Wavelet bases on a manifold

Using the decomposition method, we present in this paper constructions of multiresolution analyses on a compact Riemannian manifold M of dimension n(n∈N). These analyses are generated by a finite number of basic functions and are adapted to the study of the Sobolev spaces H¹(M) and .     

Moving immersed boundary method

A novel implicit immersed boundary method of high accuracy and efficiency is presented for the simulation of incompressible viscous flow over complex stationary or moving solid boundaries. A boundary force is often introduced in many immersed boundary methods to mimic the presence of solid boundary, such that the overall simulation can be performed on a simple Cartesian grid. The current method inherits this idea and considers the boundary force as a Lagrange multiplier to enforce the no‐slip constraint at the solid boundary, instead of applying constitutional relations for rigid bodies. Hence excessive constraint on the time step is circumvented, and the time step only depends on the discretization of fluid Navier‐Stokes equations, like the CFL condition in present work. To determine the boundary force, an additional moving force equation is derived. The dimension of this derived system is proportional to the number of Lagrangian points describing the solid boundaries, which makes the method very suitable for moving boundary problems since the time for matrix update and system solving is not significant. The force coefficient matrix is made symmetric and positive definite so that the conjugate gradient method can solve the system quickly. The proposed immersed boundary method is incorporated into the fluid solver with a second‐order accurate projection method as a plug‐in. The overall scheme is handled under an efficient fractional step framework, namely, prediction, forcing, and projection. Various simulations are performed to validate current method, and the results compare well with previous experimental and numerical studies.     

A simple nonconforming quadrilateral finite element

We introduce and analyze a simple nonconforming quadrilateral finite element and then we derive optimal a priori error estimates for arbitrary regular quadrilaterals. The idea of extension to some non-conforming elements for three-dimensional hexahedrons is also presented.     

Some of the factors involved in the Sarvazyan method for recording ultrasound field distributions with special reference to the application of ultrasound in physiotherapy

The mapping of ultrasound fields using the dye paper method is described. The mode of action by which the dye concentration is increased has been investigated. Microbubbles on the paper surface and microstreaming of dye solution seem to be essential features of the mapping method. The streaming is thought to inhibit the formation of a dye depletion layer near the paper to an extent dependent on local sound intensity A linear relation between streaming velocity and intensity is derived.     

Übertragung der Gleichstrom-Messwerte von hohem Potential auf Erdpotential mit Hilfe von Licht,und die Anwendung dieser Methode zur Regelung des Elektronenstrahles in einem Elektronenstrahlsystem

Ohne Zusammenfassung     

Olefin metathesis polymerization: Some recent developments in the precise polymerizations for synthesis of advanced materials (by ROMP,ADMET)

Recent results for synthesis of end-functionalized polymers (EFP) by using olefin metathesis polymerization have been introduced including basic characteristics in ring-opening metathesis polymerization (ROMP) of cyclic olefins and acyclic diene metathesis (ADMET) polymerization for synthesis of conjugated polymers. Several approaches were demonstrated for synthesis of EFP by living ROMP using molybdenum (exclusive coupling with aldehyde) and ruthenium catalysts (sacrificial ROMP, chain transfer). Cis specific (Z selective) ROMPs were achieved by molybdenum, ruthenium, and vanadium catalysts by the ligand modification. The catalytic synthesis of EFP with high cis selectivity has been achieved by combined ROMP with chain transfer by V(CHSiMe₃)(N-2,6-Cl₂C₆H₃)[OC(CF₃)₃](PMe₃)₂. The ADMET polymerization using molybdenum and ruthenium catalysts afforded defect-free, high molecular weight poly(arylene vinylene)s containing all trans olefinic double bonds. The methods for precise synthesis of EFPs, exhibiting unique optical properties combined with the end groups, were developed. The catalytic one-pot syntheses for EFPs have also been developed.     

N-Bromosuccinimide assisted oxidation of 5-aminopyrazoles: formation of bis diazenylderivatives

Treatment of 5-amino-4-cyanopyrazoles with N-bromosuccinimide, in DMF at rt gave azo dyes resulting from dimerization through the amino groups and further oxidation.With bromine water the dimer was also formed but, bromination occurred on the aryl ring, either at reflux or rt. Reduction of the azo group with zinc in acetic acid originated the corresponding pyrazoles.     

“Universal” CNDO/2 method (CNDO/2-U)

The Pople-Santry-Segal CNDO/2 method and the modified CNDO/2 version worked out recently by Clack for transition-metal complexes have been extended to the full periodic table.