OPAC - Pencarian Artikel Jurnal & Majalah
Menampilkan semua artikel (Halaman 6 dari 34170, Total: 341699 data)
The Game of Pass the Buck and the Markov Chain Tree Theorem
klik untuk membaca file PDF
| Pengarang | : | Jan Sedlák & Antonín Slavík |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 7) |
| Halaman | : | 615-633 |
| Abstrak | : | We describe a new approach for calculating the winning probabilities in the game of Pass the Buck on arbitrary graphs. It is based on the Markov chain tree theorem, and reduces the problem to counting arborescences in directed graphs. We investigate the game on several classes of graphs, provide short derivations of existing results, and obtain several new ones. |
Yueh-Gin Gung and Dr. Charles Y. Hu Award for 2026 to Nancy Neudauer for Distinguished Service to Mathematics
| Pengarang | : | Susan Jane Colley, Elizabeth Denne, Marcos Lopez, Perla Myers, Jeanette Shakalli & Oscar Vega |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 7) |
| Halaman | : | 611-614 |
| Abstrak | : | The Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics is the Mathematical Association of America’s (MAA) most prestigious honor for service. We are delighted and honored to present the 2026 Gung and Hu Award to Nancy Ann Neudauer, Ph.D., Professor of Mathematics at Pacific University. From her prodigious work for the MAA’s Pacific Northwest Section and nationally, to her significant teaching and mentoring across Africa, to her efforts to invigorate the field of combinatorics, especially matroid theory, Dr. Neudauer is a most worthy recipient of the Gung and Hu Award, and her work ably demonstrates the MAA’s core values of community, inclusivity, communication, and teaching and learning. |
Problems and Solutions
| Pengarang | : | Daniel H. Ullman, Daniel J. Velleman, Stan Wagon & Douglas B. West |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 388-398 |
| Abstrak | : | Abstrak tidak tersedia. |
A Visual Proof of the Parallelogram Law
| Pengarang | : | Vincent Conitzer |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 385-387 |
| Abstrak | : | In this note, we give a novel proof of the parallelogram law, relying on two superimposed tilings of the plane. |
Integration of Gauß-Type Functions in Finite Terms
| Pengarang | : | Ulrich Abel & Hartmut Siebert |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 380-384 |
| Abstrak | : | In the present paper we consider, for positive integers n, integrals of the form ∫?????(????) exp (????????+1)?????????. Using Liouville’s results, we characterize real polynomials p such that ?????(????) exp (????????+1) has an antiderivative which can be written in terms of elementary functions. For the smaller class of normal-like integrals, i.e., the special case ????=1, such a characterization was recently given in [Citation1]. In contrast to this result our criterion provides a simple algorithmic condition. |
Quadratic Reciprocity via Vandermonde Matrix
| Pengarang | : | Hongshen Chua |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 376-379 |
| Abstrak | : | This paper presents a proof of the law of quadratic reciprocity using the Vandermonde matrix and Zolotarev’s lemma. |
A Lebesgue Integral Variant of the Additive Square Problem
| Pengarang | : | Ingrid Vukusic |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 371-375 |
| Abstrak | : | The additive square problem is a relatively famous open problem in the area of combinatorics on words: Does there exist an infinite word over a finite alphabet, such that no two consecutive blocks of the same length have the same sum? In this note we solve a Lebesgue integral variant of the problem. The proof is based on Lebesgue’s density theorem. |
Computing Minimal Euclidean Functions in Imaginary Quadratic Fields
| Pengarang | : | Hester Graves |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 352-370 |
| Abstrak | : | We all should learn in our abstract algebra classes that every Euclidean domain R has a minimal Euclidean function, ????????. Our short history starts with their introduction via Motzkin’s Lemma and moves onto Lenstra’s categorization of Euclidean functions in imaginary quadratic number fields. We examine computing minimal Euclidean functions in these fields, and apply them in short, easy proofs of standard results. Using the author’s simple formula for ??????[????], the only explicitly computable minimal Euclidean function the author knows for a number field other than ?, we apply the pre-images’ geometry to give a new elementary proof affirming Lenstra’s algebraic description of these sets. Figures illustrate the definitions and arguments. |
L-Tetromino Tilings and Two-Color Integer Compositions
| Pengarang | : | Nicolas B?lohoubek & Antonín Slavík |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 341-351 |
| Abstrak | : | We find recurrent as well as explicit formulas for the number of tilings of a 2?????×4 rectangle using L-tetrominoes when only rotation of tiles is allowed. We show that the problem is equivalent to calculating the number of certain two-color integer compositions. |
The Inversion Paradox and Ranking Methods in Tournaments
| Pengarang | : | Guillaume Chèze & Etienne Fieux |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 133 (No. 4) |
| Halaman | : | 316-340 |
| Abstrak | : | This article deals with ranking methods. We study the situation where a tournament between n players ????1, ????2, …???????? gives the ranking ????1?????2???????????, but, if the results of ???????? are no longer taken into account (for example ???????? is suspended for doping), then the ranking becomes ????????−1?????????−2???????2?????1. If such a situation arises, we call it an inversion paradox. In this article, we give a sufficient condition for the inversion paradox to occur. More precisely, we give an impossibility theorem. We prove that if a ranking method satisfies three reasonable properties (the ranking must be natural, reducible by Condorcet tournaments and satisfies the long tournament property) then we cannot avoid the inversion paradox, i.e., there are tournaments where the inversion paradox occurs. We then show that this paradox can occur when we use classical methods, e.g., Borda, Massey, Colley and Markov methods. |