Successive Linearization Methods for Nonlinear Semidefinite Programs

We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method.The research of the fourth author was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science. The research of the second author was supported by the DFG (Deutsche Forschungsgemeinschaft).     

Hall subgroups of -groups need not be -groups

In this paper, we shall give examples of -groups that have Hall subgroups that are not -groups.

     

10-Gbit/s Serial Optical Interconnection for an ATM Switch

Serial optical interconnection is proposed for connections in a Torus asynchronous transfer mode switch. A cross-point switch was developed that operates at a bit rate of 20 Gbit/s. The switching operation was successfully performed using cascaded cross-point switches through an optical interconnection configuration consisting of commercial optoelectronics devices. The measured switching rate was 10 Gbit/s, and it was limited by the responses of the optoelectronics devices.     

Stochastic Komatu–Loewner evolutions and BMD domain constant

For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion $\xi \left(t\right)$ on $?\mathbb{H}$ and the slit motion $\mathbf{s}\left(t\right)$. The diffusion coefficient $\alpha$ and drift coefficient $b$ of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as ${\mathrm{SKLE}}_{\alpha ,b}$. We introduce a function $b_{\mathrm{BMD}}$ measuring the discrepancy of a standard slit domain from $\mathbb{H}$ relative to BMD. We show that ${\mathrm{SKLE}}_{\sqrt{6},?b_{\mathrm{BMD}}}$ enjoys a locality property.     

Crystallized state,thickening process,and crystal transformation of single crystal of trans-1,4-polybutadiene

The effect of heat treatment of trans-1,4-polybutadiene single crystals prepared from dilute benzene solution was studied by dilatometry, X-ray diffraction, and dynamic viscoelastic measurement. The crystal transformation temperature of the single crystal is 55.5[ddot]C, 20[ddot]C lower than that of the bulk crystallized sample. After heat treatment of the single crystal above 55.5[ddot]C, their crystal transformation temperature increases to 69.5[ddot]C. At the same time, thickening of the lamellae suddenly occurs and the viscoelastic primary absorption observed in the single crystal mat disappears. It is suggested that this means that the amorphous region attached to the single crystal rapidly crystallized above this temperature, in particular the loose loops attached to the end surface of the crystal are dragged into the crystalline phase to form tight loops as a result of the sliding diffusion of molecules along their axes. This is accompanied by the sudden thickening of the lamellae at the crystal transformation temperature. These observations confirmed more thoroughly our previous prediction that the single crystal of trans-1, 4-polybutadiene, as formed, contains loose loops. The thickening phenomena and the change in the crystal transformation temperature of the trans-1,4-polybutadiene single crystal by heat treatment are also discussed from the thermodynamic viewpoint.     

Production of hyperpolarized nuclei for MRI

The project in producing the hyperpolarized ³He and ¹⁹F are addressed in pursuit of radiation free medical diagnosis. The program for production of the hyperpolarized ³He by the brute force method with the Pomeranchuk cooling and the rapid melting of the solid 3He started a few years ago, and is still on the way, while a new program for production of the hyperpolarized ¹⁹F by means of the PHIP (ParaHydrogen Induced Polarization) has just got started. Particular attention is placed upon a new idea of the hyperpolarization catalyst to be used for ¹⁹F.     

Strain‐Promoted Double Azide Addition to Octadehydrodibenzo[12]annulene Derivatives

Octadehydrodibenzo[12]annulenes (DBAs), readily available by the oxidative acetylenic coupling of 1,2‐diethynylbenzene derivatives, were reacted with organic azides. As compared to the well‐known strain‐promoted azide‐alkyne cycloaddition (SpAAC) of 5,6,11,12‐tetradehydrodibenzo[a,e][8]annulene, the reactivity of the DBA alkynes was lower due to the lower strain energy. However, the regioselective double azide addition occurred without any side reactions under mild conditions, yielding bis‐triazole products. The structures of the products were confirmed by an X‐ray crystal structure analysis, and the reaction mechanism was studied by ¹H‐NMR spectroscopy and computational studies. It was also found that the DBAs were hardly fluorescent, while the bis‐triazole products showed a green fluorescence with quantum yields up to 5.1 %. Finally, the new strain‐promoted double azide addition to the DBAs was used for step‐growth polymerization, successfully producing a high molecular weight triazole polymer.