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Introduction to Best-Packing and Best-Covering
In this chapter we discuss two fundamental problems of discrete geometry, the best-packing problem and the best-covering problem. In Section 3.1 the...
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The Establishment of Scientific Computing as a New Discipline
At the end of the 1950s the use of computational mathematics was well established. New electronic computers had been constructed, then, with vacuum...
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Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA
We consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily...
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Quadrature formulae for the positive real axis in the setting of Mellin analysis: sharp error estimates in terms of the Mellin distance
The general Poisson summation formula of Mellin analysis can be considered as a quadrature formula for the positive real axis with remainder. For...
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Sparse operator compression of higher-order elliptic operators with rough coefficients
We introduce the sparse operator compression to compress a self-adjoint higher-order elliptic operator with rough coefficients and various boundary...
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Boundary Value Problems
This chapter is devoted to boundary value problems for ordinary differential equations. It begins with analysis of the existence and uniqueness of...
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Isogeometric Compatible Discretizations for Viscous Incompressible Flow
In this chapter, isogeometric discretizations for viscous incompressible flow are presented that satisfy the incompressibility constraint in a...
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Convergence of a linearly transformed particle method for aggregation equations
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction...
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Equivariant Index of Twisted Dirac Operators and Semi-classical Limits
Let G be a compact connected Lie group with Lie algebra g. Let M be a compact spin manifold with a G-action, and ℒ be a G-equivariant line bundle on...
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Discretization
This chapter is devoted to discretization techniques. We start with basic methods for the discretization in time. Besides simple time step**...
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Regularization of Singularities in the Weighted Summation of Dirac-Delta Functions for the Spectral Solution of Hyperbolic Conservation Laws
Singular source terms expressed as weighted summations of Dirac-delta functions are regularized through approximation theory with convolution...
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T
T 1 bis T 5, ↗ Trennungsaxiome.
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Numerical Methods for the Linear Model
If Pythagoras’ view of the world is convincing—and in today’s world everything seems to be convincing evidence of his views—the ultimate task of any...
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A numerical method for solving dynamical systems with lumped parameters which accounts for an input data error
For calculation of dynamical systems with lumped parameters, we propose and substantiate two-sided method that takes into account an input data...
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S
Sedezimalsystem, Positionssystem zur Notation von Zahlen auf der Basis von 16 Ziffern, meist als ↗ Hexadezimalsystem bezeichnet (s. d.).
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Gauss as Scientific Mediator Between Mathematics and Geodesy from the Past to the Present
The objective of the paper is to document the pioneer dimension of Gauss’s ideas, concepts, and methods in a twofold direction based on selected case...
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Reconstruction of Multiply Generated Splines from Local Average Samples
We analyze the following average sampling problem: Let h be a nonnegative measurable function supported in...
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Zeros of the Zak Transform of Totally Positive Functions
We study the Zak transform of totally positive (TP) functions. We use the convergence of the Zak transform of TP functions of finite type to prove...
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A Reduced Integration for Reissner-Mindlin Non-linear Shell Analysis Using T-Splines
We propose a reduced shell element for Reissner-Mindlin geometric non-linear analysis within the context of T-spline analysis. The shell formulation...