On numerical ranges and roots

Existence of the fractional powers is established in Banach algebra setting, in terms of the numerical ranges of elements involved. The behavior of the spectra and (for Hermitian ∗-algebras satisfying some additional hypotheses) the ∗-numerical range under taking these powers also is investigated.     

Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

CLIFFORD MARTINGALES Φ-EQUIVALENCE BETWEEN S（f） AND f^＊

ＣＬＩＦＦＯＲＤＭＡＲＴＩＮＧＡＬＥＳΦ－ＥＱＵＩＶＡＬＥＮＣＥＢＥＴＷＥＥＮＳ（ｆ）ＡＮＤｆ￥ＬＯＮＧＲＵＬＩＮ；ＱＩＡＮＴＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ．）...     

Representations, convolution square roots and spherical vectors

We extend results on square integrable representations of a locally compact group to subrepresentations of a representations induced from a character of a closed subgroup. We do so working in the framework of quotient representations of ∗-algebras.     

Analysis of combined conduction and radiation heat transfer in presence of participating medium by the development of hybrid method

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in the presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional square enclosure. A blended method where the concepts of modified differential approximation employed by combining discrete ordinate method and spherical harmonics method, has been developed for modeling the radiative transport equation. The gray participating medium is bounded by isothermal walls of two-dimensional enclosure which are considered to be opaque, diffuse and gray. The effect of various influencing parameters i.e., radiation-conduction parameter, surface emissivity, single scattering albedo and optical thickness has been illustrated. The adaptability of the present method has also been addressed.     

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.     

On error operators related to the arbitrary functions principle

The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the “arbitrary functions principle” (Poincaré, Hopf). We give extensions of this property to Rd and to the Wiener space for some approximations of the Brownian motion. This gives new approximations of the Ornstein-Uhlenbeck gradient. These results apply to the discretization of some stochastic differential equations encountered in mechanics.     

Characterization of the Surface Electrode Reaction in the Presence of Uniform Interaction: The Case of Mo(VI) Reduction in the Presence of Phenanthroline and an Excess of Fulvic Acids

Surface electrode reactions involving lateral uniform interactions between adsorbed species is studied by means of square‐wave voltammetry (SWV). Interactions are represented by the interaction product aΘ, were a is the Frumkin interaction parameter (a is positive for attraction and negative for repulsion forces) and Θ is the surface coverage. The properties of the SW voltammetric response enable detection of interactions and recognition of the type of interaction forces by a simple procedure. The influence of the interactions on the apparent electrochemical reversibility of the surface electrode reaction is studied in detail. Utilizing “quasireversible maximum” the simple methodology for estimation of the standard redox rate constant without knowing the exact value of the interaction product aΘ is developed. Theoretical predictions are illustrated and confirmed by experiments with Mo(VI) in the presence of phenantroline and an excess of fulvic acids.     

Utilization of a Copper Solid Amalgam Electrode for the Analytical Determination of Atrazine

A copper solid amalgam electrode was prepared and used for the voltammetric determination of atrazine in natural water samples by square wave voltammetry. This electrode is a convenient substitute for the hanging mercury electrode since it is selective, sensitive, reliable and inexpensive and presents low toxicity characteristic. The detection limit of atrazine obtained in pure water (laboratory samples) was shown to be lower than the maximum limit of residue established for natural water by the Brazilian Environmental Agency. The relative standard deviation for 10 different measurements was found to be only 3.98% in solutions containing 8.16×10^?6 mol L^?1 of atrazine. In polluted stream water samples, the recovery measurements were approximately 70.00%, sustaining the applicability of the proposed methodology to the analysis of atrazine in such matrices.