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## Post-Buckling Range of Plates in Axial Compression with Uncertain Initial Geometric Imperfections

### Applications of Mathematics (2002-01-01) 47: 25-44 , January 01, 2002

The method of reliable solutions alias the worst scenario method is applied to the problem of von Karman equations with uncertain initial deflection. Assuming two-mode initial and total deflections and using Galerkin approximations, the analysis leads to a system of two nonlinear algebraic equations with one or two uncertain parameters-amplitudes of initial deflections. Numerical examples involve (i) minimization of lower buckling loads and (ii) maximization of the maximal mean reduced stress.

## Dubrovin Valuation Skew Group Rings

### Acta Mathematica Sinica (2002-04-01) 18: 339-346 , April 01, 2002

Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given. Among them all the prime ideals of a Dubrovin valuation skew group ring are characterised.

## Defining Equations of G/P and Conjugacy Theorems

### Kac-Moody Groups, their Flag Varieties and Representation Theory (2002-01-01) 204: 337-368 , January 01, 2002

Fix a subset Y⊂{1,...,e} and a Y-regular weight Λ ∈ *D*_{ℤ}, i.e., A is dominant totally integral and Λ(α
_{i}^{⋁}
) iff ∈ Y.

## Smooth Manifolds over Local Algebras and Weil Bundles

### Journal of Mathematical Sciences (2002-01-01) 108: 249-294 , January 01, 2002

## Clifford Numbers and their Inverses Calculated using the Matrix Representation

### Applications of Geometric Algebra in Computer Science and Engineering (2002-01-01): 169-178 , January 01, 2002

The theory of Clifford Algebra includes a statement that each Clifford Algebra is isomorphic to a matrix representation. Several authors discuss this and in particular Ablamowicz [1] gives examples of derivation of the matrix representation. A matrix will itself satisfy the characteristic polynomial equation obeyed by its own eigenvalues. This relationship can be used to calculate the inverse of a matrix from powers of the matrix itself. It is demonstrated that the matrix basis of a Clifford number can be used to calculate the inverse of a Clifford number using the characteristic equation of the matrix and powers of the Clifford number. Examples are given for the algebras Clifford(2), Clifford(3) and Clifford(2,2).

## A Short Note on the History of Graph Drawing

### Graph Drawing (2002-01-01) 2265: 272-286 , January 01, 2002

The origins of chart graphics (e.g., bar charts and line charts) are well known [30], with the seminal event being the publication of William Playfair’s (1759-1823) *The Commercial and Political Atlas* in London in 1786 [26]. However, the origins of graph drawing are not well known. Although Euler (1707-1783) is credited with originating graph theory in 1736 [12],[20], graph drawings were in limited use centuries before Euler’s time. Moreover, Euler himself does not appear to have made significant use of graph visualizations. Widespread use of graph drawing did not begin until decades later, when it arose in several distinct contexts. In this short note we present a selection of very early graph drawings; note the apparent absence of graph visualization in Euler’s work; and identify some early innovators of modern graph drawing.

## On the complexity of the classification problem for torsion-free abelian groups of rank two

### Acta Mathematica (2002-09-01) 189: 287-305 , September 01, 2002

## 10. Applications

### Yetter-Drinfel’d Hopf Algebras over Groups of Prime Order (2002-01-01) 1789: 141-145 , January 01, 2002

10.1 Conventions

10.2 An inequality

10.3 The case of dimension 5*p*

10.4 The case of dimension 7*p*

10.5 Kaplansky’s sixth conjecture

## The Optimal Momentum Map

### Geometry, Mechanics, and Dynamics (2002-01-01): 329-362 , January 01, 2002

The presence of symmetries in a Hamiltonian system usually simplies the existence of conservation laws that are represented mathematically in terms of the dynamical preservation of the level sets of a *momentum mapping*. The symplectic or Marsden-Weinstein reduction procedure takes advantage of this and associates to the original system a new Hamiltonian system with fewer degrees of freedom. However, in a large number of situations, this standard approach does not work or is not e cient enough, in the sense that it does not use all the information encoded in the symmetry of the system. In this work, a new momentum map will be defined that is capable of overcoming most of the problems encountered in the traditional approach.

## Unique Continuation and the Cauchy Kernel

### An Introduction to Dirac Operators on Manifolds (2002-01-01) 24: 123-144 , January 01, 2002

In the previous chapters we have been occupied with the study of Dirac operators acting on functions in general. From this chapter on there will be a shift of attention: we shall be looking at monogenic functions, i.e., solutions of the equation $$ \not{\nabla }f = 0 $$ in some domain Ω.