Jove
Visualize
お問い合わせ
JoVE
x logofacebook logolinkedin logoyoutube logo
JoVEについて
概要リーダーシップブログJoVEヘルプセンター
著者向け
出版プロセス編集委員会範囲と方針査読よくある質問投稿
図書館員向け
推薦の声購読アクセスリソース図書館諮問委員会よくある質問
研究
JoVE JournalMethods CollectionsJoVE Encyclopedia of Experimentsアーカイブ
教育
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab Manual教員リソースセンター教員サイト
利用規約
プライバシーポリシー
ポリシー

関連する概念動画

Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

324
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
324
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

5.2K
The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...
5.2K
Partial Fractions01:28

Partial Fractions

256
A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
256
Real Zeros of Polynomials01:27

Real Zeros of Polynomials

219
Polynomials are algebraic expressions of terms with variables raised to non-negative integer powers. A central aspect of analyzing polynomial functions is determining their real zeros—values of the variable for which the polynomial evaluates to zero. These values represent the x-intercepts of the polynomial’s graph.The Rational Zeros Theorem lists possible rational solutions for a polynomial equation with integer coefficients. If f(x)=anxn+....+a0​, then every rational zero is...
219
Complex Zeros01:29

Complex Zeros

317
Complex zeros are the solutions to polynomial equations that include imaginary numbers, specifically, numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit defined by i2=-1. These zeros satisfy the equation P(x) = 0, where P(x) is a polynomial with real or complex coefficients. Since the complex number system includes all real numbers, it provides a complete framework for analyzing all possible roots of a polynomial.Every polynomial of degree n≥1 can be...
317
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

1.1K
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
1.1K

こちらも読む

関連記事

共著者、ジャーナル、引用グラフによってこの研究に関連する記事。

並び替え
Same journal

Automorphisms of relatively hyperbolic groups and the Farrell-Jones conjecture.

Mathematische annalen·2026
Same journal

Groups acting on trees with Tits' independence property (P): With an appendix by Stephan Tornier.

Mathematische annalen·2026
Same journal

A note on integrated local energy decay estimates for spherically symmetric black hole spacetimes.

Mathematische annalen·2026
Same journal

Higher-order regularity for a structurally damped plate equation on rough domains.

Mathematische annalen·2026
Same journal

The shifted convolution problem in function fields.

Mathematische annalen·2026
Same journal

<math><mi>b</mi></math> -Hurwitz numbers from refined topological recursion.

Mathematische annalen·2026

関連する実験動画

Updated: Feb 24, 2026

Designing CAD/CAM Surgical Guides for Maxillary Reconstruction Using an In-house Approach
08:01

Designing CAD/CAM Surgical Guides for Maxillary Reconstruction Using an In-house Approach

Published on: August 24, 2018

9.5K

Factorization norms and an inverse theorem for MaxCut

Igor Balla1, Lianna Hambardzumyan2, István Tomon3

  • 1Faculty of Mathematics and Computer Science, Leipzig University, 04109 Leipzig, Germany.

Mathematische annalen
|February 23, 2026
PubMed
まとめ

Boolean matrices with bounded gamma_2-norm or normalized trace norm contain large all-ones/all-zeros submatrices. This verifies a conjecture and yields an inverse theorem for MaxCut, showing graphs with near-maximal cuts must contain large cliques.

キーワード:
ブール行列部分行列最大カット逆定理グラフ理論組合せ論

さらに関連する動画

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.6K
Author Spotlight: Cistrome Analysis in Mouse Muscle Stem Cells
10:10

Author Spotlight: Cistrome Analysis in Mouse Muscle Stem Cells

Published on: July 7, 2023

3.3K

関連する実験動画

Last Updated: Feb 24, 2026

Designing CAD/CAM Surgical Guides for Maxillary Reconstruction Using an In-house Approach
08:01

Designing CAD/CAM Surgical Guides for Maxillary Reconstruction Using an In-house Approach

Published on: August 24, 2018

9.5K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.6K
Author Spotlight: Cistrome Analysis in Mouse Muscle Stem Cells
10:10

Author Spotlight: Cistrome Analysis in Mouse Muscle Stem Cells

Published on: July 7, 2023

3.3K

科学分野:

  • 組合せ論
  • 線形代数
  • グラフ理論

背景:

  • ブール行列は、離散数学およびコンピュータサイエンスにおける基本的な対象です。
  • γ_2ノルムおよび正規化トレースノルムは、行列の特性の主要な尺度です。
  • 最大カット問題は、グラフの頂点を分割してエッジカットを最大化することを目的としています。

研究 の 目的:

  • 有界なγ_2ノルムまたは正規化トレースノルムを持つブール行列が、線形サイズのすべて1またはすべて0の部分行列を含むことを証明すること。
  • ハンバルズﾞムヤン、ハタミ、ハタミによる予想を検証すること。
  • 最大カット問題の逆定理を確立すること。

主な方法:

  • スペクトルグラフ理論および極限組合せ論を利用すること。
  • ブール行列の構造結果を開発すること。
  • 行列ノルムの特性をグラフカット問題に適用すること。

主要な成果:

  • 有界なγ_2ノルムまたは正規化トレースノルムを持つブール行列は、線形サイズのすべて1またはすべて0の部分行列を必然的に含みます。
  • 最大カットの逆定理が確立されます。最大カットがm/2 + O(sqrt(m))以下のグラフは、Ω(sqrt(m))サイズのクリークを含む必要があります。
  • この研究は、ブール行列とその応用に関するさらなる構造的洞察を提供します。

結論:

  • この結果は、ブール行列理論における重要な予想を確認するものです。
  • 最大カットの逆定理は、特定のカット特性を持つグラフ構造に関する新しい視点を提供します。
  • この研究は、線形代数、組合せ論、および理論計算科学の概念を橋渡しするものです。