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On logarithmic norms for differential algebraic equations
Logarithmic matrix norms are well known in the theory of ordinary differential equations (ODEs) where they supply estimates for error growth and the growth of the solutions. In this paper we present a natural generalization ...
The average behaviour of greedy algorithms for the knapsack problem: General distributions
This paper is a partial generalization of the results of  for rather arbitrary distributions of coefficients. We state the main theorem concerning the average behaviour of greedy algorithms. The validity of this theorem ...
The properties of differential-algebraic equations representing optimal control problems
This paper outlines a procedure for transforming a general optimal control problem to a system of Differential-Algebraic Equations (DAEs). The Kuhn-Tucker conditions consist of differential equations, complementarity ...
A Note on Stochastic Volatility, GARCH models, and Hyperbolic Distributions
We establish a relation between stochastic volatility models and the class of generalized hyperbolic distributions. These distributions have been found to fit exceptionally well to the empirical distribution of stock ...
A Geometric Interpretation of Reduction in the Jacobians of C ab Curves
In this paper, we show that the reduction of divisors in the Jacobian of a curve $C$ can be performed by considering the intersections of a suitable projective model of $C$ with quadrics in projective space. We apply this ...
Large time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics
The anharmonic oscillator model describing the propagation of electromagnetic waves in an exterior domain containing a nonlinear dielectric medium is investigated. The system under consideration consists of a generally ...