The locating-chromatic number of a graph combines two graph concepts, namely coloring vertices and partition dimension of a graph. The locating-chromatic number is the smallest k such that G has a locating k-coloring, denoted by ${\chi }_L\left(G\right)$. This article proposes a procedure for obtaining a locating-chromatic number for an origami graph and its subdivision (one vertex on an outer edge) through two theorems with proofs.

Optimasi merupakan proses untuk mendapatkan nilai minimum atau maksimum dari sebuah fungsi, peluang, atau pencarian nilai lainnya dalam berbagai kasus. Salah satu masalah yang melibatkan proses optimasi yaitu Travelling Salesman Problem (TSP). Studi kasus pada TSP yang diteliti oleh penulis adalah terkait pendistribusian barang yang dilakukan oleh PT.Pos Indonesia di Kota Bandar Lampung. Kantor Pos Bandar Lampung sering mengalami beberapa permasalahan antara lain keterlambatan pengiriman barang, kurang puasnya pelayanan kantor pos, rute pendistribusian barang yang rumit dan lain-lain. Penyelesaian masalah TSP seperti diatas dapat diselesaikan dengan metode Algoritma Genetika. Algoritma Genetika merupakan algoritma pencarian yang didasarkan atas mekanisme seleksi alami dan evolusi biologis. Proses pencarian solusi terbaik menggunakan Algoritma Genetika dilakukan pengujian sebanyak 10 kali dengan ukpop = 30, maxgen = 100, pc = 0,95, pm = 0,01 dan operator genetika menggunakan order crossover dan inversion mutationdiperoleh hasil terbaik pada pengujian ke-8 dengan nilai fitness = 0,015032531, dengan panjang sirkuit terbaik 66,52239581 km.

This study aims to detect chicken meat contamination in beef sausage products distributed in Bandar Lampung City, Lampung Province. The selection of chicken and beef for this research is based on economic factors, as the higher price of beef compared to chicken drives the adulteration of meat products. The sausage fat was obtained using the Soxhlet extraction method with n-hexane solvent. Subsequently, the sausage fat extract was analyzed using FTIR (Fourier Transform Infrared) spectrophotometry to obtain infrared spectral data. This data was then analyzed using chemometric methods PCA (Principal Component Analysis) and PLS (Partial Least Squares). The PCA analysis results indicated that commercial sausages (AP, BP, CP, DP, and EP) and pure beef sausages showed closely clustered samples, suggesting similar physical and chemical properties with pure beef sausages. The PLS calibration set analysis yielded a model with a coefficient of determination (R2) value of 0.970409 and a root mean square error of calibration (RMSEC) parameter value of 0.09%, while the PLS validation set analysis produced a model with a coefficient of determination (R2) value of 0.963486 and a root mean square error of prediction (RMSEP) parameter value of 0.13%. Based on the PLS model predictions, it was determined that the percentage of chicken meat mixed in beef sausages circulating in the market ranged from 0.0281% to 0.1106%. This indicates a small but notable adulteration in beef sausages with chicken meat.

We study the dynamics of a two dimensional map which is derived from another two dimensional map by re-parametrizing the parameter in the system. It is shown that some of the properties of the original map can be preserved by the choice of the re-parametrization. By means of performing stability analysis to the critical points, and also studying the level set of the integrals, we study the dynamics of the re-parametrized map. Furthermore, we present preliminary results on the existence of a set where iteration starts at a point in that set, in which it will go off to infinity after finite step.

Cryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms. In particular, the Arnold’s cat and the sine-Gordon linear maps can be used in cryptographic algorithms for encoding digital images. In this article, a two-dimensional linear mKdV map derived from an ordinary difference mKdV equation will be used in a cryptographic encoding algorithm. The proposed encoding algorithm will be compared with those generated using sine-Gordon and Arnold’s cat maps via the correlations between adjacent pixels in the encrypted image and the uniformity of the pixel distribution. Note that the mKdV map is derived from the partial discrete mKdV equation with Consistency Around the Cube (CAC) properties, whereas the sine-Gordon map is derived from the partial discrete sine-Gordon equation, which does not have CAC properties.

A BN-algebra is a non-empty set $X$ with a binary operation “$\ast$” and a constant 0 that satisfies the following axioms: $\left(B1\right) x\ast x=0,$ $\left(B2\right) x\ast 0=x,$ and $\left(BN\right) \left(x\ast y\right)\ast z=\left(0\ast z\right)\ast \left(y\ast x\right)$ for all $x, y, z \in X$. A non-empty subset $I$ of $X$ is called an ideal in BN-algebra X if it satisfies $0\in X$ and if $y\in I$ and $x\ast y\in I$, then $x\in I$ for all $x,y\in X$. In this paper, we define several new ideal types in BN-algebras, namely, r-ideal, k-ideal, and m-k-ideal. Furthermore, some of their properties are constructed. Then, the relationships between ideals in BN-algebra with r-ideal, k-ideal, and m-k-ideal properties are investigated. Finally, the concept of r-ideal homomorphisms is discussed in BN-algebra.