Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

Thermally induced solid-state transformation of cimetidine. A multi-spectroscopic/chemometrics determination of the kinetics of the process and structural elucidation of one of the products as a stable N3-enamino tautomer

Exposure of cimetidine (CIM) to dry heat (160–180 °C) afforded, upon cooling, a glassy solid containing new and hitherto unknown products. The kinetics of this process was studied by a second order chemometrics-assisted multi-spectroscopic approach. Proton and carbon-13 nuclear magnetic resonance (NMR), as well as ultraviolet and infrared spectroscopic data were jointly used, whereas multivariate curve resolution with alternating least squares (MCR-ALS) was employed as the chemometrics method to extract process information. It was established that drug degradation follows a first order kinetics.     

Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.     

An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system

A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.

     

TOF-SIMS imaging of chlorhexidine-digluconate transport in frozen hydrated biofilms of the fungus Candida albicans

The diffusion of the anti-microbial chlorhexidine digluconate (CHG) has been studied in C. albicans biofilms by time-of-flight secondary-ion mass spectrometry (TOF-SIMS). C. albicans has been shown to become resistant to common anti-microbial agents, including CHG, when growing as a biofilm. Mass transport resistance within biofilms has commonly been suggested as a resistance mechanism, but measurement of transport for most anti-microbial agents in biofilms has proven extremely difficult because of the heterogeneity of the biofilms and the difficulty in detecting these agents within an intact biofilm. In this study, TOF-SIMS has been used to study the transport of CHG and glucose in a frozen hydrated biofilm. The TOF-SIMS images reveal a progression of CHG from the top of the biofilm to its base with time. Images suggest that there are channels within the biofilm and show preferential binding of CHG to cellular components of the biofilm. Additionally, both living and dead cells can be identified in the TOF-SIMS images by the sequestration of K⁺ and the presence of cell markers. This study demonstrates that TOF-SIMS has the unique potential to simultaneously observe the presence of an antimicrobial agent, concentration of nutrients, and the viability of the cell population.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Construction algorithms for polynomial lattice rules for multivariate integration

We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.

We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.

We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.

     

合作联盟资源集成计划一种新方法

合作联盟里，资源集成计划往往是联盟成员群体谈判博弈的结果。本以两人博弈为例，对联盟的资源集成计划给出一个谈判博弈模型，能够较好地模仿和反映合作联盟资源整合计划的制订过程。     

Krylov-Bogolyubov averaging of asymptotically autonomous differential equations

We apply the Krylov and Bogolyubov asymptotic integration procedure to asymptotically autonomous systems. First, we consider linear systems with quasi-periodic coefficient matrix multiplied by a scalar factor vanishing at infinity. Next, we study the asymptotically autonomous Van-der-Pol oscillator.