An integral representation for decomposable measures of measurable functions

Summary We start with a measurem on a measurable space (,A), decomposable with respect to an Archimedeant-conorm on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.The integral naturally leads to a -decomposable measurem on the space of all measurable functions from to [0, 1]. The main result of the present paper is the converse of this, namely that, under natural conditions, any -decomposable measurem on can be represented as an integral of a certain Markov-kernelK. We extend this representation to measures on which have values in a set of distribution functions.These results generalize the work done by the first author in the case of additive measures.     

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 diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

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

Call for papers

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.     

Infinite period and Hopf bifurcations for the pH-regulated oscillations in a semibatch reactor (H(2)O(2)-Cu(2+)-S(2)O(2-) (3)-NaOH system)

Dynamic behavior of the pH-regulated oscillations has been studied for the hydrogen peroxide oxidation of thiosulfate ions in the presence of trace amounts of copper(II) ions in a semibatch reactor. A solution of 0.08 M Na(2)S(2)O(3) and 0.112 M NaOH was flowed at 0.160 mL/min into 300 mL of solution containing the H(2)O(2) and Cu(2+) in a vessel. There exists a critical value of the H(2)O(2) or Cu(2+) concentrations below which the system does not oscillate. The oscillations appear due to an infinite period bifurcation at low initial concentrations of the H(2)O(2). The initial concentration of Cu(2+) may be considered as a bifurcation parameter in this case. Increase of the initial hydrogen peroxide concentration causes the pH-regulated oscillations through a nondegenerate supercritical Hopf bifurcation. The classification of bifurcations is based on the analysis of the behavior of oscillation amplitude and period at different initial concentrations of the H(2)O(2) and Cu(2+). Our results show a possibility to distinguish different scenarios for the appearance of transient oscillations in semibatch experiments. (c) 1996 American Institute of Physics.