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

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

Max-plus analysis on some binary particle systems

We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.Comment: 24 pages, 5 figures, submitted to J. Phys.

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

Pendekatan Lean Six Sigma Guna Mengurangi Waste Pada Proses Produksi Genteng Dan Paving (Studi Kasus Di PT. Malang Indah)

PT. Malang Indah merupakan salah satu Perusahaan di kota Malang yang memproduksi bahan bangunan, misalnya genteng dan paving. Penelitian ini dilakukan untuk mengidentifikasi waste apa saja yang terjadi dan upaya apa yang dapat dilakukan untuk mengurangi waste tersebut. Penelitian ini menggunakan pendekatan konsep Lean Six Sigma untuk mengidentifikasi dan meminimasi waste. Dengan pendekatan Lean Six Sigma, diharapkan waste yang terjadi di PT.Malang Indah dapat berkurang tiap bulannya. Tahapan penelitian yang dilakukan mengikuti siklus DMAIC. Tool FMEA (Failure Mode and Effect Analysis) digunakan untuk menganalisa dan dicari kemungkinan kegagalan (failure) yang akan terjadi atau yang sudah terjadi. Berdasarkan failure yang ditemukan, usulan perbaikan disusun untuk mencegah kesalahan mengatasi kesalahan yang terjadi terutama akibat human error. Usulan perbaikan disusun menggunakan tool poka yoke, dimana tool ini dapat mengantisipasi kegagalan yang mungkin terjadi dan meningkatkan ketelitian karyawan dalam bekerja. Hasil penelitian ini menunjukan adanya 6 jenis waste yang terjadi pada proses produksi genteng royal yaitu Environmental, Health, and Safety (EHS), Defect, Overproduction, Waiting, Transportation, dan Excess Processing serta 5 jenis waste yang terjadi pada proses produksi paving kotak yaitu Environmental, Health, and Safety (EHS), Defect, Overproduction, Waiting, dan Excess Processing. Usulan perbaikan yang diajukan berupa pembuatan penahan dari kayu, penempelan peringatan berbentuk poster di dinding area proses pencetakan, prosedur penumpukan dan pengangkutan produk, alat perata cetakan berbentuk (T) terbuat dari kayu, dan SOP proses pencampuran paving kotak

Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs

We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its B\"acklund transformation and the two dimensional Toda molecule equation. The method we employ in the proof can be considered as fundamental to the integrability of ultradiscrete soliton equations.Comment: 14 pages, 10 figures Added citations in v