The exact decomposition of gauge variables in lattice Yang–Mills theory

In this Letter, we consider lattice versions of the decomposition of the Yang–Mills field a la Cho–Faddeev–Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N)$\mathit{SU}(N)$ gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$. As a result, we obtain the general form of the decomposition for SU(N)$\mathit{SU}(N)$ gauge link variables and confirm the previous results obtained for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$.     

Selection of the number of regression variables; A minimax choice of generalized FPE

Summary A generalized Final Prediction Error (FPE_α)_ criterion is considered. Based onn observations, the numberk of regression variables is selected from a given range 0≦k≦K, so as to minimize . It is shown that if α tends to infinity withn, the selection is consistent but the maximum of the mean squared error of estimates of parameters diverges to infinity with the same order of divergence as that of α. A meaningful minimax choice of α exists for a regret type mean squared error, while for simple mean squared error it is trivially 0. The minimax regret choice of α converges to a constant, approximately 3.5 forK≧8 ifn−K increases simultaneously withn, otherwise it diverges to infinity withn.     

The number of labeled graphs placeable by a given permutation

Let S be a finite set and σ a permutation on S. The permutation σ* on the set of 2-subsets of S is naturally induced by σ. Suppose G is a graph and V(G), E(G) are the vertex set, the edge set, respectively. Let V(G) = S. If E(G) and σ*(E(G)), the image of E(G) by σ*, have no common element, then G is said to be placeable by σ. This notion is generalized as follows. If any two sets of {E(G), (σ¹)*(E(G)),…,(σ^l−1)* (E(G))} have no common element, then G is said to be I-placeable by σ. In this paper, we count the number of labeled graphs which are I-placeable by a given permutation. At first, we introduce the interspaced Ith Fibonacci and Lucas numbers. When I = 2 these numbers are the ordinary Fibonacci and Lucas numbers. It is known that the Fibonacci and Lucas numbers are rounded powers. We show that the interspaced Ith Fibonacci and Lucas numbers are also rounded powers when I = 3. Next, we show the number of labeled graphs which are I-placeable by a given permutation is a product of the interspaced Ith Lucas numbers. Finally, using a property of the generalized binomial series, we count the number of labeled graphs of size k which are I-placeable by σ. © 1996 John Wiley & Sons, Inc.     

Velocity and metastable state population distributions of neodymium atoms produced by laser ablation

Laser-induced fluorescence spectroscopy has been employed to characterize the plume produced in nanosecond laser ablation of metallic neodymium. The kinetic-energy distributions of the neutral and ionized atoms in the plume under both vacuum and gas environments have been investigated. The population distribution of metastable levels in the ablated atoms was also derived. The results show that some metastable states are more heavily populated than predicted by a Boltzmann-type distribution. These investigations provide preliminary data for the design of a new type of resonance photo-ionization laser ion source as well as for high-resolution laser spectroscopy of refractory elements. PACS 52.38.Mf; 33.50.Dq; 42.62.Fi     

Synthesis, photophysical and electrochemical properties of perfluoroisopropyl substituted binuclear phthalocyanine conjugated with a butadiyne linker

Synthesis of 1,3-butadiyne-bridged perfluoroisopropyl binuclear phthalocyanine 2 has been successfully achieved from unsymmetrical A₃B-type iodo-perfluoroisopropyl phthalocyanine by palladium-catalyzed cross-coupling with trimethylsilylacetylene and copper-catalyzed Glaser homo-coupling as key reactions. The dyad 2 essentially remains non-aggregated irrespective of solvent and concentration. Electrochemical analysis suggests oxidation is not possible whereas the molecule is more easily reduced. All the results are advantages for photodynamic therapy (PDT).     

Reaction mechanism for target-like products from197Au target bombarded with12C ions of energies above 100 MeV/u

Target-like products, that is,^191–200Au,^185–200Pt, and^183–195Ir, from¹⁹⁷Au target bombarded with¹²C ions at the energies of 180, 230, and 400 MeV/u were measured by using off-line gamma-ray spectrometry combined with chemical separation procedures. Spallation systematics by Rudstam reproduces well the measured cross sections for formation of platinum and iridium isotopes. It was found that the cross sections of gold nuclides increase with increase of the incident energy in the range studied and they are enhanced if compared with the reported proton-induced reaction of gold at a similar incident energy. It is suggested that the electromagnetic dissociation process plays a role for production of such gold nuclides.     

Deformation of polybutene-1 spherulites

The deformation of fresh and aged polybutene-1 spherulitic samples has been investigated by microscopic observation, interferometry, studying macroscopic and spherulitic birefringence changes, and study of light-scattering patterns. The spherulite deformation is not affine, the microscopic deformation ratio being less than the macroscopic deformation ratio of the sample and greater in the equatorial regions of the spherulite than in the polar regions. The deviation from affine deformation is less for fresh spherulites than for the aged, where void formation occurs in the equatorial part of the spherulite. This gives rise to large scattering by this part of the spherulite and to form birefringence. The spherulite birefringence and its change with elongation is dependent upon the degree of aging of the sample. The spherulite birefringence is more negative for the aged sample. In the polar regions of the spherulite, this negative birefringence decreases and turns positive at higher elongations, characteristic of a reorientation of the crystals with their optic axes turning from being perpendicular to parallel to the spherulite radius. The spherulite birefringence in the equatorial direction becomes somewhat more negative on stretching a fresh sample but less negative on stretching an aged one. Spherulite distortion and orientation changes are apparent from the light-scattering patterns of films possessing small spherulites. The changes in V_v and H_v scattering patterns upon stretch are different for the fresh and aged samples. The V_v patterns of the fresh samples decrease in intensity with time after stretching a fresh sample with the H_v patterns do not.     

Direct counting of submicrometer-sized photosynthetic apparatus dispersed in medium at cryogenic temperature by confocal laser fluorescence microscopy: estimation of the number of bacteriochlorophyll c in single light-harvesting antenna complexes chlorosomes of green photosynthetic bacteria

The number of pigments in single light-harvesting complexes (chlorosomes) were calculated by imaging single chlorosomes in a frozen buffer at cryogenic temperature with a confocal laser fluorescence microscope and pigment extraction. Chlorosomes were isolated from two types of green photosynthetic bacteria Chlorobium (Chl.) tepidum and Chloroflexus (Cfl.) aurantiacus and were individually imaged in the frozen medium. Each fluorescence spot observed mainly came from a single chlorosome and was ascribable to self-aggregates of bacteriochlorophyll (BChl) c molecules as core parts of chlorosomes. A three-dimensional distribution of fluorescence of single chlorosomes was analyzed, and the number of chlorosomes in a volume of 54,000 microm(3) was counted directly. On the basis of the results, averaged numbers of the BChl c molecules contained in a single chlorosome of Chl. tepidum and Cfl. aurantiacus were determined to be 1.4 x 10(5) and 9.6 x 10(4), respectively. The present numbers are almost comparable to those estimated by other methods (Martinez-Planells et al., Photosynth. Res. 2002, 71, 83 and Monta?o et al., Biophys. J. 2003, 85, 2560).     

Synthesis and properties of thermoplastic propyl-etherified amylose

Amylose was etherified with 1-bromopropane in DMSO. The degree of substitution (DS) was varied by altering the feed ratio of 1-bromopropane. The structures of the products were characterized by IR and 1H-NMR spectroscopy. When the molar feed ratio of 1-bromopropane to hydroxyl groups of amylose was beyond 7.5, the hydroxyl groups were completely substituted with propyl ether groups. The etherified amylose with DS 1.9 showed a glass transition temperature (T_g), and that with DS 2.3 or 3.0 showed both T_g and melting temperature (T_m) (DS 3.0 means complete substitution). The etherification imparted melt processability and solubility in nonpolar organic solvent to amylose.