Related papers: A miscellany
We overview few results which use the construction described in our paper "Telescopic actions".
We summarize recent results connecting multiloop Feynman diagram calculations to different parts of mathematics, with special attention given to the Hopf algebra structure of renormalization.
Talagrand's fundamental result on the entropy numbers is slightly improved. Our proof uses different ideas based on results from greedy approximation.
We would like to take this opportunity to thank the discussants for their thoughtful comments and encouragements on our work [arXiv:0808.1012]. The discussants raised a number of issues from theoretical as well as computational…
This is an introductory document surveying several results in polynomial approximation, known as the Bramble-Hilbert lemma.
The paper of Unal [J. Math. Phys. 59, 062104 (2018)], though worthy of attention, contains a conclusion that is in error and may mislead the efforts to extend his results. The aim of the present note is twofold: we provide a correction to…
We present the explicit formulae relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one.…
We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from this context and conclusions are derived.
We obtain some new inequalities of Chebyshev Type.
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
Lead by examples we introduce the notions of Hopf algebra and quantum group. We study their geometry and in particular their Lie algebra (of left invariant vectorfields). The examples of the quantum sl(2) Lie algebra and of the quantum…
Let $\varepsilon>0$ be a fixed small constant, ${\mathbb F}_p$ be the finite field of $p$ elements for prime $p$. We consider additive and multiplicative problems in ${\mathbb F}_p$ that involve intervals and arbitrary sets. Representative…
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
We give a short proof based on Lusztig's generalized Springer correspondence of some results of [BrCh,BaCr,P].
In this supplementary appendix we provide additional results, omitted proofs and extensive simulations that complement the analysis of the main text (arXiv:1201.0224).
We make a few comments on some misleading statements in the above paper.
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
We study the set of lengths of the horizontal chords of a continuous function. We give a new proof of Hopf's characterization of this set, and show that it implies that no matter which function we choose, at least half of the possible…
In prior joint work with Lewis, we developed a theory of enriched set-valued $P$-partitions to construct a $K$-theoretic generalization of the Hopf algebra of peak quasisymmetric functions. Here, we situate this object in a diagram of six…
We claim to resolve the P=?NP problem via a formal argument for P=NP.