Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence

We construct models for the level by level equivalence between strong compactness and supercompactness in which for κ the least supercompact cardinal and δ ≤ κ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2^δ > δ ⁺ and δ is < 2^δ supercompact. In these models, the structure of the class of supercompact cardinals can be arbitrary, and the size of the power set of κ can essentially be made as large as desired. This extends and generalizes [5, Theorem 2] and [4, Theorem 4]. We also sketch how our techniques can be used to establish a weak indestructibility result. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical flow visualization of first cycle and cyclic motion of a rigid fling-clapping wing

A flow visualization of the two-dimensional rigid fling-clap motions of the flat-plate wing is performed to get the knowledge of fling-clapping mechanism that might be employed by insects during flight. In this numerical visualization, the time-dependent Navier-Stokes equations are solved for two types of wing motion; ‘fling followed by clap and pause motion’ and ‘cyclic fling-clapping motion’. The result is observed regarding the main flow features such as the sequential development of the two families of separation vortex pairs and their movement. For the ‘fling followed by clap and pause motion’, a strong separation vortex pair of counterrotation develops in the opening between the wings in the fling phase and they then move out from the opening in the following clap phase. For ‘the cyclic fling-clapping motion’, the separation vortex pair developed in the outside space in the clap phase move into the opening in the following fling phase. The separation vortex pair in the opening developed in the fling phase of the cyclic motion is observed to be stronger than those of the ‘fling followed by clap and pause motion’. Regarding the strong fling separation vortex and the weak clap separation vortex above it in the opening, the flow pattern of the fling phase of the cyclic fling and clap motion is different to that of the fling phase of the first cycle. The flow pattern of the third cycle of the cyclic fling-clapping motion is observed to be almost same as that of the second cycle. Therefore, a periodicity of the flow pattern is established after the second cycle.     

Investigation of cold fusion in heavy water

An investigation of cold fusion of deuterium was performed by electrolyzing heavy water in a cell containing a palladium cathode while monitoring levels of tritium and neutron-capture gamma rays. No activity was detected that would indicate a sustained fusion reaction had taken place. Activities that were observed can be attributed to electrolytic enrichment and a normal cosmic-ray induced background.     

Further generalization of the Dubovicki-Milutin theorem

Combining the results of Walczak (Ref. 1) and Lasiecka (Refs. 2 and 3), we extend the well-known Dubovicki-Milutin theorem in two directions: (i) We allow for treatment of several equality constraints in optimization problems; and (ii) We assume less regularity of optimization problems by requiring the existence of external cones instead of tangent cones. An example of an optimization problem is also considered.     

Bending-torsion vibration of a partially submerged cylinder with an arbitrary cross-section

An analytical method is presented to investigate the bending-torsion vibration characteristics of a cylinder with an arbitrary cross-section and partially submerged in water. The compressibility and the free surface waves of the water are considered simultaneously in the analysis. The exact solution of structure–water interaction is obtained mathematically. Firstly, the analytical expression of the velocity potential of the water is derived by using the method of separation of variables. The unknown coefficients in the velocity potential are determined by the longitudinal and circumferential Fourier expansions along the outer surface of the cylinder and are expressed in the form of integral equations including the unknown dynamic bending deflection and torsional angle of the cylinder. Secondly, the force and torque acting on the cylinder per unit length, provided by the water, are obtained by integrating the water dynamic pressure along the circumference of the cylinder. The general solution of bending-torsion vibration of the cylinder under the water dynamic pressure is derived analytically. The integral equations included in the velocity potential of the water can be solved exactly. Finally, the eigenfrequency equation of cylinder–water interaction is obtained by means of the boundary conditions of the cylinder. Some numerical examples for elliptical columns partially submerged in water are provided to show the application of the present method.     

Epimerization, diastereoselectivity and hemilability in dicationic chiral ruthenium complexes with bidentate (PS) bisphosphine monosulfide ligands

The binding of heterobidentate P^∧S ligands introduces metal-centered chirality to the planar chiral parent complex Ru(η⁶:η¹-NMe₂C₆H₄C₆H₄PCy₂)Cl₂. Observed diastereomeric ratios for the kinetic product vary dramatically depending upon ring size of the chelate formed with the P^∧S ligand. The complexes epimerize very slowly to thermodynamic product ratios that are substantially different from the kinetic product ratios.