A case study of quantization of curves surfaces: The Myllar balloon
A complex from linear elasticity
Introduction: This article will present just one example of a general construction known as the Bernstein-Gelfand-Gelfand (BGG) resolution. It was the motivating example from two lectures on the BGG resolution given at the 19th Czech Winter School on Geometry and Physics held in Srní in January 1999. This article may be seen as a technical example to go with a more elementary introduction which will appear elsewhere [M. Eastwood, Notices Am. Math. Soc. 46, No. 11, 1368-1376 (1999)]. In fact, there...
A construction of finite-dimensional faithful representation of Lie algebra
Summary: The Ado theorem is a fundamental fact, which has a reputation of being a `strange theorem'. We give its natural proof.
A contribution to the descriptive theory of sets and spaces
A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems
Song, Yin and Zhang (Int. J. Numer. Anal. Model. 4: 127-140, 2007) discovered a remarkable property of oscillatory finite element solutions of one-dimensional convection-diffusion problems that leads to a novel numerical method for the solution of such problems. In the present paper this property is described using several figures, then a simple proof of the phenomenon is given which is much more intuitive than the technical analysis of Song et al.
A diffusion reaction system modelling spatial patterns
A direct solver for finite element matrices requiring memory places
We present a method that in certain sense stores the inverse of the stiffness matrix in memory places, where is the number of degrees of freedom and hence the matrix size. The setup of this storage format requires arithmetic operations. However, once the setup is done, the multiplication of the inverse matrix and a vector can be performed with operations. This approach applies to the first order finite element discretization of linear elliptic and parabolic problems in triangular domains,...
A duality principle for delay equations
A finite element method for a model of population dynamics with spatial diffusion
A finite element method for the computation of parametric minimal surfaces
A formal connection between projectiveness for compact and not necessarily compact completely regular spaces
A gauge theory for the Kadomtsev-Petviashvili system
A generalization of Fueter’s monogenic functions to fine domains
A generalized Leibniz rule and foundation of a discrete quaternionic analysis
A hereditarily infinite dimensional space
A high-order helicity invariant and the Rokhlin theorem
A homogeneous Hausdorff -space which is not
A K-theoretic approach to Chern-Cheeger-Simons invariants
The aim of this paper is to construct a natural mapping , , from the multiplicative -theory of a differential manifold , associated to the trivial filtration of the de Rham complex, as defined by M. Karoubi in [C. R. Acad. Sci., Paris, Sér. I 302, 321-324 (1986; Zbl 0593.55004)] to the odd cohomology . By using this mapping, the author associates to any flat complex vector bundle on characteristic classes analogous to the classes studied by S. Chern, J. Cheeger and J. Simons in [Differential...
À la mémoire de Eduard Čech
A Language Engineering Architecture for Processing Informal Mathematical Discourse
We present a modular architecture for processing informal mathematical language as found in textbooks and mathematical publications. We point at its properties relevant in addressing three aspects of informal mathematical discourse: (i) the interleaved symbolic and natural language, (ii) the linguistic, domain, and notational context, and (iii) the imprecision of the informal language. The objective in the modular approach is to enable parameterisation of the system with respect to the natural language...