Related papers: Comments on Initial Value Formulation
The convergence of self-consistent field equations in mean-field nuclear-electronic orbital methods strongly depends on the choice of initial guesses for quantum nuclei. Although several such guesses have been proposed in the literature, a…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
This is an extended abstract of my talk at the Oberwolfach Workshop "Algebraic Groups" (April 22 - 28, 2007). It is based on a joint work with H.Derksen and J.Weyman (arXiv:0704.0649v2 [math.RA]).
Commented translation of the paper "Universelle Bedeutung des Wirkungsquantums", published by Jun Ishiwara in German in the Proceedings of Tokyo Mathematico-Physical Society 8 106-116 (1915). In his work, Ishiwara, tenured at Sendai…
We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and…
Invited talk delivered at the International Conference on General Relativity and Cosmology (ICGC), Ahmedabad, India; 13 - 18 December 1991. To appear in its proceedings.
We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at…
Hilbert's 14th Problem asks the following question. Given a linear representation $ \beta: G \to \operatorname{GL}(\mathbf{V}) $ of a linear algebraic group over a field $ k $ is the ring $ S_{k}(\mathbf{V}^{\ast}) $ a finitely generated $…
This is a brief introduction on the graduate level to recent ideas in the Weinberg $(j,0)\oplus (0,j)$ formalism, appearing after presentation of the Bargamann-Wightman-Wigner-type quantum field theory by D. V. Ahluwalia {\it et al.}
The elements of Markoff triples are given by coefficients in certain matrix products defined by Christoffel words, and the Markoff injectivity conjecture, a long-standing open problem (also known as the uniqueness conjecture), is then…
This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of…
These notes originated in a series of lectures I gave in Marseille in May, 2013. I was invited to give an introduction to the isomorphism theorems, originating with Dynkin, which connect Markov local times and Gaussian processes. This is an…
We resume former discussions of the conformally invariant wave equation on a Schwarzschild background, with a particular focus on the behaviour of solutions near the 'cylinder', i.e. Friedrich's representation of spacelike infinity. This…
This survey will appear in Vol. VII of the Hendbook of Teichm{\"u}ller theory (European Mathematical Society Publishing House, 2020). It is a commentary on Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre", published in…
Machine learning currently exerts an outsized influence on the world, increasingly affecting institutional practices and impacted communities. It is therefore critical that we question vague conceptions of the field as value-neutral or…
This arXiv report provides a short introduction to the information-theoretic measure proposed by Chen and Golan in 2016 for analyzing machine- and human-centric processes in data intelligence workflows. This introduction was compiled based…
To facilitate teaching of quantum mechanics on undergraduate and even advanced secondary school levels, we present an unabridged translation of the original German text of the famous Werner Heisenberg's breakthrough paper of 1925 into Czech…
English translation of "Bemerkungen zur allgemein-relativistischen Fassung der Quantentheorie", originally published in {\em Sitzber. kgl.-preu{\ss}. Akad. Wiss. Berlin, Sitzung der phys.-math. Klasse} {\bf XXIV} (1932) 346--354.
[Note: After the first version of this manuscript was uploaded, the authors of [Berta, Brand\~ao, Gour, Lami, Plenio, Regula, and Tomamichel, Quantum 7, 1103 (2023)] pointed out an issue about a part of the claims in the previous version of…
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the…