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Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
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- Color symmetry (3)
- Middle graph (3)
- Set coloring (3)
- Sigma coloring (3)
- Zero-suppressed binary decision diagram (3)
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- Aperiodic tilings (2)
- Enumeration algorithm (2)
- HOTS (2)
- Higher-Order Thinking Skills (2)
- Mathematical app (2)
- Mobile Learning (2)
- Mobile Technology in Teaching Mathematics (2)
- Mobile technology (2)
- Numeracy Apps (2)
- STEM (2)
- Subgraph optimization (2)
- Tilings (2)
- Vertex coloring (2)
- : k-magic graphs (1)
- Absolute Mα-integrable (1)
- Abstract regular polyhedra (1)
- Annual frequency (1)
- Application (1)
- Assessment (1)
- Baire class one function (1)
- Blended learning (1)
- Cauchy extension (1)
- Chromatic number (1)
- Cognitive load scale (1)
- Color fixing groups; colored symmetrical tilings; symmetry groups of nanotubes (1)
Articles 1 - 30 of 65
Full-Text Articles in Physical Sciences and Mathematics
Cognitive Load Scale In Learning Formal Definition Of Limit: A Rasch Model Approach, Rina Oktaviyanthi, Ria Noviana Agus, Mark Lester B. Garcia, Kornkanok Lertdechapat
Cognitive Load Scale In Learning Formal Definition Of Limit: A Rasch Model Approach, Rina Oktaviyanthi, Ria Noviana Agus, Mark Lester B. Garcia, Kornkanok Lertdechapat
Mathematics Faculty Publications
Constructing proofs for the limit using the formal definition induces a high cognitive load. Common assessment tools, like cognitive load scales, lack specificity for the concept of limits. This research aims to validate an instrument tailored to assess cognitive load in students focused on the formal definition of limits, addressing the need for diverse strategies in education. The research employs a quantitative survey design with a Rasch model approach, utilizing a data collection instrument in the form of a questionnaire. Subsequently, the data are analyzed by focusing on three aspects: (1) item fit to the Rasch model, (2) unidimensionality, and …
The Set Chromatic Numbers Of The Middle Graph Of Tree Families, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio
The Set Chromatic Numbers Of The Middle Graph Of Tree Families, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio
Mathematics Faculty Publications
The neighborhood color set of each vertex v in a vertex-colored graph G is defined as the collection of the colors of all the neighbors of v. If there are no two adjacent vertices that have equal neighborhood color sets, then the coloring is called a set coloring of G. The set coloring problem on G refers to the problem of determining its set chromatic number, which refers to the fewest colors using which a set coloring of G may be constructed. In this work, we consider the set coloring problem on graphs obtained from applying middle graph, a unary …
Economic Losses From Covid-19 Cases In The Philippines: A Dynamic Model Of Health And Economic Policy Trade-Offs, Elvira P. De Lara-Tuprio, Ma. Regina Justina E. Estuar, Joselito T. Sescon, Cymon Kayle Lubangco, Rolly Czar Joseph T. Castillo, Timothy Robin Y. Teng, Lenard Paulo V. Tamayo, Jay Michael R. Macalalag, Gerome M. Vedeja
Economic Losses From Covid-19 Cases In The Philippines: A Dynamic Model Of Health And Economic Policy Trade-Offs, Elvira P. De Lara-Tuprio, Ma. Regina Justina E. Estuar, Joselito T. Sescon, Cymon Kayle Lubangco, Rolly Czar Joseph T. Castillo, Timothy Robin Y. Teng, Lenard Paulo V. Tamayo, Jay Michael R. Macalalag, Gerome M. Vedeja
Mathematics Faculty Publications
The COVID-19 pandemic forced governments globally to impose lockdown measures and mobility restrictions to curb the transmission of the virus. As economies slowly reopen, governments face a trade-off between implementing economic recovery and health policy measures to control the spread of the virus and to ensure it will not overwhelm the health system. We developed a mathematical model that measures the economic losses due to the spread of the disease and due to different lockdown policies. This is done by extending the subnational SEIR model to include two differential equations that capture economic losses due to COVID-19 infection and due …
Recursive Linear Bounds For The Vertex Chromatic Number Of The Pancake Graph, Aldrich Ellis C. Asuncion, Renzo Roel P. Tan, Christian Chan Shio, Kazushi Ikeda
Recursive Linear Bounds For The Vertex Chromatic Number Of The Pancake Graph, Aldrich Ellis C. Asuncion, Renzo Roel P. Tan, Christian Chan Shio, Kazushi Ikeda
Mathematics Faculty Publications
The pancake graph has been the subject of research. While studies on the various aspects of the graph are abundant, results on the chromatic properties may be further enhanced. Revolving around such context, the paper advances an alternative method to produce novel linear bounds for the vertex chromatic number of the pancake graph. The accompanying demonstration takes advantage of symmetries inherent to the graph, capturing the prefix reversal of subsequences through a homomorphism. Contained within the argument is the incorporation of known vertex chromatic numbers for certain orders of pancake graphs, rendering tighter bounds possible upon the release of new …
The Relative Isolation Probability Of A Vertex In A Multiple-Source Edge-Weighted Graph, Renzo Roel P. Tan, Kyle Stephen S. See, Jun Kawahara, Kazushi Ikeda, Richard De Jesus, Lessandro Estelito Garciano, Agnes Garciano
The Relative Isolation Probability Of A Vertex In A Multiple-Source Edge-Weighted Graph, Renzo Roel P. Tan, Kyle Stephen S. See, Jun Kawahara, Kazushi Ikeda, Richard De Jesus, Lessandro Estelito Garciano, Agnes Garciano
Mathematics Faculty Publications
Various measures that characterize graphs exist in literature. Insights into the properties of a graph as a whole and its components are revealed largely through graph measures, also called graph metrics. In seeking to interpret a consequential edge metric from a vertex-centric perspective, the paper advances an original measure – the relative isolation probability of a vertex. Concisely, the probability of relative isolation pertains to the likelihood of a vertex to be disconnected from all designated source vertices in a graph with probability-weighted edges. A two-step algorithm for efficient calculation is presented and evaluated. Contained within the procedure is a …
On The Frequency Module Of The Hull Of A Primitive Substitution Tiling, April Lynne D. Say-Awen, Dirk Frettlöh, Ma. Louise Antonette N. De Las Peñas
On The Frequency Module Of The Hull Of A Primitive Substitution Tiling, April Lynne D. Say-Awen, Dirk Frettlöh, Ma. Louise Antonette N. De Las Peñas
Mathematics Faculty Publications
Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal -module, where is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a …
On Twin Edge Colorings In M-Ary Trees, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino
On Twin Edge Colorings In M-Ary Trees, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino
Mathematics Faculty Publications
Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤk and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤk) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by χ′t(G …
Deployment Of Mathematical Resources To A Philippine High School Through A Community Lte Network, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Verzosa
Deployment Of Mathematical Resources To A Philippine High School Through A Community Lte Network, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Verzosa
Mathematics Faculty Publications
In the Philippines, one challenge that continues to be faced by the Department of Education in bringing educational content in a blended learning modality is the lack of internet access of the learners. This paper discusses the distribution, through a community LTE network, of mathematical resources for Grades 7 to 10 to teachers and students of a particular high school in the Philippines. It also gives details on particular technological tools (mathematical applications) that were created to help the mathematical learning of students in a remote setting.
Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino
Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino
Mathematics Faculty Publications
Lack of procedural fluency in fractions impedes access to advanced mathematical courses and limits opportunities for entry into STEM-related fields. This paper describes the design and pedagogical basis of the Moving Fractions app and supplementary fraction videos for promoting fraction learning. Moving Fractions utilizes game-design factors to draw students through a trajectory of fraction learning from part-whole comparisons to a more robust understanding of the measurement concept of fractions. The supplementary video immerses students in a broad range of fraction representations. The app and video are intended to form a fraction learning package for distribution in Philippine schools. Future work …
On The Total Set Chromatic Number Of Graphs, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz
On The Total Set Chromatic Number Of Graphs, Mark Anthony C. Tolentino, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz
Mathematics Faculty Publications
Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets. The set chromatic number χs(G) of a graph G is the minimum number of colors required in a set coloring of G. In this work, we investigate a total analog of set colorings, that is, we study set colorings of the total graph of graphs. Given a graph G = (V; E); its total graph …
Sigma Chromatic Numbers Of The Middle Graph Of Some Families Of Graphs, Jay-R Manamtam, Agnes Garciano, Mark Anthony C. Tolentino
Sigma Chromatic Numbers Of The Middle Graph Of Some Families Of Graphs, Jay-R Manamtam, Agnes Garciano, Mark Anthony C. Tolentino
Mathematics Faculty Publications
Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be …
The Set Chromatic Numbers Of The Middle Graph Of Graphs, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
The Set Chromatic Numbers Of The Middle Graph Of Graphs, Gerone Russel J. Eugenio, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Mathematics Faculty Publications
For a simple connected graph G; let c : V (G) → N be a vertex coloring of G; where adjacent vertices may be colored the same. The neighborhood color set of a vertex v; denoted by NC(v); is the set of colors of the neighbors of v. The coloring c is called a set coloring provided that NC(u) neq NC(v) for every pair of adjacent vertices u and v of G. The minimum number of colors needed for a set coloring of G is referred to as the set chromatic number of G and is denoted by χ_s(G). In …
On The Sigma Value And Sigma Range Of The Join Of A Finite Number Of Even Cycles Of The Same Order, Marie Cris A. Bulay-Og, Agnes Garciano, Reginaldo M. Marcelo
On The Sigma Value And Sigma Range Of The Join Of A Finite Number Of Even Cycles Of The Same Order, Marie Cris A. Bulay-Og, Agnes Garciano, Reginaldo M. Marcelo
Mathematics Faculty Publications
Let c be a vertex coloring of a simple; connected graph G that uses positive integers for colors. For a vertex v of G; the color sum of v is the sum of the colors of the neighbors of v. If no two adjacent vertices of G have the same color sum; then c is called a sigma coloring of G. The sigma chromatic number of G is the minimum number of colors required in a sigma coloring of G. Let max(c) be the largest color assigned to a vertex of G by a coloring c. The sigma value of …
On The Sigma Chromatic Number Of The Zero-Divisor Graphs Of The Ring Of Integers Modulo N, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
On The Sigma Chromatic Number Of The Zero-Divisor Graphs Of The Ring Of Integers Modulo N, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Mathematics Faculty Publications
The zero-divisor graph of a commutative ring R with unity is the graph Γ(R) whose vertex set is the set of nonzero zero divisors of R; where two vertices are adjacent if and only if their product in R is zero. A vertex coloring c : V (G) → Bbb N of a non-trivial connected graph G is called a sigma coloring if σ(u) = σ(ν) for any pair of adjacent vertices u and v. Here; σ(χ) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G; denoted by σ(G); is defined …
Development Of A Gamified Number Line App For Teaching Estimation And Number Sense In Grades 1 To 7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino
Development Of A Gamified Number Line App For Teaching Estimation And Number Sense In Grades 1 To 7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino
Mathematics Faculty Publications
Fraction knowledge is known to be a gatekeeper to more advanced mathematical learning. On the basis of the literature on early number learning, a number line mobile application called Catch the Carrot was designed to develop students’ knowledge of whole number and fraction magnitude. This paper aims to describe the design of the Catch the Carrot app and discusses the rationale for using number lines as representational scaffolds for developing children’s understanding of numbers, particularly their estimation and number sense skills. The gamification features of the app, as well as strategies for integration in a classroom are also presented. This …
Tilings With Congruent Edge Coronae, Ma. Louise Antonette N. De Las Peñas, Mark D. Tomenes
Tilings With Congruent Edge Coronae, Ma. Louise Antonette N. De Las Peñas, Mark D. Tomenes
Mathematics Faculty Publications
In this paper, we discuss properties of a normal tiling of the Euclidean plane with congruent edge coronae. We prove that the congruence of the first edge coronae is enough to say that the tiling is isotoxal.
Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola
Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola
Mathematics Faculty Publications
The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution; especially when application (app) design is based on sound pedagogical principles and gamification elements. However; an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison; and addition and subtraction. The integration of these apps in the …
Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola
Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola
Mathematics Faculty Publications
The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution, especially when application (app) design is based on sound pedagogical principles and gamification elements. However, an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison, and addition and subtraction. The integration of these apps in the …
Designing Performance Tasks In Mathematics Using Technological Tools, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Versoza, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino
Designing Performance Tasks In Mathematics Using Technological Tools, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Versoza, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino
Mathematics Faculty Publications
In the Philippines, the performance task is one of the major summative assessments in the K to 12 curriculum. This paper discusses how performance tasks may utilize mathematical apps within the context of blended learning. Guidelines on designing performance tasks; as well as the GRASPS framework; are discussed. Performance tasks that cut across various grade levels and strands of mathematics are presented. These involve divisibility (Numbers); integer and polynomial operations (Algebra); triangle centers (Geometry); and statistics (Statistics). The performance tasks described in this paper can provide an initial idea for the design of other summative assessments and contribute to the …
Sigma Coloring And Edge Deletions, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Sigma Coloring And Edge Deletions, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Mathematics Faculty Publications
A vertex coloring c : V(G) → N of a non-trivial graph G is called a sigma coloring if σ(u) is not equal to σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we consider the sigma chromatic number of graphs obtained by deleting one or more of its edges. In particular, we study the difference σ(G)−σ(G−e) …
Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola
Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola
Mathematics Faculty Publications
This paper reports on the Quick Images app, whose design framework is informed by research on ten-structured thinking and gamification principles. Inclusivity was also a major consideration, especially in the context of a developing country. Thus, the app was made freely available and required only moderate system requirements. Pilot studies revealed that the app has the potential to promote children’s ability to see two-digit numbers in relation to tens and ones, which is a major goal of elementary school mathematics. Collaborations with the Philippine Department of Education to ensure the app’s sustained use are also discussed.
Concerning A Decision-Diagram-Based Solution To The Generalized Directed Rural Postman Problem, Renzo Roel P. Tan, Jun Kawahara, Kazushi Ikeda, Agnes Garciano, Kyle Stephen S. See
Concerning A Decision-Diagram-Based Solution To The Generalized Directed Rural Postman Problem, Renzo Roel P. Tan, Jun Kawahara, Kazushi Ikeda, Agnes Garciano, Kyle Stephen S. See
Mathematics Faculty Publications
Decision-diagram-based solutions for discrete optimization have been persistently studied. Among these is the use of the zero-suppressed binary decision diagram, a compact graph-based representation for a specified family of sets. Such a diagram may work out combinatorial problems by efficient enumeration. In brief, an extension to the frontierbased search approach for zero-suppressed binary decision diagram construction is proposed. The modification allows for the inclusion of a class-determined constraint in formulation. Variations of the generalized directed rural postman problem, proven to be nondeterministic polynomial-time hard, are solved on some rapid transit systems as illustration. Lastly, results are juxtaposed against standard integer …
Underwater Gesture Recognition Using Classical Computer Vision And Deep Learning Techniques, Mygel Andrei M. Martija, Jakov Ivan S. Dumbrique, Prospero C. Naval Jr.
Underwater Gesture Recognition Using Classical Computer Vision And Deep Learning Techniques, Mygel Andrei M. Martija, Jakov Ivan S. Dumbrique, Prospero C. Naval Jr.
Mathematics Faculty Publications
Underwater Gesture Recognition is a challenging task since conditions which are normally not an issue in gesture recognition on land must be considered. Such issues include low visibility, low contrast, and unequal spectral propagation. In this work, we explore the underwater gesture recognition problem by taking on the recently released Cognitive Autonomous Diving Buddy Underwater Gestures dataset. The contributions of this paper are as follows: (1) Use traditional computer vision techniques along with classical machine learning to perform gesture recognition on the CADDY dataset; (2) Apply deep learning using a convolutional neural network to solve the same problem; (3) Perform …
Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas
Geometric Realizations Of Abstract Regular Polyhedra With Automorphism Group H3, Mark L. Loyola, Jonn Angel L. Aranas
Mathematics Faculty Publications
A geometric realization of an abstract polyhedron P is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Gamma. The method entails finding a real orthogonal representation of Gamma of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H3.
The Sigma Chromatic Number Of The Sierpinski Gasket Graphs And The Hanoi Graphs, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
The Sigma Chromatic Number Of The Sierpinski Gasket Graphs And The Hanoi Graphs, Agnes Garciano, Reginaldo M. Marcelo, Mari-Jo P. Ruiz, Mark Anthony C. Tolentino
Mathematics Faculty Publications
A vertex coloring c : V(G) → of a non-trivial connected graph G is called a sigma coloring if σ(u) ≠ σ(v) for any pair of adjacent vertices u and v. Here, σ(x) denotes the sum of the colors assigned to vertices adjacent to x. The sigma chromatic number of G, denoted by σ(G), is defined as the fewest number of colors needed to construct a sigma coloring of G. In this paper, we determine the sigma chromatic numbers of the …
The N-Integral, Abraham P. Racca, Emmanuel A. Cabral
The N-Integral, Abraham P. Racca, Emmanuel A. Cabral
Mathematics Faculty Publications
In this paper, we introduced a Henstock-type integral named $N$-integral of a real valued function $f$ on a closed and bounded interval $[a,b]$. The $N$-integrable functions lie entirely between Riemann integrable functions and Henstock integrable functions. It was shown that for a Henstock integrable function $f$ on $[a,b]$ the following are equivalent: \begin{enumerate} \item[$(1)$] The function $f$ is $N$-integrable; \item[$(2)$] There exists a null set $S$ for which given $\epsilon >0$ there exists a gauge $\delta$ such that for any $\delta$-fine partial division $D=\{(\xi,[u,v])\}$ of $[a,b]$ we have \[(\phi_S(D)\cap \Gamma_{\epsilon})\sum |f(v)-f(u)||v-u|<\epsilon\] where $\phi_S(D)=\{(\xi,[u,v])\in D:\xi \notin S\}$ and \[\Gamma_{\epsilon}=\{(\xi,[u,v]): |f(v)-f(u)|\geq \epsilon\}\] \end{enumerate} and \begin{enumerate} \item[$(3)$] The function $f$ is continuous almost everywhere. \end{enumerate} A characterization of continuous almost everywhere functions was also given.
Twin Chromatic Indices Of Some Graphs With Maximum Degree 3, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino
Twin Chromatic Indices Of Some Graphs With Maximum Degree 3, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino
Mathematics Faculty Publications
Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from k and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in k ) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by . In this paper, we determine the …
Sigma Chromatic Number Of Graph Coronas Involving Complete Graphs, Agnes Garciano, Maria Czarina T. Lagura, Reginaldo M. Marcelo
Sigma Chromatic Number Of Graph Coronas Involving Complete Graphs, Agnes Garciano, Maria Czarina T. Lagura, Reginaldo M. Marcelo
Mathematics Faculty Publications
Let c : V(G) → be a coloring of the vertices in a graph G. For a vertex u in G, the color sum of u, denoted by σ(u), is the sum of the colors of the neighbors of u. The coloring c is called a sigma coloring of G if σ(u) ≠ σ(v) whenever u and v are adjacent vertices in G. The minimum number of colors that can be used in a sigma coloring of G is called the sigma chromatic …
Designing Mobile Apps To Promote Numeracy And Statistical Reasoning, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Versoza
Designing Mobile Apps To Promote Numeracy And Statistical Reasoning, Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Versoza
Mathematics Faculty Publications
Developing countries typically do not perform well in international benchmarks of mathematics achievement. This may be partially explained by students’ immersion in classrooms characterized by superficial strategies or rote-learning methods. This paper reports on the design of mobile applications (apps) developed by the authors as part of an ongoing project funded by a national government agency and intended to promote structural thinking and statistical reasoning. It describes the general features of the apps, as well as the pedagogical principles upon which the apps’ designs were anchored on. These principles are grounded on research and established practices on number sense and …
On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino
On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino
Mathematics Faculty Publications
A vertex coloring c : V(G) → of a non-trivial connected graph G is called a set coloring if NC(u) ≠ NC(v) for any pair of adjacent vertices u and v. Here, NC(x) denotes the set of colors assigned to vertices adjacent to x. The set chromatic number of G, denoted by χs (G), is defined as the fewest number of colors needed to construct a set coloring of G. In this paper, we study the set chromatic number in relation to two graph operations: …