Asymptotic behavior of semigroups of ρ-non-expansive and holomorphic mappings on the Hilbert Ball

We study generated semigroups of those self-mappings of the Hilbert ball which are non-expansive with respect to the hyperbolic metric. We find optimal convergence rates for such semigroups to interior stationary and boundary sink points. Since the hyperbolic metric is not defined on the boundary, the usual approach treats these two cases separately. In contrast with this practice, we use a special non-Euclidean “distance” (which induces the original topology) to present a unified theory. Our approach leads to new results even in the one-dimensional case. When the semigroups consist of holomorphic self-mappings, we obtain the rather unexpected phenomenon of universal rates of convergence of an exponential type. In particular, in the case of a boundary sink point we establish a continuous analog of the celebrated Julia–Wolff–Carathéodory theorem. Received: January 3, 2001; in final form: November 28, 2001?Published online: October 30, 2002     

Spatial dependencies of wind power and interrelations with spot price dynamics

Wind power has seen strong growth over the last decade and increasingly affects electricity spot prices. In particular, prices are more volatile due to the stochastic nature of wind, such that more generation of wind energy yields lower prices. Therefore, it is important to assess the value of wind power at different locations not only for an investor but for the electricity system as a whole. In this paper, we develop a stochastic simulation model that captures the full spatial dependence structure of wind power by using copulas, incorporated into a supply and demand based model for the electricity spot price. This model is calibrated with German data. We find that the specific location of a turbine – i.e., its spatial dependence with respect to the aggregated wind power in the system – is of high relevance for its value. Many of the locations analyzed show an upper tail dependence that adversely impacts the market value. Therefore, a model that assumes a linear dependence structure would systematically overestimate the market value of wind power in many cases. This effect becomes more important for increasing levels of wind power penetration and may render the large-scale integration into markets more difficult.     

A nonlinear truck model and its treatment as a multibody system

A planar vertical truck model with nonlinear suspension and its multibody system formulation are presented. The equations of motion of the model form a system of differential-algebraic equations (DAEs). All equations are given explicitly, including a complete set of parameter values, consistent initial values, and a sample road excitation. Thus the truck model allows various investigations of the specific DAE effects and represents a test problem for algorithms in control theory, mechanics of multibody systems, and numerical analysis. Several numerical tests show the properties of the model.     

Second order random fields over l p with homogeneous and isotropic increments

Summary A random field over l _p is a stochastic process X(t), where t is an element of l _p .It is said to have homogeneous and isotropic increments if E(X(t) – X(s)) ² is a function of t-s. The subject of this work is the spectral theory of such processes. The main results are: a representation of the field as a series of filtered, orthogonal processes with a real time parameter; a representation as a white noise integral over l _p ;limit theorems for the average of X over a sphere; and, finally, filtering of the orthogonal components.In particular, we mention: (1) The averages over spheres of increasing dimension converge in quadratic mean for p=2 but not for 0<p<2. (2) The limiting distribution of a fixed coordinate of a point uniformly distributed over the l _p -unit sphere in n-space, n , has the density [2(1/p+1)p ^1/p ]^–1exp(-¦x¦ ^p /P).This paper represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship of the National Science Foundation Grants NSF-GP-7378 and NSF-GW-2049.     

Enthalpies of ligation of Co2+ and Cu2+ to epimeric threonines and isoleucines

The enthalpies of protonation of epimeric threonines and isoleucines were determined calorimetrically at 298.15 K in 0.1 mol dm^?3 NaNO₃. The enthalpies of ligation of the same ligands with Co²⁺ and Cu²⁺ were determined under the same conditions.     

Fitzpatrick functions,cyclic monotonicity and Rockafellar’s antiderivative

Several deeper results on maximal monotone operators have recently found simpler proofs using Fitzpatrick functions. In this paper, we study a sequence of Fitzpatrick functions associated with a monotone operator. The first term of this sequence coincides with the original Fitzpatrick function, and the other terms turn out to be useful for the identification and characterization of cyclic monotonicity properties. It is shown that for any maximal cyclically monotone operator, the pointwise supremum of the sequence of Fitzpatrick functions is closely related to Rockafellar’s antiderivative. Several examples are explicitly computed for the purpose of illustration. In contrast to Rockafellar’s result, a maximal 3-cyclically monotone operator need not be maximal monotone. A simplified proof of Asplund’s observation that the rotation in the Euclidean plane by π/n$\pi /n$ is n$n$-cyclically monotone but not (n+1)$(n+1)$-cyclically monotone is provided. The Fitzpatrick family of the subdifferential operator of a sublinear and of an indicator function is studied in detail. We conclude with a new proof of Moreau’s result concerning the convexity of the set of proximal mappings.     

Multiple Blocking Sets and Arcs in Finite Planes

This paper contains two main results relating to the size ofa multiple blocking set in PG(2, q). The first gives a verygeneral lower bound, the second a much better lower bound forprime planes. The latter is used to consider maximum sizes of(k, n)-arcs in PG(2, 11) and PG(2, 13), some of which are determined.In addition, a summary is given of the value of m_n(2, q) forq 13.