the value of kT is much smaller than the width of the excitedstate energy distribution. At the same time, in the system investigated there is a classical relationship between phosphorescence and delayed fluorescence, i.e., the rate coefficient for the reaction of triplettriplet annihilation is a constant.     

Analyzing Microdomains in Biological Membranes Using Fluorescence Techniques

It is becoming increasingly clear that various lipids and proteins in the plasma membrane are not distributed homogeneously but are organized in compositionally and functionally variable microdomains. Fluorescence techniques have contributed significantly to our understanding of membrane structure and function. Here we review recent studies using fluorescence methods to detect membrane domains in intact cells. We also discuss the current limitations in the available techniques and the models used to interpret experimental data.     

Cosmological surrealism: More than “eternal reality” is needed

Inflationary cosmology makes the universe eternal and provides for recurrent universe creation, ad infinitum — making it also plausible to assume that our Big Bang was also preceeded by others, etc.. However, GR tells us that in the parent universe's reference frame, the newborn universe's expansion will never start. Our picture of reality in spacetime has to be enlarged.Wolfson Distinguished Chair in Theoretical Physics.Also on leave from the University of Texas, Center for Particle Physics, Austin, Texas.     

The quantum theory of multipole radiation in a dielectric

The potentials of an electromagnetic field of multipoles in a dielectric, which is realized by a dielectric sphere having a perfectly conducting surface, are derived. The diagonal values of the energy for thez component of the angular momentum and the square of the angular momentum of the field are determined and also the ratio between thez component of the angular momentum and the energy and the ratio between the square of the angular momentum and the square of the energy. It is shown that the total angular momentum can be divided in the usual way into orbital and spin parts but that these parts cannot be interpreted as the orbital and spin angular momentum because their eigenvalues cannot be the eigenvalues of any operator of infinitesimal rotation. In the commutation rules of a multipole field the vector character of the field is to a certain extent suppressed and the spin of the photon in a state with a certain value of the energy, parityz component of the angular momentum and the square of the angular momentum is not defined.

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, . ,z— , , z— . , , , , , - . , ,z— .

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In conclusion the author thanks Dr. . Muziká for directing the work, F. Samek for valuable remarks and discussion and J. Kvasnica for help in preparing the paper for publication and for adding a number of remarks.