Affine minimal hypersurfaces of rotation

We give a complete list of affine minimal surfaces inA ³ with Euclidean rotational symmetry, completing the treatise given in [1] and prove that these surfaces have maximal affine surface area within the class of all affine surfaces of rotation satisfying suitable boundary conditions. Besides we show that for rotationally symmetric locally strongly convex affine minimal hypersurfaces inA ⁿ ,n4, the second variation of the affine surface area is negative definite under certain conditions on the meridian.     

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.

     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

The job-shop problem and immediate selection

The job-shop problem is one of the most difficult NP-hard scheduling problems. A 10×10-problem published in 1963 has been solved only recently by Carlier and Pinson using a branch and bound method. Other branch and bound algorithms have been developed recently. The efficiency of all these branch and bound methods relies on the concept of immediate selection which allows to introduce order relations on the setI of all operations to be processed on the same machine before branching. We present new algorithms for immediate selection. Among them are

1. anO(max {n logn,f})-algorithm for fixing all disjunctions induced by cliques;
2. anO(n ²)-algorithm based on concepts which are different from those used by Carlier and Pinson.

Here,n is the number of operations inI andf is the number of induced order relations.     

Time-resolved vibrational spectroscopy

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Time-resolved vibrational spectroscopy     

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.     

Density computations for real quadratic units

In order to study the density of the set of positive integers for which the negative Pell equation is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadratic orders. A fast algorithm that computes 2-class groups rather than units is used. It is random polynomial-time in as the factorization of is a natural part of the input for the values of we encounter. The data obtained provide convincing numerical evidence for the density heuristics for the negative Pell equation proposed by the second author. In particular, an irrational proportion of the real quadratic fields without discriminantal prime divisors congruent to 3 mod 4 should have a fundamental unit of norm .

     

Nonlocal forces of inertia in cosmology

This paper reviews the origin of inertia according to Mach's principle and Weber's law of gravitation. The resulting theory is based on simultaneous nonlocal gravitational interactions between particles in the solar system and others in the remote universe beyond the Milky Way galaxy. It explains the precession of the perihelion of Mercury. A most important implication of the Mach-Weber theory of the force of inertia is the necessity for a large amount of uniformly distributed matter in the galactic universe. This matter could be the source of the cosmic background radiation. Nonlocal inertia forces are compatible with a static universe and also with an expanding universe but the latter would demand slow changes in the mass of particles and the gravitational constant.     

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.