Generalized entropy optimization problems and the existence of their solutions

In the present study we have formulated a generalization of entropy optimization problems (GEOP), proposed sufficient conditions for the existence of solution. We have suggested also a new method based on a priori evaluations and Newton's methods for calculation of Langrange multipliers. Mentioned method allows calculating Langrange multipliers by starting from arbitrary initial point for Newton's approximations of constructed auxiliary equation. The solution of auxiliary equation is chosen as initial point for second constructed auxiliary equation. The recurring mentioned process for finite time leads to achieve an initial point for Newton's approximations of given equation and allows to find its unknown solution.     

A geometric characterisation of resonance in Hopf bifurcation from relative equilibria

We give a new characterisation of resonance in Hopf bifurcation from relative equilibria in systems with compact symmetry group. This characterisation provides a full geometric explanation of the resonance phenomenon. In addition, we develop techniques based on normal form theory to give a complete solution to the associated bifurcation problem.     

Uncertainty evaluation of the spectral UV irradiance evaluated by using the UVSPEC radiative transfer model

The radiative transfer models allow calculating the spectral UV irradiance from some set of measured input quantities linked with the surface reflectivity, the solar zenith angle, the ozone column and the characteristics of clouds and aerosols. The spectral irradiance yielded by a model is influenced by errors in the measurement of the input quantities. In this paper, the influences of these errors are characterized and compared with other systematic effects through an uncertainty analysis. We evaluated the uncertainty of the spectral UV irradiance rendered by the UVSPEC model, under cloudless sky conditions. In order to express the uncertainty of the output quantities (the global, direct and diffuse irradiances) in terms of the standard uncertainties of the input quantities, we used a Monte Carlo-based uncertainty propagation technique. We found that the uncertainty of the irradiance in the UV-B part of the spectrum was strongly influenced by the uncertainty attributed to the ozone column datum. Moreover, the uncertainities associated with the aerosol parameters accounted for most of the UV-A global irradiance uncertainty; the latter increased from about 4% under low aerosol conditions, up to about 14% in case of polluted air. We conclude that the UV irradiance evaluation through radiative transfer models requires paying special attention to the assessment of the aerosols properties.     

Phase recovery from fringe patterns using the continuous wavelet transform

Interferometry is well established as an optical technique in which a measurand is encoded as the phase of a periodically varying intensity pattern. In view of the inherent accuracy of interferometry, many methods have been developed to retrieve the phase from images of the fringe pattern. Our focus in this paper is one such technique—the continuous wavelet transform (CWT). We begin by reviewing the CWT and the space–spatial–frequency localisation properties of wavelets. We show that a path which follows the maximum modulus of the CWT (the wavelet ridge) gives the instantaneous fringe frequency as a function of spatial displacement. The phase is automatically and trivially obtained, without discontinuities, by integration. Examples of practical wavelets are given and algorithms to isolate the wavelet ridge reviewed.     

Abelian Subgroups of Garside Groups

In this article, we show that for every abelian subgroup H of a Garside group, some conjugate g ^?1 Hg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.     

NorTRACK product tracking system—development and implementation

This paper presents the experience gained by developers and users with implementation and operation of NorTRACK^TM, a real-time computerized product tracking system. A Programmable Logic Controller (PLC) collects and transfers data in real time to NorTRACK’s Oracle^TM database on a Windows NT^TM server network. After extensive development and Beta testing at MDS Nordion’s Canadian Irradiation Centre in Montreal, Canada, NorTRACK was installed in January 1997 with a new irradiation facility in Ethicon Endo-Surgery Inc.’s Albuquerque plant in the United States. NorTRACK communicates with the irradiator control and safety system, the plant's central manufacturing database, an innovative pallet staging and tote loading robot, and an automated dosimetry reading system. This integrated system allows the sterilization facility to monitor the irradiator operation and the flow of many products, through varied processing modes, continuously and reliably. As a result of operating with NorTRACK, both MDS Nordion’s CIC facility and the Endo-Surgery manufacturing site, are beginning to realize unique benefits in their respective operations. MDS Nordion is also initiating several future product enhancements and additional productivity modules. This paper describes the NorTRACK system, the various stages of the development project and Beta tests, and the experience of the users to date in their operations.     

Free Subgroups in the Units of ℤ[K 8 × C p ]

Abstract

Marciniak and Sehgal (Marciniak, Z., Sehgal, S. K. (1997). Constructing free subgroups of integral group rings units. Proc. Amer. Math. Soc.125(4):1005–1009) constructed free subgroups in U(?[G]) whenever Ghas a non normal finite subgroup. In this paper we construct free subgroups in U(?[G]), where Gis a group whose subgroups are all normal.     

Mod p classification of Shimura F ‐crystals

Let k be an algebraically closed field of positive characteristic p. We first classify the D ‐truncations mod p of Shimura F ‐crystals over k and then we study stratifications defined by inner isomorphism classes of these D ‐truncations. This generalizes previous works of Kraft, Ekedahl, Oort, Moonen, and Wedhorn. As a main tool we introduce and study Bruhat F ‐decompositions; they generalize the combined form of Steinberg theorem and of classical Bruhat decompositions for reductive groups over k (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Imaginary quadratic function fields

In Bautista-Ancona and Diaz-Vargas (2006) [B-D] a characterization and complete listing is given of the imaginary quadratic extensions K of k(x), where k is a finite field, in which the ideal class group has exponent two and the infinite prime of k(x) ramifies. The objective of this work is to give a characterization and list of these kind of extensions but now considering the case in which the infinite prime of k(x) is inert in K. Thus, we get all the imaginary quadratic extensions of k(x), in which the ideal class group has exponent two.