2020年6月2日 -Paritosh Mokhasi,内核开发,算法R&d

使用整数优化建设和解决Wolfram语言的数独游戏manbet万博app

Sudoku is a popular game that pushes the player’s analytical, mathematical and mental abilities. Solving sudoku problems has long been discussed onWolfram Community,并出现了一些精彩的代码提出了解决数独问题。要添加到讨论中,我将演示几个特点,是新的数学Version 12.1, including how this game can be solved as an integer optimization problem using the functionLinearOptimization,以及如何生成新的数独游戏。

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May 6, 2020 —Tigran Ishkhanyan, Algorithms R&D

数学was initially built to be a universal solver of different mathematical tasks for everything from school-level algebraic equations to complicated problems in real scientific projects. During the past 30 years of development, over250 mathematical functionshave been implemented in the system, and in the recent release ofVersion 12.1of themanbet万博appWolfram语言, we’ve added many more, ranging from the elementarySinfunction to the advancedHeunfunctions.

From Sine to Heun: 5 New Functions for Mathematics and Physics in the Wolfram Language

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April 29, 2020 —丸山浩二, Sales Engineer

非线形偏微分方程式への有限要素法の适用

数学12有powerful functionality for solving partial differential equations (PDEs) both symbolically and numerically. This article focuses on, among other things, the finite element method (FEM)–based solver for nonlinear PDEs that has been newly implemented in Version 12. After briefly reviewing basic syntax of themanbet万博appWolfram语言for PDEs, including how to designate Dirichlet and Neumann boundary conditions, we will delineate how Mathematica 12 finds the solution of a given nonlinear problem with FEM. We then show some examples in physics and chemistry, such as the Gray–Scott model and the time-dependent Navier–Stokes equation. More information can be found in the Wolfram Language tutorial “Finite Element Programming”,基于本文的大部分。


1. はじめに

Wolfram Research社の旗舰制品である数学は,5000を超える组み込み关数を有するWolfram语言を駆manbet万博app动する。数理モデリング,解析の基本となる常·偏微分方程式の分野においては,これらをシンボリックに,あるいは数値的に解くための强力なソルバを搭载している。最近は有限要素法(FEM)を利用した数値的求解机能が大幅に强化され,偏微分方程式(PDE)を任意の领域上で解いたり,固有値·固有关数を求めたりすることが可能となった。ここでは,最新のバージョン12における非线形偏微分方程式のFEMによる求解を中心に,现実的な问题に応用する上での流れを例とともに绍介する。なお,有限要素法を用いて非线形PDEを解くワークフローの详细,コードはすべて公开されている.Mathematicaのmanbet万博app钨ドキュメント内で,チュートリアル“FiniteElementProgramming”を参照いただきたい.

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April 14, 2020 —Stephen Wolfram

沃尔夫勒姆物理项目的可视摘要manbet万博app

我从没有想到这

这是意想不到的,令人惊讶,对我来说非常刺激。为了公平起见,在一定程度我一直朝着这个近50年。但它只是在它终于走到了一起过去几个月。而且它的更精彩,漂亮,比我想象的。

在许多方面,它在自然科学的终极问题:如何做我们的宇宙的工作?是否有一个基本的理论?一个令人难以置信的金额已经想通了关于过去几百年物理学。但是,即使一切的已经完成,并且这是非常令人印象深刻,我们还是,毕竟这个时候,没有物理的一个真正的基础理论。

Back when Iused do theoretical physics for a living, I must admit I didn’t think much about trying to find a fundamental theory; I was more concerned about what we could figure out based on the theories we had. And somehow I think I imagined that if there was a fundamental theory, it would inevitably be very complicated.

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February 12, 2020 —Ed Pegg Jr, Editor, Wolfram Demonstrations Project

New Bound for Sparse Rulers Proof using the Wolfram Language

The sparse ruler problem has been famously worked on byPaul Erdős,Marcel J. E. Golay,John Leech,艾尔弗雷德·雷尼,László RédeiandSolomon W. Golomb, among many others. The problem is this: what is the smallest subsetofso that the unsigned pairwise differences ofgive all values from 1 to? One way to look at this is to imagine a blank yardstick. At what positions on the yardstick would you add 10 marks, so that you can measure any number of inches up to 36?

Another simple example isof size 3, which has differences,and。The sets of size 2 have only one difference. The minimal subsetis not unique; the differences ofalso give

Part of what makes the sparse ruler problem so compelling is its embodiment in an object inside every schoolchild’s desk—and its enduring appeal lies in its deceptive simplicity. Read on to see precisely just how complicated rulers, marks and recipes can be.

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January 9, 2020 —George Beck,文档和媒体系统

数论是一种非常古老的学科,在现代已经分流到各个大区域。其中之一是堆垒数论,像这样的问题:是时候prime the sum of two squares? Primes are part of the more classical area now calledmultiplicative number theory,从而费尔马的这一问题表明,这两个地区有着密切的联系。我在这个博客讨论的问题是加法和乘法数论的混合,用线性代数的冲刺。

An Intriguing Identity: Connecting Distinct and Complete Integer Partitions

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November 21, 2019
Gabriele Dian, Visiting Scholar, Algorithms R&D
SAGEX, Early Stage Researcher, Durham University, UK

It’s rare to hear polygons mentioned in a physics class, even in higher education. This may seem unexpected given the fundamental role they play in mathematics. However, over the last few years, polygons have come to the front line in many areas of theoretical physics, helping us understand the laws of nature with their astonishing beauty.

这是在粒子物理学,其中一个新的几何对象已经发现将被连接到粒子动力学领域尤其如此:在amplituhedron。It represents a novelty not only in physics but also in mathematics, generalizing the concept of a convex polygon. In this blog post, I will first discuss its relation to particle physics, and then how to visualize its geometry using themanbet万博appWolfram语言

Visualizing the amplituhedron

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2019年10月1日 -Stephen Wolfram

Announcing the Rule 30 Prizes

The Story of Rule 30

怎么能什么that simple produce something that complex? It’s been nearly 40 years since Ifirst saw rule 30- 但它仍然让我感到吃惊。很久以前,它成为我个人的所有时间最喜爱的科学发现,多年来它改变了我的世界观,使我all sorts of science, technology, philosophy and more

但是,即使经过这么多年,还是有很多我们不知道的规则30.基本的事情,我已经决定,现在是时候尽我所能来刺激发现更多的人出来的过程。所以,从今天开始,我提供的奖金$ 30,000的回答了有关第30条的三个基本问题。

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2019年7月25日 -Keren Garcia, Algorithms R&D

Building Uniform Polyhedra for Version 12

Since I started working at Wolfram, I’ve been a part of several different projects. ForVersion 12, my main focus was replicating models of the uniform polyhedra with themanbet万博appWolfram语言以确保数据符合一定的标准,使我们的模型精确,包括以创建每个实体的适当网格模型精确坐标,一致的面部朝向和封闭区域。

Working with visual models of polyhedra is one thing, but analyzing them mathematically proved to be much more challenging. Starting with reference models of the polyhedra, I found that the Wolfram Language made mathematical analysis of uniform polyhedra particularly efficient and easy.

首先,什么真的是多面体,和我们为什么要在乎?在版本12中,我们可以探索多面体是什么,以及如何,他们已经赢得了他们的继续发生在我们的想象。

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2019年7月2日 -Jon McLoone,主任,技术交流与战略

How I Used Last-Mover Advantage to Make Money

这个星期,我赢了一些钱,将数学策略,完全不可预测的赌博游戏。但在此之前我解释我是如何,需要给去年发优势的一些背景。

Some time ago, I briefly considered doing some analysis of the dice game Yahtzee. But I was put off by the discovery that several papers (includingthis one)已经列举了整场比赛状态图创造最大化分数的期望值的策略(这是254.59)。

However, maximizing the expected value of the score only solves the solo Yahtzee game. In a competitive game, and in many other games, we are not actually trying to maximize our score—we are trying to win, and these are not always the same thing.

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