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Uniform L 1 error bounds for semi-discrete finite element solutions of evolutionary integral equations

Lin, Qun, Xu, Da, Zhang, Shuhua (2012)

Applications of Mathematics 2012

In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem u t + ∫ 0 t β ( t - s ) A u ( s ) d s = 0 , u ( 0 ) = v , t > 0 , where A is an elliptic partial-differential operator and β ( t ) is positive, nonincreasing and log-convex on ( 0 , ∞ ) with 0 ≤ β ( ∞ ) < β ( 0 + ) ≤ ∞ . Error estimates are derived in the norm of L t 1 ( 0 , ∞ ; L x 2 ) , and some estimates for the first order time derivatives of the errors are also given.

Universal enveloping algebras and quantization

Grabowski, Janusz (1993)

Proceedings of the Winter School "Geometry and Physics"

It is shown how the universal enveloping algebra of a Lie algebra L can be obtained as a formal deformation of the Kirillov-Souriau Poisson algebra C ∞ ( L * ) of smooth functions on the dual of L . This deformation process may be viewed as a “quantization” in the sense of F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer [Ann. Phys. 111, 61-110 (1978; Zbl 0377.53024) and ibid., 111-151 (1978; Zbl 0377.53025)]. The result presented is a somewhat more elaborate version of earlier findings...

Universal spaces

Schori, R. M. (1967)

General Topology and its Relations to Modern Analysis and Algebra

Use of a differential evolution algorithm for the optimization of the heat radiation intensity

Mlýnek, Jaroslav, Knobloch, Roman, Srb, Radek (2015)

Application of Mathematics 2015

This article focuses on the heat radiation intensity optimization on the surface of an aluminium shell mould. The outer mould surface is heated by infrared heaters located above the mould and the inner mould surface is sprinkled with a special PVC powder. This is an economic way of producing artificial leathers in the automotive industry (e.g. the artificial leather on car dashboards). The article includes a description of a mathematical model that allows us to calculate the heat radiation intensity...

Vector fields and connection on fibred manifolds

Dekrét, Anton (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] In a previous paper [Cas. Pestovani Mat. 115, No.4, 360-367 (1990)] the author determined the set of the vector fields on TM by which connections on TM can be constructed. In this paper, he generalizes some of such constructions to the case of vector fields on fibred manifolds, giving several examples.

Viscosity solutions to a new phase-field model for martensitic phase transformations

Zhu, Peicheng (2015)

Application of Mathematics 2015

We investigate a new phase-field model which describes martensitic phase transitions, driven by material forces, in solid materials, e.g., shape memory alloys. This model is a nonlinear degenerate parabolic equation of second order, its principal part is not in divergence form in multi-dimensional case. We prove the existence of viscosity solutions to an initial-boundary value problem for this model.

Volume and area renormalizations for conformally compact Einstein metrics

Graham, Robin C. (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Let X be the interior of a compact manifold X ¯ of dimension n + 1 with boundary M = ∂ X , and g + be a conformally compact metric on X , namely g ¯ ≡ r 2 g + extends continuously (or with some degree of smoothness) as a metric to X , where r denotes a defining function for M , i.e. r > 0 on X and r = 0 , d r ≠ 0 on M . The restrction of g ¯ to T M rescales upon changing r , so defines invariantly a conformal class of metrics on M , which is called the conformal infinity of g + . In the present paper, the author considers conformally compact metrics...

Wallman's method

Schröder, J. (1977)

General topology and its relations to modern analysis and algebra IV

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