Nonvanishing at spatial extremity solutions of the defocusing nonlinear Schrödinger equation

We show local existence of certain type of solutions for the Cauchy problem of the defocusing nonlinear Schrödinger equation with pure power nonlinearity, in various cases of open sets, unbounded or bounded. These solutions do not vanish at the boundary or at infinity. We also show, in certain cases, that these solutions are unique and global.     

Representation formulae of general solutions in the theory of hemitropic elasticity

We consider the steady state oscillation equations of the theoryof elasticity of hemitropic materials. We derive general representationformulae for the displacement and microrotation vectors by meansof six scalar metaharmonic functions. These formulae are veryconvenient and useful in many particular problems for domainswith concrete geometry. Here we consider two canonical transmissionproblems for piecewise homogeneous bodies with spherical interfacesand with the help of the representation formulae construct explicitsolutions in the form of absolutely and uniformly convergentseries. The representations can also be applied to multi-layeredbodies with spherical and cylindrical interfaces.     

3D elastic scattering theorems for point-generated dyadic fields

The problem of scattering of elastic spherical waves by a rigid body, cavity or a penetrable obstacle in 3D linear elasticity is considered. For two point sources, dyadic far-field pattern generators are defined, which are used for the formulation of a general scattering theorem. The main reciprocity principle and mixed scattering relations are also established. We provide the necessary energy considerations, presenting relative energy functionals and expressions for the differential and the scattering cross section due to point-source dyadic incidence. Finally, an application of the general scattering theorem for appropriate locations of the point source leads to an optical theorem. Copyright © 2007 John Wiley & Sons, Ltd.     

Designed study of the effect of different reaction parameters on the catalytic determination of iron(III)

Summary The paper deals with the optimization of a catalytic determination of Fe(III) in trace amounts. The optimization is performed by the orthogonal experimental design and includes five reaction variables (pH, concentration of oxidant, concentration of substrate, ionic strength of solution, temperature). The rank of the variables is found and commented and a practically satisfactory statistical model is derived.

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Untersuchung der Wirkung verschiedener Reaktionsparameter auf die katalytische Eisen(III)-Bestimmung

     

On an inequality in probability

Inequalities are obtained forΣⁿ_im1P(A₁) when P(A₁A₁) 1? i < j ? n are known. The result improves an elementary inequality due to Erdös, Neveu, Renyi and Zybrzyck.     

The D-optimal saturated designs of order 22

This paper attempts to prove the D-optimality of the saturated designs X${}^1$ and X${}^{11}$ of order 22, already existing in the current literature. The corresponding non-equivalent information matrices M${}^1$=(X${}^1$)${}^T$X${}^1$ and M${}^{11}$=(X${}^{11}$)${}^T$X${}^{11}$ have the maximum determinant. Within the application of a specific procedure, all symmetric and positive definite matrices M of order 22 with determinant the square of an integer and $\ge$det(M${}^1$) are constructed. This procedure has indicated that there are 26 such non-equivalent matrices M, for 24 of which the non-existence of designs X such that X${}^T$X =M is proved. The remaining two matrices M are the information matrices M${}^1$ and M${}^{11}$.     

Distributed caching over heterogeneous mobile networks

Sharing content over a mobile network through opportunistic contacts has recently received considerable attention. In proposed scenarios, users store content they download in a local cache and share it with other users they meet, e.g., via Bluetooth or WiFi. The storage capacity of mobile devices is typically limited; therefore, identifying which content a user should store in her cache is a fundamental problem in the operation of any such content distribution system. In this work we propose Psephos, a novel mechanism for determining the caching policy of each mobile user. Psephos is fully distributed: users compute their own policies individually, in the absence of a central authority. Moreover, it is designed for a heterogeneous environment, in which demand for content, access to resources, and mobility characteristics may vary across different users. Most importantly, the caching policies computed by our mechanism are optimal: we show that Psephos maximizes the system’s social welfare. To the best of our knowledge, our work is the first to address caching with heterogeneity in a fully distributed manner.     

LIBS using dual- and ultra-short laser pulses

Pre-ablation dual-pulse LIBS enhancement data for copper, brass and steel using ns laser excitation are reported. Although large enhancements are observed for all samples, the magnitude of the enhancement is matrix dependent. Whereas all of the dual-pulse studies used ns laser excitation we see interesting effects when using ps and fs laser excitation for single-pulse LIBS. LIBS spectra of copper using 1.3 ps and 140 fs laser pulses show much lower background signals compared to ns pulse excitation. Also, the atomic emission decays much more rapidly with time. Because of relatively low backgrounds when using ps and fs pulses, non-gated detection of LIBS is shown to be very effective. The plasma dissipates quickly enough using ps and fs laser pulses, that high pulse rates, up to 1000 Hz, are effective for increasing the LIBS signal, for a given measurement time. Finally, a simple near-collinear dual-pulse fiber-optic LIBS probe is shown to be useful for enhanced LIBS measurements. Received: 1 August 2000 / Revised: 2 November 2000 / Accepted: 8 November 2000