Pub Date : 2019-07-01DOI: 10.37516/adv.math.sci.2019.0074
Rachanna R Kanabur, S. K. Giregol, Basavaraj M. Koujalagi, Edake Yogesh Sidaraya
Throughout this paper simple and undirected graphs are considered. Let G = (V,E) be such a graph. The structure of a chemical compound can be represented by a graph whose vertex and edge specify the atom and bonds respectively. In this paper we compute certain topological indices of silicate chain.
{"title":"ON THE INVARIANT OF NEW DEGREE-BASED TOPOLOGICAL INDICES OF SILICATE CHAIN GRAPH","authors":"Rachanna R Kanabur, S. K. Giregol, Basavaraj M. Koujalagi, Edake Yogesh Sidaraya","doi":"10.37516/adv.math.sci.2019.0074","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0074","url":null,"abstract":"Throughout this paper simple and undirected graphs are considered. Let G = (V,E) be such a graph. The structure of a chemical compound can be represented by a graph whose vertex and edge specify the atom and bonds respectively. In this\u0000paper we compute certain topological indices of silicate chain.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"309 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77781272","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 : 2019-06-15DOI: 10.37516/adv.math.sci.2019.0050
D. Sarma, B. Tripathy
In this article we construct a fuzzy topology on a non-empty set X called mixed semi-pre fuzzy topology from two given fuzzy topological spaces on X with the help of fuzzy semi-prequasi-neighborhood of a fuzzy point.
{"title":"MIXED SEMI-PRE FUZZY TOPOLOGICAL SPACES","authors":"D. Sarma, B. Tripathy","doi":"10.37516/adv.math.sci.2019.0050","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0050","url":null,"abstract":"In this article we construct a fuzzy topology on a non-empty set X called mixed semi-pre fuzzy topology from two given fuzzy topological spaces on X with the help of fuzzy semi-prequasi-neighborhood of a fuzzy point.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84819330","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 : 2019-06-12DOI: 10.37516/adv.math.sci.2019.0072
R. Vigneswaran, S. Thilaganathan
We consider a phase space stability error control for numerical simulation of dynamical systems. Standard adaptive algorithm used to solve the linear systems perform well during the finite time of integration with fixed initial condition and performs poorly in three areas. To overcome the difficulties faced the Phase Space Error control criterion was introduced. A new error control was introduced by R. Vigneswaran and Tony Humbries which is generalization of the error control first proposed by some other researchers. For linear systems with a stable hyperbolic fixed point, this error control gives a numerical solution which is forced to converge to the fixed point. In earlier, it was analyzed only for forward Euler method applied to the linear system whose coefficient matrix has real negative eigenvalues. In this paper we analyze forward Euler method applied to the linear system whose coefficient matrix has complex eigenvalues with negative large real parts. Some theoretical results are obtained and numerical results are given.
{"title":"PHASE SPACE ERROR CONTROL WITH VARIABLE TIME-STEPPING ALGORITHMS APPLIED TO THE FORWARD EULER METHOD FOR AUTONOMOUS DYNAMICAL SYSTEMS","authors":"R. Vigneswaran, S. Thilaganathan","doi":"10.37516/adv.math.sci.2019.0072","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0072","url":null,"abstract":"We consider a phase space stability error control for numerical simulation of dynamical systems. Standard adaptive algorithm used to solve the linear systems perform well during the finite time of integration with fixed initial condition and performs poorly in three areas. To overcome the difficulties faced the Phase Space Error control criterion was introduced. A new error control was introduced by R. Vigneswaran and Tony Humbries which is generalization of the error control first proposed by some other researchers. For linear systems with a stable hyperbolic fixed point, this error control gives a numerical solution which is forced to converge to the fixed point. In earlier, it was analyzed only for forward Euler method applied to the linear system whose coefficient matrix has real negative eigenvalues. In this paper we analyze forward Euler method applied to the linear system whose coefficient matrix has complex eigenvalues with negative large real parts. Some theoretical results are obtained and numerical results are given.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86287507","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 : 2019-06-02DOI: 10.37516/adv.math.sci.2019.0052
M. Arunmaran, K. Kannan
Zadeh established the concept of fuzzy set based on the characteristic function. Foundation of fuzzy set theory was introduced by him. Throughout this paper, 𝑀𝑛(𝐹) denotes the set of all fuzzy matrices of order 𝑛 over the fuzzy unit interval [0,1]. Inaddi tion (𝑀𝑛 (𝐹), 𝜃) dis called as fuzzy 𝛼 −normed linear space. The objective of this paper is to investigate the relationships between convergent sequences and fuzzy 𝛼 −normed linear space. The set of all fuzzy points in 𝑀𝑛 (𝐹) is denoted by 𝑃∗(𝑀𝑛(𝐹)). For a fuzzy 𝛼 −normed linear space (𝑀𝑛 (𝐹), 𝜃), we have |𝜃(𝑃𝐴)𝛼 −𝜃(𝑃𝐵)𝛼 | ≤ 𝜃(𝑃𝐴,𝑃𝐵)𝛼. Besides 𝜃 is a continuous function on 𝑀𝑛 (𝐹). That is, if 𝑃𝐴𝑛 → 𝑃𝐴 as 𝑛 → ∞ then 𝜃(𝑃𝐴𝑛 )𝛼 → 𝜃(𝑃𝐴)𝛼 as 𝑛 → ∞, where 𝑃𝐴𝑛 is a sequence in (𝑀𝑛 (𝐹), 𝜃). Hence, 𝜃 is always bounded on 𝑀𝑛(𝐹). Next we introduce the following result: Let 𝑃𝐴𝑛 , 𝑃𝐵𝑛 ∈ 𝑃 ∗ (𝑀𝑛(𝐹)) with 𝑃𝐴𝑛 and 𝑃𝐵𝑛 converge to 𝑃𝐴 and 𝑃𝐵 respectively as 𝑛 → ∞. Then 𝑃𝐴𝑛 + 𝑃𝐵𝑛 converge to 𝑃𝐴 + 𝑃𝐵 as 𝑛 → ∞. Furthermore, we are able to compare two different fuzzy 𝛼 −norms with convergent sequence. The result states that for a fuzzy 𝛼 −normed linear space (𝑀𝑛(𝐹), 𝜃), we have 𝜃(𝑃𝐴)𝛼1 ≥ 𝑀𝜃(𝑃𝐴 )𝛼2 , for some 𝑀 > 0 and 𝑃𝐴 ∈ 𝑃 ∗ (𝑀𝑛(𝐹)). If 𝑃𝐴𝑛 converges to 𝑃𝐴 under fuzzy 𝛼1 −norm then 𝑃𝐴𝑛 converges to 𝑃𝐴 under fuzzy 𝛼2 −norm. Moreover, if (𝑀𝑛 (𝐹), 𝜃) has finite dimension then it should be complete. Through these results, we are able to get clear understanding about the concept fuzzy 𝛼 −normed linear space and its properties.
{"title":"SOME RESULTS RELATED WITH FUZZY a −NORMED LINEAR SPACE","authors":"M. Arunmaran, K. Kannan","doi":"10.37516/adv.math.sci.2019.0052","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0052","url":null,"abstract":"Zadeh established the concept of fuzzy set based on the characteristic function. Foundation of fuzzy set theory was introduced by him. Throughout this paper, 𝑀𝑛(𝐹) denotes the set of all fuzzy matrices of order 𝑛 over the fuzzy unit interval [0,1]. Inaddi tion (𝑀𝑛 (𝐹), 𝜃) dis called as fuzzy 𝛼 −normed linear space. The objective of this paper is to investigate the relationships between convergent sequences and fuzzy 𝛼 −normed linear space. The set of all fuzzy points in 𝑀𝑛 (𝐹) is denoted by 𝑃∗(𝑀𝑛(𝐹)). For a fuzzy 𝛼 −normed linear space (𝑀𝑛 (𝐹), 𝜃), we have |𝜃(𝑃𝐴)𝛼 −𝜃(𝑃𝐵)𝛼 | ≤ 𝜃(𝑃𝐴,𝑃𝐵)𝛼. Besides 𝜃 is a continuous function on 𝑀𝑛 (𝐹). That is, if 𝑃𝐴𝑛 → 𝑃𝐴 as 𝑛 → ∞ then 𝜃(𝑃𝐴𝑛 )𝛼 → 𝜃(𝑃𝐴)𝛼 as 𝑛 → ∞, where 𝑃𝐴𝑛 is a sequence in (𝑀𝑛 (𝐹), 𝜃). Hence, 𝜃 is always bounded on 𝑀𝑛(𝐹). Next we introduce the following result: Let 𝑃𝐴𝑛 , 𝑃𝐵𝑛 ∈ 𝑃 ∗ (𝑀𝑛(𝐹)) with 𝑃𝐴𝑛 and 𝑃𝐵𝑛 converge to 𝑃𝐴 and 𝑃𝐵 respectively as 𝑛 → ∞. Then 𝑃𝐴𝑛 + 𝑃𝐵𝑛 converge to 𝑃𝐴 + 𝑃𝐵 as 𝑛 → ∞. Furthermore, we are able to compare two different fuzzy 𝛼 −norms with convergent sequence. The result states that for a fuzzy 𝛼 −normed linear space (𝑀𝑛(𝐹), 𝜃), we have 𝜃(𝑃𝐴)𝛼1 ≥ 𝑀𝜃(𝑃𝐴 )𝛼2 , for some 𝑀 > 0 and 𝑃𝐴 ∈ 𝑃 ∗ (𝑀𝑛(𝐹)). If 𝑃𝐴𝑛 converges to 𝑃𝐴 under fuzzy 𝛼1 −norm then 𝑃𝐴𝑛 converges to 𝑃𝐴 under fuzzy 𝛼2 −norm. Moreover, if (𝑀𝑛 (𝐹), 𝜃) has finite dimension then it should be complete. Through these results, we are able to get clear understanding about the concept fuzzy 𝛼 −normed linear space and its properties.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"606 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86052630","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 : 2019-06-02DOI: 10.37516/adv.math.sci.2019.0051
M. Arunmaran, K. Kannan
In this paper, we introduce the concept “Quotient bi-space” in bitopological spaces. In addition, we investigate the results related with quotient bi-space. Moreover, we have discussed the results related with pairwise regular and normal spaces in bitopological space. For a non-empty set X, we can define two topologies (these may be same or distinct topologies) τ1 and τ2 on X. Then, the triple (X, τ1 , τ2 ) is known as bitopological space. Let (X, τ1 , τ2 ) be bitopological space, (Y, σ1 , σ2 ) be trivial bitopological space and f : (X, τ1 , τ2 ) → (Y, σ1 , σ2 ) be onto map. Then f is τ1 τ2 −continuous map. If η = {G (σ − open set in Y ) : f ^{−1} (G) is τ1 τ2 − open in X} then η is a topology on Y . Moreover, if (Y, σ, σ) be a quotient bi-space of (X, τ1 , τ2) under f : (X, τ1 , τ2 ) → (Y, σ, σ) and g : (Y, σ, σ) → (Z, η1 , η2 ) be a map, then, gis σ − continuous if and only if g ◦ f : (X, τ1 , τ2 ) → (Z, η1 , η2 ) is τ1 τ2 −continuous. Let (X, τ1 , τ2) be bitopological space and A be τ1 τ2 − compact subset of pairwise Hausdorff space X. Then, A is τ1 τ2 − closed set. Finally, we have discussed the following : Let (X, τ1 , τ2 ) be bitopological space and τ1 τ2 −compact pairwise Hausdorff space. Then, the space (X, τ1 , τ2 ) is pairwise normal.
{"title":"DISCUSSION ON QUOTIENT BI-SPACE AND ON PAIRWISE REGULAR AND NORMAL SPACES IN BITOPOLOGICAL SPACES","authors":"M. Arunmaran, K. Kannan","doi":"10.37516/adv.math.sci.2019.0051","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0051","url":null,"abstract":"In this paper, we introduce the concept “Quotient bi-space” in bitopological spaces. In addition, we investigate the results related with quotient bi-space. Moreover, we have discussed the results related with pairwise regular and normal spaces in bitopological space. For a non-empty set X, we can define two topologies (these may be same or distinct topologies) τ1 and τ2 on X. Then, the triple (X, τ1 , τ2 ) is known as bitopological space. Let (X, τ1 , τ2 ) be bitopological space, (Y, σ1 , σ2 ) be trivial bitopological space and f : (X, τ1 , τ2 ) → (Y, σ1 , σ2 ) be onto map. Then f is τ1 τ2 −continuous map. If η = {G (σ −\u0000open set in Y ) : f ^{−1} (G) is τ1 τ2 − open in X} then η is a topology on Y . Moreover, if (Y, σ, σ) be a quotient bi-space of (X, τ1 , τ2) under f : (X, τ1 , τ2 ) → (Y, σ, σ) and g : (Y, σ, σ) → (Z, η1 , η2 ) be a map, then, gis σ − continuous if and only if g ◦ f : (X, τ1 , τ2 ) → (Z, η1 , η2 ) is τ1 τ2 −continuous. Let (X, τ1 , τ2) be bitopological space and A be τ1 τ2 − compact subset of pairwise Hausdorff space X. Then, A is τ1 τ2 − closed set. Finally, we have discussed the following : Let (X, τ1 , τ2 ) be bitopological space and τ1 τ2 −compact pairwise Hausdorff space. Then, the space (X, τ1 , τ2 ) is pairwise normal.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81687137","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 : 2019-05-28DOI: 10.37516/adv.math.sci.2019.0042
Nita H. Shah, P. Pandya, A. Suthar
The cut-throat competition to be the best individual is coming out to be social issue in the hi-tech world. Society increases this pressure by imposing their expectation. Both these issues result into imbalance situations which results stress and depression in an individual. The life style adds more depression. The relation between depression due to social pressure and get relief from this needs medication is modelled in this research. The formulation is done with the help of system of nonlinear differential equations. The fraction (threshold) of individuals suffering from depression who needs medication is computed. The stress-free equilibrium and its stability are analysed.
{"title":"CURTAILING SEVERITY OF DEPRESSION DUE TO SOCIAL PRESSURE BY MEDICATION","authors":"Nita H. Shah, P. Pandya, A. Suthar","doi":"10.37516/adv.math.sci.2019.0042","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0042","url":null,"abstract":"The cut-throat competition to be the best individual is coming out to be social issue in the hi-tech world. Society increases this pressure by imposing their expectation. Both these issues result into imbalance situations which results stress and depression in an individual. The life style adds more depression. The relation between depression due to social pressure and get relief from this needs medication is modelled in this research. The formulation is done with the help of system of nonlinear differential equations. The fraction (threshold) of individuals suffering from depression who needs medication is computed. The stress-free equilibrium and its stability are analysed.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90465068","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 : 2019-01-07DOI: 10.37516/adv.math.sci.2019.0071
Omar Abu-gdere, M. Rashid
The aim of this paper is to prove the existence common fixed point for compatible mapping of type (A) in Non-Archimedean Menger PM-space and we introduced new conditions for this type.
{"title":"COMMON FIXED POINT THEOREMS FOR COMPATIBLE MAPPINGS OF TYPE (A) IN NON-ARCHIMEDEAN MENGER PM-SPACES","authors":"Omar Abu-gdere, M. Rashid","doi":"10.37516/adv.math.sci.2019.0071","DOIUrl":"https://doi.org/10.37516/adv.math.sci.2019.0071","url":null,"abstract":"The aim of this paper is to prove the existence common fixed point for compatible mapping of type (A) in Non-Archimedean Menger PM-space and we introduced new conditions for this type.","PeriodicalId":53941,"journal":{"name":"Advances and Applications in Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89403637","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}
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