American journal of applied mathematics and statistics最新文献

{"title":"On Approximate Controllability of Second Order Fractional Impulsive Stochastic Differential System with Nonlocal, State-dependent Delay and Poisson Jumps","authors":"K. Thiagu","doi":"10.11648/J.AJAM.20210902.13","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210902.13","url":null,"abstract":"The main scope of this paper is to focus the approximate controllability of second order (q∈(1,2]) fractional impulsive stochastic differential system with nonlocal, state-dependent delay and Poisson umps in Hilbert spaces. The existence of mild solutions is derived by using Schauder fixed point theorem. Sufficient conditions for the approximate controllability are established by under the assumptions that the corresponding linear system is approximately controllable and it is checked by using Lebesgue dominated convergence theorem. The main results are completly based on the results that the existence and approximate controllability of the fractional stochastic system of order 1<q≤2 and are derived by using stochastic analysis theory, fixed point technique, q-order cosine family {Ca(t)}t≥0, new set of novel sufficient conditions and methods adopted directly from deterministic fractional equations for the second order nonlinear impulsive fractional nonlocal stochastic differential systems with state-dependent delay and Poisson jumps in Hildert space H. Finally an example is added to illustrate the main results.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75799157","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":"Generalised Rational αs-Meir-Keeler Contraction Mapping in S-metric Spaces","authors":"Shanu Poddar, Y. Rohen","doi":"10.12691/AJAMS-9-2-2","DOIUrl":"https://doi.org/10.12691/AJAMS-9-2-2","url":null,"abstract":"In this paper, we introduce the concept of generalised rational αs-Meir-Keeler contraction mapping on S-metric spaces. The existence of fixed points is also discussed.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"62 1","pages":"48-52"},"PeriodicalIF":0.0,"publicationDate":"2021-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78036352","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 Künneth Formula for the Embedded Homology","authors":"Chonghu Wang","doi":"10.11648/J.AJAM.20210901.15","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210901.15","url":null,"abstract":"Hypergraph is an important model for complex networks. A hypergraph can be regarded as a virtual simplicial complex with some faces missing and it is the key hub to connect the simplicial complex in topology and graph in combinatorics. The embedded homology groups of hypergraphs are new developments in mathematics in recent years, and the embedded homology groups of hypergraphs can reflect the topological and geometric characteristics of complex network which can not be reflected by the associated simplicial complex of hypergraphs. Kunneth formulas describe the homology or cohomology of a product space in terms of the homology or cohomology of the factors. In this paper, we prove that the infimum chain complex of tensor products of free R-modules generated by hypergraphs is isomorphic to the tensor product of their respective infimum chain complexes, and give an analogues of Kunneth formula for hypergraphs by classical algebraic Kunneth formula based on the embedded homology groups of hypergraphs, which provides a theoretical basis for further study of cohomology theory of hypergraphs. In fact, the Kunneth formula here can be extended to the Kunneth formula of embedded homology of graded abelian groups of chain complexes, which can be used to extend the Kunneth formula for digraphs with coefficients in a field.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"3 1","pages":"31"},"PeriodicalIF":0.0,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89695502","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":"The Fermionic-bosonic Representations of A(M-1,N-1)-graded Lie Superalgebras","authors":"Lingyu Yu","doi":"10.11648/J.AJAM.20210902.12","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210902.12","url":null,"abstract":"Lie groups, Lie algebras and their representation theories are important parts of mathematical physics. They play a crucial character in symmetries. As a generalization of Lie algebra, Lie superalgebras are from the comprehending and description for supersymmetry of mathematical physics. Unlike the semisimple Lie algebras, understanding the representation theory of Lie superalgebras is a difficult problem. Lie superalgebras graded by root supersystems are Lie superalgebras of great significance. In recent years, the representations of types B(m,n), C(n), D(m,n), P(n) and Q(n)-graded Lie superalgebras coordinatized by quantum tori have been studied. In this paper, we construct fermionic-bosonic representations for a class of A(M-1,N-1)-graded Lie superalgebras coordinatized by quantum tori with nontrivial central extensions. At first, we introduce the background of the research on the graded Lie superalgebras and present some basics on it. Then, a set of bases for A(M-1,N-1)-graded Lie superalgebras and the multiplication operations among them are given specifically to present the construction of the vector space. By using the tensor product of fermionic and bosonic module, the operators and their operation relations are derived. Finally, we obtain a brief and pretty representation theorem of A(M-1,N-1)-graded Lie superalgebras with nontrivial central extensions.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"107 1","pages":"44"},"PeriodicalIF":0.0,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77418185","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":"Two-Stage Artificial Neural Network Regression Modelling for Wheezing Risk Factors Among Children - A Case Study of Gatundu Hospital, Kenya","authors":"Thomas Mageto, J. Onyango","doi":"10.12691/AJAMS-9-2-1","DOIUrl":"https://doi.org/10.12691/AJAMS-9-2-1","url":null,"abstract":"In Kenya wheezing that leads to asthma development in most cases remain under-diagnosed and under-treated. Currently there is no public supported wheezing and asthma care programmes to optimize care for patients with asthma which greatly compounds diagnosis and treatment of the disease. The aim of this study is therefore to consider and analyse the covariates of childhood wheezing among children below 10 years of age in Kenya, a case study of Gatundu hospital in order to improve the provision of wheezing and asthma care services in medical facilities. The possible risk factors in the study are selected from three major groups of demographic, socioeconomic and geographical location factors related to childhood wheezing. The longitudinal secondary data obtained from Gatundu hospital in Kenya were collected and a total of 584 complete cases were recorded. The predictor variables considered in the study include age of children in months, gender, exclusive breastfeeding, exposure to tobacco smoking, difficult living conditions, residence, atopy, maternal age and preterm births. Due to the binary nature of response variable in which data is recorded as presence or absence of wheezing, the risk factors were modelled using multiple logistic regression and Artificial Neural Network Models. Simple random samples of sizes n = 385 without replacement were selected and p-values at 5% level of significance for the variables were recorded. In multiple logistic regression, the five variables identified as possible risk factors for modelling with p-value less than or equal to 0.05 were selected that includes age of children, exclusive breastfeeding, exposure to tobacco smoking, difficult living conditions and residence that recorded p-values of 0.0151, 0.0000, 0.0071, 0.0274 and 0.0410. The best multiple logistic linear regression model selected was based on Akaike Information Criterion (AIC) criterion that recorded null deviance, residual deviance and AIC of 502.44, 179.57 and 191.57 respectively. The precision and accuracy of the multiple logistic regression model were recorded as 89.2% and 93.3% respectively. The Artificial Neural Network was considered for modelling as well, the model with one-hidden layer with four neurons in the hidden layer recorded precision of 97.1% and accuracy of 39.4% while the rest of the models with one hidden layer recorded precision and accuracy of 0.0% and 65.1% respectively. The Artificial Neural Network model with two-hidden layers were also considered and the Network with one neuron in both layers was selected as better performing model with precision and accuracy of 88.2% and 93.3%. The developed two-stage logistic Artificial Neural Network was found to have better performance compared to multiple linear logistic regression and Artificial Neural Networks since it recorded precision and accuracy of 97.1% and 99.0% respectively and hence recommended for consideration in modelling the risk factor of wheezing among children in Ke","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"9 1","pages":"38-47"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90936479","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":"Michael, Dowker, Worrell, Banerjee Theorems Extended to Multifunctions","authors":"Terrence A. Edwards, J. E. Joseph, B. Nayar","doi":"10.11648/J.AJAM.20210902.11","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210902.11","url":null,"abstract":"E. Michael, in 1957, proved that the pracompactness is preserved by continuous closed functions from a space onto another. Michael’s proof is an immediate consequence of his characterization of paracompact spaces as those spaces with the property that each open cover of the space has a closure preserving refinement. Normality and transfinite induction were used to produce this characterization. J. M. Worrell, in 1985, proved, using the well-ordering principle, that continuous closed images of metacompact spaces are metacompact, as a consequence of a characterization of metacompact spaces he established earlier the same year. C. H. Dowker and R. N. Banerjee have provided the corresponding results for countable paracompactnes and countable metacompactness. In this article we extend these results for continuous, image closed and onto multifunctions. A result due to Joseph and Kwack that all open sets in Y have the form g(V) - g(X - V); where V is open in X, if g : X → Y is continuous, closed and onto (2006), is extended to image-closed, continuous, multifunctions. Such multifunctions as well as a characterization that a space is paracompact (metacompact) if and only if every ultrafilter of type P (M) converges, proved, in 1918, by Joseph and Nayar, is used to give generalizations of the invariance of paracompactness and metacompactness under continuous closed surjections to multifunctions.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"344 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77146763","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":"Reviving the Sphinx by Means of Constants - Codes in a Creative Space","authors":"Hristo Smolenov","doi":"10.11648/J.AJAM.20210901.14","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210901.14","url":null,"abstract":"This paper deals with ancient codes embedded in world famous artefacts like the Sphinx and pyramids on the plateau of Giza. The same spatial codes are to be found materialized in the most ancient processed gold on Earth – the treasure trove of Varna Necropolis (4600 – 4200 BC). Amazing is the match found between those two groups of artefacts, bearing in mind that the gold from Varna Necropolis is at least 2000 years older than the pyramids. But the prototype of their sacred measure – the so called royal cubit – emerges in the system of measures related to the famous Varna Necropolis. It is there that I have been able to identify the prototypes of universal constants like the Golden ratio and Pi. The synergy of those two constants is there for us to uncover – for instance Pi times the Golden ratio. It is the simplest one in an array of complex proportions which come into effect in regard to primeval gold artefacts as well as pyramids. Surprisingly, the synergy of Pi with an exotic variant of the Golden ratio allows for the inference of a specific number, which matches the Inverse Fine structure constant. For this inference the ratio between the Planck-length and the Light second will be a starting point. On the one hand is the minimum span in the Space-time continuum (the Planck length), and on the other hand - the distance covered by light in vacuum within one second of time (the Light second). The sacred measure of pyramids is the royal cubit comprised of 28 equal parts called “fingers”. The length of the Great Sphinx comprises 140 royal cubits. It can be viewed as a super-measure from which the sizes of the three main pyramids on the plateau of Giza obtain. Suppose we were to divide this super-measure (the Sphinx-length) in 28 equal parts by analogy with the royal cubit being divided in 28 fingers. The result would be a span of 5 royal cubits. I maintain that (the Planck-length) times (10 to the power of 35) times (the Golden ratio number) yields 5 royal cubits, slightly longer than 0.523 meters each. Wishing to get closer to the actual length of the Sphinx, we might as well use a variant of the Golden ratio – the square root of (13/8 x 21/13) whereby 8, 13, 21 are consecutive Fibonacci numbers.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"42 1","pages":"20"},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86764596","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 Class of Generalized Operator Quasi-Equilibrium Problems","authors":"A. Raouf, R. Gupta, Shivani Sharma","doi":"10.11648/J.AJAM.20210901.13","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210901.13","url":null,"abstract":"In this work, introduce and study a generalized operator quasi-equilibrium problems (in short, OQEP) in the setting of topological vector spaces. We prove some new existence results for the solution of this problem by applying C(f)-quasiconvex, escaping sequence in Hausdorff topological vector spaces. The results of this paper can generalize and unify previously known corresponding results of this area.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"140 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86146508","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":"Students' Conception on Multiple Integrals of a Function of Several Variables: A Case of Adama Science and Technology University","authors":"Eyasu Gemechu, Amanuel Mogiso, Y. Hussein, Gedefa Adugna","doi":"10.11648/J.AJAM.20210901.12","DOIUrl":"https://doi.org/10.11648/J.AJAM.20210901.12","url":null,"abstract":"The study was conducted at Adama Science and Technology University to investigate students' conceptual understanding in learning Applied Mathematics II in general and multiple integrals in particular. A case study research design was employed on a Mechanical engineering group one student. This group was randomly selected through simple random sampling techniques. The number of students involved in this study was 50. Qualitative data were collected through reasoning part of the multiple choice items of the pre-test and interview items of the post-test were analyzed using APOS analysis based on proposed genetic decompositions. These tools were intended to investigate the conceptual understanding of students and the way they justify their answers. The study shows that the majority of the students' conception of multiple integrals could be categorized under action level whereas a few students were categorized under process conception. Students' conceptual understanding on multiple integrals of a function of two variables is a straight forward as that of a function of a single variable, which reveals that students have not developed a new schema for a function of two variables, as different from a function of a single variable. The majority of the respondents was poor at extending previous concepts to the new concept and had difficulty to represent multiple integrals using graph. Thus; the researchers recommended the utilization of an appropriate instructional approach in order to scaffold students' conceptual understanding of multiple integrals.","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85174604","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 Brief Elementary Proof for Fermat’s Last Theorem Using Ramanujan-Nagell Equation","authors":"P. Seetharaman","doi":"10.12691/AJAMS-9-1-4","DOIUrl":"https://doi.org/10.12691/AJAMS-9-1-4","url":null,"abstract":"Fermat's Last Theorem states that it is impossible to find natural numbers A, B and C satisfying the equation (where is any integer ). Fermat himself proved the theorem for the index and Euler proved for [1]. In the equation we hypothesize that all r, s and are non-zero integers, and prove the theorem by the method of contradiction. Merly for supporting the proof in the above equation, we include another equation without loss of generality, we assert that both and as non-zero integers; a non-zero integer; and irrational. By trial and error method, we have created transformation equations to the above two equations, into which we have incorporated the Ramanujan-Nagell Equation and on solving the two transformation equations with the aid of Ramanujan--Nagell Equation, we prove the theorem by showing","PeriodicalId":91196,"journal":{"name":"American journal of applied mathematics and statistics","volume":"3 1","pages":"24-27"},"PeriodicalIF":0.0,"publicationDate":"2021-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80201719","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}