Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

A Simple Theory of Condensation

A simple assumption of an emergence in gas of small atomic clusters consisting of $c$ particles each, leads to a phase separation (first order transition). It reveals itself by an emergence of ``forbidden'' density range starting at a certain temperature. Defining this latter value as the critical temperature predicts existence of an interval with anomalous heat capacity behaviour $c_p\propto\Delta T^{-1/c}$. The value $c=13$ suggested in literature yields the heat capacity exponent $\alpha=0.077$.Comment: 9 pages, 1 figur

A quadratic stability result for singular switched systems with application to anti-windup control

In this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A−ghT , and where one of the matrices is singular. We then apply this result in a study of a feedback system with a saturating actuator

On the infrared freezing of perturbative QCD in the Minkowskian region

The infrared freezing of observables is known to hold at fixed orders of perturbative QCD if the Minkowskian quantities are defined through the analytic continuation from the Euclidean region. In a recent paper [1] it is claimed that infrared freezing can be proved also for Borel resummed all-orders quantities in perturbative QCD. In the present paper we obtain the Minkowskian quantities by the analytic continuation of the all-orders Euclidean amplitudes expressed in terms of the inverse Mellin transform of the corresponding Borel functions [2]. Our result shows that if the principle of analytic continuation is preserved in Borel-type resummations, the Minkowskian quantities exhibit a divergent increase in the infrared regime, which contradicts the claim made in [1]. We discuss the arguments given in [1] and show that the special redefinition of Borel summation at low energies adopted there does not reproduce the lowest order result obtained by analytic continuation.Comment: 19 pages, 1 figur

The Wright ω Function

This paper defines the Wright ω function, and presents some of its properties. As well as being of intrinsic mathematical interest, the function has a specific interest in the context of symbolic computation and automatic reasoning with nonstandard functions. In particular, although Wright ω is a cognate of the Lambert W function, it presents a di#erent model for handling the branches and multiple values that make the properties of W difficult to work with. By choosing a form for the function that has fewer discontinuities (and numerical difficulties), we make reasoning about expressions containing such functions easier. A final point of interest is that some of the techniques used to establish the mathematical properties can themselves potentially be automated, as was discussed in a paper presented at AISC Madrid [3]

Exact Solution for Relativistic Two-Body Motion in Dilaton Gravity

We present an exact solution to the problem of the relativistic motion of 2 point masses in $(1+1)$ dimensional dilaton gravity. The motion of the bodies is governed entirely by their mutual gravitational influence, and the spacetime metric is likewise fully determined by their stress-energy. A Newtonian limit exists, and there is a static gravitational potential. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.Comment: 6 pages, latex, 3 figure

Generation of Cosmological Seed Magnetic Fields from Inflation with Cutoff

Inflation has the potential to seed the galactic magnetic fields observed today. However, there is an obstacle to the amplification of the quantum fluctuations of the electromagnetic field during inflation: namely the conformal invariance of electromagnetic theory on a conformally flat underlying geometry. As the existence of a preferred minimal length breaks the conformal invariance of the background geometry, it is plausible that this effect could generate some electromagnetic field amplification. We show that this scenario is equivalent to endowing the photon with a large negative mass during inflation. This effective mass is negligibly small in a radiation and matter dominated universe. Depending on the value of the free parameter of the theory, we show that the seed required by the dynamo mechanism can be generated. We also show that this mechanism can produce the requisite galactic magnetic field without resorting to a dynamo mechanism.Comment: Latex, 16 pages, 2 figures, 4 references added, minor corrections; v4: more references added, boundary term written in a covariant form, discussion regarding other gauge fields added, submitted to PRD; v5: matched with the published versio

The Effect of Negative-Energy Shells on the Schwarzschild Black Hole

We construct Penrose diagrams for Schwarzschild spacetimes joined by massless shells of matter, in the process correcting minor flaws in the similar diagrams drawn by Dray and 't Hooft, and confirming their result that such shells generate a horizon shift. We then consider shells with negative energy density, showing that the horizon shift in this case allows for travel between the heretofore causally separated exterior regions of the Schwarzschild geometry. These drawing techniques are then used to investigate the properties of successive shells, joining multiple Schwarzschild regions. Again, the presence of negative-energy shells leads to a causal connection between the exterior regions, even in (some) cases with two successive shells of equal but opposite total energy.Comment: 12 pages, 10 figure

Methods for Partitioning Data to Improve Parallel Execution Time for Sorting on Heterogeneous Clusters

International audienceThe aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For uniformly related processors (processors speeds are related by a constant factor), we develop a constant time technique for mastering processor load and execution time in an heterogeneous environment and also a technique to deal with unknown cost functions. For non uniformly related processors, we use a technique based on dynamic programming. Most of the time, the solutions are in O(p) (p is the number of processors), independent of the problem size n. Consequently, there is a small overhead regarding the problem we deal with but it is inherently limited by the knowing of time complexity of the portion of code following the partitioning