We determine the L p-L q-estimate of the linear equations of thermoelasticity for rhom-bic media in R 2. For this purpose we will transform the equations to an evolution equation showing that this equation has a unique solution with the help of the semigroup theory. In order to obtain the L p-L q-estimate, we will first apply the Fourier transformation to the evolution equation, thus determinin...

We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear time-dependent term is involved in the resulting equation. Two new numerical a...

Let C be a smooth projective curve in P1 × P1 of genus g 6= 4, and assume that it is birationally equivalent to a curve defined by a Laurent polynomial that is non-degenerate with respect to its Newton polygon ∆. Then we show that the convex hull ∆(1) of the interior lattice points of ∆ is a standard rectangle, up to a unimodular transformation. Our main auxiliary result, which we believe to be...

We compare three different methods for direct energy minimization in electronic structure calculations where the gradient of the energy functional with respect to the molecular orbitals is available. These methods make use of the preconditioned gradient to increase robustness. An orbital transformation is used to ensure that the orthogonality constraint on the orbitals remains satisfied when us...

The problem of minimizing an L2-sensitivity measure subject to L2norm dynamic-range scaling constraints for state-space digital filters is formulated. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form...

We present the gradient and Hessian of the trace of the multivariate Cramér-Rao bound (CRB) formula for unknown impinging angles of plane waves with non-unitary beamspace measurements,. These gradient and Hessian can be used to find the optimal beamspace transformation matrix, i.e., the optimum beamsteering angles, using the Newton-Raphson iteration. These trace formulas are particularly useful...

In this paper, we present a full Newton step feasible interior-pointmethod for circular cone optimization by using Euclidean Jordanalgebra. The search direction is based on the Nesterov-Todd scalingscheme, and only full-Newton step is used at each iteration.Furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

Abstract: The problem of minimizing an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints for two-dimensional (2-D) separable-denominator digital filters is formulated. The constrained optimization problem is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, an efficient quasi-Newton algorithm is applied with closed-form fo...

In this paper we prove that there exists a Zariski dense open subset U defined over Q in the parameter space of one-variable rational functions with prescribed l poles with fixed orders, such that for every geometric point f in U(Q), the L-function of exponential sum of f at p has Newton polygon approaches the Hodge polygon as p approaches infinity. This result generalizes some result in [13] a...

After discretization in time with the implicit Euler method and in space with the Box method (c.f. [2]), we end up with a nonlinear system of equations. Newton’s method is used to solve these systems, where the required Jacobians are obtained by automatic differentiation (AD) (c.f. [3]). In contrast to approximate Jacobians via finite differences, AD gives exact Jacobians through a source code ...