The Bohl Spectrum for Linear Nonautonomous Differential Equations

We develop the Bohl spectrum for nonautonomous linear differential equations on a half line, which is a spectral concept that lies between the Lyapunov and the Sacker–Sell spectra. We prove that the Bohl spectrum is given by the union of finitely many intervals, and we show by means of an explicit example that the Bohl spectrum does not coincide with the Sacker–Sell spectrum in general even for bounded systems. We demonstrate for this example that any higher-order nonlinear perturbation is exponentially stable (which is not evident from the Sacker–Sell spectrum), but we show that in general this is not true. We also analyze in detail situations in which the Bohl spectrum is identical to the Sacker–Sell spectrum.     

Constrained predictive synchronization of discrete-time chaotic Lur’e systems with time-varying delayed feedback control

This paper presents a predictive synchronization method for discrete-time chaotic Lur’e systems with input constraints by using time-varying delayed feedback control. Based on the model predictive control scheme, a delay-dependent stabilization criterion is derived for the synchronization of chaotic systems that is represented by Lur’e systems with input constraints. By constructing a suitable Lyapunov–Krasovskii functional and combining with a reciprocally convex combination technique, a delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The control inputs are obtained by solving a min-max problem subject to cost monotonicity, which is expressed in terms of LMIs. The effectiveness of the proposed method will be verified throughout a numerical example.     

Stability of Semi-implicit Finite Volume Scheme for Level Set Like Equation

We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation(image selective smoothing model) given by Alvarez et al.(Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer.Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes,unconditionally stable in L∞ and W1,2(W1,1) sense in isotropic(anisotropic) diffusion domain.     

A new acylated triterpene from the roots of Chaenomeles japonica

A new acylated triterpene together with prunasin, (-)-epicatechin, daucosterol, and three triterpenes, ursolic, oleanolic, and pomolic acids was isolated from the root of Chaenomeles japonica (THUNB.) LINDL. (Rosaceae) and determined to be 3-O-(E)-3, 5-dihydroxycinnamoylursolic acid on the basis of NMR and FAB-MS experiments.     

Solution-phase hexasaccharide synthesis using glucosyl iodides

[reaction: see text] Oligosaccharides composed of 1,6-glucosyl residues have been prepared from glucosyl iodides. The reactions are highly stereoselective, giving the alpha-glycosides as the only isolated products in yields ranging from 84% to 94%. Oligomer synthesis can take place in an iterative 1 + 1 + 1 fashion or in a convergent manner where dimer iodides serve as donors for higher order acceptors.     

Circular Summations of Theta Functions in Ramanujan's Lost Notebook

Let f(a, b) denote Ramanujan's symmetric theta function. In his Lost Notebook, Ramanujan claimed that the circular summation of n-th powers of f satisfies a factorization of the form f(a, b)F(ab). He listed elegant identities for n = 2, 3, 4, 5 and 7. We present alternative proofs of his claims.     

Synthesis of Cu2O coated Cu nanoparticles and their successful applications to Ullmann-type amination coupling reactions of aryl chlorides

We synthesized uniform Cu2O coated Cu nanoparticles from the thermal decomposition of copper acetylacetonate followed by air oxidation and used these nanoparticles as catalysts for Ullmann type amination coupling reactions of aryl chlorides     

Complete conditions for entanglement transfer

We investigate the conditions to entangle two qubits interacting with local environments driven by a continuous-variable correlated field. We find the conditions to transfer the entanglement from the driving field to the qubits both in dynamical and steady-state cases. We see how the quantum correlations initially present in the driving field play a critical role in the entanglement-transfer process. The system we treat is general enough to be adapted to different physical setups.     

Golmaenone, a new diketopiperazine alkaloid from the marine-derived fungus Aspergillus sp

A new diketopiperazine alkaloid, golmaenone (1). and related alkaloids, neoechinulin A (2). and L-alanyl-L-tryptophan anhydride (3). have been isolated from the culture broth of the marine-derived fungus Aspergillus sp. The structure and absolute stereochemistry of the new compound (1). was assigned by spectroscopic methods and the advanced Marfey's method. Compounds 1 and 2 exhibited a significant radical scavenging activity against 1,1-diphenyl-2-picrylhydrazyl (DPPH) with IC(50) values of 20 and 24 microM, respectively, which are similar to the positive control, ascorbic acid (IC(50), 20 microM). Compounds 1 and 2 also showed an ultraviolet-A (UV-A) (320--390 nm) protecting activity with ED(50) values of 90 and 170 microM, respectively, which are more active than oxybenzone (ED(50), 350 microM) currently being used as sunscreen.