On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

The representation of conditional expectations of non-Gaussian noise

For Wiener spaces conditional expectations and $L^{2}$-martingales w.r.t. the natural filtration have a natural representation in terms of chaos expansion. In this note an extension to larger classes of processes is discussed. In particular, it is pointed out that orthogonality of the chaos expansion is not required.

Selection-mutation balance models with epistatic selection

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Oxygen precipitation in Czochralski grown silicon heat treated at 525 degrees C

The diffusion of interstitial oxygen In silicon at 525 degrees C is studied using time-of-flight small-angle neutron scattering (SANS) to separate the elastic scattering from oxygen-containing aggregates from the inelastic scattering from neutron-phonon interactions. The growth of oxygen-containing aggregates as a function of time gives a diffusion coefficient, D, calculated from Ham's theory, that is I factor of similar to 3.8 +/- 1.4 times higher than that expected by extrapolation of higher and lower temperature data (D = 0.13 exp(-2.53 eV kT(-1)) cm(2) s(-1)). This result confirms previous observations of enhanced diffusion at intermediate temperatures (400 degrees C-650 degrees C) although the magnitude of the enhancement we find is Much smaller than that reported by some others.

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

Conservative upwind difference schemes for the Euler equations for real gas flows in a duct

In a recent paper [P. Glaister, Conservative upwind difference schemes for compressible flows in a Duct, Comput. Math. Appl. 56 (2008) 1787–1796] numerical schemes based on a conservative linearisation are presented for the Euler equations governing compressible flows of an ideal gas in a duct of variable cross-section, and in [P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480] schemes based on this philosophy are presented for real gas flows with slab symmetry. In this paper we seek to extend these ideas to encompass compressible flows of real gases in a duct. This will incorporate the handling of additional terms arising out of the variable geometry and the non-ideal nature of the gas.

Variance estimation with Chao's sampling scheme

We show that the Hájek (Ann. Math Statist. (1964) 1491) variance estimator can be used to estimate the variance of the Horvitz–Thompson estimator when the Chao sampling scheme (Chao, Biometrika 69 (1982) 653) is implemented. This estimator is simple and can be implemented with any statistical packages. We consider a numerical and an analytic method to show that this estimator can be used. A series of simulations supports our findings.

Knowledge communication and translation- A knowledge transfer model

Purpose – The purpose of this paper is to propose a process model for knowledge transfer in using theories relating knowledge communication and knowledge translation. Design/methodology/approach – Most of what is put forward in this paper is based on a research project titled “Procurement for innovation and knowledge transfer (ProFIK)”. The project is funded by a UK government research council – The Engineering and Physical Sciences Research Council (EPSRC). The discussions are mainly grounded on a thorough review of literature accomplished as part of the research project. Findings – The process model developed in this paper has built upon the theory of knowledge transfer and the theory of communication. Knowledge transfer, per se, is not a mere transfer of knowledge. It involves different stages of knowledge transformation. Depending on the context of knowledge transfer, it can also be influenced by many factors; some positive and some negative. The developed model of knowledge transfer attempts to encapsulate all these issues in order to create a holistic framework. Originality/value of paper – An attempt has been made in the paper to combine some of the significant theories or findings relating to knowledge transfer together, making the paper an original and valuable one.

Application of semiquantitative proteomics techniques to the Maillard reaction

Proteomic tools-in particular, mass spectrometry (MS)-have advanced significantly in recent years, and the identification of proteins within complex mixtures is now a routine procedure. Quantitative methods of analysis are less well advanced and continue to develop. These include the use of stable isotope ratio approaches, isotopically labeled peptide standards, and nonlabeling methods. This paper summarizes the use of MS as a proteomics tool to identify and semiquantify proteins and their modified forms by using examples of relevance to the Maillard reaction. Finally, some challenges for the future are presented.