Related papers: Analytical Guide and updates for "Cardinal Arithme…
This contains a list of (mostly very minor) corrections to the book Introduction to Symplectic Topology, Clarendon Press, Oxford, (1995), together with rewritten versions of two lemmas and some additional comments.
The preliminary material of the monograph (arXiv:1607.03852) written by the first two authors contains two major imprecisions that necessitates a number of (in the end harmless) changes throughout the entire text. One is about…
This set of notes provides some additional explanatory material on the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type.
Recent advancements in Retrieval-Augmented Generation have significantly enhanced code completion at the repository level. Various RAG-based code completion systems are proposed based on different design choices. For instance, gaining more…
This is a revised version of Sh:430, section 6.
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
This is the first part of a series of papers aiming to show how trigonometry and analytic tools can help into tackling demanding Olympiad geometry problems. We present several novel techniques for tackling hard problems from various…
The present note is an answer to complains of E.Weitz on [Sh:371]. We present a corrected version of a part of chapter VIII of " Cardinal Arithmetic".
Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4…
A comprehensive listing of over 230 references related to Cartesian to geodetic coordinate transformations are provided. The references are coarsely sorted and DOI:s or URL:s are provided to the extent possible to facilitate studies of the…
We describe a algorithms and their implementations that calculate local and global Schur indices of ordinary irreducible characters of finite groups, cyclotomic algebras over abelian number fields, and rational quaternion algebras. These…
This is a draft of a book about algorithms for performing arithmetic, and their implementation on modern computers. We are concerned with software more than hardware - we do not cover computer architecture or the design of computer…
The main phases of applied statistical work are discussed in general terms. The account starts with the clarification of objectives and proceeds through study design, measurement and analysis to interpretation. An attempt is made to extract…
Our Chapter in the upcoming Volume I: Computer Science and Software Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales and Jorge L. Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical,…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
Series solutions for a large family of single equation Dyson-Schwinger equations are given as expansions over decorated rooted connected chord diagrams. The analytic input to the new expansions are the expansions of the regularized…
This paper presents an updated biography of Samgamagr\=ama M\=adhava incorporating viewpoints expounded by scholars in the recent past and collecting together in one place more details about his works culled from recent researches into his…
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
This note covers two parts. The first one provides an errata to the paper "Numerical and analytical modeling of busbar systems". We mainly give the correction for three equations affected by a typographical mistake. Despite the corrections…