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All Journal Jurnal Pendidikan Indonesia Electronic Journal of Graph Theory and Applications (EJGTA) Indonesian Journal of Mathematics Education The Indonesian Journal of Social Studies InPrime: Indonesian Journal Of Pure And Applied Mathematics Journal of Fundamental Mathematics and Applications (JFMA) Indonesian Journal Of Educational Research and Review

Leomarich F Casinillo

Visayas State University

Author-ID : 2384407

Humanities Computer Science & IT Decision Sciences, Operations Research & Management Education Electrical & Electronics Engineering Mathematics Social Sciences Other

Published : 14 Documents Claim Missing Document

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Articles

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A note on Fibonacci and Lucas number of domination in path Leomarich F Casinillo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.2.11

Let G = (V(G), E(G)) be a path of order n ≥ 1. Let fm(G) be a path with m ≥ 0 independent dominating vertices which follows a Fibonacci string of binary numbers where 1 is the dominating vertex. A set F(G) contains all possible fm(G), m ≥ 0, having the cardinality of the Fibonacci number Fn + 2. Let Fd(G) be a set of fm(G) where m = i(G) and Fdmax(G) be a set of paths with maximum independent dominating vertices. Let lm(G) be a path with m ≥ 0 independent dominating vertices which follows a Lucas string of binary numbers where 1 is the dominating vertex. A set L(G) contains all possible lm(G), m ≥ 0, having the cardinality of the Lucas number Ln. Let Ld(G) be a set of lm(G) where m = i(G) and Ldmax(G) be a set of paths with maximum independent dominating vertices. This paper determines the number of possible elements in the sets Fd(G), Ld(G), Fdmax(G) and Ldmax(G) by constructing a combinatorial formula. Furthermore, we examine some properties of F(G) and L(G) and give some important results.

Some New Notes on Mersenne Primes and Perfect Numbers Leomarich F Casinillo
Indonesian Journal of Mathematics Education Vol 3, No 1 (2020): Indonesian Journal of Mathematics Education
Publisher : Universitas Tidar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31002/ijome.v3i1.2282

Mersenne primes are specific type of prime numbers that can be derived using the formula , where is a prime number. A perfect number is a positive integer of the form where is prime and is a Mersenne prime, and that can be written as the sum of its proper divisor, that is, a number that is half the sum of all of its positive divisor. In this note, some concepts relating to Mersenne primes and perfect numbers were revisited. Further, Mersenne primes and perfect numbers were evaluated using triangular numbers. This note also discussed how to partition perfect numbers into odd cubes for odd prime . Also, the formula that partition perfect numbers in terms of its proper divisors were constructed and determine the number of primes in the partition and discuss some concepts. The results of this study is useful to better understand the mathematical structure of Mersenne primes and perfect numbers.

A Note on Full and Complete Binary Planar Graphs Emily L Casinillo; Leomarich F Casinillo
Indonesian Journal of Mathematics Education Vol 3, No 2 (2020): Indonesian Journal of Mathematics Education
Publisher : Universitas Tidar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31002/ijome.v3i2.2800

Let G=(V(G), E(G)) be a connected graph where V(G) is a finite nonempty set called vertex-set of G, and E(G) is a set of unordered pairs {u, v} of distinct elements from V(G) called the edge-set of G. If is a connected acyclic graph or a connected graph with no cycles, then it is called a tree graph. A binary tree Tl with l levels is complete if all levels except possibly the last are completely full, and the last level has all its nodes to the left side. If we form a path on each level of a full and complete binary tree, then the graph is now called full and complete binary planar graph and it is denoted as Bn, where n is the level of the graph. This paper introduced a new planar graph which is derived from binary tree graphs. In addition, a combinatorial formula for counting its vertices, faces, and edges that depends on the level of the graph was developed.

Knowledge Acquisition Practices and Reading Comprehension Skills of the Learners in Hilongos South District, Leyte Division, Philippines Ginna F Tavera; Leomarich F Casinillo
Jurnal Pendidikan Indonesia Vol 9 No 3 (2020)
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat

The main purpose of this study was to determine the knowledge acquisition practices and reading comprehension of the learners in Hilongos South District, Leyte Division, Philippines. This study adopted the descriptive-survey and correlational method of research. This method tried to explore and describe the prevailing knowledge acquisition practices obtained in a particular place or situation; the reading level of the learners in terms of prior knowledge and vocabulary, and their reading comprehension as well as the extent of relationship among the variables was portrayed. The analysis and interpretation of the data led to the following findings: the knowledge acquisition practices of learners, teachers and parents were all very satisfactory, the learners had satisfactory prior knowledge and very satisfactory vocabulary level, the reading comprehension of the learner-respondents was very satisfactory. Furthermore, there were significant relationships between knowledge acquisition practices of learners and their prior knowledge, vocabulary and knowledge acquisition practices of teachers versus vocabulary level of the learners. There were also significant relationships between prior knowledge and vocabulary to the reading comprehension of the learners.

On Characterizing School Leaders: Evidence from Hindang District, Leyte Division, Philippines Leomarich F Casinillo; Michael G Suarez
Jurnal Pendidikan Indonesia Vol 10 No 2 (2021)
Publisher : Lembaga Penelitian dan Pengabdian kepada Masyarakat

This study was conducted to characterize school leaders at Hindang District, Leyte Division, Philippines. By complete enumeration, the study considered all active elementary teachers at Hindang District. Primary data was collected through a developed structured questionnaire in regards to the various characteristics of a school leader which serves as an independent variable of the study. On the other hand, secondary data was collected at Department of Education regarding the elementary school classifications at Hindang District as follows: good, better and outstanding. With the aid of ordered logit models, the study highlighted some influencing factors of school classification governed by school leaders. Results showed that on the average, elementary schools in Hindang District are considered to be “better” based on the DepEd classification. This implies that these schools have a room for improvement with the help of an effective school leaders. Based on the constructed ordered logit models, it is shown that a personal attribute of a school leader has an inverse effect in outstanding school classification. In addition, it is revealed that result-focus, teamwork and people development were significant factors in achieving an outstanding performance in school. Hence, a leader must be a results driven that has the ability to create momentum based on their ultimate goal. Furthermore, school leaders must set clear directions, establish expectations since they are in a position to shape the goals, direction and structure of schools.

Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs Leomarich F Casinillo; Leo A Mamolo
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v2i2.15845

AbstractThis paper developed a simple but elegant formula for the series of consecutive square of natural numbers under alternating signs. Furthermore, this study investigated the said formula under odd and even number of terms and discuss some important results.Keywords: consecutive -squares; alternating signs; odd and even terms. AbstrakDalam paper ini kita membangun formula yang sederhana namun elegan untuk menghitung jumlah deret berganti-tanda dari kuadrat bilangan-bilangan asli berurutan. Kita akan menyelidiki formula untuk kasus banyaknya suku ganjil maupun genap dan mendiskusikan beberapa hasil yang penting.Kata kunci: -kuadrat berurutan; berganti-tanda; bersuku ganjil dan bersuku genap.

On Triangular Secure Domination Number Emily L Casinillo; Leomarich F Casinillo; Jorge S Valenzona; Divina L Valenzona
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v2i2.15996

Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m). A dominating set T of V(T_m) is a secure dominating set of T_m if for each u ϵ V(T_m)\T, there exists v ϵ T such that uv ϵ E(T_m) and the set (T\{u})ꓴ{v} is a dominating set of T_m. The minimum cardinality of a secure dominating set of T_m, denoted by γ_s(T_m) is called a secure domination number of graph T_m. A secure dominating number γ_s(T_m) of graph T_m is a triangular secure domination number if γ_s(T_m) is a triangular number. In this paper, a combinatorial formula for triangular secure domination number of graph T_m was constructed. Furthermore, the said number was evaluated in relation to perfect numbers.

Econometric Evidence on Self-Determination Theory in Learning Calculus Among Agribusiness Students Leomarich F Casinillo; Emily L Casinillo
The Indonesian Journal of Social Studies Vol 3 No 1 (2020): July
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/ijss.v3n1.p1-12

Self-determination theory is a study of individual interest and motivation which plays a vital role in good and productive performance in learning. This study focus on the agribusiness students motivation in learning Calculus as part of their curriculum. Using econometric models, this study identified some statistically significant factors of motivation. The study employed 121 agribusiness students as respondents using stratified random sampling in the first semester of SY 2019-2020. Results revealed that most of the agribusiness students are motivated in learning calculus. Female student is more likely motivated compared to male students. Females are more focusing on their studies while males are affected by online games. The study revealed that learning attitude and health are significant factors of motivation in learning. Also, students experience in calculus makes them creative in the classroom which positively contributes to their interest. Perhaps, this students makes or invents new ideas in the learning environment. Results documented that problems encountered in the classroom does not affects their interest in learning. Furthermore, results showed that their perception to their calculus teacher is relatively high which is a significant factor to their motivation. In fact, their teachers are the most important factor that contributes to their level of achievement in Calculus, more important than any other school resources.

NEW COUNTING FORMULA FOR DOMINATING SETS IN PATH AND CYCLE GRAPHS Leomarich F Casinillo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020)
Publisher : Diponegoro University

Let G=(V(G), E(G)) be a path or cycle graph. A subset D of V(G) is a dominating set of G if for every u element of V(G)\D, there exists v element of D such that uv element of E(G), that is, N[D]=V(G). The domination number of G, denoted by gamma(G), is the smallest cardinality of a dominating set of G. A set D_1 subset of V(G) is a set containing dominating vertices of degree 2, that is, each vertex is internally stable. A set D_2 subset of V(G) is a set containing dominating vertices where one of the element say a element of D_2, and the rest are of degree 2. A set D_3 subset of V(G) is a set containing dominating vertices in which two of the elements say b, c element of D_3, deg(b)=deg(c)=1. This paper developed a new combinatorial formula that determines the number of ways of putting a dominating set in a path and cycle graphs of order n>=1 and n>=3, respectively. Further, a combinatorial function P^1_G(n), P^2_G(n) and P^3_G(n) that determines the probability of getting the set D_1, D_2, and D_3, respectively in graph G of order n were constructed.

A SHORT NOTE ON FIBONACCI NUMBERS IN A GENERALIZED PYTHAGOREAN TRIPLES Emily L Casinillo; Leomarich F Casinillo
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 1 (2021)
Publisher : Diponegoro University

This paper aims to construct a new formula that generates a Fibonacci numbers in a generalized Pythagorean triples. In addition, the paper formulates some Fibonacci identities and discuss some important findings.

Co-Authors Divina L Valenzona Emily L Casinillo Ginna F Tavera Jorge S Valenzona Leizl F Abrantes Leo A Mamolo Michael G Suarez

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