The minimal degree of plane models of algebraic curves and double coverings

Let C be a smooth irreducible projective curve of genus g and s(C, 2) (or simply s(2)) the minimal degree of plane models of C. We show the non-existence of curves with s(2) = g for g ≥ 10, g ≠ 11. Another main result is determining the value of s(2) for double coverings of hyperelliptic curves. We also give a criterion for a curve with big s(2) to be a double covering.     

Approximation algorithms for the weighted independent set problem in sparse graphs

The approximability of the unweighted independent set problem has been analyzed in terms of sparseness parameters such as the average degree and inductiveness. In the weighted case, no corresponding results are possible for average degree, since adding vertices of small weight can decrease the average degree arbitrarily without significantly changing the approximation ratio. In this paper, we introduce two weighted measures, namely weighted average degree and weighted inductiveness, and analyze algorithms for the weighted independent set problem in terms of these parameters.     

CONSERVATION LAWS IN FINITE MICROCRACKING BRITTLE SOLIDS

This paper addresses the conservation laws in finite brittle solids with microcracks. The discussion is limited to the 2-D cases. First, after considering the combination of the Pseudo-Traction Method and the indirect Boundary Element Method, a versatile method for solving multi-crack interacting problems in finite plane solids is proposed, by which the fracture parameters （SIF and path-independent integrals） can be calculated with a desirable accuracy. Second, with the aid of the method proposed, the roles the conservation laws play in the fracture analysis for finite microcracking solids are studied. It is concluded that the conservation laws do play important roles in not only the fracture analysis but also the analysis of damage and stability for the finite microcracking system. Finally, the physical interpretation of the M-integral is discussed further. An explicit relation between the M-integral and the crack face area, i.e., M = GS, has been discovered using the analytical method, which can shed some light on the Damage Mechanics issues from a different perspective.     

Biomimetic Synthesis of Metal Ion‐Doped Hierarchical Crystals Using a Gel Matrix: Formation of Cobalt‐Doped LiMn2O4 with Improved Electrochemical Properties through a Cobalt‐Doped MnCO3 Precursor

We have synthesized spinel type cobalt‐doped LiMn₂O₄ (LiMn_2?yCo_yO₄, 0≤y≤0.367), a cathode material for a lithium‐ion battery, with hierarchical sponge structures via the cobalt‐doped MnCO₃ (Mn_1‐xCo_xCO₃, 0≤x≤0.204) formed in an agar gel matrix. Biomimetic crystal growth in the gel matrix facilitates the generation of both an homogeneous solid solution and the hierarchical structures under ambient condition. The controlled composition and the hierarchical structure of the cobalt‐doped MnCO₃ precursor played an important role in the formation of the cobalt‐doped LiMn₂O₄. The charge–discharge reversible stability of the resultant LiMn_1.947Co_0.053O₄ was improved to ca. 12 % loss of the discharge capacity after 100 cycles, while pure LiMn₂O₄ showed 24 % loss of the discharge capacity after 100 cycles. The parallel control of the hierarchical structure and the composition in the precursor material through a biomimetic approach, promises the development of functional materials under mild conditions.     

Screening of C60 crystallization using a microfluidic system

We have carried out screening of C60 crystallization using a simple liquid/liquid interfacial precipitation method in a microfluidic device. By controlling the time, temperature, and concentration, various metastable phases of C60 crystals were found, including tubes, spheres, open-ended hollow columns, stars, branches, and trees. The obtained C60 crystal shapes are similar to those of snow crystals. These findings suggest an urgent need to screen C60 crystallization for the development of fullerene C60 drugs.     

Excited state geometry optimizations by analytical energy gradient of long-range corrected time-dependent density functional theory

An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.     

Direct photon measurement at RHIC-PHENIX

Results on direct photon measurements from the PHENIX experiment at RHIC are presented. The direct photon yields for P _T >6GeV/c as a function of centrality in Au+Au collisions at $\sqrt {s_{NN} } = 200$ GeV are found to be consistent with NLO pQCD calculation scaled by the number of binary collisions. The results suggest that the photons observed are emitted from the initial stage of hard scattering. Comparisons with several theoretical calculations are also presented.     

N-Acetylaspartate concentrations in the thalami of neuropathic pain patients and healthy comparison subjects measured with (1)H-MRS

We investigated the absolute concentration of N-acetylaspartate (NAA) in the thalami of neuropathic pain patients and healthy comparison subjects by single-voxel proton magnetic resonance spectroscopy ((1)H-MRS). (1)H-MRS was performed with a 1.5-T MR system on a voxel in the thalamus bilaterally in 9 neuropathic pain patients and 14 healthy control subjects. We measured the absolute concentration of NAA using a linear combination model. The NAA concentration in the thalamus decreased significantly on the contralateral side in seven patients and on the ipsilateral side in two patients, as compared with the mean NAA concentration of the healthy control subjects. The NAA concentrations in two patients who did not respond to standard pain treatments were extremely decreased. Our results using (1)H-MRS suggest that neuropathic pain seems to be associated with an abnormal balance of the neural activity in the thalamus. The NAA concentration of the thalamus may be related to the efficacy of therapy. (1)H-MRS may serve as a useful noninvasive tool for evaluating thalamic neural activity in neuropathic pain patients.     

Cerium isotope effects in Ce(III) malate and lactate complex formation studied by long-distance displacement chromatography

Isotope effects of cerium were observed in malate and lactate complex formations during the long-distance displacement chromatographic processes at 313 K. Heavier isotopes were found fractionated in the frontal edges of the Ce adsorption bands in both the systems, registering a preference of the heavier isotopes for the Ce(III) complexes in the solution phase over the simply hydrated Ce(III) ions in the resin phase. The fractionation coefficients epsilon for the 136Ce/140Ce, 138Ce/140Ce and 142Ce/140Ce isotopic pairs were 7.1 x 10(-6), 5.2 x 10(-6) and -2.1 x 10(-6) for the malate system, and 4.8 x 10(-6), 4.5 x 10(-6) and-2.6 x 10(-6) for the lactate system, respectively. They all show the mass-dependent law if the deviation of epsilon for the 138Ce/140Ce pair was considered merely due to the isobaric interference in Ce isotopic ratio measurements, suggesting the molecular vibration, rather than the nuclear field shift, mainly contributes to the Ce isotope effects in the complex formation systems. The absolute values of epsilon between the two systems are comparable, suggesting no instinct difference in structural properties between Ce malate and lactate complexes involved.