Estimates for functions of two commuting infinite matrices and applications

We consider a matrix valued function of two infinite commuting matrices generating bounded operators in a Banach space. Sharp estimates for the norm and entries are derived. Applications of the obtained estimates to differential equations are also discussed.     

Diastereo-controlled Diels–Alder cycloadditions of erythrose benzylidene-acetal 1,3-butadienes by 4-substituted-1,2,4-triazoline-3,5-dione: Evidence for the stereoelectronic effects on the dienes

Erythrose benzylidene-acetal 1,3-butadienes are studied as partners in Diels–Alder cycloadditions. A high diastereofacial improvement is found in cases where both the alcohol function is protected and a π–π interaction between the diene and dienophile is possible. Several competing factors have been studied independently in order to explain its influence on the selectivity of the cycloadditions.     

Computing Complex Airy Functions by Numerical Quadrature

Integral representations are considered of solutions of the Airy differential equation w –zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations, which are evaluated by the trapezoidal rule. In a second method an integral representation is evaluated by using generalized Gauss–Laguerre quadrature; this approach provides a fast method for computing Airy functions to a predetermined accuracy. Comparisons are made with well-known algorithms of Amos, designed for computing Bessel functions of complex argument. Several discrepancies with Amos' code are detected, and it is pointed out for which regions of the complex plane Amos' code is less accurate than the quadrature algorithms. Hints are given in order to build reliable software for complex Airy functions.     

Inclusion of Polyphenol Oxidase Substrates in β-Cyclodextrin: A 1 H-NMR Study

A ¹H-NMR study of the interactionsbetween -cyclodextrin (-CD) and included phenolic molecules (chloragenic acid and caffeic acid ) in aqueous medium is reported. The results confirm that inclusion occurs. Data analysis by the continuous variation method shows that all the complexes have 1 : 1 stoichiometries. Values for the apparent association constants of the inclusion compounds are estimated and compared with previously reported values.     

Sum-frequency generation in dissipative systems: experimental evidence for optical wave patterns

We report a new mechanism for the secondary instabilities of traveling wave patterns in dissipative systems. In close analogy to nonlinear optics and plasma physics, it is a process of three-wave interaction that leads to sum-frequency generation. The primary traveling wave gives rise to two additional wave components, an upper and a lower frequency. We outline the mechanism and we show that this process does occur for wave patterns obtained in an optical experiment.     

Spiral wave generation in heterogeneous excitable media

As the coupling in a heterogeneous excitable medium is reduced, three different types of behavior are encountered: plane waves propagate without breaking up, plane waves break up into spiral waves, and plane waves block. We illustrate these phenomena in monolayers of chick embryonic heart cells using calcium sensitive fluorescent dyes. Following the addition of heptanol, an agent that reduces the electrical coupling between cells, we observe breakup of spiral waves. These results are modeled in a heterogeneous cellular automaton model in which the neighborhood of interaction is modified.     

On the loss of information due to fuzziness in experimental observations

The absence of exactness in the observation of the outcomes of a random experiment always entails a loss of information about the experimental distribution. This intuitive assertion will be formally proved in this paper by using a mathematical model involving the notions of fuzzy information and fuzzy information system (as intended by Tanaka, Okuda and Asai) and Zadeh's probabilistic definition. On the basis of this model we are first going to consider a family of measures of information enclosing some well-known measures, such as those defined by Kagan, Kullback-Leibler and Matusita, and then to establish methods for removing the loss of information due to fuzziness by increasing suitably the number of experimental observations.     

Life prediction of thermally cracked railway wheels: Growth estimation of cracks with arbitrary shape

A computer program for railway wheel life prediction has been developed incorporating an elastoplastic calculation of both the residual stress field induced by shoe-braking and the superposed alternating rolling contact stresses. The possibilities of unstable propagation of surface cracks, crack arrest, fatigue propagation through a complex stress field and crack detention on reaching the threshold value have been accounted for. An approximate method for crack growth prediction is used providing bounds for instantaneous crack front position and estimations of crack shape within short computing times. Some examples of application for an UIC R7 wheel are presented.