Related papers: Wolf Barth (1942--2016)
On August 4 this year, Tsung-Dao Lee, a renowned theoretical physicist of Chinese origin, passed away at the age of 97. His most famous discovery dates back to 1956, when -- together with Chen-Ning Yang -- he postulated that parity symmetry…
In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the…
Recently, a new generalized family of infinite-dimensional $ \widetilde{W} $ algebras, each associated with a particular element of a commutative subalgebra of the $ W_{1+\infty} $ algebra, was described. This paper provides a comprehensive…
The authors T.Harima, J.C.Migliore, U.Nagel and J.Watanabe characterized the Hilbert function of algbebras with the Lefschetz property. We extend this characterization to algebras with the Lefschetz property m times. We also give upper…
We survey briefly the life and work of P. L. Chebyshev, and his ongoing influence. We discuss his contributions to probability, number theory and mechanics, his pupils and mathematical descendants, and his role as the founding father of…
We confirm a conjecture of Guth concerning the maximal number of $\delta$-tubes, with $\delta$-separated directions, contained in the $\delta$-neighborhood of a real algebraic variety. Modulo a factor of $\delta^{-\varepsilon}$, we also…
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumerative results for intersecting varieties defined by rank…
E. Opdam introduced the tool of spectral transfer morphism (STM) of affine Hecke algebras to study the formal degrees of unipotent discrete series representations. He established a uniqueness property of STM for the affine Hecke algebras…
We define Schwartz functions, tempered functions and tempered distributions on (possibly singular) real algebraic varieties. We prove that all classical properties of these spaces, defined previously on affine spaces and on Nash manifolds,…
We give a selective survey of topics in algebraic deformation theory ranging from its inception to current times. Throughout, the numerous contributions of Murray Gerstenhaber are emphasized, especially the common themes of cohomology,…
In this paper, we exploit some geometric-differential techniques to prove the strong Lefschetz property in degree $1$ for a complete intersection standard Artinian Gorenstein algebra of codimension $6$ presented by quadrics. We prove also…
Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials.…
The article surveys the known results and conjectures about the analytic properties of dispersion relations and Fermi surfaces for periodic equations of mathematical physics and their spectral incarnations.
We present a polynomial partitioning theorem for finite sets of points in the real locus of an irreducible complex algebraic variety of codimension at most two. This result generalizes the polynomial partitioning theorem on the Euclidean…
Theorems of Barth-Lefschetz type describe restrictions on the topology of varieties of small codimension. R. Schoen and J. Wolfson, using Morse theory on a path space, have described a technique to prove theorems of this kind for complex…
Given a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic.…
We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic…
In this paper, we present two types of Lefschetz numbers in the topology of digital images. Namely, the simplicial Lefschetz number $L(f)$ and the cubical Lefschetz number $\bar L(f)$. We show that $L(f)$ is a strong homotopy invariant and…
The topic of this paper is, on the one hand to introduce algebraic analysis results of \'Etienne B\'ezout (1730- 1783) not as we know them today but as he found them in his time, and on the other hand to emphasize his innovating viewpoints.…
These are expanded notes from graduate courses about Lie algebras and Chevalley groups held at the University of Stuttgart. In the 1950s Chevalley showed how linear groups over arbitrary fields could be obtained~ -- ~by a uniform procedure~…