Related papers: Hirotaka's problem 028
This is an update of my problem list.
This is an update on, and expansion of, our paper Open problems on $\beta\omega$ in the book Open Problems in Topology.
How can we predict the difficulty of a Sudoku puzzle? We give an overview of difficulty rating metrics and evaluate them on extensive dataset on human problem solving (more then 1700 Sudoku puzzles, hundreds of solvers). The best results…
We solve some decision problems for timed automata which were recently raised by S. Tripakis in [ Folk Theorems on the Determinization and Minimization of Timed Automata, in the Proceedings of the International Workshop FORMATS'2003, LNCS,…
These notes provide an opportunity to discover the beauty of Bourbaki set theory, and I hope that they will facilitate the task to those who find it difficult to read this book, one of the most critical elements of the mathematics of…
In this paper, we will solve the Reifenberg Plateau Problem in Hilbert space.
We determine topological complexity of a series of finite spaces which is weakly homotopy equivalent to a circle $S^1$, and give a finite space $X$ satisfying the inequality tc$(X) <$ cat$(X {\times} X)$. This answers two conjectures on…
Details for known solutions of some geometric and algebraic problems with the help of origami are presented: two theorems of Haga, the general cubic equation, especially the heptagon equation, doubling the cube as well as the trisection of…
The text is a synthetic presentation of the state of the knowledge about the capitulation for the class-groups of numbers fields, shortly before the demonstration by Suzuki of the main conjecture on this question.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
A negative solution of Problem 188 posed by Max Eidelheit in {\it the Scottish Book} concerning superpositions of separately absolutely continuous functions is presented. We discuss here his and some related problems which have also…
This document compiles problems proposed and discussed during the problem session at the conference Foliations and Diffeomorphism Groups (CIRM, 2024), organized by H\'el\`ene Eynard-Bontemps, Ga\"el Meigniez, Sam Nariman, and Mehdi Yazdi.…
We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We provide infinitely many solutions of a Dirichlet problem on balls.
In this note we present the solution of Problem H-691 (The Fibonacci Quarterly, 50 (1) 2012) with some corrections and more details. The solution involves three nontrivial integrals whose evaluations are given here.
This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and…
The finite-genus solutions for the Hirota's bilinear difference equation are constructed using the Fay's identities for the theta-functions of compact Riemann surfaces.
We consider several algorithmic problems concerning geodesics in finitely generated groups. We show that the three geodesic problems considered by Miasnikov et al [arXiv:0807.1032] are polynomial-time reducible to each other. We study two…
In this paper we study random optimization problems where random functions are investigated in sample paths. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.