An ore-type condition for the existence ofk-factors in graphs

Letk be a positive integer, and letG be a graph of ordern withn 4k – 5,kn even and minimum degree at leastk. We prove that if the degree sum of each pair of nonadjacent vertices is at leastn, thenG has ak-factor.     

Nanophotonic droplet: a nanometric optical device consisting of size- and number-selective coupled quantum dots

Although recent advances in fabrication technologies have allowed the realization of highly accurate nanometric devices and systems, most approaches still lack uniformity and mass-production capability sufficient for practical use. We have previously demonstrated a novel technique for autonomously coupling heterogeneous quantum dots to induce particular optical responses based on a simple phonon-assisted photocuring method in which a mixture of quantum dots and photocurable polymer is irradiated with light. The cured polymer sequentially encapsulates coupled quantum dots, forming what we call a nanophotonic droplet. Recently, we found that each quantum dot in the mixture is preferably coupled with other quantum dots of similar size due to a size resonance effect of the optical near-field interactions between them. Moreover, every nanophotonic droplet is likely to contain the same number of coupled quantum dots. In this paper, we describe the basic mechanisms of autonomously fabricating nanophotonic droplets, and we examine the size- and number-selectivity of the quantum dots during their coupling process. The results from experiments show the uniformity of the optical properties of mass-produced nanophotonic droplets, revealed by emission from the contained coupled quantum dots, due to the fundamental characteristics of our method.     

Upper and Lower Bounds on Maximum Nonlinearity of n-input m-output Boolean Function

The paper presents lower and upper bounds on the maximumnonlinearity for an n-input m-output Booleanfunction. We show a systematic construction method for a highlynonlinear Boolean function based on binary linear codes whichcontain the first order Reed-Muller code as a subcode. We alsopresent a method to prove the nonexistence of some nonlinearBoolean functions by using nonexistence results on binary linearcodes. Such construction and nonexistence results can be regardedas lower and upper bounds on the maximum nonlinearity. For somen and m, these bounds are tighter than theconventional bounds. The techniques employed here indicate astrong connection between binary linear codes and nonlinear n-input m-output Boolean functions.     

Investigation of scattering of elastic waves by cylinders in 1-3 piezocomposites

The scattering behavior of P-waves in piezoelectric composites with 1–3 connectivity is studied. The method of wave function expansion is adopted for the theoretical derivations. Analytical expressions are obtained for the distributions of mechanical displacement in z-direction along the circumferences of piezoelectric cylinders. These solutions are used to study the influence of each element of the stiffness matrix and the piezoelectric matrix on the various resonant modes of vibration. Numerical results obtained indicate that perturbations of the elements c₄₄ and e₁₅ significantly affect resonant frequencies and amplitudes, perturbations of c₁₁ and c₁₂ have pronounced effects on resonant modes of high frequencies also. However, the resonant modes are not so sensitive to the perturbations of c₁₃, e₃₁ and e₃₃. The dynamic characteristics of 1–3 connectivity piezoelectric composites exposed here are meaningful for the design and manufacture of sensor/actuator elements by this kind of composites as well as the on-line health monitoring of the mechanical properties variations of the composites itself.     

Nanometric summation architecture based on optical near-field interaction between quantum dots

A nanoscale data summation architecture is proposed and experimentally demonstrated based on the optical near-field interaction between quantum dots. Based on local electromagnetic interactions between a few nanometric elements via optical near fields, we can combine multiple excitations at a certain quantum dot, which allows construction of a summation architecture. Summation plays a key role for content-addressable memory, which is one of the most important functions in optical networks.     

Propagation of thickness-twist waves in a piezoelectric ceramic plate with unattached electrodes

We analyze the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with air gaps between the plate surfaces and two electrodes. These waves are also called anti-plane or shear-horizontal waves with one displacement component only. An exact solution is obtained from the equations of the linear theory of piezoelectricity. Dispersion relations of the waves are obtained and plotted. Results show that the wave frequency or speed is sensitive to the air gap thickness. This effect can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.     

Reaction dynamics of excited 2-(3-benzoylphenyl)propionic acid (ketoprofen) with histidine

Photoreaction dynamics of 2-(3-benzoylphenyl)propionic acid (ketoprofen, KP), one of nonsteroidal anti-inflammatory drugs, with histidine in a phosphate buffer solution (pH 7.4) was investigated with the laser flash photolysis. The deprotonated form of KP (KP(-)) was decarboxylated via UV laser excitation to form a carbanion. It was found that histidine accelerates the protonation reaction of the carbanion to 3-ethylbenzophenone ketyl biradical (3-EBPH) for the first time. The experimental results of the photoreaction of KP with alanine as well as the photoreaction of KP with 4-methylimidazole (a part of the side chain of histidine) in methanol, clearly showed that the protonated form of histidine is a key species for the protonation reaction of the carbanion. These series of the initial reactions should result in the occurrence of photosensitization in vivo. The reaction mechanism was discussed in detail.     

Collision-energy-resolved penning ionization electron spectroscopy of phenylacetylene and diphenylacetylene by collision with He*(2(3)s) metastable atoms

Penning ionization of phenylacetylene and diphenylacetylene upon collision with metastable He*(2(3)S) atoms was studied by collision-energy-/electron-energy-resolved two-dimensional Penning ionization electron spectroscopy (2D-PIES). On the basis of the collision energy dependence of partial ionization cross-sections (CEDPICS) obtained from 2D-PIES as well as ab initio molecular orbital calculations for the approach of a metastable atom to the target molecule, anisotropy of interaction between the target molecule and He*(2(3)S) was investigated. For the calculations of interaction potential, a Li(2(2)S) atom was used in place of He*(2(3)S) metastable atom because of its well-known interaction behavior with various targets. The results indicate that attractive potentials localize in the pi regions of the phenyl groups as well as in the pi-conjugated regions of the acetylene group. Although similar attractive interactions were also found by the observation of CEDPICS for ionization of all pi MOs localized at the C[triple bond]C bond, the in-plane regions have repulsive potentials. Rotation of the phenyl groups about the C[triple bond]C bond can be observed for diphenylacetylene because of a low torsion barrier. So the examination of measured PIES was performed taking into consideration the change of ionization energies for conjugated molecular orbitals.     

Highly efficient total synthesis of the marine natural products (+)-avarone, (+)-avarol, (-)-neoavarone, (-)-neoavarol and (+)-aureol

Biologically important and structurally unique marine natural products avarone (1), avarol (2), neoavarone (3), neoavarol (4) and aureol (5), were efficiently synthesized in a unified manner starting from (+)-5-methyl-Wieland-Miescher ketone 10. The synthesis involved the following crucial steps: i) Sequential BF(3)Et(2)O-induced rearrangement/cyclization reaction of 2 and 4 to produce 5 with complete stereoselectivity in high yield (2 --> 5 and 4 --> 5); ii) strategic salcomine oxidation of the phenolic compounds 6 and 8 to derive the corresponding quinones 1 and 3 (6 --> 1 and 8 --> 3); and iii) Birch reductive alkylation of 10 with bromide 11 to construct the requisite carbon framework 12 (10 + 11 --> 12). An in vitro cytotoxicity assay of compounds 1-5 against human histiocytic lymphoma cells U937 determined the order of cytotoxic potency (3 > 1 > 5 > 2 > 4) and some novel aspects of structure-activity relationships.     

A synchrotron X‐ray study of triclinic LiCa2Nb3O10 with perovskite‐type slabs

The triclinic superstructure of a small crystal of LiCa₂Nb₃O₁₀, lithium dicalcium triniobium decaoxide, has been investigated by synchrotron X‐ray diffraction. The unit cell is an almost rectangular parallelepiped, although there is a 0.245° offset from orthogonality for β. The structure essentially belongs to a homologous series of Li[Na_n?3Ca₂Nb_nO_3n+1] with n = 3, where the moiety in square brackets has a perovskite‐type slab structure. The superstructure has a doubled unit‐cell volume with respect to the tetragonal aristotype. The NbO₆ octahedra are rotated about axes parallel to [110] by approximately 10°. Adjacent slabs are connected by Li atoms and are geo­metrically related by 4₂ pseudosymmetry lying parallel to c . There are twice as many sites as Li atoms, providing a variation of population at these Li sites.