Search results for "Mathematica"

On the Background to Hilbert’s Paris Lecture “Mathematical Problems”

2018

Much has been written about the famous lecture on “Mathematical Problems” (Hilbert 1901) that David Hilbert delivered at the Second International Congress of Mathematicians, which took place in Paris during the summer of 1900 (Alexandrov 1979; Browder 1976). Not that the event itself evoked such great interest, nor have many writers paid particularly close attention to what Hilbert had to say on that occasion. What mattered – both for the text and the larger context – came afterward. Mathematicians remember ICM II and Hilbert’s role in it for just one reason: this was the occasion when he unveiled a famous list of 23 problems, a challenge to those who wished to make names for themselves in …

On Taylor coefficients of entire functions integrable against exponential weights

2001

A New Family of Deformations of Darboux-Pöschl-Teller Potentials

2004

The aim of this Letter is to present a new family of integrable functional-difference deformations of the Schrodinger equation with Darboux–Poschl–Teller potentials. The related potentials are labeled by two integers m and n, and also depend on a deformation parameter h. When h→ 0 the classical Darboux–Poschl–Teller model is recovered.

A Method of Conversion of some Coefficient Inverse Parabolic Problems to a Unified Type of Integral-Differential Equation

2011

Coefficient inverse problems are reformulated to a unified integral differential equation. The presented method of conversion of the considered inverse problems to a unified Volterra integral-differential equation gives an opportunity to distribute the acquired results also to analogous inverse problems for non-linear parabolic equations of different types.

Rectifiability and singular integrals

1995

Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach

2011

In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.

Arm Space Decomposition as a Strategy for Tackling Large Scale Multi-armed Bandit Problems

2013

Recent multi-armed bandit based optimization schemes provide near-optimal balancing of arm exploration against arm exploitation, allowing the optimal arm to be identified with probability arbitrarily close to unity. However, the convergence speed drops dramatically as the number of bandit arms grows large, simply because singling out the optimal arm requires experimentation with all of the available arms. Furthermore, effective exploration and exploitation typically demands computational resources that grow linearly with the number of arms. Although the former problem can be remedied to some degree when prior knowledge about arm correlation is available, the latter problem persists. In this…

An Improved Method for Estimating the Time ACF of a Sum of Complex Plane Waves

2010

Time averaging is a well-known technique for evaluating the temporal autocorrelation function (ACF) from a sample function of a stochastic process. For stochastic processes that can be modelled as a sum of plane waves, it is shown that the ACF obtained by time averaging can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs result from the autocorrelation of the individual plane waves, while the CTs are due to the cross-correlation between different plane wave components. The CTs cause an estimation error of the ACF. This estimation error increases as the observation time decreases. For the practically important case that the observation time interval is limited, we pr…

Parallel Genetic Solution for Multiobjective MDO

1997

Publisher Summary This chapter reviews a multiobjective, multidisciplinary design optimization of two-dimensional airfoil designs. The control points on leading and trailing edges remain fixed, and the y-coordinates of the other control points are allowed to change during the optimization process. The grid for the Euler solver depends continuously and smoothly on the design parameters. The number of nodes and elements in the mesh might vary according to design because the meshes for the Helmholtz solver are done using the local fitting. The computations are made on an IBM SP2 parallel computer using high-performance switch and the MPICH message-passing library. As gradients are not required…

Weak Maximum Principle and Application to Swimming at Low Reynolds Number

2018

We refer to [9, 42, 46] for more details about the general concepts and notations introduced in this section.