Molecular speciation of microparticles: application of pattern recognition techniques to laser microprobe mass spectrometric data

Attempts were made to enhance the ability of laser microprobe mass spectrometry (LAMMS) to identify molecular species in individual microparticles by applying pattern recognition methods. Principal component analysis (PCA) and canonical discriminant analysis were applied to LAMMS data for nickel-containing environmental particles. Detailed comparison of the two statistical methods demonstrated the utility of PCA. The successful application was highly dependent on the use of appropriate spectral normalization and feature extraction techniques prior to PCA. Although the test system involved only a small number of standard compounds, the LAMMS data were complicated by the effects of intra-particle heterogeneity common to environmental samples and by instrumental limitations. Pattern recognition techniques provided more accurate quantitative assignments of molecular species than were available by qualitative inspection of characteristic cluster ions or by simple spectral subtraction to compare particle data with a library of standard compounds. Results were substantiated by comparison with bulk analysis studies using wet chemical techniques.     

Generalized nonlinear models of suspension bridges

This paper generalizes some results established in [J. Malík, Nonlinear models of suspension bridges, J. Math. Anal. Appl., in press]. The geometric nonlinearity connected with the torsion of a road bed is included in the generalized model. The basic variational equations are derived from the principle of minimum energy. The existence of a solution to the generalized problem is proved. The existence is based on the Brouwer fixed-point theorem.     

Worst-case distribution analysis of stochastic programs

We show that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution. This extends the so-called ``Uniformity Principle' of Barmish and Lagoa (1997) where the objective function is the indicator function of a convex symmetric set.     

Vector Ekeland’s variational principle in an <Emphasis Type="Italic">F</Emphasis>-type topological space

In this paper, we first give a vector-valued version of Brézis and Browder’s scalar general principle. We then apply the vector-valued general principle to study a vector Ekeland’s variational principle in a F-type topological space, which unifies and improves the corresponding vector-valued Ekeland’s variational results in complete metric space. This project was partially supported by the Research Grants Council of Hong Kong (BG771) and National Natural Science Foundation of China (70501015, 70401006).     

A priori bounds for elliptic equations

In this paper we study the relationship existing between the maximum principle and the principal eigenvalue of second order elliptic operators and the expected exit times of the corresponding diffusions. A probabilistic approach is discussed that provides a good understanding of classical results established analytically. We also obtain an Alexandrov-Bakelman-Pucci type of estimate using similar methods.     

New developments in the application of Pontryagin's Principle for the hydrothermal optimization

^** Email: bayon{at}uniovi.es In this paper we have developed a much simpler theory than previousones that resolves the problem of the optimization of hydrothermalsystems. The problem involves non-holonomic inequality constraints.In particular, we have established a necessary condition forthe stationary functions of the functional. We shall use Pontryagin'sMinimum Principle as the basis for proving this theorem, settingout our problem in terms of optimal control in continuous time,with the Lagrange-type functional. This theorem allows us toelaborate the optimization algorithm that leads to the determinationof the optimal solution of the hydrothermal system. We generalizethe problem, taking into account a cost associated with thewater, to then set out and solve the corresponding Bolza's problem.Finally, we present an example employing the algorithm developedfor this purpose with the ‘Mathematica’ package.     

Positive Solutionsofp-LaplaceEquation Involving Critical Sobolev Exponent

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Light intensity modulation fiber-optic sensor for curvature measurement

A light intensity modulation fiber-optic sensor, which can measure curvature directly, has been developed. It is suitable for the measurement of thin, embedded or highly flexible structures. An experimental analysis on the static and dynamic characteristics of sensor has been undertaken. The results show that the output voltage has polarity and a good linear relationship with curvature when the curvature radius is larger than 60 mm. The mathematical model relating the relative output loss, parameters of sensitive zone’s configuration (depth, number, height and half angle of tooth) and bending radius is described analytically based on the geometric optics. Curvature fiber-optic sensors can be used to build a quasi-distributed fiber-optic sensor system, which can measure curvature and torsion angle simultaneously.     

Maximal inequalities for a continuous semimartingale

Let X =( X t ) t S 0 be a continuous semimartingale given by d X t = f ( t ) w ( X t )d d M ¢ t + f ( t ) σ ( X t )d M t , X 0 =0, where M =( M t , F t ) t S 0 is a continuous local martingale starting at zero with quadratic variation d M ¢ and f ( t ) is a positive, bounded continuous function on [0, X ), and w , σ both are continuous on R and σ ( x )>0 if x p 0. Denote X 𝜏 * =sup 0 h t h 𝜏 | X t | and J t = Z 0 t f ( s ) } ( X s )d d M ¢ s ( t S 0) for a nonnegative continuous function } . If w ( x ) h 0 ( x S 0) and K 1 | x | n σ 2 ( x ) h | w ( x )| h K 2 | x | n σ 2 ( x ) ( x ] R , n >0) with two fixed constants K 2 S K 1 >0, then under suitable conditions for } we show that the maximal inequalities c p , n log 1 n +1 (1+ J 𝜏 ) p h Á X 𝜏 * Á p h C p , n log 1 n +1 (1+ J 𝜏 ) p (0< p < n +1) hold for all stopping times 𝜏 .     

An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg's Uncertainty Principle

We present "one-dimensional" Fourier theory on commutative groups T hH , 0 h h < X , 0< H h X within the framework of the so-called calculus on measure chains (or time scales). Depending on certain values of the graininess h and length H of the group the four classical types of Fourier transform are covered: Fourier integral ( T 0 X = R ), Fourier series ( T 1 X = Z ), Fourier analysis of periodic functions ( T 0,2 ~ = S 1 (0) unit circle) and discrete Fourier transform ( T 1 N = Z N ). We will present Fourier theory on these groups in a unified manner. This also allows to closely track the roles of the graininess h and length H of the group--especially for h M 0 and H M X . In the final part of the paper, we investigate the solution of a fundamental equation on T hH , which can be considered as a generalization of the Gauss function. It finally leads to a version of the Heisenberg uncertainty principle, which extends the classical one, valid for T 0 X = R , to the case T hH , where either h >0 or H < X .