Papers by Michael Baldado Jr.
Journal of Education and Practice, 2016
The velocity of a moving object is different when measured from a stationary frame of reference a... more The velocity of a moving object is different when measured from a stationary frame of reference and on a moving frame of reference (see the famous train experiment and the Michelson-Morley experiment). Because velocity is relative to the frame of reference, so do the concepts of "distance" and "time". Thus, were born the concepts of relativistic mass, relativistic distance, and the notion of time dilation, which practically revolutionized Newton's classical Physics (Muller, General Theory of Relativity, 1958). In this paper, we investigate how the fractal dimension of the same natural geometric object changes relative to the distance from which a picture of the object is taken.
European Journal of Pure and Applied Mathematics, 2019
Corrigendum 2010 Mathematics Subject Classifications: 54-XX Key Words and Phrases: β-open sets, β... more Corrigendum 2010 Mathematics Subject Classifications: 54-XX Key Words and Phrases: β-open sets, β I-open sets, β I-compactness, cβ I-compactness, β Ihyperconnectedness and cβ I-hyperconnectednes * Corresponding author.
European Journal of Pure and Applied Mathematics, 2021
Let R be a ring with identity 1R. A subset J of R is called a γ-set if for every a ∈ R\J,there ex... more Let R be a ring with identity 1R. A subset J of R is called a γ-set if for every a ∈ R\J,there exist b, c ∈ J such that a+b = 0 and ac = 1R = ca. A γ-set of minimum cardinality is called a minimum γ-set. In this study, we identified some elements of R that are necessarily in a γ-sets, and we presented a method of constructing a new γ-set. Moreover, we gave: necessary and sufficient conditions for rings to have a unique γ-set; an upper bound for the total number of minimum γ-sets in a division ring; a lower bound for the total number of minimum γ-sets in a division ring; necessary and sufficient conditions for T(x) and T to be equal; necessary and sufficient conditions for a ring to have a trivial γ-set; necessary and sufficient conditions for an image of a γ-set to be a γ-set also; necessary and sufficient conditions for a ring to have a trivial γ-set; and, necessary and sufficient conditions for the families of γ-sets of two division rings to be isomorphic.
European Journal of Pure and Applied Mathematics
A nonempty set G is a g-group [with respect to a binary operation ∗] if it satisfies the followin... more A nonempty set G is a g-group [with respect to a binary operation ∗] if it satisfies the following properties: (g1) a ∗ (b ∗ c) = (a ∗ b) ∗ c for all a, b, c ∈ G; (g2) for each a ∈ G, there exists an element e ∈ G such that a ∗ e = a = e ∗ a (e is called an identity element of a); and, (g3) for each a ∈ G, there exists an element b ∈ G such that a ∗ b = e = b ∗ a for some identity element eof a. In this study, we gave some important properties of g-subgroups, homomorphism of g-groups, andthe zero element. We also presented a couple of ways to construct g-groups and g-subgroups.
European Journal of Pure and Applied Mathematics, 2021
Let G = (V, E) be a graph of order 2n. If A ⊆ V and hAi ∼= hV \Ai, then A is said to be isosp... more Let G = (V, E) be a graph of order 2n. If A ⊆ V and hAi ∼= hV \Ai, then A is said to be isospectral. If for every n-element subset A of V we have hAi ∼= hV \Ai, then we say that G is spectral-equipartite. In [1], Igor Shparlinski communicated with Bibak et al., proposing a full characterization of spectral-equipartite graphs. In this paper, we gave a characterization of disconnected spectral-equipartite graphs. Moreover, we introduced the concept eccentricity-equipartite graphs.
International Journal of Contemporary Mathematical Sciences
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International Mathematical Forum
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Pure Mathematical Sciences
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European Journal of Pure and Applied Mathematics
Let X be a topological space and I be an ideal in X. A subset A of a topological space X is calle... more Let X be a topological space and I be an ideal in X. A subset A of a topological space X is called a β-open set if A ⊆ cl(int(cl(A))). A subset A of X is called β-open with respect to the ideal I, or βI -open, if there exists an open set U such that (1) U − A ∈ I, and (2) A − cl(int(cl(U))) ∈ I. A space X is said to be a βI -compact space if it is βI -compact as a subset. An ideal topological space (X, τ, I) is said to be a cβI -compact space if it is cβI -compact as a subset. An ideal topological space (X, τ, I) is said to be a countably βI -compact space if X is countably βI -compact as a subset. Two sets A and B in an ideal topological space (X, τ, I) is said to be βI -separated if clβI (A) ∩ B = ∅ = A ∩ clβ(B). A subset A of an ideal topological space (X, τ, I) is said to be βI -connected if it cannot be expressed as a union of two βI -separated sets. An ideal topological space (X, τ, I) is said to be βI -connected if X βI -connected as a subset. In this study, we introduced the...
Turkish Journal of Analysis and Number Theory, 2016
This paper investigates D−sets of groups in relation to structure-preserving maps. It shows conne... more This paper investigates D−sets of groups in relation to structure-preserving maps. It shows connections between non-involutions of groups and the concept of D−sets. In particular, we prove that the existence of a semigroup isomorphism between the families of D−sets of two groups is equivalent to an existence of a special type of bijection between the subsets containing all elements of orders greater than two of the groups.
Advanced Topics of Topology [Working Title]
Let XτI be an ideal topological space. A subset A of X is said to be β-open if A⊆clintclA, and it... more Let XτI be an ideal topological space. A subset A of X is said to be β-open if A⊆clintclA, and it is said to be βI-open if there is a set O∈τ with the property 1O−A∈I and 2A−clintclO∈I. The set A is called βI-compact if every cover of A by βI-open sets has a finite sub-cover. The set A is said to be cβI-compact, if every cover Oλ:λ∈Λ of A by β-open sets, Λ has a finite subset Λ0 such that A−∪Oλ:λ∈Λ0∈I. The set A is said to be countably βI-compact if every countable cover of A by βI-open sets has a finite sub-cover. An ideal topological space XτI is said to be βI∗-hyperconnected if X−cl∗A∈I for every non-empty βI-open subset A of X. Two subsets A and B of X is said to be βI-separated if clβIA∩B=∅=A∩clβB. Moreover, A is called a βI-connected set if it can’t be written as a union of two βI-separated subsets. An ideal topological space XτI is called βI-connected space if X is βI-connected. In this article, we give some important properties of βI-open sets, βI-compact spaces, cβI-compact...
Copyright c © 2014 Joris N. Buloron et al. This is an open access article distributed under the C... more Copyright c © 2014 Joris N. Buloron et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A subset D of a group G is called a D-set if every element of G which is not in D has its inverse in D. In this paper, we gave some of the properties of a D-set. Mathematics Subject Classification: 20Dxx
A path P connecting two vertices u and v in a totally colored graph G is called a rainbow total-p... more A path P connecting two vertices u and v in a totally colored graph G is called a rainbow total-path between u and v if all elements in , except for u and v, are assigned distinct colors. A total-colored graph is rainbow total-connected if it has a rainbow total-path between every two vertices. The rainbow total-connection number of a graph G is the minimum colors such that G is rainbow total-connected. In this paper, we gave the rainbow total-connection number of sunflower graph and lotus inside circle graph.
L et be a simple graph. A set is called a secure dominating set of a graph if for every vertex... more L et be a simple graph. A set is called a secure dominating set of a graph if for every vertex , there exists such that is dominating. It is a super secure dominating set if The minimum cardinality of a super secure dominating set in , denoted by , is called the super secure domination number of . In this paper, we initiate the study of the concept and give some important results.
European Journal of Mathematics and Applications, 2021
Let G be a graph. An eternal 1-secure set in a graph G is a set S0 ⊆ V (G) with the property that... more Let G be a graph. An eternal 1-secure set in a graph G is a set S0 ⊆ V (G) with the property that for any k ∈ N and any sequence 〈v1, v2, . . . , vk〉 of vertices of G, there exists a sequence 〈u1, u2, . . . , uk〉 of vertices of G with ui ∈ Si−1 and either ui equal to or adjacent to vi, such that each set Si = (Si−1\{ui}) ∪ {vi} is dominating in G. The eternal 1-security number of G, denoted by σ1(G), is the minimum cardinality of an eternal 1-secure set in G. In this paper we characterized all graphs G with σ1(G) = 1 and all graphs G with σ1(G) = |V (G)|. Eternal 1-security numbers of the corona and cartesian products of some graphs are also determined/given. Mathematics Subject Classification: 05C12
European Journal of Pure and Applied Mathematics, 2016
A subset D of a group G is a D -set if every element of G , not in D , has its inverse in D . Le... more A subset D of a group G is a D -set if every element of G , not in D , has its inverse in D . Let A be a non-empty subset of G . A smallest D -set of G that contains A is called a D -set generated by A , denoted by . Note that may not be unique. This paper characterized sets A with unique and sets whose number of generated D -sets is equal to the index minimum.
We examine the power-law distribution with fractional exponents as a parent distribution of a ran... more We examine the power-law distribution with fractional exponents as a parent distribution of a random sample. The phase plot (xt, xt+1) of the random sample is shown to behave like fractals as defined by Mandelbrot (1967). Two (2) features of fractals are discussed as possible replacement of the mean (μ) and the standard deviation (σ) in describing fractals since the two quantities may not exist for low dimensional fractals 0 < d< 2. The two (2) features are the quantiles and ruggedness measure via fractal derivatives and integrals.
The velocity of a moving object is different when measured from a stationary frame of reference a... more The velocity of a moving object is different when measured from a stationary frame of reference and on a moving frame of reference (see the famous train experiment and the Michelson-Morley experiment). Because velocity is relative to the frame of reference, so do the concepts of “distance” and “time”. Thus, were born the concepts of relativistic mass, relativistic distance, and the notion of time dilation, which practically revolutionized Newton’s classical Physics (Muller, General Theory of Relativity, 1958). In this paper, we investigate how the fractal dimension of the same natural geometric object changes relative to the distance from which a picture of the object is taken. Keywords: Fractal dimension, Distance, Fractal
L et be a graph . A subset D of G is a p-dominating set of G if for all , where is the set of ... more L et be a graph . A subset D of G is a p-dominating set of G if for all , where is the set of all vertices which are adjacent to x. The p-domination number of G, denoted by , is the minimum cardinality of p-dominating sets of G. The p-reinforcement number of G, denoted by , is the minimum number of edges in that has to be added to G in order to reduce the p-domination number of the resulting graphs. In this study, we gave a tight upperbound for the p-domination number of the join of graphs, the p-domination number of a complete and any graph, the 2-domination number and 3-domination number of fans, and the 2-reinforcement number and 3-reinforcement number of fans.
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Papers by Michael Baldado Jr.