Evolution of non-uniformly seeded warm clouds in idealized turbulent conditions

We present a mean-field model of cloud evolution that describes droplet growth due to condensation and collisions and droplet loss due to fallout. The model accounts for the effects of cloud turbulence both in a large-scale turbulent mixing and in a microphysical enhancement of condensation and collisions. The model allows for an effective numerical simulation by a scheme that is conservative in water mass and keeps accurate count of the number of droplets. We first study the homogeneous situation and determine how the rain-initiation time depends on the concentration of cloud condensation nuclei (CCN) and turbulence level. We then consider clouds with an inhomogeneous concentration of CCN and evaluate how the rain initiation time and the effective optical depth vary in space and time. We argue that over-seeding even a part of a cloud by small hygroscopic nuclei, one can substantially delay the onset and increase the amount of precipitation.

Tuneable compensator of dispersion and slope using non-uniformly strained chirped fibre grating

Summary form only given. A novel method for tuning the second and the third order dispersion using a simple multi-point bending device has been demonstrated. A simple model has been developed that allows to calculate the exact bending profile required for compensation for the given values of dispersion and dispersion slope.

Tuneable compensator of dispersion and slope using non-uniformly strained chirped fibre grating

Summary form only given. A novel method for tuning the second and the third order dispersion using a simple multi-point bending device has been demonstrated. A simple model has been developed that allows to calculate the exact bending profile required for compensation for the given values of dispersion and dispersion slope.

The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.

Abstract Subdifferential Calculus and Semi-Convex Functions

∗ The work is partially supported by NSFR Grant No MM 409/94.

On Typical Compact Convex Sets in Hilbert Spaces

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).

Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.

Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

MSC 2010: 30C45, 30C55

Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.