Related papers: Parallel Weighings
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
This paper explores the number of parallelograms that appear in a billiard path that enters one corner of a rectangle and leaves a second corner of a rectangle as a function of the normalized dimensions of the rectangle.
We introduce and analyze several variations of Penney's game aimed to find a more equitable game.
Suppose you are given a graph $G=(V,E)$ with a weight assignment $w:V\rightarrow\mathbb{Z}$ and that your objective is to modify $w$ using legal steps such that all vertices will have the same weight, where in each legal step you are…
Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.
Short introduction to the gauge/gravity duality
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be…
Coins are frequently used in everyday life at various places like in banks, grocery stores, supermarkets, automated weighing machines, vending machines etc. So, there is a basic need to automate the counting and sorting of coins. For this…
Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.
This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.
I construct a new universal differential equation (B), in the sense of Rubel. That is, its solutions approximate to arbitrary accuracy any continuous function on any interval of the real line.
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
We solve the PBW-like problem of normal ordering for enveloping algebras of direct sums.
The aim of boosting is to convert a sequence of weak learners into a strong learner. At their heart, these methods are fully sequential. In this paper, we investigate the possibility of parallelizing boosting. Our main contribution is a…
The prisoners and hats puzzle, or simply the hat puzzle, is a family of games in which a group of prisoners are each assigned a colored hat and are asked to guess the color of their own hat. Various versions of the puzzle arise depending on…
In this paper, we define some weighted sums of the alternating multiple $T$-values (AMTVs), and study several duality formulas for them by using the tools developed in our previous papers. Then we introduce the alternating version of the…
Guo-Niu Han [arXiv:2006.14070 [math.CO]] has introduced a new combinatorial object named standard puzzle. We use digraphs to show the relations between numbers in standard puzzles and propose a skeleton model. By this model, we solve the…