Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization

The regularized Newton method (RNM) is one of the efficient solution methods for the unconstrained convex optimization. It is well-known that the RNM has good convergence properties as compared to the steepest descent method and the pure Newton’s method. For example, Li, Fukushima, Qi and Yamashita showed that the RNM has a quadratic rate of convergence under the local error bound condition. Recently, Polyak showed that the global complexity bound of the RNM, which is the first iteration k such that ‖∇ f(x _k )‖≤ε, is O(ε ⁻⁴), where f is the objective function and ε is a given positive constant. In this paper, we consider a RNM extended to the unconstrained “nonconvex” optimization. We show that the extended RNM (E-RNM) has the following properties. (a) The E-RNM has a global convergence property under appropriate conditions. (b) The global complexity bound of the E-RNM is O(ε ⁻²) if ∇ ² f is Lipschitz continuous on a certain compact set. (c) The E-RNM has a superlinear rate of convergence under the local error bound condition.     

E expansion for a Fermi gas at infinite scattering length

We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over E = 4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/epsilon(F) =1/2 (E 3/2) + 1/16 (E 5/2) lnE -0.0246E (5/2) + ... and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu =2E(-1) - 0.691 + ... . The minimum of the fermion dispersion curve is located at |p|=(2mepsilon(0))(1/2), where epsilon_(0)/mu=2+O(E). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.     

Reminiscences of research on the chemistry and biology of natural sterols in insects,plants and humans

Natural sterols often occur as a heterogeneous mixture of homologs, which had disturbed the progress of steroid research. Development and application of GC methodology overcame this difficulty and enabled us to obtain detailed sterol profiles. Together, fine synthesis of stereo-defined isomers and homologs of steroids having oxygenated side chains allowed us to compare them with natural samples as well as to investigate structure-activity relationship. Advance of HPLC technology also facilitated the determination of the stereochemical structure of naturally occurring steroidal compounds, which were obtained only in minute amounts. This review highlights three topics out of our steroid research that have been performed mainly at Tokyo Institute of Technology around 1970–1990. These are sterol metabolism in insects focusing on the mechanism of the conversion of plant sterols to cholesterol and ecdysone biosynthesis, the synthesis and biochemical research of active forms of vitamin D₃ derivatives, and the synthesis and microanalysis of plant hormone brassinosteroids.     

Magnetic neutron scattering magnetic behaviour of a low-carrier density Kondo-lattice system ceas

Abstract

We have determined the magnetic structure of a low-carrier Kondo-lattice system CeAs, and have observed a softening of the crystalline electric field excitations. Despite the prediction of a recent magnetic polaron model in which CeAs and CeP are expected to show a stacking order of T₇ and T₈ layers, CeAs does not show such a stacking structure under pressure. The ordering in the intermediate phase is a regular ferromagnetic order and that of the low-temperature phase is a canted type-I AF.     

Cu-catalyzed regio- and stereoselective sulfonylation of multi-substituted allenes

Regio- and stereoselective sulfonylation of allenes under Cu catalysis is described. Allenyl sp carbons exclusively react with TsCN to give the corresponding alkenyl sulfones. The reaction is initiated by addition of tosyl radical to form benzyl radical intermediates, which determines the reaction pathway. The structure of the products is highly dependent on the substituents on allenes.     

Nickel-catalyzed [2 + 2] cycloaddition reaction using bisallenes

A nickel-catalyzed [2 + 2] cycloaddition of bisallenes has been described. Simple bisallenes are employed for the formation of “head to head” cycloadducts in the presence of Ni(0) with xantphos. The dienyl moiety in a product were applicable for various [4 + 2] cycloaddition reactions. Allene-allenamides under Ni-xantphos system gave the tricyclic compounds through sequential [2 + 2]–[4 + 2] cycloaddition reaction in highly stereoselective manner.     

Efficient and low-noise single-photon detection in 1550 nm communication band by frequency upconversion in periodically poled LiNbO3 waveguides

We demonstrate 1500 nm band single-photon detection with low dark-count noise and a potentially high efficiency, which may allow long distance and high-bit-rate quantum key distribution. By developing frequency upconversion devices based on periodically poled lithium niobate waveguides, which are specifically designed to use a pump wavelength longer than that of communication-band photons, we completely eliminate the dark-count noise caused by parasitic nonlinear processes in the waveguide. We observed an internal conversion efficiency as high as 40% and demonstrated scaling down to the single photon level while maintaining a background dark-count rate of 10(2)s(-1).     

Atomistic nitriding processes of titanium thin films due to nitrogen-implantation

Nitrogen ions (N₂⁺) with 62 keV were implanted into the as-deposited Ti film composed of mainly (1 1 0)-oriented TiH_x and (0 3 · 5)-oriented hcp-Ti at room temperature, which results in the epitaxial formation of (1 1 0)-oriented and (0 0 1)-oriented TiN_y, respectively. The electron energy loss spectroscopy experiments elucidate that in the early N-implanting stage the release of hydrogen constituting TiH_x gives rise to the shift of the loss peak due to plasmon excitation to lower loss energy side. On the other hand, the energy loss peaks due to plasmon excitation for nitriding of hcp-Ti gradually shifted to higher energy side with increasing dose. Through the N-invasion into the octahedral sites of hcp-Ti with larger space and lower electron density, the hcp-fcc transformation of Ti sublattices is induced by the shift of the (0 0 · 1)-plane in the 〈0 1 ⋅ 0〉 direction of hcp-Ti promoted by the forming of the strong Ti-N bonds including the π-type covalent bonds, and by the weakening of the Ti-Ti bonds. Furthermore, the inheritance of square atomic arrangement and the movement of the N atom to other neighboring O-site in the transformed fcc-Ti sublattice are responsible for the epitaxial growth of TiN_y. The atomistic processes of the epitaxial growth of TiN_y are discussed with the aid of the molecular orbital calculations.     

Recoil effects in high-energy photoemission beyond single-site approximation

Recoil effects of photoelectrons excited by high-energy X-rays are studied beyond the simplest approximation where elastic scatterings of photoelectrons are completely neglected (single-site approximation). At first we have shown that the simple free atom energy shift is accurately obtained within the harmonic and the single-site approximations. Beyond the single-site approximation, this simple formula does not work, but still simple classically acceptable formula can be used to explain the recoil energy shift. Illustrative numerical calculations show that the energy shifts caused by the photoelectron diffraction amounts to 5–8 meV for graphite-like carbon and about 100 meV for LiI₆${\text{LiI}}_6$ cluster at _?k=5${?}_k=5$–7 keV, and show oscillations as functions of the photoelectron energy. Furthermore we discuss the recoil effects in photoemission from extended levels by use of the tight-binding approach. Our approach naturally provides not only Debye–Waller factors but also the recoil factors. In addition to the phonon excitation, we also study the recoil effects associated with plasmon losses where intrinsic and extrinsic processes can interfere each other. Only the latter can contribute to the recoil energy shift.     

Acoustic energy harvesting using an electromechanical Helmholtz resonator

This paper presents the development of an acoustic energy harvester using an electromechanical Helmholtz resonator (EMHR). The EMHR consists of an orifice, cavity, and a piezoelectric diaphragm. Acoustic energy is converted to mechanical energy when sound incident on the orifice generates an oscillatory pressure in the cavity, which in turns causes the vibration of the diaphragm. The conversion of acoustic energy to electrical energy is achieved via piezoelectric transduction in the diaphragm of the EMHR. Moreover, the diaphragm is coupled with energy reclamation circuitry to increase the efficiency of the energy conversion. Lumped element modeling of the EMHR is used to provide physical insight into the coupled energy domain dynamics governing the energy reclamation process. The feasibility of acoustic energy reclamation using an EMHR is demonstrated in a plane wave tube for two power converter topologies. The first is comprised of only a rectifier, and the second uses a rectifier connected to a flyback converter to improve load matching. Experimental results indicate that approximately 30 mW of output power is harvested for an incident sound pressure level of 160 dB with a flyback converter. Such power level is sufficient to power a variety of low power electronic devices.