Multi-Center Vector Field Methods for Wave Equations

We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is the repulsiveness or nontrapping conditions on the flow corresponding to the wave equation. Thus this method is limited to potential perturbations which are repulsive, that is the radial derivative pointing away from the origin. In this work, we generalize this method to include potentials which are repulsive relative to a line in space (in three or higher dimensions), among other cases. This method is based on constructing multi-centered vector fields as multipliers, cancellation lemmas and energy localization.     

The Initial-boundary Value Problem for the Ostrovsky-Vakhnenko Equation on the Half-line

We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that the solution u(x,t) can be recovered from its initial and boundary values via the solution of a vector Riemann-Hilbert problem formulated in the plane of a complex spectral parameter z.     

Adaptive complete synchronization of chaotic dynamical network with unknown and mismatched parameters

In this paper, an adaptive controller is designed to synchronize the chaotic dynamical network with unknown and mismatched parameters. Based on the invariance principle of differential equations, some generic sufficient conditions for asymptotic synchronization are obtained. In order to demonstrate the effectiveness of the proposed method, an example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.     

Complex network study of Asian Go players

Tournaments of the game of Go can be represented as a directed network in which the vertices are players and a directed link is pointing from the winner to the loser for each game. In this article, we present some interesting results for the network of Asian Go players, which is composed of 756 Go players and 9473 tournaments. It is found that the topological structure of this network displays the small-world property and a significant rich-club phenomenon where high-degree nodes are tightly interconnected. In addition, we consider the weighted version of the network, and find the weights obey power-law distributions, while the strengths follow stretched exponential distributions. The time evolution of the network structure is studied and the corresponding results discussed. The analysis of this work provides a deeper understanding for the competition network structure of Asian Go players.     

Enhanced superprism effect based on positive/negative lateral shift of reflective beam in a Fabry-Perot filter

It is found that when a light beam is incident obliquely on a thin film Fabry-Perot filter (FPF) from different incident media (air or substrate), the reflective beam will be shifted in both the forward and the backward directions. Based on this inverted spatial dispersion effect, two thin film FPFs with different directional lateral shifts are assembled to get a thin film superprism with a wider dispersion band. The thin film samples are fabricated as well as tested, and the results are in approximate agreement with numerical simulation.     

Schematic design of a complex thin-film luminescent screen usable for vacuum fluorescent and field emission display

Based on the facts related to solid-state cathodoluminescence, mixed excitation, and serial excitation recently discovered in our laboratory, a fundamental schematic design and a series of different schematic elaborated designs are proposed for protection from electron accumulation, reasonable use of a luminescent screen, and enhancement of light intensity.     

Quantitative Time-Resolved Fluorescence Spectrum of the Cortical Sarcoma and the Adjacent Normal Tissue

The difference in time-resolved fluorescence spectrum between the cortical sarcoma and the adjacent normal tissue was studied in both experimental and theoretical ways. The Clinical data were obtained in vivo using a time-resolved fluorescence spectrometer employing a single fiber-optic probe for excitation and detection. Tissue was modeled as s-180 sarcoma tumor surrounded with normal muscle and was mediated by the Palladium-porphyrin photosensitizer (Pd-TCPP). The emitted fluorescence was considered as arising from the tumor tissue or the normal muscle, due to the presence of the photosensitizer. A computational code which could simulating time-resolved fluorescence emission was presented and applied to comparing fluorescence decay of photosensitizer in different stages of tumor growth. In this code the different stages of the tumor was modeled through changing the time τ, the delay of the fluorescence photon emission and z _max, the thickness of the tumor. It was found in the in vivo experiment that the fluorescence from tumor tissue decayed more quickly than from the adjacent normal muscle. For the ten rats in the first experiment day, the mean decay constant of tumor T _s and normal tissue T _n were 554 and 526 μs, respectively. And T _s increased with the tumor growth, from 554 μs in the first day to 634 μs in the eighth day while T _s kept steady. It was believed that the more adequate oxygen supplied by the normal tissue can more effectively quench the fluorescence and in the normal tissue the photosensitizer lifetime is smaller. As a result the simulated time-resolved fluorescence spectrum of normal tissue showed more quickly decay. And the thickness of the tumor can also delay the fluorescence decay. Both the experimental and simulated results indicated that the germination of the tumor would increase the decay constant of the time-resolved fluorescence spectrum. So decay constant of the tumor tissue spectrum should be larger than that of adjacent normal tissue for the reason of hypoxia and overgrouth. This fact could be of use in the tumor diagnoses.     

Calcium Ion-Induced Stabilization and Refolding of Agkisacutacin from <Emphasis Type="Italic">Agkistrodon Acutus</Emphasis> Venom Studied by Fluorescent Spectroscopy

Agkisacutacin isolated from the venom of Agkistrodon acutus is a coagulation factor IX / coagulation factor X-binding protein with marked anticoagulant- and platelet-modulating activities. Ca²⁺ ion-induced stabilization and refolding of Agkisacutacin have been studied by following fluorescent measurements. Ca²⁺ ions not only increase the structural stability of agkisacutacin against GdnHCl denaturation, but also induce its refolding. The GdnHCl-induced unfolding of the apo-agkisacutacin and the purified agkisacutacin is a single-step process with no detectable intermediate state. Ca²⁺ ions play an important role in the stabilization of the structure of agkisacutacin. Ca²⁺-stabilized agkisacutacin exhibits higher resistance to GdnHCl denaturation than the apo-agkisacutacin. It is possible to induce refolding of the unfolded apo-agkisacutacin merely by adding 1 mM Ca²⁺ ions without changing the concentration of the denaturant. The kinetic result of Ca²⁺-induced refolding provides evidences for that agkisacutacin consists of at least two refolding phases and the first phase of Ca²⁺-induced refolding should involve the formation of the compact Ca²⁺-binding site regions, and subsequently, the protein undergoes further conformational rearrangements to form the native structure.     

1H NMR Reassignment for Z/E-Benzomalvins B and Absolute Configuration of Benzomalvin C

Chemistry of Natural Compounds - Benzomalvins B, C, and E (1, 2, and 3) were simultaneously obtained from the marine fungus Aspergillus sp. isolated from the soft coral Sinularia sp., collected...