Remarks on the decay of the local energy for semilinear wave equation

In this note, we prove the global well posedness and the local energy decay for semilinear wave equation with small data.     

Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space

Using Cesari's approach, we prove the existence of optimal controls for a class of systems governed by differential inclusions on a Banach space having the Radon-Nikodym property. Theorem 3.1 gives the existence result for optimal relaxed controls under fairly general assumptions on the system and the admissible controls. This result depends on a fundamental result (Theorem 2.1) that proves the existence of mild solutions of differential inclusions on a Banach space, which has also independent interest. Further, the preparatory results, such as Lemma 3.1 and Lemma 3.2, are also useful in the study of time-optimal and terminal control problems.For illustration of the results, we present two examples, one on distributed controls for a class of systems governed by nonlinear parabolic equations and the other on boundary controls with discontinuous boundary operator.This work is supported in part by the National Science and Engineering Council of Canada under Grant No. 7109.     

DC electrical resistivity for CoxNi5/3−xSb1/3Fe1O4 ferrites

The DC electrical resistivity (p) was studied for Co substituted SbNi ferrites as a function of temperature and composition. The experimental results showed that DC resistivity, Curie temperature and activation energies for electrical conduction increase as Co-ion substitution decreases. The DC electrical conductivity increases as temperature increases. The real part of dielectric constant (e') was found to be inversely proportional to the root mean square value of the electrical resistivity.     

Optimization of laser welding of DP/TRIP steel sheets using statistical approach

Generally, the quality of a weld joint is directly influenced by the welding input parameter settings. Selection of proper process parameters is important to obtain the desired weld bead profile and quality. In this research work, numerical and graphical optimization techniques of the CO₂ laser beam welding of dual phase (DP600)/transformation induced plasticity (TRIP700) steel sheets were carried out using response surface methodology (RSM) based on Box–Behnken design. The procedure was established to improve the weld quality, increase the productivity and minimize the total operation cost by considering the welding parameters range of laser power (2–2.2 kW), welding speed (40–50 mm/s) and focus position (?1 to 0 mm). It was found that, RSM can be considered as a powerful tool in experimental welding optimization, even when the experimenter does not have a model for the process. Strong, efficient and low cost weld joints could be achieved using the optimum welding conditions.     

Discreteness of space from GUP II: Relativistic wave equations

Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrödinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one-dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. In this Letter, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected Klein–Gordon and Dirac equations, and for the latter, to two and three dimensions. We again arrive at quantization of box length, area and volume and an indication of the fundamentally grainy nature of space. We discuss possible implications.     

New Spectrofluorimetric Method for Determination of Cephalosporins in Pharmaceutical Formulations

Simple, accurate and sensitive spectrofluorimetric method has been proposed for the determination of three cephalosporins, namely; cefixime (cefi), cephalexine (ceph), cefotaxime sodium (cefo) in pharmaceutical formulations. The method is based on a reaction between cephalosporins with 1, 2-naphthoquinone-4-sulfonic (NQS) in alkaline medium, at pH values of 12.0 for cefi and 13.0 for ceph and cefo to give highly fluorescent derivatives extracted with chloroform and subsequently measured at 600,580 and 580 nm after excitation at 520,455 and 490 nm for cefi, ceph and cefo respectively. The optimum experimental conditions have been studied. Beer’s law is obeyed over the concentrations of 10–35 ng/mL, 10–60 ng/mL and 20–45 ng/mL for cefi,ceph and cefo, respectively. The detection limits were 2.02 ng/mL, 2.09 ng/mL and 2.30 ng/mL for cefi, ceph and cefo, respectively, with a linear regression correlation coefficient of 0.9987, 0.9995 and 0.9991 and recoveries in range from 98.5-107.04, 95.17-101.00 and 95.00-109.55% for cefi, ceph and cefo, respectively. This method is simple and can be applied for the determination of cefi, ceph and cefo in pharmaceutical formulations in quality control laboratories.     

Non-vacuum field desorption ion source implemented under super-atmospheric pressure

Standard field desorption (FD) ionization is implemented under high vacuum condition. In this paper, non-vacuum FD is performed under a super-atmospheric pressure environment using untreated tungsten wires as FD emitter, and the ion source was coupled to a commercial linear ion trap mass spectrometer. The operating pressure of the ion source was 6 bars which was high enough to provide sufficient dielectric strength to the working gas so that the high voltage that was required for FD could be applied to the emitter without occurrence of electrical discharge. Non-volatile sample deposited on the bare tungsten wire FD emitter was heated by flowing direct current through the emitter. Similar to vacuum FD, the formation of conical protrusion of the liquefied sample layer under the strong electric field was also observed. Using the present ion source, high pressure field-desorption of polar neutral compounds, organic salts and ionic liquids is demonstrated. Copyright ? 2012 John Wiley & Sons, Ltd.     

Existence of unimodular elements in a projective module

(1) Let R be an affine algebra over an algebraically closed field of characteristic 0 with $\dim (R)=n$. Let P be a projective $A=R[T_1,?,T_k]$-module of rank n with determinant L. Suppose I is an ideal of A of height n such that there are two surjections $\alpha :P?I$ and $?:L\oplus A^{n?1}?I$. Assume that either (a) $k=1$ and $n\ge 3$ or (b) k is arbitrary but $n\ge 4$ is even. Then P has a unimodular element (see 4.1, 4.3).(2) Let R be a ring containing $\mathbb{Q}$ of even dimension n with height of the Jacobson radical of $R\ge 2$. Let P be a projective $R[T,T^{?1}]$-module of rank n with trivial determinant. Assume that there exists a surjection $\alpha :P?I$, where $I?R[T,T^{?1}]$ is an ideal of height n such that I is generated by n elements. Then P has a unimodular element (see 3.4).     

A New Approach for Synthesis of Low‐moisture Glycidyl Azide Polymer

In this work, low‐moisture glycidyl azide polymer (GAP) was successfully prepared using a modified two‐step method. The modified method resembles the structure of the classical two‐step method, which is widely used to prepare the GAP. Firstly, epichlorohydrin (ECH) is polymerized into polyepicholorohydrin (PECH), which is subjected afterward to azidation step using sodium azide (NaN₃). Interestingly, minimizing the water content in the final GAP product, which is a challenging when dealing with GAP as a rocket propellant binder, was effectively achieved by utilizing low boiling point solvents instead of the relatively high boiling point Dimethyl formamide (DMF), monitoring the volatility of ECH and controlling the exothermicity of the reaction. Prepared GAP samples were investigated using Fourier transformer infra‐red (FT‐IR), gel‐permeation chromatography (GPC) and elemental analysis apparatus (CHNS) were used to characterize the product. The moisture % in the final product was examined using the Karl‐Fisher Technique. Results showed the successful preparation of GAP with low water content (<0.01 %), high average molecular weight (> 2000 g · mol^–1), 42.82 % nitrogen, a viscosity of 3484 cP at 20 °C, yield ranges between 95–98 % and a polydispersity index of 1.2. The prepared GAP is promising for replacement of the classical GAPs in the energetic materials applications.     

Mesenchymal Stem Cells: a Promising Therapeutic Tool for Acute Kidney Injury

Applied Biochemistry and Biotechnology - Acute kidney injury (AKI) is a rapid loss of renal function. It has high mortality rates. Still, renal replacement therapy is considered the best solution...