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Veronica, Rahayu Budhiati
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STRUKTUR DAN SIFAT-SIFAT K-ALJABAR Nugroho, Deni; Veronica, Rahayu Budhiati; Mashuri, Mashuri
Unnes Journal of Mathematics Vol 6 No 1 (2017)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v6i1.13066

Abstract

K-aljabar merupakan struktur aljabar <G,*,⊙,e>, di mana G merupakan grup terhadap operasi biner * dengan elemen identitas e, operasi ⊙ didefinisikan oleh ∀x,y∈G,x⊙y=x*y-1, dan memenuhi kelima aksioma dari K-aljabar. Konsep yang diterapkan dalam K-aljabar hampir sama dengan konsep dalam grup. Jika dalam grup terdapat subgrup dan homomorfisma grup, maka dalam K-aljabar terdapat K-subaljabar dan K-homomorfisma. Penelitian ini membahas mengenai struktur dan sifat-sifat yang terkait dengan K-aljabar, K-subaljabar, dan K-homomorfisma. Tujuan penelitian ini adalah menjelaskan struktur dan sifat-sifat dari kajian K-aljabar, K-subaljabar, dan K-homomorfisma. Penelitian ini menggunakan metode kajian pustaka, dengan cara mengumpulkan berbagai sumber dan teorema-teorema yang mendukung pada kajian K-aljabar. Pada penelitian ini dapat disimpulkan: 1) Dalam K-aljabar berlaku sifat-sifat berikut; hukum kanselasi; Suatu K-aljabar <G,*,⊙,e> dikatakan komutatif jika ∀x,g∈G berlaku g⊙(e⊙x)=x⊙(e⊙g) 2) K-subaljabar memiliki sifat sebagai berikut; misalkan <G,*,⊙,e> K-aljabar dan g∈G. Jika H suatu subgrup dari G, maka Hg2={g⊙(g⊙x)│x∈H} adalah suatu K-subaljabar dari <G,*,⊙,e>. 3) Homomofisma K-aljabar φ:K1→K2 memiliki sifat-sifat sebagai berikut; ∀x1∈K1,x2∈K2 berlaku φ(e1)=e2; φ(e1⊙x1 )=e1⊙φ(x1 ); φ(x1⊙x2)=e1⇔φ(x1)=φ(x2); dan jika H1 adalah K-subaljabar dari K1 maka φ(K1) adalah K-subaljabar dari K2. K-algebra is an algebraic structure <G,*,⊙,e>, when G is a group of the binary operation * with identity element e, the operation ⊙ defined by ∀x,y∈G,x⊙y=x*y-1, and fulfill the five axioms of K-algebra. The concept is applied in the K-algebra is similar to the concept of the group. If in the group there is a subgroup and group homomorphism, then in K-algebra is K-subalgebra and K-homomorphism. This study discusses the structure and properties associated with the K-algebra, K-subalgebra, and K-homomorphism. The purpose of this study is to explain the structure and properties of the study of K-algebra, K-subalgebra, and K-homomorphism. This study used literature review, by collecting a variety of sources and theorems that support the study of K-algebra. In this study it can be concluded: 1) In K-algebra have following properties; applicable with cancelation law; K-algebra <G,*,⊙,e> is commutative if ∀x,g∈G apply g⊙(e⊙x)=x⊙(e⊙g). 2) K-subalgebra have the following properties; eg <G,*,⊙,e> K-algebra and g∈G. If H subgroup of G, then Hg2={g⊙(g⊙x)│x∈H} is K-subalgebra of <G,*,⊙,e>. 3) K-algebra homomorphism φ:K1→K2 has properties follows; ∀x1∈K1,x2∈K2 apply φ(e1)=e2; φ(e1⊙x1 )=e2⊙φ(x1); φ(x1⊙x2 )=e2⇔φ(x1)=φ(x2); and if H1 is K-subalgebra of K1 then φ(K1) is K-subalgebra of K2.
NILAI EIGEN DAN VEKTOR EIGEN MATRIKS ATAS ALJABAR MAX-PLUS Tunisa, Kholipah; Wijayanti, Kristina; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Vol 6 No 2 (2017)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v6i2.20483

Abstract

Penelitian ini membahas mengenai menentukan nilai eigen, vektor eigen dari matriks tak tereduksi atas aljabar max-plus dan sifat -sifatnya. Metode yang digunakan adalah studi pustaka. Pada penelitian ini disimpulkan: 1) Nilai eigen dan vektor eigen dari matriks tak tereduksi atas aljabar max-plus dapat ditentukan dengan langkah-langkah berikut. (i) Menghitung A pangkat k, untuk k dari 1 sampai n, dengan n ordo matriks persegi (ii) Menghitung nilai eigen dengan yaitu maksimum seper k dikali trace dari A pangkat k pada langkah (i). (iii) Memilih sirkuit (c,c) yang merupakan sirkuit kritis di G(A). (iv) Menghitung matriks B dan B bintang. (v) Memilih vektor eigen dari A yang merupakan kolom ke-c dari matriks B bintang. 2) Sifat-sifat dari nilai eigen dan vektor eigen dari matriks tak tereduksi atas aljabar max-plus sebagai berikut. Vektor eigen dari matriks tak tereduksi tidak tunggal, Nilai eigen dan vektor eigen dari matriks tak tereduksi adalah berhingga. Nilai eigen dari matriks tak tereduksi tunggal. Nilai eigen dari matriks transpose sama dengan nilai eigen dari matriks asalnya Nilai eigen dari A pangkat k sama dengan nilai eigen dari A dipangkatkan k.
PENERAPAN ALJABAR MAX-PLUS PADA PENGATURAN SISTEM ANTRIAN TRAFFIC LIGHT Wibowo, Andi; Wijayanti, Kristina; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Vol 7 No 2 (2018)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v7i2.21338

Abstract

Penelitian ini bertujuan untuk mengatur sistem antrian traffic light menggunakan aljabar max-plus. Penelitian ini berdasarkan data kepadatan arus dan data durasi traffic light pada persimpangan. Kemudian, disusun graf yang menggambarkan kondisi persimpangan dan merepresentasikan arah dari pergerakan masing-masing jalur. Selanjutnya disusun aturan sinkronisasi yang sesuai dengan graf dan pemodelan dari aljabar max-plus. Langkah berikutnya adalah membahas penjadwalan yang periodik dari barisan keadaan sistem traffic light. Analisis dari model aljabar max-plus sistem antrian traffic light menggunakan algoritma power diperoleh periode rata-rata durasi lampu hijau tiap fase adalah detik. Hasil analisis memperoleh hasil perhitungan untuk persimpangan Jarakah Semarang dengan . Berdasarkan periode tersebut, durasi traffic light lebih proporsional dari data primer dan sesuai dengan kepadatan masing-masing simpang di persimpangan Jarakah Semarang. Sedangkan untuk persimpangan Lotte Mart Semarang diperoleh hasil dan berdasarkan periode tersebut menunjukkan durasi traffic light menjadi lebih optimal untuk mengurai kepadatan kendaraan yang melintasi persimpangan tersebut.
Students' mathematical communication skill in co-op co-op type of cooperative learning model reviewed by productive disposition Utami, Ika Wahyu Putri; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Education Vol 10 No 1 (2021): Unnes Journal of Mathematics Education
Publisher : Department of Mathematics, Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujme.v10i1.46130

Abstract

The purpose of this study are examine the effectiveness of co-op co-op type of cooperative learning model on the mathematical communication skill of 8th grade students, determine the effect of productive disposition on students' mathematical communication skill in co-op co-op type of cooperative learning model, and describe students' mathematical communication skill reviewed by productive disposition in co-op co-op type of cooperative learning model. The research method used is mixed method. The results showed that: 1) the mathematical communication skill of 8th grade students in co-op co-op type of cooperative learning model achieved classical completeness criteria, 2) the average of mathematical communication skill of 8th grade students in the co-op co-op type of cooperative learning model achieved minimum completeness criteria, 3) there is an effect of productive disposition on mathematical communication skill in the co-op type of cooperative learning model, 4) subjects with high productive disposition are able to achieve one indicator well and five indicators are achieved imperfectly. Subjects with medium productive disposition are able to achieve all indicators of mathematical communication skill imperfectly. Subjects with low productive disposition are able to achieve four indicators of mathematical communication skill imperfectly.
Analysis of the Mathematical Representation Ability of Class VIII Students in terms of Self Regulated Learning with the Inductive Discovery Learning Model Putri, Arbai Syahidarahma; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Education Vol 10 No 3 (2021): Unnes Journal of Mathematics Education
Publisher : Department of Mathematics, Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujme.v10i3.54039

Abstract

The aim of this study was to determine the mathematical representation ability of class VIII students in terms of self regulated learning with the Inductive Discovery Leraning Model. This type of research is a mix methods research with a concurrent embedded desaign (unbalanced mix). The population in this study were class VIII students of SMP Negeri 40 Semarang in the academic year 2020/2021. The data collection technique used triangulation, comparing the data obtained from interviews, obsservations, and final tests of mathematical representation abilities. The research subjects selected were 6 students, consisting of 2 students with high self regulated learning, 2 students with medium self regulated learning, and 2 students with low self regulated learning. The results of the study indicate that students with high self regulated learning have high mathematical representation abilities, students with medium self regulated learning have medium mathematical representation abilities, and students with low self regulated learning have low mathematical representation abilities.
Mathematical Communication Ability with Brain-Based Learning Model in Terms of Gender Pertiwi, Hana; RD, Nuriana; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Education Vol 10 No 3 (2021): Unnes Journal of Mathematics Education
Publisher : Department of Mathematics, Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujme.v10i3.54140

Abstract

Mathematical communication ability is one of the basic skills standards in mathematics. However, mathematical communication ability with students is still low. This can be seen from the work of students who still have difficulty expressing mathematical problems with mathematical symbols and have difficulty interpreting mathematical ideas in writing. It seems that students find it difficult to express mathematical ideas into writing. This study aims to (1) determine the attainment of the classic dimension of the ability of mathematics students to communicate through the Brain-Based Learning model (2) compared the ability of mathematics based on gender through the Brain-Based Learning model (3) to describe the ability of mathematics students to communicate through gender. This study uses a mix method with a sequential Explanatory. The population is the eighth grade high school student of State 31 at the same time. The sample in this study is a class VIII B student determined by random sampling techniques. The subject of this study was taken on the basis of the student gender. There are six students, three male students and three female students. The results of this study show that: (1) the ability of students to communicate mathematically in Pythagorean matter through the Brain-Based Learning model reaches the classical dimension (2) there is no significant difference in the ability of students to communicate mathematically between men and women through the Brain-Based Learning model (3) Women are better at explaining the idea of the situation and the mathematical relationship in writing with real things, images, graphics, and algebra, and also women are better at creating concepts, formulating arguments, and generalization than men. But in terms of connecting real things, images, and diagrams to the idea of mathematics and also in terms of expressing everyday events in language or the symbol of mathematics between students and girls there is no significant difference.
PENENTUAN NILAI EIGEN SUATU MATRIKS DENGAN METODE PANGKAT (POWER METHOD) Herviani, Benedikta Putri; Isnarto, Isnarto; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Vol 8 No 2 (2019)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v8i2.30091

Abstract

Penelitian ini membahas mengenai penentuan nilai eigen dominan dan tak dominan suatu matriks dengan metode pangkat (power method). Metode penelitian yang digunakan adalah dengan kajian pustaka. Pada penelitian ini disimpulkan: 1) Nilai eigen dominan suatu matriks A dengan metode pangkat langsung ditentukan dengan langkah-langkah berikut. (i) Menentukan sebarang vektor taknol x0. (ii) Mencari vektor yk = Axk untuk k = 0, dan vektor xk+1 untuk k = 0 yaitu membagi yk dengan λ(k+1), elemen yk dengan nilai mutlak terbesar. (iii) Mencari vektor yk dan xk+1 untuk k dari 1 sampai n hingga λ(k) mendekati λ(k+1). (2) Nilai eigen tak dominan suatu matriks A dengan metode pangkat invers ditentukan dengan mencari nilai eigen dominan A invers dimisalkan λinvers, dan nilai eigen tak dominan A adalah 1 dibagi λinvers. (3) Nilai eigen tak dominan suatu matriks A dengan metode pangkat tergeser ditentukan dengan mencari nilai eigen dominan A yang digeser dimisalkan λshifted dengan nilai geseran s, dan nilai eigen tak dominan A adalah λshifted ditambah s. (4) Nilai eigen dominan suatu matriks A dengan metode pangkat invers tergeser ditentukan dengan mencari nilai eigen dominan A yang diinvers dan digeser dimisalkan λshiftedinvers dengan nilai s dan nilai eigen dominan A adalah 1 dibagi λshiftedinvers ditambah s.
JARINGAN MATRIKS (MATRIX NETWORK) DAN KEISTIMEWAANNYA Dito, Aliffia Putri; Veronica, Rahayu Budhiati; Mashuri, Mashuri
Unnes Journal of Mathematics Vol 9 No 1 (2020)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v9i1.30555

Abstract

Penelitian ini membahas mengenai pembentukan jaringan matriks, karakteristik-karakteristik yang dimiliki jaringan matriks dan penerapan jaringan matriks dalam genetika. Tujuan penelitian ini adalah untuk mengetahui (1) bagaimana pembentukan jaringan matriks, (2) karakteristik apa saja yang dimiliki jaringan matriks. Hasil dari penelitian ini adalah untuk mendeskripsikan peluang mikrostatik pada saat transisi gen.
Penerapan metode AHP sebagai sistem pendukung keputusan pemilihan tempat kerja Nugroho, Ade Oktafiawan; Veronica, Rahayu Budhiati
Unnes Journal of Mathematics Vol 10 No 1 (2021)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v10i1.44631

Abstract

This study aims to create a decision support method that is useful for undergraduate graduates to choose a workplace that suits their interests and abilities as well as to produce a computer program for a decision support system to choose a workplace that suits what the graduates want the scholar.The method used is a literature study, which is carried out by reading and analyzing books and journals related to decision support systems to choose a workplace using the Analytical Hierarchy Process (AHP) method. The purpose of this literature study method is to obtain references, making it easier to carry out this research. After the literature study method, the writer will collect the respondent’s data which will be processed using the AHP method. The next stage is to analyze the problem with the AHP method. By using the AHP method and studying the steps of the AHP, in order to obtain the priority order of the most appropriate business entities to be selected, which are sorted according to the total value of the Global Priority Table from the largest to the total weight value equivalent And finally the authors produced a computer program to determine the workplace called the PHP-based Workplace Decision Support System (DSS).
Co-Authors Amalludin, Subuh ANDI WIBOWO Bambang Eko Susilo Devita Anggraini Dito, Aliffia Putri Dwijanto Dwijanto, Dwijanto Emi Pujiastuti Hana Pertiwi Hardi Suyitno Hartriani, Novita Herviani, Benedikta Putri Isnarto, Isnarto Kartono - Kristina Wijayanti Mashuri Mashuri Nugroho, Ade Oktafiawan Nugroho, Deni Nurkaromah Dwidayati, Nurkaromah Permatasari, Gilang Anjar Pratiwi, Dyah Ayu Putri, Arbai Syahidarahma Putriaji Hendikawati RD, Nuriana St. Budi Waluya Sunarmi Sunarmi Tayani, Mevi Tunisa, Kholipah Utami, Eka Nurul Utami, Ika Wahyu Putri Wicaksono, Wahyu Budi Yuliani, Selvia