Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

A note on a result by M. Bognár concerning the Hahn--Mazurkiewicz Theorem

Summary In this note we use Theorem 2.4 in<span lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>[1]to give a very short proof of a recent result due to M. Bognár (Theorem A in [3]). We also prove that Bognár's result is in fact equivalent to the classical Hahn-Mazurkiewicz Theorem. Finally we give generalizations in the non-compact setting.     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

Submanifolds associated with graphs

In this paper we present an interesting relationship between graph theory and differential geometry by defining submanifolds of almost Hermitian manifolds associated with certain kinds of graphs. We show some results about the possibility of a graph being associated with a submanifold and we use them to characterize CR-submanifolds by means of trees. Finally, we characterize submanifolds associated with graphs in a four-dimensional almost Hermitian manifold.

     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

The Gross-Neveu model at finite temperature at next-to-leading order in the 1/N expansion

We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under renormalization group transformations. The model is used as a playground to investigate various features of field theory at finite temperature. For example we verify that, as expected from general arguments, the cancellation of ultraviolet divergences takes place at finite temperature without the need for introducing counterterms beyond those of zero temperature. As well known, the discrete chiral symmetry of the (1+1)-dimensional model is spontaneously broken at zero temperature and restored, in leading order, at some temperature T_c; we find that the 1/N approximation breaks down for temperatures below T_c: as the temperature increases, the fluctuations become eventually too large to be treated as corrections, and a Landau pole invalidates the calculation of the effective potential in the vicinity of its minimum. Beyond T_c, the 1/N expansion becomes again regular: it predicts that in leading order the system behaves as a free gas of massless fermions and that, at the next-to-leading order, it remains weakly interacting. In the limit of large temperature, the pressure coincides with that given by perturbation theory with a coupling constant defined at a scale of the order of the temperature, as expected from asymptotic freedom.     

Balanced contributions for TU games with awards and applications

Calleja et al. [Calleja, P., Borm, P., Hendrickx, R., 2005. Multi-issue allocation situations. European Journal of Operational Research 164, 730–747] introduced multi-issue allocation situations with awards. In this paper, we extend the classical model of cooperative games with transferable utility to the cooperative games with transferable utility and awards. We define a run-to-the-bank rule for cooperative games with transferable utility and awards and characterise it in terms of a property of balanced contributions. We apply our main result to bankruptcy problems and multi-issue allocation situations with awards.     

Comparisons of pharynx, source, formant, and pressure characteristics in operatic and musical theatre singing

Belting, a vocal technique typically cultivated in musical theatre singing, differs timbrally from operatic singing in many interesting respects. The underlying phonatory differences have not been previously investigated in detail. Yet, belting is frequently associated with disturbances of voice function. Articulatory and phonatory characteristics are investigated in a female subject who is a professional singer (co-author JL) trained in both the operatic and belting styles and in an intermediate vocal technique (“mixed”). This article presents data obtained from this subject by video-fiberoptic observation of the pharynx, inverse filtering of airflow, and measurement of subglottal pressure. The results reveal that belting was characterized by very high subglottal pressures and sound levels, and apparently also by a comparatively high degree of glottal adduction. Comparisons with other investigations of related aspects of belting and operatic singing support the assumption that the data obtained from our subject are representative for these vocal techniques.     

Structural study of methyl 2,6-diphenyl-N-methyl-4-oxopiperidine-3,5-dicarboxylate enolic forms

The methyl 2,6-diphenyl-1-methyl-4-oxopiperidine-3,5-dicarboxylates 1 were synthesized by the Mannich procedure from methyl 3-oxoglutarate, benzaldehyde and methylamine. Keto-enol tautomerism as well as configurational isomerism at C-2 were observed. The stereochemistry of the Ib and Ic enolic forms were determined by ¹H and ¹³C nmr data.