A note on the nonexistence of monotonic steady solutions of the Kuramoto-Sivashinsky equation

We present a simple proof of the nonexistence of monotonic solutions derived from the Kuramoto-Sivashinsky equation. Although our method restricts the range of parameters, it has the advantage of applicability to other equations, which includes a model of dendritic growth of needle crystals.

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Sunto In questo lavoro, presentiamo una semplice dimostrazione di non esistenza di soluzioni monotone per l’equazione di Kuramoto-Sivashinsky. Sebbene il nostro metodo restringa il range dei parametri, esso ha il vantaggio di essere applicabile anche ad equazioni aventi interesse fisico quali descriventi un modello locale di solidificazione.

     

A structured pattern matrix algorithm for multichain Markov decision processes

In this paper, we are concerned with a new algorithm for multichain finite state Markov decision processes which finds an average optimal policy through the decomposition of the state space into some communicating classes and a transient class. For each communicating class, a relatively optimal policy is found, which is used to find an optimal policy by applying the value iteration algorithm. Using a pattern matrix determining the behaviour pattern of the decision process, the decomposition of the state space is effectively done, so that the proposed algorithm simplifies the structured one given by the excellent Leizarowitz’s paper (Math Oper Res 28:553–586, 2003). Also, a numerical example is given to comprehend the algorithm.     

High‐pressure Brillouin study of the elastic properties of rare‐gas solid xenon at pressures up to 45 GPa

The pressure dependences of three adiabatic elastic constants, adiabatic bulk modulus, refractive index, and elastic anisotropy, as well as Cauchy deviation of fcc solid Xe have been determined up to 10 GPa at 296 K by high‐pressure Brillouin scattering spectroscopy. The characteristics of elastic properties at high pressure of rare‐gas solid Xe are investigated by comparison with the previous studies on Ne, Ar, and Kr. Above 10 GPa, the occurrence of splitting in the Brillouin signals and the direction dependence of acoustic velocities for solid Xe clearly show partial phase transformation to the hcp structure reported by the previous X‐ray diffraction and Raman scattering studies. The shear elastic modulus in the hcp phase of solid Xe has also been estimated at pressures up to 45 GPa by using the pressure dependence of the Raman wavenumber shift for the E_2g mode. Copyright © 2008 John Wiley & Sons, Ltd.     

Design of Photostable,Activatable Near‐Infrared Photoacoustic Probes Using Tautomeric Benziphthalocyanine as a Platform

Near‐infrared (NIR) imaging techniques have attracted significant attention for biological and medicinal applications due to the ability of NIR to penetrate deeply into tissues. However, there are very few stable, activatable molecular probes that can utilize NIR light in the wavelength range beyond 800 nm. Herein, we report a new activatable NIR system for photoacoustic imaging based on tautomeric benziphthalocyanines (BPcs). We found that the existence of a free hydroxyl group is crucial for NIR absorption of BPcs. Synthesized water‐soluble hydroxy BPcs exhibited high photostability and no fluorescence, which are desirable features for photoacoustic imaging. We synthesized BPcs in which the free hydroxyl group was masked by an esterase‐labile or an H₂O₂‐labile group. The photoacoustic signals of these hydroxy‐masked BPcs were increased upon NIR excitation at 880 nm in the presence of esterase or H₂O₂, respectively. These are rare examples of activatable probes utilizing NIR light at around 900 nm.     

Ordered Microporous Surface Films Formed by Core‐Shell‐Type Nanospheres

Summary: Polymer nanospheres are synthesized by free‐radical dispersion copolymerization of methyl methacrylate (MMA) and ethylene glycol dimethacrylate (EGDM) with a methacryloyl‐terminated polystyrene (PS‐MC) macromonomer in cyclohexane. Such polymer nanospheres are stabilized sterically with polystyrene (PS)‐grafted chains in cyclohexane at temperatures greater than 34 °C (the Θ temperature for PS). Ordered microporous surface films are constructed by casting these core‐shell‐type nanospheres from hot cyclohexane solution at 20 °C. The results indicate the possibility of fixation or encapsulation of functional materials after microporous patterning of the core‐shell‐type nanospheres.

SEM photograph of a vertical section of a hexagonal micropore film obtained here.     

Identification of the interface of a large protein-protein complex using H/D exchange and Fourier transform ion cyclotron resonance mass spectrometry

An infrared multiphoton dissociation (IRMPD) spectrum, obtained by Fourier transform ion cyclotron resonance mass spectrometry (FTICRMS), was used to dissociate and to identify fragment ions from recombinant human interleukin-6 (IL-6; 21 KDa). The entire sequence was assigned by a single IRMPD experiment, and the observed fragment ions reflected the IL-6 secondary structure. This method was combined with H/D off-exchange to identify IL-6 and anti-human IL-6 mouse monoclonal antibody MH166 (150-kDa) binding sites in the IL-6 molecule. To facilitate the data analysis, the protein complex formation and the hydrogen exchange were performed with an immobilized antibody. Quenching of the hydrogen exchange reaction and collection of the deuterated IL-6 were performed by elution under acidic conditions to measure the mass spectrum directly. IL-6 was dissociated by using IRMPD, and the interface of IL-6 bound to anti-IL-6 antibody MH166 was determined to analyze the deuterium incorporation level of each fragment ion. Thus, two discontinuous regions, Leu 126-Lys 131 and Asp 160-Met 184, were identified as the antibody binding sites. These regions are adjacent to each other on the tertiary structures determined by NMR and X-ray analyses.     

Synthesis of 2,3-disubstituted indole using palladium(II)-catalyzed cyclization with alkenylation reaction

The reaction of ethyl 2-ethynylphenylcarbamate derivative with alkenes in the presence of a palladium(II) catalyst, copper dichloride and tetrabutylammonium fluoride (TBAF) produced 2-substituted 3-ethenylindoles during refluxing. The intramolecular cyclization reaction of ethyl 2-ethynylphenylcarbamates, which have an ethenyl part in the ethynyl group, was also used to produce carbazole derivatives.     

The total absolute curvature of an equiaffine immersion

For an equiaffine immersion of general codimension, we recently defined the Lipschitz-Killing curvature, where we fix a transversal bundle and a transversal volume element. The main purpose of this paper is to show that the integration of the absolute value of the Lipschitz-Killing curvature is independent of the choices of a transversal bundle and a transversal volume element.