On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature

In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group Γ is said to be rigid, if Γ determines its boundary up to homeomorphisms of a CAT(0) space on which Γ acts geometrically. C. Croke and B. Kleiner have constructed a non-rigid CAT(0) group. As an application of the splitting theorems for CAT(0) spaces, we obtain that if Γ₁ and Γ₂ are rigid CAT(0) groups then so is Γ₁ × Γ₂.     

Towards a Measurement of the n=2 Lamb Shift in Hydrogen-like Nitrogen Using an Electron Beam Ion Trap

Hyperfine Interactions - Using a 14C16O2 laser the 2s 1/2–2p 3/2 (fine structure – Lamb shift) transition has been induced in 14N6+ ions trapped in an electron beam ion trap. Prospects...     

Implementation of quantum gate operations in molecules with weak laser fields

We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision.     

Substituent effects on the tautomer ratios between the hydra-zone imine and diazenyl enamine forms in 3-(arylhydra-zono)methyl-2-oxo-1,2-dihydroquinoxalines. Correlation of the hammett constants σp with the tautomeric equilibrium constants KT

The 3-(arylhydrazono)methyl-2-oxo-1,2-dihydroquinoxalines 1a-e and 2a-i showed tautomeric equilibria between the hydrazone imine A and diazenyl enamine B forms in dimethyl sulfoxide media. The sub-stituent effects on the tautomer ratios of A to B in compounds 1a-e and 2a-i were studied by the nmr spec-troscopy. The electron-donating or electron-withdrawing p-substituents R¹ in compounds 2a-i represented a tendency to increase the ratios of the tautomer A or the tautomer B , respectively, exhibiting the linear correlation of the Hammett constants σ_p (-0.17 to +0.78) with the tautomer ratios of A to B or the tautomeric equilibrium constants K_T. However, the presence of the ester group R² in compounds 1a-e induced the exclusive existence of the tautomer A regardless of the nature of the p-substituents R¹. In the tautomeric thermodynamic study, the elevating temperature increased the ratios of the hydrazone imine tautomer A in compounds 2a-i . The tautomeric thermodynamic parameters ΔG°, ΔH° and ΔS° were derived from the van't Hoff plots for compounds 2a , b , h , i , wherein the entropy term dominated the free-energy difference between the A and B tautomers.     

A simple collision algorithm for arbitrarily shaped objects in particle-resolved flow simulation using an immersed boundary method

In the present study, we proposed a simple collision algorithm, which can be handled arbitrarily shaped objects, for flow solvers using the immersed boundary method (IBM) based on the level set and ghost cell methods. The proposed algorithm can handle the collision of the arbitrarily shaped object with little additional computational costs for the collision calculation because collision detection and calculation are performed using the level set function and image point, which are incorporated into the original IBM solver. The proposed algorithm was implemented on the solid-liquid IBM flow solver and validated by simulations of the flow over an isolated cylinder and sphere. Also, grid and time step size sensitivity on the total energy conservation of objects were investigated in cylinder-cylinder, cylinder-red-blood-cells-shaped (RBC-shaped) objects, sphere-sphere, and sphere-flat plate interaction problems. Through validation, good agreement with previous studies, grid and time step size convergence, and sufficient total energy conservation were confirmed. As a demonstration, the drafting, kissing, and tumbling processes were computed, and it was confirmed that the present result by the proposed method is similar to the previous computations. In addition, particle-laden flow in a channel including obstacles with collision and adhesion phenomena and the interaction of cylinders and wavy-wall were computed. The results of these simulations reveal the capability of solving a flow containing arbitrarily shaped moving objects with collision phenomena by a simple proposed method.     

A Study of the Application of Photoexcited TiO2 Particle to Cancer Treatment

The purpose of the present paper is to introduce such a new application of photoexcited TiO₂ to the area of biology that has been investigated in our laboratory. The behavior of cultured celles on the photoexcied TiO₂ electrode surface and the cell killing effect of photoexcited TiO₂ particles are described. And the possible application of this cell killing effect of photoexcited TiO₂ particles to cancer treatment is discussed.     

Semiconductor acousto-electric potential detection using a force microscope

Acousto-electric force microscopy (AEFM), developed as a technique for high-resolution mapping of carrier characteristics in solids is described. This technique is based on an acousto-electric voltage (AEV) detection scheme where AEV pulses are obtained from the cantilever deflection caused by the electrostatic force acting between the cantilever tip and the sample surface. AEFM appears to be feasible, but an improved AEV detection scheme is required.