Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4870
Jhon Cris Bonifacio, Clarence Joy Andaya, Daryl Magpantay
This paper defines a new class of graphs using the spanning subgraphs of a cycle graph as vertices. This class of graphs is called $j$-edge intersection graph of cycle graph, denoted by $E_{C_{(n,j)}}$. The vertex set of $E_{C_{(n,j)}}$ is the set of spanning subgraphs of cycle graph with $j$ edges where $n geq 3$ and $j$ is a nonnegative integer such that $1 leq j leq n$. Moreover, two distinct vertices are adjacent if they have exactly one edge in common. $E_{C_{(n,j)}}$ is considered as a simple graph. Furthermore, $E_{C_{(n,j)}}$ is characterized by the value of $j$ that is when $j=1$ or $lceil frac{n}{2} rceil < j leq n$ and $2 leq j leq lceil frac{n}{2} rceil$. When $j=1$ or $lceil frac{n}{2} rceil < j leq n$, the new graph only produced an empty graph. Hence, the proponents only considered the value when $2 leq j leq lceil frac{n}{2} rceil$ in determining the order and size of $E_{C_{(n,j)}}$. Moreover, this paper discusses necessary and sufficient conditions where the $j$-edge intersection graph of $C_n$ is isomorphic to the cycle graph. Furthermore, the researchers determined a lower bound for the independence number, and an upper bound for the domination number of $E_{C_{(n,j)}}$ when $j=2$.
{"title":"On the j-Edge Intersection Graph of Cycle Graph","authors":"Jhon Cris Bonifacio, Clarence Joy Andaya, Daryl Magpantay","doi":"10.29020/nybg.ejpam.v16i4.4870","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4870","url":null,"abstract":"This paper defines a new class of graphs using the spanning subgraphs of a cycle graph as vertices. This class of graphs is called $j$-edge intersection graph of cycle graph, denoted by $E_{C_{(n,j)}}$. The vertex set of $E_{C_{(n,j)}}$ is the set of spanning subgraphs of cycle graph with $j$ edges where $n geq 3$ and $j$ is a nonnegative integer such that $1 leq j leq n$. Moreover, two distinct vertices are adjacent if they have exactly one edge in common. $E_{C_{(n,j)}}$ is considered as a simple graph. Furthermore, $E_{C_{(n,j)}}$ is characterized by the value of $j$ that is when $j=1$ or $lceil frac{n}{2} rceil < j leq n$ and $2 leq j leq lceil frac{n}{2} rceil$. When $j=1$ or $lceil frac{n}{2} rceil < j leq n$, the new graph only produced an empty graph. Hence, the proponents only considered the value when $2 leq j leq lceil frac{n}{2} rceil$ in determining the order and size of $E_{C_{(n,j)}}$. Moreover, this paper discusses necessary and sufficient conditions where the $j$-edge intersection graph of $C_n$ is isomorphic to the cycle graph. Furthermore, the researchers determined a lower bound for the independence number, and an upper bound for the domination number of $E_{C_{(n,j)}}$ when $j=2$.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4830
Felipe Jr Raypan Sumalpong, M. Frondoza, N. L. Sayson
In a plain vanilla option, its holder is given the right, but not the obligation, to buy or sell the underlying stock at a specified price (strike price) at a predetermined date. If the exercise date is at maturity, the option is called a European; if the option is exercised anytime prior to maturity, it is called an American. In a British option, the holder can enjoy the early exercise feature of American option whereupon his payoff is the ‘best prediction’ of the European payoff given all the information up to exercise date under the hypothesis that the true drift of the stock equals a specified contract drift. In this paper, in contrast to the constant interest rate and constant volatility assumptions, we consider the British option by assuming that the economic state of the world is described by a finite state continuous-time Markov chain. Also, we provide a solution to a free boundary problem by using PDE arguments. However, closed form expression for the arbitrage-free price are not available in our setting.
{"title":"British Put Option On Stocks Under Regime-Switching Model","authors":"Felipe Jr Raypan Sumalpong, M. Frondoza, N. L. Sayson","doi":"10.29020/nybg.ejpam.v16i3.4830","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4830","url":null,"abstract":"In a plain vanilla option, its holder is given the right, but not the obligation, to buy or sell the underlying stock at a specified price (strike price) at a predetermined date. If the exercise date is at maturity, the option is called a European; if the option is exercised anytime prior to maturity, it is called an American. In a British option, the holder can enjoy the early exercise feature of American option whereupon his payoff is the ‘best prediction’ of the European payoff given all the information up to exercise date under the hypothesis that the true drift of the stock equals a specified contract drift. In this paper, in contrast to the constant interest rate and constant volatility assumptions, we consider the British option by assuming that the economic state of the world is described by a finite state continuous-time Markov chain. Also, we provide a solution to a free boundary problem by using PDE arguments. However, closed form expression for the arbitrage-free price are not available in our setting.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48359907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4793
Hulsen T. Sarapuddin, Jocelyn P. Vilela
This study introduces the concept of Gamma-ideals and Gamma-submonoids of Gamma-monoids and investigates their relationships with the existing Gamma-order-ideals. Moreover, quotient of Gamma-monoids and isomorphism theorems via Gamma-submonoids are proved.
{"title":"On Gamma-Ideals, Gamma-Submonoids and Isomorphism Theorems of Gamma-Monoids via Gamma-Submonoids","authors":"Hulsen T. Sarapuddin, Jocelyn P. Vilela","doi":"10.29020/nybg.ejpam.v16i3.4793","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4793","url":null,"abstract":"This study introduces the concept of Gamma-ideals and Gamma-submonoids of Gamma-monoids and investigates their relationships with the existing Gamma-order-ideals. Moreover, quotient of Gamma-monoids and isomorphism theorems via Gamma-submonoids are proved. ","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45196589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4733
C. Boonpok, M. Thongmoon
This paper deals with the notion of $delta p(Lambda,p)$-open sets. Some properties of $delta p(Lambda,p)$-open sets and $delta p(Lambda,p)$-closed sets are investigated. Moreover, several characterizations of $delta p(Lambda,p)$-$mathscr{D}_1$ spaces and $delta p(Lambda,p)$-$R_0$ spaces are established.
{"title":"$delta p(Lambda,p)$-open Sets in Topological Spaces","authors":"C. Boonpok, M. Thongmoon","doi":"10.29020/nybg.ejpam.v16i3.4733","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4733","url":null,"abstract":"This paper deals with the notion of $delta p(Lambda,p)$-open sets. Some properties of $delta p(Lambda,p)$-open sets and $delta p(Lambda,p)$-closed sets are investigated. Moreover, several characterizations of $delta p(Lambda,p)$-$mathscr{D}_1$ spaces and $delta p(Lambda,p)$-$R_0$ spaces are established.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42817370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4792
Supaknaree Sattaso, P. Prasertsang, T. Prasertsang
In this study, solutions of higher-order differential equations with polynomial coefficients(HODEPCs) were obtained by applying the $G_{alpha}$-transform. Based on some characterizations, the solutions of HODEPCs were investigated. With the general solution of the HODEPCs, the curves of the general solution can be shown in several examples.
{"title":"Using $G_{alpha}$-transform to Study Higher-order Differential Equations with Polynomial Coefficients","authors":"Supaknaree Sattaso, P. Prasertsang, T. Prasertsang","doi":"10.29020/nybg.ejpam.v16i3.4792","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4792","url":null,"abstract":"In this study, solutions of higher-order differential equations with polynomial coefficients(HODEPCs) were obtained by applying the $G_{alpha}$-transform. Based on some characterizations, the solutions of HODEPCs were investigated. With the general solution of the HODEPCs, the curves of the general solution can be shown in several examples.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44286797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4800
J. Jawdat
In this paper, we study strong coproximinality in Bochner $L^p$-spaces and in the Köthe Bochner function space $E(X)$. We investigate some conditions to be imposed on the subspace $G$ of the Banach space $X$ such that $L^{p}left(mu,G right)$ is strongly coproximinal in $L^{p}left(mu,X right), 1 leq p
本文研究了Bochner $L^p$ -空间和Köthe Bochner函数空间$E(X)$中的强近性。我们研究了在Banach空间$X$的子空间$G$上，使$L^{p}left(mu,G right)$在$L^{p}left(mu,X right), 1 leq p
{"title":"Strong Coproximinality in Bochner $L^p$-Spaces and in Köthe Spaces","authors":"J. Jawdat","doi":"10.29020/nybg.ejpam.v16i3.4800","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4800","url":null,"abstract":"In this paper, we study strong coproximinality in Bochner $L^p$-spaces and in the Köthe Bochner function space $E(X)$. We investigate some conditions to be imposed on the subspace $G$ of the Banach space $X$ such that $L^{p}left(mu,G right)$ is strongly coproximinal in $L^{p}left(mu,X right), 1 leq p <infty$. On the other hand, we prove that if $G$ is a separable subspace of $X$ then $G$ is strongly coproximinal in $X$ if and only if $E(G)$ is strongly coproximinal in $E(X)$, provided that $E$ is a strictly monotone Köthe space. This generalizes some results in the literature. Some other results in this direction are also presented.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43460442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4806
M. V., Kalyani Desikan
Core-satellite graphs Θ(c, s, η) ∼= Kc ▽ (ηKs) are graphs consisting of a central clique Kc (the core) and η copies of Ks (the satellites) meeting in a common clique. They belong to the class of graphs of diameter two. Agave graphs Θ(2, 1, η) ∼= K2 ▽ (ηK1) belong to the general class of complete split graphs, where the graphs consist of a central clique K2 and η copies of K1 which are connected to all the nodes of the clique. They are the subclass of Core-satellite graphs. Let μ(G) be the spectral radius of the signless Laplacian matrix Q(G). In this paper, we have obtained the greatest lower bound and the least upper bound of signless Laplacian spectral radius of Agave graphs. These bounds have been expressed in terms of graph invariants like m the number of edges, n the number of vertices, δ the minimum degree, ∆ the maximum degree, and η copies of the satellite. We have made use of the approximation technique to derive these bounds. This unique approach can be utilized to determine the bounds for the signless Laplacian spectral radius of any general family of graphs. We have also obtained Nordhaus-Gaddum type inequality using the derived bounds.
{"title":"New Improved Bounds for Signless Laplacian Spectral Radius and Nordhaus-Gaddum Type Inequalities for Agave Class of Graphs","authors":"M. V., Kalyani Desikan","doi":"10.29020/nybg.ejpam.v16i3.4806","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4806","url":null,"abstract":"Core-satellite graphs Θ(c, s, η) ∼= Kc ▽ (ηKs) are graphs consisting of a central clique Kc (the core) and η copies of Ks (the satellites) meeting in a common clique. They belong to the class of graphs of diameter two. Agave graphs Θ(2, 1, η) ∼= K2 ▽ (ηK1) belong to the general class of complete split graphs, where the graphs consist of a central clique K2 and η copies of K1 which are connected to all the nodes of the clique. They are the subclass of Core-satellite graphs. Let μ(G) be the spectral radius of the signless Laplacian matrix Q(G). In this paper, we have obtained the greatest lower bound and the least upper bound of signless Laplacian spectral radius of Agave graphs. These bounds have been expressed in terms of graph invariants like m the number of edges, n the number of vertices, δ the minimum degree, ∆ the maximum degree, and η copies of the satellite. We have made use of the approximation technique to derive these bounds. This unique approach can be utilized to determine the bounds for the signless Laplacian spectral radius of any general family of graphs. We have also obtained Nordhaus-Gaddum type inequality using the derived bounds.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42263195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4825
Noel Lacpao
In this paper, the Hurwitz-Lerch poly-Cauchy and poly-Bernoulli polynomials are defined using polylogarithm factorial function. Some properties of these types of polynomials were also established. Specifically, two different forms of explicit formula of Hurwitz-Lerch type poly-Cauchy polynomials were obtained using Stirling numbers of the first and second kinds and an explicit formula of Hurwitz-Lerch type poly-Bernoulli polynomials was established using the Stirling numbers of the first kind.
{"title":"Some Explicit Formula of Hurwitz Lerch type Poly-Cauchy Polynomials and Poly-Bernoulli Polynomials","authors":"Noel Lacpao","doi":"10.29020/nybg.ejpam.v16i3.4825","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4825","url":null,"abstract":"In this paper, the Hurwitz-Lerch poly-Cauchy and poly-Bernoulli polynomials are defined using polylogarithm factorial function. Some properties of these types of polynomials were also established. Specifically, two different forms of explicit formula of Hurwitz-Lerch type poly-Cauchy polynomials were obtained using Stirling numbers of the first and second kinds and an explicit formula of Hurwitz-Lerch type poly-Bernoulli polynomials was established using the Stirling numbers of the first kind.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42994726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4824
Arash Pourkia
We present explicit descriptions for the swap gate and the iswap gate in any arbitrary dimension $d geq 2$, in terms of permutation matrices. Moreover, we unify these gates by introducing a more general gate xSWAP which includes SWAP and iSWAP for $x=1$ and $x=i$ (i.e. $sqrt{-1}$), respectively. The higher dimensional xSWAP e.g., the swap and iswap gates for $d > 2$ serve as quantum logic gates that operate on two $d$-level qudits. For $d=2$, it is well known that iSWAP unlike SWAP is universal for quantum computing. We will prove this fact for xSWAP in any dimension $d$, when $x neq pm 1$. Our explicit representation of xSWAP by a permutation matrix facilitates the proof, greatly.
{"title":"A Note on Quantum Gates SWAP and iSWAP in Higher Dimensions","authors":"Arash Pourkia","doi":"10.29020/nybg.ejpam.v16i3.4824","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4824","url":null,"abstract":"We present explicit descriptions for the swap gate and the iswap gate in any arbitrary dimension $d geq 2$, in terms of permutation matrices. Moreover, we unify these gates by introducing a more general gate xSWAP which includes SWAP and iSWAP for $x=1$ and $x=i$ (i.e. $sqrt{-1}$), respectively. The higher dimensional xSWAP e.g., the swap and iswap gates for $d > 2$ serve as quantum logic gates that operate on two $d$-level qudits. For $d=2$, it is well known that iSWAP unlike SWAP is universal for quantum computing. We will prove this fact for xSWAP in any dimension $d$, when $x neq pm 1$. Our explicit representation of xSWAP by a permutation matrix facilitates the proof, greatly.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48692352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4848
Farene Loida Alfeche, Victor Barraza, Sergio R. Canoy
In this paper, we revisit the concept of (normalized) closeness centrality of a vertex in a graph and investigate it in some graphs under some operations. Specifically, we derive formulas that compute the closeness centrality of vertices in the shadow graph, complementary prism, edge corona, and disjunction of graphs.
{"title":"Closeness Centrality of Vertices in Graphs Under Some Operations","authors":"Farene Loida Alfeche, Victor Barraza, Sergio R. Canoy","doi":"10.29020/nybg.ejpam.v16i3.4848","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4848","url":null,"abstract":"In this paper, we revisit the concept of (normalized) closeness centrality of a vertex in a graph and investigate it in some graphs under some operations. Specifically, we derive formulas that compute the closeness centrality of vertices in the shadow graph, complementary prism, edge corona, and disjunction of graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46149309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：