Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

On the invariant representation of spin tensors with applications

The invariant representation of the spin tensor defined as the rotation rate of a principal triad for a symmetric and non-degenerate tensor is derived on the basis of the general solution of a linear tensorial equation. The result can be naturally specified to study the. spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics. A remarkable formula which relates the generalized stress conjugate to the generalized strain in Hill's sense. to Cauchy stress, is obtained in invariant form through the work conjugate principle. Particularly, a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes of strain arc not fixed during deformation.

A single amino acid defines cross-species reactivity of tree shrew (Tupaia belangeri) CD1d to human invariant natural killer T (iNKT) cells

P>The non-classical major histocompatibility complex (MHC) class I molecule CD1d presents lipid antigens to invariant natural killer T (iNKT) cells, which are an important part of the innate immune system. CD1d/iNKT systems are highly conserved in evoluti

Exploring consensus mRNA secondary (folding) structure units by stochastic sampling and folding simulation

It is extremely difficult to explore mRNA folding structure by biological experiments. In this report, we use stochastic sampling and folding simulation to test the existence of the stable secondary structural units of-mRNA, look for the folding units, and explore the probabilistic stabilization of the units. Using this method, We made simulations for all possible local optimum secondary structures of a single strand mRNA within a certain range, and searched for the common parts of the secondary structures. The consensus secondary structure units (CSSUs) extracted from the above method are mainly hairpins, with a few single strands. These CSSUs suggest that the mRNA folding units could be relatively stable and could perform specific biological function. The significance of these observations for the mRNA folding problem in general is also discussed. (c) 2004 Elsevier B.V. All rights reserved.

Application of polyurethane foam units and calorimetry to microbial monitoring in Lake Donghu

Combined with the national standard biomonitoring method (polyurethane foam units method), calorimetry was applied to study the metabolic activities of PFU microbial communities in fresh water to determine the effects of anthropotgenic stresses on the activity of the microbial community. Comparisons were made at four sampling stations with different eutrophic status in Lake Donghu. Water quality variables, species number of protozoa, abundances of microorganisms, biomass, heterotrophy indexes and diversity indexes are reported. The heat rate-time curves of the native and concentrated PFU microbial communities were determined at 28 degrees C. Growth rate, measured maximum power output and total heat were calculated from the heat rate-time curves. The values of metabolic variables are higher at the more eutrophic stations, which suggests that organic pollution increases the activity of PFU microbial communities. The metabolic variables are in good agreement with chemical and biotic variables. And calorimetry will be useful for biomonitoring of the PFU microbial community. (C) 2005 Elsevier B.V. All rights reserved.

Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle. (C) 2010 Optical Society of America

The thermal fatigue resistance of vermicular cast iron coupling with H13 steel units by cast-in process

This paper focuses on improving the thermal fatigue resistance on the surface of vermicular cast iron coupling with inserted H13 steel blocks that had different cross sections, by cast-in processing. The microstructure of bionic units was examined by scanning electron microscope. Micro-hardness and thermal fatigue resistance of bionic samples with varied cross sections and spacings were investigated, respectively. Results show that a marked metallurgical bonding zone was produced at interface between the inserted H13 steel block and the parent material - a unique feature of the bionic structure in the vermicular cast iron samples. The micro-hardness of the bionic samples has been significantly improved. Thermal resistance of the samples with the circular cross section was the highest and the bionics sample with spacing of 2 mm spacing had a much longer thermal fatigue life, thus resulting in the improvement for the thermal fatigue life of the bionic samples, due to the efficient preclusion for the generation and propagation of crack at the interface of H13 block and the matrix. Crown Copyright (c) 2010 Published by Elsevier Ltd. All rights reserved.

Knotted wave dislocation with the hopf invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the phi-mapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.