Collatz conjecture or 3N+1 problem by Lothar Collatz can be described as follows: For any positive integer N, a subsequent term is obtained from the previous term as follows: if N is even, the next term is one half of the previous term, but if the previous term is odd, then the next term is multiplied by 3 and added to 1. Repeat this process to the result over and over again. The conjecture is that no matter the positive integer N, the sequence will always reach 1. This paper attempts to present a new approach known as the “Unitary Series” approach, it is an approach that proves Collatz conjecture to be true. The key idea of this new approach focuses on the infinite loop (1, 4, 2) generated by any positive integer N if it indeed obeys Collatz algorithm and thus reducible to 1. This proof of Collatz algorithm for the problem is proposed and numerical example is given to show its feasibility. With this new approach, the proof of the conjecture is given.
Keyword: Collatz, 3n+1, conjecture, series, unitary.

The research paper seeks to distinguish how applications of artificial intelligence were utilized during the outbreak of the Coronavirus.  Where the facts proved to the conditions of acceleration and facilitation to which these applications contributed, especially in terms of data and information analysis, and to draw accurate results. A tremendous amount of information directly related to the Coronavirus, in addition to the largest amount of information related to diseases close to it, as it provides an effective reading based on comparison and inventory. It has been called the applications of artificial intelligence and machine learning, in reducing the element of time, whether in terms of discovering the genetic strain of the virus or at the level of vaccine manufacture. While these applications have proven their utmost benefit in monitoring the movement of the epidemic and limiting the speed of its spread.

Since Bruntland Comission report established the concept of sustainable development , the manufacturing and mine industry have been in effort to obtain and extend their planning in implementing sustainable manufacturing for them to meet the sustainable management criterion laid down by  ISO 14000 series standards. These criterion have been explained and established to determine and evaluate the key performance indicators for manufacturing flow. The aim of this paper is to examine a case study in order to understand manufacturing procedure stages  of steel industry in the context of its sustainable practices.  Energy analysis and natural minerals such as Iron ore have been shown as main key performances for this paper.

Research with the title Analysis of Associative Meaning in the novel not Cinta Cinderella by Ussy Sulistiawati and Andika Pratama offers to describe the types of associative meanings. This type of research used in this research is descriptive qualitative. The data in this study consisted of words, phrases and sentences that contained associative meaning in the Novel not Cinta Cinderella. The data source is in the form of character dialogue including the introduction to the text. This study uses three studies, namely research on the provision of data, data analysis, and analysis of results.