{"title":"Size Multipartite Ramsey Numbers for Small Paths vs. K2,n","authors":"C. Jayawardene","doi":"10.22457/apam.v19n1a1","DOIUrl":"https://doi.org/10.22457/apam.v19n1a1","url":null,"abstract":"","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128213114","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}
{"title":"Mathematical Modelling on the Effects of Drug Abuse to the Societies","authors":"Fikiri Lucas Matonya, D. Kuznetsov","doi":"10.22457/apam.591v19n1a4","DOIUrl":"https://doi.org/10.22457/apam.591v19n1a4","url":null,"abstract":"Drug abuse remains to be the global burden causing a large number of death and disability, it is now termed as a significant threat to public health for both developed and developing coun tries. This work presents a mathematical model as a new approach towards understanding and controlling the drug abuse in Tanzania. The mathematical model to study the effect of drug abuse in the society is developed and analyzed in this study. The model’s transmission process is considered as a social contact process between susceptible individuals and drug users based on the epidemiology principles. The model used the factors that were identified through feasi bility study as the significant factors that control the dynamics of drug abused population in the particular society. The model is analyzed using next generation matrix method the numberof new drug users that one drug user can produce in the entire period of abuse is computed and identifies as an epidemic threshold value, R0. Using R0 the condition for existence and stabil ity of stationary point is established. Using numerical simulation, the dynamical behavior of the model is explored and the result shows the significant contribution by the rate of adequate contact between the susceptible individual and the drug user, and the rate of recovery of drug user after rehabilitation as the major factors or players that dictate the dynamics of drug user population in the society. The model is finally analyzed to study the dynamical behavior of the drug abuse when control is applied, the result shows the drug users are minimized significantly. The result signifiesthe importance of early control of the drug abuse problem through establish ment of the strict laws that will narrow the possibility of this bad practice in societies. It is then vividly justified that, key result arising from this model is that prevention is indeed better than cure.","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128535208","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}
{"title":"All the Solutions of the Diophantine Equations (p + 1) x – py = z2 andpy - (p + 1) x = z2 when p is Prime and x + y = 2, 3, 4","authors":"N. Burshtein","doi":"10.22457/apam.599v19n1a6","DOIUrl":"https://doi.org/10.22457/apam.599v19n1a6","url":null,"abstract":"","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126572590","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}
{"title":"On Solutions of the Diophantine Equations $p^4 + q^4 = z^2$ and $p^4-q^4= z^2$ when p and q are Primes","authors":"N. Burshtein","doi":"10.22457/apam.594v19n1a1","DOIUrl":"https://doi.org/10.22457/apam.594v19n1a1","url":null,"abstract":". In this article, we consider the equations p 4 + q 4 = z 2 and p 4 - q 4 = z 2 when p , q are primes and z is a positive integer. We establish that p 4 + q 4 = z 2 has no solutions for all primes 2 ≤ p < q . For p 4 - q 4 = z 2 when 2 ≤ q < p , it is shown: (i) For q = 2 the equation has no solutions. (ii) The equation z 2 = p 4 – q 4 = ( p 2 – q 2 )( p 2 + q 2 ) is impossible when each factor is equal to a square. (iii) When each factor is not a square, conditions which must be satisfied simultaneously are determined for p 2 and q 2 . For all primes p < 2100, these conditions are not fulfilled simultaneously. It is conjectured for all primes p > 2100 and q > 2 that the equation has no solutions.","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131951404","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}
{"title":"A Type of the Cauchy-Euler Equations: Distinct Complex Roots","authors":"G. Sritanratana, Atiwath Chanram","doi":"10.22457/apam.601v19n1a10","DOIUrl":"https://doi.org/10.22457/apam.601v19n1a10","url":null,"abstract":"","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"36 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134225926","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}
{"title":"Generalized Birkhoff Center of Almost Distributive Lattices","authors":"Berhanu Assaye Alaba","doi":"10.22457/APAM.600V19N1A14","DOIUrl":"https://doi.org/10.22457/APAM.600V19N1A14","url":null,"abstract":"In this paper we define sectional Birkhoff center for an Almost Distributive Lattice not necessarily with maximal elements; as a Birkhoff center of its principal ideals. Moreover we extend this result and define the generalized Birkhoff center of an ADL not necessarily with maximal elements. We give a necessary and sufficient condition for an ADL to be relatively complemented in terms of its sectional Birkhoff centers. Also we define and characterize sectionaly complemented ideals and sectional factor congruences using sectional Birkhoff centers. MSC-2010: 06D99 Key words: Birkhoff center of ADLs; Sectional Birkhoff center of ADLs; generalized Birkhoff center of ADLs.","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131230057","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}
{"title":"Degree Based Connectivity F-Indices of Nanotubes","authors":"V. Kulli","doi":"10.22457/apam.v18n2a10","DOIUrl":"https://doi.org/10.22457/apam.v18n2a10","url":null,"abstract":"","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"8 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116673622","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}
{"title":"On Solutions to the Diophantine Equation p^2 + q^2 = z^4","authors":"N. Burshtein","doi":"10.22457/apam.v18n2a2","DOIUrl":"https://doi.org/10.22457/apam.v18n2a2","url":null,"abstract":"","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116588489","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}
{"title":"Epimorphisms and Ideals of Distributive Nearlattices","authors":"M. A. Gandhi, S. S. Khopade, Y. S. Pawar","doi":"10.22457/apam.v18n2a5","DOIUrl":"https://doi.org/10.22457/apam.v18n2a5","url":null,"abstract":"","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117261875","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}
{"title":"On the Diophantine Equation {(q^2 )^n }^x+p^y= z^2 where q is any Prime Number and p is an Odd Prime Number","authors":"S. Gautam, H. Kishan, Satish Kumar","doi":"10.22457/apam.v18n2a1","DOIUrl":"https://doi.org/10.22457/apam.v18n2a1","url":null,"abstract":"","PeriodicalId":305863,"journal":{"name":"Annals of Pure and Applied Mathematics","volume":" 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113949731","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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