Existence and Exponential Decay of Solutions for a Wave Equation with Integral Nonlocal Boundary Conditions of Memory Type

In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results.     

A 3–10 GHz Ultra Wideband Receiver LNA in 0.13 \mu m CMOS

A fully integrated low-power, low-complexity ultra wideband (UWB) 3–10 GHz receiver front-end in standard 130 nm CMOS technology is proposed for UWB radar sensing applications. The receiver front-end consists of a full UWB band low-noise amplifier and an on-chip diplexer. The on-chip diplexer has a 1 dB insertion loss and provides a \(-\) 30 dB isolation. The diplexer switch was co-designed with the receiver input matching network to optimize the power matching while simultaneously achieving good noise matching performance. The receiver low-noise amplifier provides a 3–10 GHz bandwidth input matching and a power gain of 17 dB. The overall receiver front-end consumes an average power of 13 mW. The core area of the transceiver circuit is 500 \(\mu \) m by 700 \(\mu \) m.     

Structural variability of endotoxins from R-type isogenic mutants of Shigella sonnei

The structural variations in the rough-type endotoxins [lipopolysaccharides (LPSs)] of Shigella sonnei mutant strains (S. sonnei phase II-4303, R41, 562H and 4350) were investigated by Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and tandem MS. A series of S. sonnei mutants had previously been the subject of analytical studies on the biosynthesis of heptose components in the core oligosaccharide region of LPSs. This study gives a complete overview on the structures of the full core and lipid A of S. sonnei mutant strains by MS. We found that the LPSs of the isogenic rough mutants were formed in a step-like manner containing 0:1:2:3 heptose in the deep core region of 4350, 562H, R41 and 4303, respectively, and the longest LPS from the mutant S. sonnei 4303 contained also five hexoses. The structural variations in the lipid A moiety and in the oligosaccharide part of the intact LPS were followed by MALDI-TOF-MS/MS. For the dissolution and the ionization of the samples, 2,5-dihydroxybenzoic acid in citric acid solution was applied as matrix. The detailed evaluation of the mass spectra indicates heterogeneity in the lipid part due to the differences in the phosphate and fatty acid composition.     

On energy estimates for second order hyperbolic equations with Levi conditions for higher order regularity

We consider energy estimates for second order homogeneous hyperbolic equations with time dependent coefficients. The property of energy conservation, which holds in the case of constant coefficients, does not hold in general for variable coefficients; in fact, the energy can be unbounded as t → ∞ in this case. The conditions to the coefficients for the generalized energy conservation (GEC), which is an equivalence of the energy uniformly with respect to time, has been studied precisely for wave type equations, that is, only the propagation speed is variable. However, it is not true that the same conditions to the coefficients conclude (GEC) for general homogeneous hyperbolic equations. The main purpose of this paper is to give additional conditions to the coefficients which provide (GEC); they will be called as C ^k -type Levi conditions due to the essentially same meaning of usual Levi condition for the well-posedness of weakly hyperbolic equations.     

Oleanolic triterpene saponins from the roots of Panax bipinnatifidus

Ten oleanane-type saponins (1-10), including three new compounds, namely bifinosides A-C (1-3), were isolated from the roots of Panax bipinnatifidus SEEM. Their structures were elucidated on the basis of chemical and spectroscopic methods.     

Control of ZnO morphologies on carbon nanotube electrodes and electrocatalytic characteristics toward hydrazine

We controlled the morphologies of zinc oxide (ZnO) nanostructures on single-walled carbon nanotube electrodes by an electrochemical deposition method and investigated the dependence of the electrocatalytic characteristics toward hydrazine on the different morphologies. ZnO nanorods provided high electrocatalytic activity with unique electrochemical behaviours, associated with the H(+) ion generated by the electro-oxidation of hydrazine.     

Ionic liquid-assisted carboxylation of amines by CO2: a mechanistic consideration

The catalytic roles of ionic liquids (ILs) in the syntheses of 1,3-disubstituted ureas from the carboxylation of amines by CO(2) were experimentally and theoretically investigated. The carboxylation reaction of n-butylamine was greatly facilitated by the presence of an IL and the catalytic activity of the IL was strongly affected by the nucleophilicity of the anion. Computational study on the mechanistic aspects of the carboxylation with methylamine with or without the presence of an IL, 1-ethyl-3-methylimidazolium chloride, implies that the activation energies of the transition states and the intermediate ionic species could be lowered significantly through the multi-interactions of the carbonyl group of CO(2) with both cations and anions of the ILs.     

Local shrinkage and stress induced by thermo-oxidation in composite materials at high temperatures

The paper is concerned with the modelling, simulation and experimental characterisation of local shrinkage strains and stresses induced by thermo-oxidation phenomena in the IM7/977-2 carbon/epoxy composite material at elevated temperatures. The oxygen concentration and mechanical fields were established through a coupled model constructed from a unified multiphysical approach and the thermodynamics of irreversible processes. The model was implemented in the ABAQUS^® finite element commercial code. Simulations of thermo-oxidation-induced matrix shrinkage were run at a local scale, i.e., the scale of the elementary constituents of the composite, the fibre and the matrix. The experimental assessment was done at the same scale, and the local matrix shrinkage profiles were measured by confocal interferometric microscopy.A good agreement was found between the simulated and measured profiles, validating the unified model. The thermo-oxidation induced stress field was analysed to understand the influence of the environment on the onset of damage in composite materials at elevated temperature.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

Sequence-based necessary second-order optimality conditions for semilinear elliptic optimal control problems with nonsmooth data

Positivity - The main goal of this note is to formulate sequence-based necessary second-order optimality conditions for a semilinear elliptic optimal control problem, with a pointwise pure state...