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All Journal Jurnal Sains dan Teknologi JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Square : Journal of Mathematics and Mathematics Education Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Operations Research: International Conference Series International Journal of Multidisciplinary Research and Literature (IJOMRAL) Bulletin of Applied Mathematics and Mathematics Education Jurnal Matematika Integratif
Ari Wardayani, Ari
Universitas Jenderal Soedirman
Humanities Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Engineering Environmental Science Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Library & Information Science Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Journal : Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)

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KARAKTERISTIK SEGITIGA LUCAS Nurshiami, Siti Rahmah; Wardayani, Ari; Setiani, Kana Hasmi
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 11 No 1 (2019): JMP Edisi Juni 2019
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Lucas triangle is an array of coeficients of a polynomial forming a pattern which is similar to Pascal triangle. This research studies Lucas triangle and its properties. The research results show that every row in Lucas triangle is begun by the number 1 and is ended by the number 2,  the sum of the first n terms of number of 1th column is equal to the number at th row, 2nd column. Besides, the number at nth row and  th column of Lucas triangle is  for , the sum of the first n terms of number of jth column is equal to the number at th row,  column for . The number of Lucas triangle is the sum of two number terms in preceded row, that is the number at  th row,  and the number at th row, . Then, the sum of coefficients of each  row of Lucas triangle is .
KARAKTERISTIK SEGITIGA LUCAS Siti Rahmah Nurshiami; Ari Wardayani; Kana Hasmi Setiani
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 11 No 1 (2019): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2020.12.1.1933

Abstract

Lucas triangle is an array of coeficients of a polynomial forming a pattern which is similar to Pascal triangle. This research studies Lucas triangle and its properties. The research results show that every row in Lucas triangle is begun by the number 1 and is ended by the number 2, the sum of the first n terms of number of 1th column is equal to the number at th row, 2nd column. Besides, the number at nth row and th column of Lucas triangle is for , the sum of the first n terms of number of jth column is equal to the number at th row, column for . The number of Lucas triangle is the sum of two number terms in preceded row, that is the number at th row, and the number at th row, . Then, the sum of coefficients of each row of Lucas triangle is . Full Article
KARAKTERISTIK SEGITIGA LUCAS Nurshiami, Siti Rahmah; Wardayani, Ari; Setiani, Kana Hasmi
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 11 No 1 (2019): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2020.12.1.1933

Abstract

ABSTRACT. Lucas triangle is an array of coeficients of a polynomial forming a pattern which is similar to Pascal triangle. This research studies Lucas triangle and its properties. The research results show that every row in Lucas triangle is begun by the number 1 and is ended by the number 2, the sum of the first n terms of number of 1th column is equal to the number at (n+1)th row, 2nd column. Besides, the number at nth row and (n-2)th column of Lucas triangle is (n-1)^2 for n≥2, the sum of the first n terms of number of jth column is equal to the number at (n+1)th row, (j+1)^th column for j≥1. The number of Lucas triangle is the sum of two number terms in preceded row, that is the number at (n-1)th row, (j-1)^th and the number at (n-1)th row, j^th. Then, the sum of coefficients of each n^th row of Lucas triangle is .Keywords: Pascal triangle, Lucas number, Lucas triangle. ABSTRAK. Segitiga Lucas merupakan susunan koefisien-koefisien dari suatu polinomial yang disusun membentuk pola segitiga memyerupai segitiga Pascal. Penelitian ini mengkaji segitiga Lucas dan karakteristik dari segitiga Lucas. Hasil penelitian menunjukkan bahwa, setiap baris pada segitiga Lucas diawali dengan angka 1 dan diakhiri dengan angka 2, jumlah dari n suku bilangan pertama pada kolom ke-1 sama dengan bilangan pada baris ke- kolom ke-2. Selain itu, bilangan pada baris ke- kolom ke- pada segitiga Lucas adalah untuk , jumlah n suku bilangan pertama pada kolom ke-j sama dengan bilangan pada baris ke- kolom ke- untuk . Bilangan pada segitiga Lucas merupakan penjumlahan dari dua suku bilangan pada baris sebelumnya, yaitu bilangan pada baris ke- kolom ke- dan bilangan pada baris ke- kolom ke-j. Kemudian, jumlah koefisien setiap baris ke-n pada segitiga Lucas adalah .Kata Kunci: Segitiga Pascal, Bilangan Lucas, Segitiga Lucas
KONSEP DASAR HIPERGRAF DAN SIFAT-SIFATNYA Putri, Faiq Fauziya; Triyani, Triyani; Wardayani, Ari
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 12 No 2 (2020): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2020.12.2.3619

Abstract

ABSTRACT. This article discusses fundamental properties of hypergraphs. Hypergraphs are generalization of graph which hyperedges, edges in hypergraph, can join more than two vertices. The fundamental properties in this article are the vertices degrees, connection in hypergraphs, and dual hypergraph. connectivity in hypergraphs in this article are walks, trails, strict trails, path, and cycles. In the end of this article, we present a few examples of problems that can be represented by hypergraph.Keywords: hypergraph, connectivity in hypergraph, dual hypergraph ABSTRAK. Artikel ini membahas mengenai konsep dasar hipergraf dan sifat-sifatnya. Hipergraf merupakan generalisasi dari graf dimana hyperedge, istilah sisi pada hipergraf, dapat menghubungkan lebih dari dua titik. Sifat-sifat dasar yang disajikan pada artikel ini berkaitan dengan derajat titik, keterhubungan dalam hipergraf, dan dual hipergraf pada hipergraf tak berarah. Keterhubungan dalam hipergraf berupa jalan, trail, strict trail, lintasan, dan cycle. Pada bagian akhir artikel, disajikan beberapa contoh permasalahan yang dapat direpresentasikan dengan hipergraf.Kata kunci: hipergraf, keterhubungan dalam hipergraf, dual hipergraf
SOME PROPERTIES OF SUBSEMIHYPERGROUPS wardayani, Ari; Cerinda, Mitha; Sihwaningrum, Idha; Estri, Mutia nur; Sidik, Wuryatmo Ahmad
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 13 No 2 (2021): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2021.13.2.4905

Abstract

ABSTRACT. In this paper we will present two properties of subsemihypergroups. The first property is a relation between subsemihypergroups and semihypergroup. This property enable us to get the second property, which provides a relation between subsemihypergroups and regular semihypergroups.Keywords: semihypergroup, subsemihypergroup, regular. ABSTRAK. Pada makalah ini disajikan dua buah sifat subsemihypergrup. Sifat pertama adalah hubungan antara subsemihypergrup dan semihypergrup. Berdasarkan sifat ini, selanjutnya diperoleh sifat kedua yakni hubungan antara subsemihipergrup dan semihipergrup reguler.Kata Kunci: semihipergrup, subsemihipergrup, reguler
SEMIGRUP REGULER DAN SIFAT-SIFATNYA Istikaanah, Najmah; Wardayani, Ari; Renny, Renny; Nurahmadhani, Ambar Sari; Sb., Agustini Tripena Br.; Triyani, Triyani
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 13 No 2 (2021): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2021.13.2.4968

Abstract

ABSTRACT. This article discusses some properties of regular semigroups. These properties are especially concerned with the relation of the regular semigroups to groups, idempoten semigroups and invers semigroups. This article also discusses the Cartesian product of two regular semigroups where it is concluded that the Cartesian product of two regular semigroups is a regular semigroup, a group must be a regular semigroup. In addition, idempotent semigroups and inverse semigroups are also regular semigroups.Keywords: idempoten semigroup, inverse semigroup, regular semigroup, Cartesian product ABSTRAK. Artikel ini membahas tentang sifat-sifat semigrup reguler. Sifat-sifat ini khususnya berkenaan dengan keterkaitan semigrup reguler dengan grup, semigrup idempoten, dan semigrup invers. Pada artikel ini juga dibahas mengenai hasil kali Cartesius dari dua semigrup regular dimana diperoleh kesimpulan bahwa hasil kali Cartesius dua semigrup reguler merupakan semigrup reguler, suatu grup pasti merupakan semigrup regular. Selain itu, semigrup idempoten dan semigrup invers juga merupakan semigrup regular.Kata kunci: semigrup idempoten, semigrup invers, semigrup reguler, hasil kali kartesius.
Co-Authors Achfasarty, Kiran Nirmala Agung Prabowo Binafsie, Latifah Ibda Cerinda, Mitha Chumaedi Sugihandardji Dian Pratama Erni Widiyastuti Gunawan Gunawan Gunawan Gunawan Guswanto, Bambang Hendriya Idha Sihwaningrum Irham Taufiq, Irham Jaka Wijaya Kusuma Kana Hasmi Setiani Maryani, Sri Mutia Nur Estri, Mutia Nur Najmah Istikaanah Najmah Istikaanah Niken Larasati Nurahmadhani, Ambar Sari Nurul Istiqomah Putri, Faiq Fauziya Renny Renny Sb., Agustini Tripena Br. Setiani, Kana Hasmi Sidik, Wuryatmo Ahmad Siti Rahmah Nurshiami, Siti Rahmah Sri Maryani Suhariman, Fikrianto Suroto Suroto Suroto Suroto Triyani Triyani Triyani Triyani Zahratunnisa, Siti Fauziah