Global solutions for a semilinear,two‐dimensional Klein‐Gordon equation with exponential‐type nonlinearity

We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a semilinear Klein‐Gordon equation in two space dimensions. Our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method. © 2006 Wiley Periodicals, Inc.     

Uniform Existence of the Integrated Density of States for Randomly Weighted Hamiltonians on Long-Range Percolation Graphs

We consider random Hamiltonians defined on long-range percolation graphs over $\mathbb {Z}^{d}$ . The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula.     

Bio-guided Purification and Mass Spectrometry Characterisation Exploring the Lysozyme-like Protein from Enterococcus lactis Q1, an Unusual Marine Bacterial Strain

Applied Biochemistry and Biotechnology - Lactic acid bacteria produce various antibacterial peptides such as bacteriocins that are active against pathogenic and spoilage microorganisms. Very little...     

Purification and Biochemical Characterization of a New Protease Inhibitor from Conyza dioscoridis with Antimicrobial,Antifungal and Cytotoxic Effects

The main objective of the current study was the extraction, purification, and biochemical characterization of a protein protease inhibitor from Conyza dioscoridis. Antimicrobial potential and cytotoxic effects were also examined. The protease inhibitor was extracted in 0.1 M phosphate buffer (pH 6–7). Then, the protease inhibitor, named PDInhibitor, was purified using ammonium sulfate precipitation followed by filtration through a Sephadex G-50 column and had an apparent molecular weight of 25 kDa. The N-terminal sequence of PDInhibitor showed a high level of identity with those of the Kunitz family. PDInhibitor was found to be active at pH values ranging from 5.0 to 11.0, with maximal activity at pH 9.0. It was also fully active at 50 °C and maintained 90% of its stability at over 55 °C. The thermostability of the PDInhibitor was clearly enhanced by CaCl₂ and sorbitol, whereas the presence of Ca²⁺ and Zn²⁺ ions, Sodium taurodeoxycholate (NaTDC), Sodium dodecyl sulfate (SDS), Dithiothreitol (DTT), and β-ME dramatically improved the inhibitory activity. A remarkable affinity of the protease inhibitor with available important therapeutic proteases (elastase and trypsin) was observed. PDInhibitor also acted as a potent inhibitor of commercial proteases from Aspergillus oryzae and of Proteinase K. The inhibitor displayed potent antimicrobial activity against gram+ and gram- bacteria and against fungal strains. Interestingly, PDInhibitor affected several human cancer cell lines, namely HCT-116, MDA-MB-231, and Lovo. Thus, it can be considered a potentially powerful therapeutic agent.     

Local solvability and loss of smoothness of the Navier–Stokes–Maxwell equations with large initial data

The existence of a local-in-time unique solution and loss of smoothness of a full Magneto-Hydro-Dynamics (MHD) system are considered for periodic initial data. The result is proven using Fujita–Kato’s method in ${?}^1$ based (for the Fourier coefficients) functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to Maxwell’s equations. A loss of smoothness result is shown for the velocity and magnetic field. It comes from the damped-wave operator which does not have any smoothing effect.     

Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics

In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics. In this paper we show that for certain class of initial data the corresponding smooth solutions of the inviscid (non-viscous) primitive equations, if they exist, they blow up in finite time. Specifically, we consider the three-dimensional inviscid primitive equations in a three-dimensional infinite horizontal channel, subject to periodic boundary conditions in the horizontal directions, and with no-normal flow boundary conditions on the solid, top and bottom boundaries. For certain class of initial data we reduce this system into the two-dimensional system of primitive equations in an infinite horizontal strip with the same type of boundary conditions; and then we show that for specific sub-class of initial data the corresponding smooth solutions of the reduced inviscid two-dimensional system develop singularities in finite time.     

Design and Stereoselective Synthesis of ProM‐2: A Spirocyclic Diproline Mimetic with Polyproline Type II (PPII) Helix Conformation

With the aim of developing polyproline type II helix (PPII) secondary‐structure mimetics for the modulation of prolin‐rich‐mediated protein–protein interactions, the novel diproline mimetic ProM‐2 was designed by bridging the two pyrrolidine rings of a diproline (Pro–Pro) unit through a Z‐vinylidene moiety. This scaffold, which closely resembles a section of a PPII helix, was then stereoselectively synthesized by exploiting a ruthenium‐catalyzed ring‐closing metathesis (RCM) as a late key step. The required vinylproline building blocks, that is, (R)‐N‐Boc‐2‐vinylproline (Boc=tert‐butyloxycarbonyl) and (S,S)‐5‐vinylproline‐tert‐butyl ester, were prepared on a gram scale as pure stereoisomers. The difficult peptide coupling of the sterically demanding building blocks was achieved in good yield and without epimerization by using 2‐(1H‐7‐azabenzotriazol‐1‐yl)‐1,1,3,3‐tetramethyluronium hexafluorophosphate (HATU)/N,N‐diisopropylethylamine (DIPEA). The RCM proceeded smoothly in the presence of the Grubbs II catalyst. Stereostructural assignments for several intermediates were secured by X‐ray crystallography. As a proof of concept, it was shown that certain peptides containing ProM‐2 exhibited improved (canonical) binding towards the Ena/VASP homology 1 (EVH1) domain as a relevant protein interaction target.     

卫星系统中的混沌控制

对于非线性扰动系统对指令信号的跟踪问题,提出解析条件和实现方法.对在反馈中包含线性动力和非线性两部份的非线性扰动设备进行了研究,设备的非线性部份和扰动是未知的但是有界的.提出控制卫星天平动角的算法,用图示对该算法作了说明.     

On the buckling of elastic plates

The Föppl-von Kármán equations are used toexplore the onset of linear instability and the subsequent nonlineardevelopment of buckling patterns in a flat elastic plate dueto an imposed shear or body force such as gravity. Experimentalresults are also presented for a clamped and sheared sheet ofNeoprene rubber and these compare favourably with theory.     

Random Polyesteramides Based on Glycolic Acid and β-Alanine

A series of random polyesteramides (PEAs) within a range of molar composition from 90/10 to 10/90 were synthesized by a direct melt polycondensation of glycolic acid and β-alanine. Their structures were fully characterized by NMR spectroscopy. The resulting copolymers are amorphous and present increasing glass transition temperatures at increasing β-alanine contents. The copolymers were also characterized by, FTIR, TGA and viscosimetry measurements.