On the initial value problem of a periodic box-ball system

We show that the initial value problem of a periodic box-ball system can be solved in an elementary way using simple combinatorial methods.Comment: 9 pages, 2 figure

Correlation function for a periodic box-ball system

We investigate correlation functions in a periodic box-ball system. For the two point functions of short distance, we give explicit formulae obtained by combinatorial methods. We give expressions for general N-point functions in terms of ultradiscrete theta functions.Comment: 13 pages, 2 figures, submitted to J. Phys. A: Math. Theo

Model Regresi Dummy Indeks Prestasi Akademik Mahasiswa Program Studi Matematika Faperta Unimor

One indicator that can be used as a determinant in the quality of higher education is the academic achievement of students. Grade Point Average (GPA) is a measure of the academic performance. GPA gained students can not be separated from the quality of the incoming student input at the college. This study discusses some of the indicators that can be used as a measure of the quality of student input from the academic side, such as the National Examination (NE), the origin of school (public / private), gender and type of college entrance exam (SNMPTN test, SBMPTN test and independent institution test). Because some of these indicators are qualitative so the data analysis used regression analysis with dummy variables. Research conducted on students of Mathematics Study Program, Faculty of Agriculture, Timor University, class of 2017 to class of 2021. From the data processing, obtained regression model: . From the data analysis, concluded that the female students of Mathematics Study Program, Faculty of Agriculture, Timor University, coming from public schools and type of college entrance exam is SNMPTN have the greatest tendency to obtain high GPA compared with other students. In addition,  for the regression equation obtained above was 38.2% means that the independent variable in the model can explain the diversity of the GPA of 38.2%

KAJIAN TEOREMA BOLZANO-WEIERSTRASS UNTUK MENGKONSTRUKSI BARISAN YANG KONVERGEN DI R^n DAN APLIKASINYA DALAM PEMBUKTIAN TEOREMA EKSISTENSI MAX-MIN

A sequence is a function from the set of natural numbers to the set of real numbers . In sequences there is the concept of sequence convergence. Testing the convergence of a sequence can be done using the Bolzano-Weierstrass Theorem. This theorem states that every finite sequence has a convergent sequence. The relationship between convergent sequences and finite sequences is also important to study further. Apart from being used to prove the convergence of sequences, the Bolzano-Weirstrass Theorem can also be applied to prove the Max-Min Existence Theorem. This research was conducted to examine the relationship between convergent sequences and finite sequences, the relationship between convergence and continuous functions and the relationship between continuous functions and max-min values ​​with the aim of constructing a convergent sequence in R^n and its application in proving the Max-Min Existence Theorem. This research is a literature study. This research was conducted through a literature review of books and other literature. From the literature review, the materials are then discussed in depth. The results of the literature study show that a convergent sequence is a finite sequence, but a finite sequence is not necessarily convergent. In determining the convergence of a sequence using the Bolzano-Weierstrass Theorem, it is necessary to first show the limitations of the sequence. Furthermore, to prove the Max-Min Existence Theorem it is necessary to require that the sequence is finite and then this theorem can be proven using the Bolzano-Weierstrass Theorem and Apit Theorem. Keywords: Monotonous Sequence, Finite Sequence, Continuity, Bolzano-Weierstrass Theorem, Max-Min Existence Theorem

Penjadwalan Tenaga Kerja Tiga Shift Berkendala Libur Hari Minggu Dan Satu Hari Setelah Shift Tiga

Peningkatan permintaan menunjukkan pertumbuhan bisnis yang baik dari Perusahaan, namun terkendala oleh kapasitas produksi yang dimiliki.Utilitas mesin di pabrik pupuk organik, PT X,belum maksimal dan baru dipergunakan kurang dari 70%. Peningkatan kapasitas produksi dengan menaikkan utilisasi mesin dan menambahkan tenaga kerja dari 2 shift menjadi 3 shift, memerlukan penjadwalan tenaga kerja yang efektif. . Penelitian ini menggunakan algoritma Tibrewala, Philippe dan Browne yang telah dimodifikasi. Modifikasi algoritma bertujuan untuk mengakomodasi waktu produksi 3 shift perhari dengan 6 hari perminggu, di mana tenaga kerja bekerja 5 hari perminggu dengan pergantian 3 shift serta libur 2 hari yaitu di hari Minggu sesuai kebijakan Perusahaan dan 1 hari setelah shift 3.Modifikasi algoritma mengubah dan menambahkan dari tiga langkah menjadi lima langkah, mengubah format tabel tabular penjadwalan tenaga kerja untuk tiga shift, serta mengubah aturan pemilihan hari libur.Mempergunakan algoritma yang telah dimodifikasi, penelitian ini menjadwalkan tenaga kerja sebanyak 85 orang yang meliputi 45 orang di mesin Crusher, 29 orang di mesin Pan Granulator dan 11 orang di mesin Cooler. Overstaffing yang terjadi pada mesin Crusher sebanyak 9 man-days (ekuivalen dengan 1,8 orang), Pan Granulator sebanyak 1 man-days (ekuivalen dengan 0,2 orang),Cooler sebanyak 1 man-days (ekuivalen dengan 0,2 orang). Penjadwalan tenaga kerja selama 3 shift dalam 6 hari kerja perminggu diharapkan dapat meningkatkan utilitas mesin hingga 85,71% dengan kapasitas produksi hingga 216 ton pupuk organik perminggu.Kata kunci (keywords): Utilitas, Kapasitas, Penjadwalan tenaga kerja, Algoritma Tibrewala Philippe & Browne, Modifikasi algoritma

Tropical Krichever construction for the non-periodic box and ball system

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur

A crystal theoretic method for finding rigged configurations from paths

The Kerov--Kirillov--Reshetikhin (KKR) bijection gives one to one correspondences between the set of highest paths and the set of rigged configurations. In this paper, we give a crystal theoretic reformulation of the KKR map from the paths to rigged configurations, using the combinatorial R and energy functions. This formalism provides tool for analysis of the periodic box-ball systems.Comment: 24 pages, version for publicatio

Pelatihan Pembuatan Aplikasi E-raport dengan Menggunakan Microsoft Office Excel Bagi Guru-guru SD di Wilayah Insana Fafinesu

The activity of filling in school data, student data, and student final grades in report card at elementary schools in the Insana Fafinesu District, Timor Tengah Utara Regency has been carried out in handwriting (conventional), which have some constraints such as taking a long time to processing grades, has a tendency to miscalculation if the student report card is lost or damaged, it does not have documentation/ back-up documents. For teachers who have sloppy handwriting, it will be difficult for a parent to read. One software that can be used in making student report cards is Microsoft Office Excel. This software is easy to understand and can overcome problems in making student report cards such as the length of time for processing grades, the tendency of grade processing error, difficulties in reading teacher writing by parents, and overcoming problems with documentation/backup documents. This service activity aims to provide training in making e-report card applications using Microsoft Excel for elementary school teachers in the Insana Fafinesu area, Timor Tengah Utara Regency. The methods used in this activity are workshops and ongoing mentoring. As a result, teachers better understand the functions in Microsoft Excel that are useful in the process of filling out student report cards, each teacher succeeds in making their own e-reports, and they agree that e-reports with Microsoft Excel are more efficient and effective than filling out report cards manually (conventional) and will use e-reports in their respective schools. The next plan for this service activity will be an application for Teacher Performance Assessment (TPA) and Employee Work Targets (EWT). &nbsp

Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations

There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba--Takagi--Takenouchi and another way is the 10-elimination approach due to Mada--Idzumi--Tokihiro. In this paper, we describe precisely interrelations between these two approaches.Comment: 16 pages, final version, minor revisio

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page