Hasil Pencarian  ::  Simpan CSV :: Kembali

"Tesis ini membahas mengenai sifat-sifat matriks yang terdapat pada suatu matriks Sudoku. Matriks Sudoku merupakan matriks yang memenuhi aturan yang berlaku pada permainan Sudoku. Jika diberikan suatu matriks Sudoku tertentu, maka dengan menggunakan operasi elementer, transpos, dan operasi rotasi 90° searah jarum jam, dapat dibentuk matriks-matriks Sudoku yang lain. Sedangkan sifat-sifat yang dikaji adalah sifat-sifat umum yang terdapat pada suatu matriks seperti, determinan, transpos, nilai eigen, simetri atau tidak simetri, normal atau non normal.

---

This thesis discussed about properties of Sudoku matrix. Sudoku matrix is a matrix which is verified by a rule of Sudoku game. If a Sudoku matrix is given, then the other Sudoku matrices can be obtained by using an elementary operation, transpose, and rotation 90°. This thesis also explored about properties of matrix such as, determinant, transpose, eigenvalues, symmetric or nonsymmetric, normal or nonnormal."

"Permainan Sudoku merupakan permainan yang populer saat ini. Permainan Sudoku merupakan suatu permainan penempatan angka-angka 1 hingga 9 pada matriks berukuran dengan syarat di tiap baris, tiap kolom, dan di setiap submatriks hanya berisi angka 1 hingga 9 tepat satu kali (Taalman, 2007).Dalam skripsi ini dibuat permainan Sudoku dengan lima tingkat kesulitan yang dibuat dari satu matriks Sudoku dengan menggunakan algoritma digging holes. Permainan Sudoku yang dibuat diharapkan jika dikerjakan akan menghasilkan matriks Sudoku yang unik. Untuk mengecek keunikan digunakan program Sudoku solver. Untuk membuat variasi dari permainan Sudoku yang telah dibuat dilakukan proses penambahan variasi.

---

Sudoku game is a popular game nowadays. Sudoku is a game that put numbers start from 1 until 9 into a matrix with rules in every line, in every column,and in every sub matrix only has number 1 until 9 once. In this small thesis,Sudoku game with 5 difficulty levels will be made from a Sudoku matrix by using digging holes algorithm. Sudoku games, when it is solved, supposed to only have a unique Sudoku matrix. A Sudoku solver program is being used to check Sudoku uniqueness. For Sudoku games variation, there is a proses named propagating."

"Matriks anti ketetanggaan merupakan salah satu matriks representasi dari suatu graf berarah, tetapi sifat-sifatnya masih belum banyak diketahui karena masih baru diperkenalkan. Sehingga, pada penelitian ini dibahas sifat-sifat dari matriks anti ketetanggaan suatu graf berarah dan graf garis berarahnya. Sifat-sifat yang dibahas yaitu hasil representasi dari perpangkatan matriks anti ketetanggaan suatu graf berarah yang mungkin mempunyai digon atau gelang berarah, determinan dan polinomial karakteristik dari matriks anti ketetanggaan suatu graf berarah yang mempunyai digon berarah, dan hubungan polinomial karakteristik matriks anti ketetanggaan suatu graf berarah asiklik sederhana dan graf garis berarahnya. Kemudian, pada penelitian ini ditunjukkan bahwa tidak ada hubungan antara suatu graf berarah selain asiklik dan graf garis berarahnya dengan memberikan counterexample-nya.

---

Antiadjacency matrix is one of the representation matrices of a directed graph, but its properties are still not widely known because it has just been introduced. Thus, in this study, we discuss the properties of the antiadjaceny matrix of a digraph and its line digraph. The properties discussed are the results of the representation of powering the antiadjaceny matrix of a digraph which may have directed digon(s) or loop(s), the determinant and characteristic polynomial of an anti-adjacent matrix of a digraph that has directed digon(s), and the characteristic polynomial relationship of the antiadjaceny matrix of a simple acyclic digraph. and the line digraph. Then, in this study, it was shown that there is no relationship between a directed graph other than acyclic and a directed line graph by providing its counterexample."

"Graf merupakan himpunan simpul dan busur dengan setiap busurnya menghubungkan dua simpul. Graf dapat direpresentasikan dalam sebuah matriks. Matriks representasi graf di antaranya yaitu matriks ketetanggaan, matriks jarak, matrik kehadiran, dan matriks Laplacian. Matriks ketetanggaan merepresentasikan ada tidaknya busur yang menghubungkan dua buah simpul. Matriks jarak merepresentasikan jarak lintasan terpendek antara dua simpul pada graf. Pada graf berdiameter dua, yaitu jarak terpanjang di antara dua simpul adalah dua. Graf berdiameter dua di antaranya yaitu graf bipartit, graf roda, dan graf kipas. Pada tesis ini akan dibahas hubungan antara matriks ketetanggaan dan matriks jarak dari suatu graf berdiameter dua, dan sifat-sifat matriks jarak pada graf berdiameter dua, serta polinomial karakteristik dari matriks jarak pada kelas graf khusus berdiameter dua yaitu graf bipartit lengkap 𝐾𝑛,𝑛.

---

Graph is the set of vertices and edges where each edge connects two vertices. The graph can be represented by a matrix. There are several matrix representation of graph, such as adjacency matrix, distance matrix, incidence matrix, and Laplacian matrix. The adjacency matrix represents the presence or absence of an arc connecting two vertices. Distance matrix represent the shortest path between two vertices on a graph. The example of two-diameter graphs are bipartite graphs, wheel graphs, and fan graphs. In this thesis we discuss the relationship between the adjacency matrix and the distance matrix of a two-diameter graph, and the properties of the distance matrix in the twodiameter graph, and the characteristic polynomial of the distance matrix of special family of two-diameter graph that is complete bipartite graph 𝐾𝑛,𝑛."

"ABSTRAKLATAR BELAKANG. Memori kerja merupakan ranah kognisi yang bertanggungjawabterhadap sebagian besar masalah kognisi yang dialami seorangusia lanjut.Tujuan penelitian ini adalah untuk mengetahui manfaat mengisiSudoku terhadap fungsi memori kerja dan fungsi kognisi global usia lanjut. METODE. Desain studi adalah uji klinis tidak tersamar. Subjek merupakanwarga Panti Sosial TresnaWerda I dan III DKI Jakarta yang diambil secarakonsekutif kemudian dibagi acak menjadi dua kelompok, perlakuan dan kontrol.Kelompok perlakuan melakukan latihan Sudoku 3x/minggu selama 12 minggu.Memori kerja dinilai dengan Trail Making Test part B (TMT-B), fungsi kognisiglobal dinilai dengan Montreal Cognitive Assesment versi bahasa Indonesia(MoCA-Ina). HASIL. Terdapat 24 subjek pada kelompok perlakuan dan 27 subjek padakelompok kontrol. Terdapat 13 subjek yang memberikan kesan positif terhadaplatihan Sudoku. Penurunan waktu penyelesaian TMT-B sebesar 11,1 detik padakelompok perlakuan dan 18,8 detik pada kelompok kontrol, meskipun tidakdidapatkan perbedaan bermakna antar kedua kelompok (p = 0,816). Terdapat 8subjek (33,3%) dari kelompok perlakuan dan 11 subjek (40,7%) dari kelompokkontrol yang mengalami peningkatan nilaiMoCA-Ina (p = 0,530). KESIMPULAN. Sudoku belum terbukti dapat meningkatkan fungsi memorikerja dan fungsi kognisi global pada usia lanjut sehat, namun peningkatan fungsimemori kerja yang terlihat pada kedua kelompok menandakan adanya plastisitasneural pada usia lanjut yang bermanfaat untuk pemeliharaan fungsi kognitif.

---

ABSTRACTBACKGROUND. Working memory deficit is responsible for most of thecognitive problem experienced by older adults.The aim of the present study was todetermine whether Sudoku training might improves these deficits and if so,whether such changes might be transferred to other cognitive domains.METHODS. This was non-blinding randomized controlled trial. Subjects wereconsecutively taken from Panti Sosial TresnaWerda I dan III DKI Jakarta afterseries of screening. All subjects were assessed with Indonesian version ofMontreal Cognitive Assessment (MoCA-Ina) for cognitive function and TrailMaking Test part B (TMT-B) for working memory. The experimental group wasgiven 12 weeks of cognitive alternate-day training based on Sudoku exercises.RESULTS. There are 24 subjects in experimental group and 27 subjects incontrol group. Nine subjects from each group showed improvement in the TMT-Bcompletion time, although this difference were not statistically significant(experimental group 11.1s Vs control group 18.8s; p = 0.816). There were 8subjects (33.3 %) on experimental group and 11 subjects (40.7 %) on controlgroup had increment in MoCA-Ina scores (p = 0.530). Thirteen subjects reportedimprovements in memory, attention and concentration span.CONCLUSIONS. The use of Sudoku as one of the cognitive training tools on elderly still need further study and discussion regarding limitation of this presentstudy. But the improvement of working memory function as seen in resultprovides potential brain plasticity for maintaining cognitive function in elderly. ;BACKGROUND. Working memory deficit is responsible for most of thecognitive problem experienced by older adults.The aim of the present study was todetermine whether Sudoku training might improves these deficits and if so,whether such changes might be transferred to other cognitive domains.METHODS. This was non-blinding randomized controlled trial. Subjects wereconsecutively taken from Panti Sosial TresnaWerda I dan III DKI Jakarta afterseries of screening. All subjects were assessed with Indonesian version ofMontreal Cognitive Assessment (MoCA-Ina) for cognitive function and TrailMaking Test part B (TMT-B) for working memory. The experimental group wasgiven 12 weeks of cognitive alternate-day training based on Sudoku exercises.RESULTS. There are 24 subjects in experimental group and 27 subjects incontrol group. Nine subjects from each group showed improvement in the TMT-Bcompletion time, although this difference were not statistically significant(experimental group 11.1s Vs control group 18.8s; p = 0.816). There were 8subjects (33.3 %) on experimental group and 11 subjects (40.7 %) on controlgroup had increment in MoCA-Ina scores (p = 0.530). Thirteen subjects reportedimprovements in memory, attention and concentration span.CONCLUSIONS. The use of Sudoku as one of the cognitive training tools on elderly still need further study and discussion regarding limitation of this presentstudy. But the improvement of working memory function as seen in resultprovides potential brain plasticity for maintaining cognitive function in elderly. ;BACKGROUND. Working memory deficit is responsible for most of thecognitive problem experienced by older adults.The aim of the present study was todetermine whether Sudoku training might improves these deficits and if so,whether such changes might be transferred to other cognitive domains.METHODS. This was non-blinding randomized controlled trial. Subjects wereconsecutively taken from Panti Sosial TresnaWerda I dan III DKI Jakarta afterseries of screening. All subjects were assessed with Indonesian version ofMontreal Cognitive Assessment (MoCA-Ina) for cognitive function and TrailMaking Test part B (TMT-B) for working memory. The experimental group wasgiven 12 weeks of cognitive alternate-day training based on Sudoku exercises.RESULTS. There are 24 subjects in experimental group and 27 subjects incontrol group. Nine subjects from each group showed improvement in the TMT-Bcompletion time, although this difference were not statistically significant(experimental group 11.1s Vs control group 18.8s; p = 0.816). There were 8subjects (33.3 %) on experimental group and 11 subjects (40.7 %) on controlgroup had increment in MoCA-Ina scores (p = 0.530). Thirteen subjects reportedimprovements in memory, attention and concentration span.CONCLUSIONS. The use of Sudoku as one of the cognitive training tools on elderly still need further study and discussion regarding limitation of this presentstudy. But the improvement of working memory function as seen in resultprovides potential brain plasticity for maintaining cognitive function in elderly. ;BACKGROUND. Working memory deficit is responsible for most of thecognitive problem experienced by older adults.The aim of the present study was todetermine whether Sudoku training might improves these deficits and if so,whether such changes might be transferred to other cognitive domains.METHODS. This was non-blinding randomized controlled trial. Subjects wereconsecutively taken from Panti Sosial TresnaWerda I dan III DKI Jakarta afterseries of screening. All subjects were assessed with Indonesian version ofMontreal Cognitive Assessment (MoCA-Ina) for cognitive function and TrailMaking Test part B (TMT-B) for working memory. The experimental group wasgiven 12 weeks of cognitive alternate-day training based on Sudoku exercises.RESULTS. There are 24 subjects in experimental group and 27 subjects incontrol group. Nine subjects from each group showed improvement in the TMT-Bcompletion time, although this difference were not statistically significant(experimental group 11.1s Vs control group 18.8s; p = 0.816). There were 8subjects (33.3 %) on experimental group and 11 subjects (40.7 %) on controlgroup had increment in MoCA-Ina scores (p = 0.530). Thirteen subjects reportedimprovements in memory, attention and concentration span.CONCLUSIONS. The use of Sudoku as one of the cognitive training tools on elderly still need further study and discussion regarding limitation of this presentstudy. But the improvement of working memory function as seen in resultprovides potential brain plasticity for maintaining cognitive function in elderly. "

"Euclidean Distance Matrix (EDM) mempunyai hubungan dengan matriks semidefinit positif yang mana hubungan tersebut direpresentasikan oleh fungsiτ dan fungsi K, dengan τ dan K merupakan fungsi yang saling invers (H. Kurata & P. Tarazaga, 2011). Sedangkan istilah dan notasi mayorisasi itu sendiri pertama kali diperkenalkan oleh Hardy, Littlewood, & Polya (1934) untuk mengungkapkan suatu vektor x dikatakan "less spread out" dibanding vektor Y.Pada skripsi ini akan dipelajari bagaimana hubungan matriks semidefinit positif B1 dan B2 jika diketahui bahwa vektor dengan elemen nilai-nilai eigen matriks EDM D1 dimayorisasi oleh vektor dengan elemen nilai-nilai eigen matriks EDM D2 dengan Bi (i=1,2) bersesuaian dengan Di(i=1,2).

---

There is a relationship between Euclidean Distance Matrix (EDM) and positive semidefinite matrix, which is represented τ function and K function, with τ and K are mutually inverse (H. Kurata & P. Tarazaga, 2011). Meanwhile the term and notation of majorization was first introduced by Hardy, Littlewood, and Polya (1934), to express how the vector X is said to be "less spread out" than the vector Y.

In this paper, it will be studied how the relationship between the positive semidefinit matrix B1 and B2, if it is known that a vector with elements eigenvalues of the EDM D1 is majorized by a vector with elements eigenvalues of the EDM D2, where Bi(i=1,2) corresponds to Di(i=1,2)."

"Misalkan adalah suatu graf berarah yang acyclic dengan ( ) * +. Matriks adjacency dari graf berarah adalah matriks [ ] yang berukuran yang didefinisikan dengan, untuk jika terdapat busur berarah dari ke dan untuk selainnya. Matriks disebut sebagai matriks antiadjacency dari graf berarah dengan adalah matriks yang berukuran dengan semua entrinya adalah . Pada tesis ini diberikan sifat-sifat dari polinomial karakteristik matriks antiadjacency dari graf berarah yang acyclic dan gabungan beberapa graf berarah yang acyclic . Selain hal tersebut juga diberikan spektrum matriks antiadjacency dari beberapa kelas graf berarah yang acyclic yaitu graf bipartit lengkap berarah ⃗⃗ dengan , graf bintang berarah keluar ⃗⃗ dengan , graf bintang berarah masuk ⃗⃗ dengan , graf lintasan lengkap berarah ⃗ ⃗⃗⃗ ⃗ dengan , gabungan graf bipartit lengkap berarah ⃗⃗ ⋃ ⃗⃗ dengan , gabungan graf bintang berarah keluar ⋃ ⃗⃗ dengan dan gabungan graf bintang berarah masuk ⋃ ⃗⃗ dengan .

---

Let be an directed acyclic graph with ( ) * +. The adjacency matrix of directed graph is a matrix [ ] of order , such that if there is an edge from to then , otherwise . The matrix will be called antiadjacency matrix of directed graph with is a matrix of order with all entries are . In this thesis is given properties of characteristic polynomial antiadjacency matrix of directed acyclic graph and union of some directed acyclic graphs . In addition, here are also given spectrum of antiadjacency matrix from some classes of directed acyclic graphs that are complete bipartite directed graph ⃗⃗ with , out-star directed graph ⃗⃗ with , in-star directed graph ⃗⃗ with , complete path directed graph ⃗ ⃗⃗⃗ ⃗ with , union of complete bipartite directed graphs ⃗⃗ ⋃ ⃗⃗ with , union of out-star directed graphs ⋃ ⃗⃗ with and union of in-star directed graphs ⋃ ⃗⃗ with ."

"Misalkan T adalah gelanggang matriks segitiga formal dan T[z; θ, d] adalah gelanggang polinomial miring atas T. Dengan mempelajari homomorfisma khusus dan derivasi miring pada gelanggang matriks segitiga formal, dapat dibuktikanbahwa gelanggang polinomial miring T[z; θ, d] memiliki representasi matriks segitiga formal.

---

Let T be a formal triangular matrix ring and T[z; θ, d] be a skew polynomial ring over T. By studying a particular ring homomorphism and skew derivation on formal triangular matrix ring, one can show that the skew polynomial ring T[z; θ, d] has formal triangular matrix representation."