Related papers: Corrigendum for "Almost vanishing polynomials and …
A function g, with domain the natural numbers, is a quasi-polynomial if there exists a period m and polynomials p_0,p_1,...,p_{m-1} such that g(t)=p_i(t) for t=i mod m. Quasi-polynomials classically -- and "reasonably" -- appear in Ehrhart…
It is shown that the corrections of $\alpha^2$ order to the total cross sections for interaction of elementary hydrogen-like atoms with target atoms, reported in the previously published paper [S.Mrowczynski, Phys.Rev. D36, 1520 (1987)], do…
This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027
We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a log factor. We present algorithms for three special cases,…
In the present article, we have given a corrigendum to our paper ``On (p,q)-analogue of Bernstein operators" published in Applied Mathematics and Computation 266 (2015) 874-882.
We correct a mistake in the paper "On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields " by A. Borel, J.-P. Labesse, J. Schwermer that appeared in Compositio Mathematica, 102 (1996), 1-40.
The reconstruction approach [Shu C.W.: {\em SIAM Rev.} {\bf 51} (2009) 82--126] for the numerical approximation of $f'(x)$ is based on the construction of a dual function $h(x)$ whose sliding averages over the interval…
In the paper [Hong-Shi Zong, Wei-Min Sun, Phys. Lett. B 640 (2006) 196], the authors claim that our proof of the inconsistency of the ladder approximation to QCD [Phys. Lett. B 611 (2005) 129] was incorrect. However, their claim is based on…
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
This paper has been withdrawn since it is identical to the paper math.QA/0601267. It was posted by mistake.
We provide a numerical refutation of the developments of Fiorini et al. (2015)* for models with disjoint sets of descriptive variables. We also provide an insight into the meaning of the existence of a one-to-one linear map between…
We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.
In this paper we describe how to improve the performance of the symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the multiplicity structure and refining approximate isolated singular solutions in the breadth one case. By…
A toric polyhedron is a reduced closed subscheme of a toric variety that are partial unions of the orbits of the torus action. We prove vanishing theorems for toric polyhedra. We also give a proof of the $E_1$-degeneration of Hodge to de…
We correct a mistake regarding almost complex structures on Hilbert schemes of points in surfaces in arXiv:1510.02449. The error does not affect the main results of the paper, and only affects the proofs of invariance of equivariant…
This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described…
This article has been withdrown by the author.
This paper provides full \Matlab-code and informal correctness proofs for the lexicographic reverse search algorithm for convex hull calculations. The implementation was tested on a 1993 486-PC for various small and some larger, partially…
Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite…
This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs…