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Asuransi dan Redistribusi Pendapatan Sebuah Pemikiran Analisa Teori Ekonometri
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 692-697 |
| Abstrak | : | - |
Perang dan Damai : Dari Yankee Imperialisme Hingga Hegemony Russia
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 687-691 |
| Abstrak | : | - |
Sweet Division Problems: From Chocolate Bars to Honeycomb Strips
| Pengarang | : | Tomislav Doslic & Luka Podrug |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 2) |
| Halaman | : | 162-170 |
| Abstrak | : | We consider finite portions of the regular hexagonal lattice and count the ways of dividing narrow strips of such a lattice into a given number of parts. We prove that such divisions are enumerated by the odd-indexed Fibonacci numbers, thus providing a new combinatorial interpretation of that sequence. We offer three different proofs of this result. Consequently, we obtain a new combinatorial proof of a well-known Fibonacci-related identity. At the end of the paper, we interpret our results in the context of graph compositions and indicate some possible directions for further research. |
"Negara Kaya" dan "Kemajuan Peradaban" Pada Jaman Jepang Modern
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 681-686 |
| Abstrak | : | - |
Some Lie Algebra Structures on Symmetric Powers
| Pengarang | : | Yin Chen |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 2) |
| Halaman | : | 150-161 |
| Abstrak | : | Let k be a field of any characteristic, V a finite-dimensional vector space over k, and ?????????(????*) be the d-th symmetric power of the dual space ????*. Given a linear map ???? on V and an eigenvector w of ????, we prove that the pair (????,????) can be used to construct a new Lie algebra structure on ?????????(????*). We prove that this Lie algebra structure is solvable, and in particular, it is nilpotent if ???? is a nilpotent map. We also classify the Lie algebras for all possible pairs (????,????), when ????=? and V is two-dimensional. |
Fourier Series for Nonperiodic Functions
| Pengarang | : | Rodrigo Lopez Pouso |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 2) |
| Halaman | : | 134-149 |
| Abstrak | : | We introduce a small change in the definition of the Fourier series so that we can guarantee the coincidence with the given function at the endpoints of the interval even if the function does not assume the same value at the endpoints. This definition of the Fourier series also eliminates the Gibbs phenomenom at the endpoints of the interval and proves useful in the resolution of antiperiodic and mixed boundary value problems with linear partial differential equations. |
Peran Kreativitas dan Inovasi Jepang Dalam Pembangunan
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 673-680 |
| Abstrak | : | - |
Flip a Coin, Get an Annular Function
| Pengarang | : | Curtis Barnhart, Russell Howell, Isaac Jessop & Samuel Tang |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 2) |
| Halaman | : | 122-133 |
| Abstrak | : | A certain class of holomorphic functions in the unit disk can be put into a one-to-one correspondence with a subset of the interval [0,1]. We show that the measure of this subset is either zero or one. We also uncover some symmetry properties of this subset, then exhibit an uncountable collection of numbers belonging to it as well as to its complement. |
INVENTARISASI GULMA LAHAN KERING DI NTT DAN KEMUNGKINAN MELUASNYA DALAM POLA BERTANI TRADISIONAL
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Ilmu dan Budaya |
| Volume / Edisi | : | VIII-9, JUNI (No. 9) |
| Halaman | : | 663-672 |
| Abstrak | : | - |
An Equilateral Triangle of Side > n Cannot be Covered by n2 + 1 Unit Equilateral Triangles Homothetic to it
| Pengarang | : | Jineon Baek & Seewoo Lee |
| Nama Majalah/Jurnal | : | The American Mathematical Monthly |
| Volume / Edisi | : | 132 (No. 2) |
| Halaman | : | 113-121 |
| Abstrak | : | John Conway and Alexander Soifer showed that an equilateral triangle T of side slightly longer than n can be covered by ????2+2 unit equilateral triangles. They also conjectured that it is impossible to cover T with ????2+1 unit equilateral triangles, no matter how close the side of T is to n. While the Conway–Soifer conjecture remains open, we prove an important case where the sides of the triangles used for covering are parallel to the sides of T (e.g., ? and ?). That is, we show that if all unit equilateral triangles are required to be homothetic to T, then the minimum number of unit equilateral triangles that can cover T of side slightly longer than n is exactly ????2+2. Our proof generalizes to covering T by (not necessarily equilateral) triangles of base one parallel to the x-axis and height equal to that of a unit equilateral triangle. Using our method, we also determine the largest side length ????+1/(????+1) (resp. ????+1/????) of T such that the equilateral triangle T can be covered by ????2+2 (respectively ????2+3) unit equilateral triangles homothetic to T. |