Route Optimization of the Towns of Pampanga Using Hamiltonian Path

Kristian Paul A. Trasga and Ivy Gay O. Salvador

Travelling is one of the hottest activities today. Everyone, especially the youth, loves to travel and explore various places. The objective of the study is to determine Hamiltonian paths around the towns of Pampanga and to formulate a path that minimizes the travel distance, fare and time through iterations.
The researcher used descriptive expository type of research in this study. The descriptive part was used to analyze the graph made on the map of Pampanga while expository part was used to apply the Hamiltonian path in determining the optimized solution in terms of distance, fare and time. This study produced optimum solutions which consist of 20 different minimized paths in terms of distance, fare and time, traversing all the towns of Pampanga with different starting town. The optimized route obtained in terms of distance from Porac to Masantol is 300.5 km. In terms of fare, from Apalit to Masantol is 437 pesos and the time from Angeles to Masantol is 484 min. Based on the results drawn, the researcher recommends this study to others researchers who would like to find and explore other provinces in the country using Hamiltonian path. Other researchers may also find a program to generate the optimized routes.

A Proposed Algorithm and Program in Representing a Number as a Sum of Least Possible Square

John Kenneth T. Simbulan and Jocell D. Calma

The main objective of the study was to develop an algorithm and program in representing a number as a sum of least possible squares. Specifically it sought to explain how the proposed algorithm was developed, to demonstrate the algorithm and program, and to describe the evaluation of the respondents in using the proposed algorithm and program in terms of completeness, clarity and correctness. This descriptive research was conducted at the College of Arts and Sciences of Pampanga state Agricultural University. The evaluators of the study were faculty members of the Department of Sciences- Mathematics and Physics. The proposed algorithm and program were developed by Studying the characteristics of the natural numbers when they are represented by two squares, three squares and four squares. The proposed algorithm was demonstrated in four steps and it was programmed using the Visual Studio C# Software. The respondents evaluated the proposed algorithm and program and the procedure using a five-point scale. In terms of completeness, correctness and clarity, the evaluators gave a rating of an excellent. Based on the findings of the study, the researcher recommends that future researchers could develop another algorithm in representing any number as a sum of least possible squares. In addition, students and teachers may use the study as reference in studying and teaching number theory, particularly in sum of squares.

Designs of Music Chords Through Cayley Graphs

Regine B. Publico and Aiza D. Villavicencio

The main objective of this study was to create permutation out of music chords, construct graphs and produce sounds/melody from the permutation of each major chords. The researcher used descriptive-explanatory type or research. The study was done by observing the construction of different major chords, and trying to produce the permutation using symmetric group of 3 for the construct ion of Cayley graphs and applying the touched of music by creating melody out of the permutation of each major chords. Finding of the Study showed that the permutation of S_3 can be generated by the composition of major chords notes. Then, the generators of the permutation of S_n were used to construct a Cayley graphs. Permutations were then arranged by the use of notes concept to form or create sounds/melody. Based on the findings and conclusion, the researcher recommends to the future researchers to use the different minor chords to as an object where symmetric group can be formed, using the other way in creating melody presentation or by extracting mathematical concepts from the sounds created.

Proposed Algorithms and Program in Transformation

Reuel A. Pomarca and Jessie H. Licup

The main objectives of this study were to generalize algorithms and create a program of the proposed algorithms. The specific objectives of the proposed algorithms were center of rotation, center of dilation, the image under Glide reflection, and the image under Glide dilation. The study used descriptive expository type of research. The descriptive part is consisted of the evaluation of the respondents of proposed algorithms and program by its completeness, clarity and correctness. The expository part of the research is the development and demonstration of the proposed algorithms and program. As the conclusion, the researcher created 4 algorithms in different transformations, and also generalized them into formulas. The proposed algorithms were developed by the used underlying concepts of geometry and the program developed by using Visual studio as software. As the recommendation, the other researcher may use other programming software that can create a visual illustration of the transformation.

Characterizing Heavy Rainfall Events in Pampanga

Catherene B. Lopez and Alvin M. Supan

The main objective of this study was to characterize the heavy rainfall events in Pampanga from 1976-2005. It aimed to identify the grid/s that frequently experience the incidences of heavy rainfall. Also, aimed to analyze the month/s do the heavy rainfall occur in Pampanga and to determine the significant differences of the three (3) decade/periods. This study provide additional knowledge and awareness to the members of the community regarding heavy rainfall, and as a guide to improve the agriculture production as well as the livelihood of the people in Pampanga. This study was conducted at the Regional Climate System (RCS) in Manila Observatory, Quezon city where the dataset from Aphrodite of daily rainfall from 1976-2005 were taken. It was calculated on the different grid points of Pampanga using the latitude, longitude and threshold of rainfall. The number or count of events above the heavy and extreme thresholds, the 90th percentile refer as heavy while 95th percentile, referred as extreme events. Based on the results, there were three months, July, August,

Understanding Climate Variability in Pampanga

Jovith E. Herbas and Ivy Gay O. Salvador

The main objective of this study was to analyse and describe the climate variability in Pampanga. The researcher aims to increase the awareness of the people of Pampanga about this issue as its extremes have something to do with the primary source of livelihood. The researcher used descriptive and inferential methods of research. Results of the study showed that there were variations and changes in seasonal, annual and decadal bases. The researcher found out that the results in rainfall satisfy the Modified Coronas Classification wherein Pampanga belongs to climate type 1. Climate type 1 states that the dry season is occurring from November to February and wet season on the rest of the months. Temperature results showed that the temperature in Pampanga is influenced by northeast monsoon from November to February. It can be observed on the result that the mentioned months earlier have colder temperature, than the rest of the year. Moreover, temperature, rainfall and time have no significant relationship as tested. Hence, rainfall and temperature cannot be predicted by time. Also, rainfall is not a significant predictor of temperature and vice versa. Based on the results of the study, the researcher recommends that the future researchers may analyze the climate variability in other localities and may analyze the effects of extremes to the source of livelihood of the people of Pampanga.

Spatial and Temporal Analysis of Meteorological drought Events in Pampanga

Jevelson S. Bambico and Aldrin P. Mendoza

Drought is one of the most damaging environmental phenomena. In general, drought is the lack of precipitation over a period of time. The main objective of the study was to analyze drought event more particular meteorological drought in Pampanga using spatial and temporal analysis. The researcher aimed to locate where and when the drought events particularly occurred to help the community, especially the agriculture sector of Pampanga in developing a contingency plan in case of drought phenomenon. The researcher, use descriptive method of research. Two different statistical tools were employed in identifying and classifying droughts namely: a.) Standardized Precipitation Index (SPI) and b.) PAGASA drought classification. The results showed that there were identified droughts in the different grids of Pampanga. The heat map of SPI and PAGASA showed different drought classification. For the SPI, the most prone in the in droughts is grid 120.625-14.875. Meanwhile, for PAGASA, the most prone in droughts are grid 120.625-15.125 and 120.875-15.125. For the recommendations, the future researchers may: a. study the impact of droughts in the respective regions or province, b. locate specific towns were droughts happen and c. predict the future drought events.

Evaluation of the Performance of Cordex-Sea Regional Climate Models in Simulating the Climate of Pampanga

Marie Fe G. Gomez and Lenie G. Magat

The main objective of this study is to evaluate the performance of RCMs from Coordinated Regional Climate Downscaling Experiment program – Southeast Asia (CORDEX-SEA) to simulate the temperature and rainfall over Pampanga. The output from four RCMs came from one Global Climate Models (GCM) which is the CMIP5 data. The RCMs are evaluated against observed data from the APHRODITE. The evaluation was based on determining how well the RCMs reproduce climatological trends, probability distribution function, bar graph histogram, and boxplot of the temperature and rainfall. Statistical measures of model performance that include the median, minimum, maximum, mean, standard deviation, p-value and trend analysis were used. The conclusion of this study showed that in terms of temperature, generally, the RCMs failed to reproduce the annual temperature of Pampanga at 0.01 significant level. However, when the ANOVA test was done for the data which were separated per quarter it was found out that for January – March, CNRM-CM5 is comparable with observed data. From April to June and July to September, CSIRO-Mk3.6 is comparable with observed data. From October to December, MPI-ESM-MR is comparable with observed data. In terms of precipitation, the RCM that best captures the annual observed data is CSIRO-Mk3.6. Based on the conclusion, the researcher recommends other researchers to use other sets of data to evaluate their respective regions or province.

Mathematical Modeling of the Production of PSAU Water Purifying Facility

Mar-Jay S. Antonio and Aldrin P. Mendoza

Mathematical modeling is the process of using various mathematical structures, such as graphs equations, diagrams, scatterplots, and tree diagram to represent real world situation (Annenberg Foundation, 2017). For instance, mathematical modeling may be employed in business production. With this, the researcher aimed to determine the optimum profit of PSAU Water Purifying Facility through mathematical modeling. The study, used descriptive-expository type of research in achieving and discussing the results in understandable and clearly way. The mathematical modeling of the production of PSAU water purifying facility aimed to solve the optimum solution based on the traditional solving and the objective function that maximizes the profit of the PSAU water purifying facility. The mathematical modeling of the production of PSAU Water Purifying Facility was completed through the use of Excel Solver and AMPL Program. Based on the results and conclusion the researcher would like to recommend to the future researcher to use another programming language to find the optimum solution. Also, future researcher May implement the model in the water facility of the PSAU to see if it is effective or not.