A New Technique for Preserving Conservation Laws

Foundations of Computational Mathematics - This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We...     

Representations of double coset hypergroups and induced representations

The principal goal of this paper is to investigate the representation theory of double coset hypergroups. IfK=G//H is a double coset hypergroup, representations ofK can canonically be obtained from those ofG. However, not every representation ofK originates from this construction in general, i.e., extends to a representation ofG. Properties of this construction are discussed, and as the main result it turns out that extending representations ofK is compatible with the inducing process (as introduced in [7]). It follows that a representation weakly contained in the left-regular representation ofK always admits an extension toG. Furthermore, we realize the Gelfand pair (where are a local field andR its ring of integers) as a polynomial hypergroup on ℕ₀ and characterize the (proper) subset of its dual consisting of extensible representations.     

Densest packings of eleven congruent circles in a circle

In 1969 Pirl provided the densest packings ofn equal circles in a circle forn 10. We will prove the optimality for the packings that were conjectured forn=11. The proof is based on elementary combinatorial and analytical techniques.     

Über lineare Unabhängigkeit

It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w ₁ + ... + w _m over , wherew ₁,...,w _m are given real numbers. In particular, if this dimension ism, i.e. ifw ₁,...,w _m are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade.

     

Jets

This is a discussion of concentrated large-scale flows in planetary atmospheres and oceans, argued from the viewpoint of basic geophysical fluid dynamics. We give several elementary examples in which these flows form jets on rotating spheres. Jet formation occurs under a variety of circumstances: when flows driven by external stress have a rigid boundary which can balance the Coriolis force, and at which further concentration can be caused by the beta effect; when there are singular lines like the line of vanishing windstress or windstress-curl, or the Equator; when compact sources of momentum, heat or mass radiate jet-like beta plumes along latitude circles; when random external stirring of the fluid becomes organized by the beta effect into jets; when internal instability of the mass field generates zonal flow which then is concentrated into jets; when bottom topographic obstacles radiate jets, and when frontogenesis leads to shallow jet formation. Essential to the process of jet formation in stratified fluids is the baroclinic life cycle described in geostrophic turbulence studies; there, conversion from potential to kinetic energy generates eddy motions, and these convert to quasibarotropic motions which then radiate and induce jet-like large-scale circulation. Ideas of potential vorticity stirring by eddies generalize the notion of Rossby-wave radiation, showing how jets embedded in an ambient potential vorticity gradient (typically due to the spherical geometry of the rotating planet) gain eastward momentum while promoting broader, weaker westward circulation. Homogenization of potential vorticity is an important limit point, which many geophysical circulations achieve. This well-mixed state is found in subdomains of the terrestrial midlatitude oceans, the high-latitude circumpolar ocean, and episodically in the middle atmosphere. Homogenization expels potential vorticity gradients vertically to the top and bottom of the fluid, and sideways to the edges of flow domains or gyres; in both these ways is jet formation enhanced.     

Reducibility behavior of polynomials with varying coefficients

LetK be a number field, and leth∈K[Y] be a polynomial of degreen. Fix an integer 0≤i≤n and compare the set ν of those integersa ofK such thath(Y)−aY ⁱhas a root inK with the set of those integersa, such thath(Y)−aY ⁱis reducible overK. Ifi is coprime ton, then we classify the rare cases where ν is not cofinite in . The main tools are a theorem of Siegel about integral points on algebraic curves and the theory of finite groups.     

Probing Higgs boson — and supersymmetry-induced CP violation in top quark production by (un-) polarized electron-positron collisions

We consider, both for unpolarized and longitudinally polarized electron beams, the reaction $e^ + e^ - \to t\bar t$ with subsequent semileptonict and nonleptonic $\bar t$ decay and vice versa and investigate optimized angular correlations which are sensitive to CP non-conservation in the $t\bar t$ production vertex. We calculate these correlations for two-Higgs-doublet extensions and the minimal super-symmetric extension of the Standard Model (SM) with CP violation beyond the Kobayashi-Maskawa phase. While the sensitivity of the optimal correlation for tracing dispersive CP effects is enhanced with longitudinally polarized electron beams, we find that the sensitivity of the best correlation for probing absorptive CP effects is almost independent of the polarization degree.     

Bivoltametric titrations using electrodes with innovative geometry

Electrodes with different surface areas were investigated for the determination of reversible, quasireversible, irreversible or electroinactive substrates. Two kinds of electrodes were constructed, a helical electrode with a given asymmetry and a platinum array electrode with a variable area. These electrodes were applied for the cerimetry of ammonium iron(II) sulfate and for the bromatometry of various organic substances. The theoretically derived effects on the shape of the voltametric titration curve are verified experimentally. It is possible to sharpen one side of the peak and to broaden the other side, depending on the system and the side of the peak one is interested in. It is possible to improve the bivoltametric determination of hydroquinone, benzocaine and sulfaguanidine by bromatometry by the directed employment of electrodes of different areas. For the bromatometric determination of electrochemically irreversible substrates the use of the electrode geometries proposed is a way to obtain a sharp bend and a steep decrease of titration curves with low values of the constant current which is a basic requirement for the accuracy.