Derivatives of the Evans function and (modified) Fredholm determinants for first order systems

The Evans function is a Wronskian type determinant used to detect point spectrum of differential operators obtained by linearizing PDEs about special solutions such as traveling waves, etc. This work is a sequel to the paper “Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves”, published by F. Gesztesy, K. Zumbrun and the second author in J. Math. Pures Appl. 90 , 160–200 (2008), where the Evans and Jost functions for the Schrödinger equations have been considered. In the current work, we study the Evans function for the general case of linear ODE systems, and choose it to agree with the modified Fredholm determinant of the respective Birman‐Schwinger type integral operator. The Evans function is thus the determinant of the matrix composed of the so‐called generalized Jost solutions. These are the solutions of the homogeneous perturbed differential equation which are asymptotic to some reference solutions of the unperturbed equation. One of the main results of the current paper is a formula for the derivative of the Evans function for the first order systems. Its proof uses a matrix composed of the newly introduced modified Jost solutions. These are the solutions of an inhomogeneous perturbed differential equation with the inhomogeneous term constructed by means of the above‐mentioned generalized Jost solutions.     

China ASON Network Migration Scenarios and Their Quantitative Analysis

This paper proposes two migration scenarios from China rin g networks to ASON mesh networks . In our quantitative analysis with ASON/GMPLS simulator, a subnetwork protection scheme achieved best balanced performance in resource utilization and restoration time.     

Humidity sensor based on localized surface plasmon resonance of multilayer thin films of gold nanoparticles linked with myoglobin

Layer-by-layer self-assembled multilayer thin films of gold nanoparticles (GNPs) linked with myoglobin (Mb) show substantial sensitivity to humidity at room temperature according to measurements of localized surface plasmon resonance (LSPR) absorption that relies on the interparticle interaction present in the film. The sensor response is reversible, with response and recovery times as low as 5 s. The sensing mechanism is as follows: as the ambient humidity changes, Mb molecules change their size, making the GNP-to-GNP spacing and thereby the interparticle interaction change; the change in the interparticle interaction causes a change in the LSPR absorption of the multilayer thin film. We found that the LSPR band of the multilayer thin film was almost insensitive to both the surrounding refractive index and the adlayer thickness, rendering the multilayer-film-based humidity sensor highly immune to ambient disturbances.     

Reversible photostructural change in chalcogenide glass films observed in infrared absorption spectra

Measurement of infrared absorption spectra in amorphous chalcogenide films revealed changes which can be closely related with the reversible photostructural change. The changes came out in intensity of absorption peak situated near 650 cm^-1 as well as definite change in infrared fundamental absorption peak. The absorption peak intensity near 650 cm^-1 showed considerable decrease by annealing, while it recovered initial value after light exposure. The change was shown to be in close correspondence with the well known reversible optical absorption edge shift.     

Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions

The central limit (or fluctuation) phenomena are discussed in the interacting diffusion system. The tightness in the Kolmogorov-Prokhorov sense is proved for a sequence of distribution valued processes arising from finite particle systems. Further, the stochastic differential equation for the limit process is derived by constructing an infinite dimensional Brownian motion.     

De Rham-Hodge-Kodaire decomposition in ∞-dimensions

Dedicated to Professor Haruo Suzuki on the occasion of his sixtieth birthday     

Applications of molecular mechanics to alkyl radicals

The MM2 force field has been extended to alkyl radicals. The known structures and conformational energy relationships are well reproduced for many simple radicals, and predictions were made for 1-butyl, 2-butyl, cyclopentyl, cyclohexyl and others. Heats of formation were also studied.     

pH-Responsive shrinkage/swelling of a supramolecular hydrogel composed of two small amphiphilic molecules

A pH-responsive volume-change function was successfully introduced into a supramolecular hydrogel that contained GalNAc-appended (GalNAc=N-acetylgalactosamine) glutamate ester 1 by the simple mixing of it with an appropriate amount of 2 a or 2 b amphiphilic carboxylic acid. In the 1:1 mixture (1:2), the hydrogel swelled under neutral pH conditions, but shrank to almost half of its original volume under acidic pH conditions. The structure and pH response of the mixed hydrogel were characterized by using X-ray diffraction (XRD), confocal laser scanning microscopy (CLSM), transmission or scanning electron microscopy (TEM, SEM), and Fourier transform IR (FTIR) spectroscopy. Well-developed fibers formed a stable hydrogel by self-assembly, and under acidic conditions the charge of the carboxylic acid terminal (from the carboxylate anion) was neutralized and then these fibers became densely packed. This macroscopic pH response was also applied to the pH-triggered release of bioactive substances. In this mixed supramolecular hydrogel, the hydrogelator 1 provides a stable hydrogel structure and the additive 2 acts as a commander that is sensitive to an environmental pH signal. The present supramolecular copolymerization strategy should be useful for the construction of novel, stimuli-responsive, soft materials.