New methodologies in trace analysis of volatile organic compounds

Two methods for sampling and concentration of volatile organic compounds are reported. In the first method, traps coated with a very thick film (ca. 100 μm) of cross-linked silicone stationary phase are employed. Such thick films can be prepared with a modified dynamic coating procedure, which is briefly described. The low phase ratio traps can be utilized for enrichment of volatiles from gaseous as well as aqueous matrices. The second technique is based on chromatographic evaporation of a solvent in a capillary tube, where the process is sustained by a repeated sample injection and a cyclic flow reversal. In this way, large solvent volumes can be handled by a small volume system. Under optimal conditions, when using a solvent barrier, quantitative recovery is possible even for compounds of comparatively high volatility. Another important application of the technique is extraction of trace components from gases such as headspace samples, polluted air, etc.     

Solutions in Sobolev spaces of vector refinement equations with a general dilation matrix

In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space W_p^k(ℝ^s) (1≤p≤∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented. Rate of convergence of vector cascade algorithms in a Sobolev space W_p^k(ℝ^s) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the L_p (1≤p≤∞) critical smoothness exponent of a refinable function vector without the assumption of stability on the refinable function vector. As a consequence, we show that if a compactly supported function vector φ∈L_p(ℝ^s) (φ∈C(ℝ^s) when p=∞) satisfies a refinement equation with a finitely supported matrix mask, then all the components of φ must belong to a Lipschitz space Lip(ν,L_p(ℝ^s)) for some ν>0. This paper generalizes the results in R.Q. Jia, K.S. Lau and D.X. Zhou (J. Fourier Anal. Appl. 7 (2001) 143–167) in the univariate setting to the multivariate setting. Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 42C20, 41A25, 39B12. Research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant G121210654.     

Tunneling Radiation of a Torus-Like Black Hole in Anti-de Sitter Space-Time

An extension of the Parikh-Wilczek's semi-classical quantum tunneling method, the tunneling radiation of the charged particle from a torus-like black hole is investigated. Difference from the uncharged mass-less particle, the geodesics of the charged massive particle tunneling from the black hole is not light-like, but determined by the phase velocity. The derived result shows that the tunneling rate depends on the emitted particle's energy and electric charge, and takes the same functional form as uncharged particle. It proves also that the exact emission spectrum is not strictly pure thermal, but is consistent with the underlying unitary theory. PACS Numbers: 04.70.Dy, 97.60.Lf, 05.30.Ch.     

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

1IntroductionThispaperisconcernedwithpositivesolutionOfthesemilinearheatequationswithlocalizedreactionssubjecttoeitherinitialconditions(Cauchyproblem)ortheinitialandboundary-value(DirichletorNeumanntype)conditionswherenisaboundeddomaininRe,icEO.Equations(1.1)canbethoughtofasamodeltodescribesomephysicalphenomena(heatpropagation,chemicalreaction)inwhichthenonlinearreactionsinadynndcalsystemtakesplaceonlyatasinglesite.InthesequelforconvenienceweshallsamplycalltheCauchy,initial-Direchlet,orini…     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

Representing the mean residual life in terms of the failure rate

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem—namely that of expressing the mean residual life in terms of the failure rate—typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.     

Flow Search Approach and New Bounds for the m-Step Linear Conjugate Gradient Algorithm

A flow search approach is presented in this paper. In the approach, each iterative process involves a subproblem, whose variables are the stepsize parameters. Every feasible solution of the subproblem corresponds to some serial search stages, the stepsize parameters in different search stages may interact mutually, and their optimal values are determined by evaluating the total effect of the interaction. The main idea of the flow search approach is illustrated via the minimization of a convex quadratic function. Based on the flow search approach, some properties of the m-step linear conjugate gradient algorithm are analyzed and new bounds on its convergence rate are also presented. Theoretical and numerical results indicate that the new bounds are better than the well-known ones.     

Evaluation of the Kushida Method of short-term earthquake prediction

Kushida and Kushida found that FM radio waves from stations at distances over-the-horizon are received before earthquakes. Based on this finding, since the mid-1990’s, the Kushidas have been practicing “Earthquake Precursor Detection Experiment”. The performance of the Kushida method during 2000–2003 has been evaluated by checking their predictions against the actual seismicity. During the period, there were 92 Kushida predictions mentioning the possibility of M ≥ 5.5 event, whereas there were 49 M ≥ 5.5 earthquakes in the Japanese region. If the criteria for successful prediction are set as: the errors in date is less than one day, epicentral position is roughly within specified area, and error in M is less than 0.5, the success rate was 20% and the alarm rate was 12%. If we relax the criteria to: the errors in dates within 10 days, epicenter within additional 100 km of specified area and the magnitude error less than 1.0, the success rate was 40% and the alarm rate was 27%. These rates may look insufficient for a practical prediction method. Considering, however, the fact that no other short-term prediction has ever been made in Japan so far it is a significant achievement. Moreover, it was found that in almost all failed predictions, meaningful signals were detected although the interpretations were incorrect. This indicates that the method is promising provided further investigation is carried out. The same evaluation at the M ≥ 6.0 level showed that the general performance was similar to the M ≥ 5.5 level, except that both success rate and alarm rate were lower at the M ≥ 6.0 level. If this unexpected finding is real, it might be inherent to the methodology using scattering of short-wave length radio waves as suggested by M. Hayakawa and may contain important information in understanding the earthquake physics and LAI-coupling. The results of the present study indicate strongly that the earthquake prediction research using anomalous transmission of VHF FM radio waves should be enhanced in parallel with complementary research in other frequency ranges.     

Study on the dispersion characteristic of the plasma-loaded relativistic BWO

The dispersion characteristic of the plasma-loaded relativistic backward wave oscillator has been analyzed. The theoretical model has been established and the numerical calculations accord with the experimental results, which provides some useful suggestions on the designing of slow-wave structure of BWO.     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…