Asian Research Journal of Mathematics最新文献_第2页

A Detailed Proof of the Strong Goldbach Conjecture Based on Partitions of a New Formulation of a Set of Even Numbers 基于偶数集合新公式分区的强哥德巴赫猜想的详细证明

Asian Research Journal of Mathematics Pub Date : 2024-04-10 DOI: 10.9734/arjom/2024/v20i4793

Daniel Sankei, Loyford Njagi, Josephine Mutembei

{"title":"A Detailed Proof of the Strong Goldbach Conjecture Based on Partitions of a New Formulation of a Set of Even Numbers","authors":"Daniel Sankei, Loyford Njagi, Josephine Mutembei","doi":"10.9734/arjom/2024/v20i4793","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i4793","url":null,"abstract":"The Strong Goldbach's conjecture, a fundamental problem in Number Theory, asserts that every even integer greater than 2 can be expressed as the sum of two prime numbers. Despite significant efforts over centuries, this conjecture remains unproven, challenging the core of mathematics. The known algorithms for attempting to prove or verify the conjecture on a given interval [a,b] consist of finding two sets of primes Pi and Pj such that Pi+Pj cover all the even numbers in the interval [a,b]. However, the traditional definition of an even number as 2n for n ∈ ℕ (where ℕ is the set of natural numbers), has not provided mathematicians with a straightforward method to obtain all Goldbach partitions for any even number of this form. This paper introduces a novel approach to the problem, utilizing all odd partitions of an even number of a new formulation of the form Eij = ni + nj + (nj - ni)n or alln ∈ ℕ. By demonstrating that there exist at least a pair of prime numbers in these odd partitions, the fact that the sum of any two prime numbers is even and there exists infinitely many prime numbers, this paper provides a compelling proof of the conjecture. This breakthrough not only solves a long-standing mathematical mystery but also sheds light on the structure of prime numbers.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"225 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140720044","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}

引用次数: 0

Analysis of Norm-Attainability and Convergence Properties of Orthogonal Polynomials in Weighted Sobolev Spaces 加权索波列夫空间中正交多项式的规范可达性和收敛性分析

Asian Research Journal of Mathematics Pub Date : 2024-04-09 DOI: 10.9734/arjom/2024/v20i4792

Mogoi N. Evans, A. Wanjara, Samuel B. Apima

引用次数: 0

Solution of Laplace Equation by Modified Differential Transform Method 用修正微分变换法求解拉普拉斯方程

Asian Research Journal of Mathematics Pub Date : 2024-03-29 DOI: 10.9734/arjom/2024/v20i3790

R. S. M. Kularathna, N. Kajan, T. Jeyamugan, S. Thilaganathan

引用次数: 0

Fixed Point Theorems for Kannan Interpolative, Riech Interpolative and Dass-Gupta Interpolative Rational type Contractions in A-Metric Spaces A 度量空间中 Kannan 互推、Riech 互推和 Dass-Gupta 互推有理类型收缩的定点定理

Asian Research Journal of Mathematics Pub Date : 2024-02-28 DOI: 10.9734/arjom/2024/v20i2782

Sheetal Yadav, Manoj Ughade, D. Singh, Manoj Kumar Shukla

引用次数: 0

The Minimum Superior Dominating Energy of Graphs 图形的最小优势支配能

Asian Research Journal of Mathematics Pub Date : 2024-02-21 DOI: 10.9734/arjom/2024/v20i1781

Tejaskumar R., A. Ismayil

引用次数: 0

Modelling Mortality in Kenya 肯尼亚死亡率模型

Asian Research Journal of Mathematics Pub Date : 2024-01-23 DOI: 10.9734/arjom/2024/v20i1777

Jackson K. Njenga, I. C. Kipchirchir

{"title":"Modelling Mortality in Kenya","authors":"Jackson K. Njenga, I. C. Kipchirchir","doi":"10.9734/arjom/2024/v20i1777","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i1777","url":null,"abstract":"This research work seeks to analysis the mortality trend experienced in Kenya over the sample period 1950 to 2021 using a multidimensional modeling framework. Life table functions, namely; life expectancy, survival function and age at death distribution are applied to depict mortality characteristics. Life expectancy and survival rate have significantly improved. There has been a shift in mortality status from a high mortality population, to an intermediate stage and mortality risk factors have increased across age. Mortality concentration curve and index within the Lorenz curve and Gini coefficient framework are used to analyze the lifespan inequality. Lifespan inequality is high with negligible improvements over time. Gompertz force of mortality is then estimated, which is statistically significant at 5% level. Deaths at exact age 25 is about 35 per ten thousand, with the rate death rate increasing by 6.09% per year starting from age 25. Under the assumptions of stable population, where the mortality and fertility functions are independent of time, Malthusian parameter is estimated which is less than zero for selected years. Kenya is a shrinking population and death rate decrease with increase in Malthusian parameter. Finally, to model long-term mortality rate forecast, Lee-Carter model is estimated. The model is statistically significant at 5% level explaining 78.4% of the variations. Expected life expectancy at a given age is projected to increase, with life expectancy at birth in 2030 and 2071 being 65.6 and 70.5 years respectively.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"147 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140498083","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}

引用次数: 0

Oscillatory Solution of a Convolutional Volterra Integral Equation 卷积 Volterra 积分方程的振荡解法

Asian Research Journal of Mathematics Pub Date : 2023-12-28 DOI: 10.9734/arjom/2023/v19i12772

Henry Otoo, W. Obeng-Denteh, Lewis Brew

引用次数: 0

Estimation of the Probability of Earthquakes Return Period in Zimbabwe Using Gumbel’s Extreme Value Theory Method 利用 Gumbel 的极值理论方法估算津巴布韦地震重现期的概率

Asian Research Journal of Mathematics Pub Date : 2023-12-28 DOI: 10.9734/arjom/2023/v19i12771

Atsu, J. U., Abong, A. A.

{"title":"Estimation of the Probability of Earthquakes Return Period in Zimbabwe Using Gumbel’s Extreme Value Theory Method","authors":"Atsu, J. U., Abong, A. A.","doi":"10.9734/arjom/2023/v19i12771","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i12771","url":null,"abstract":"Using Gumbel's extreme value theory method, this study looked into the probability of the largest earthquakes for different return periods in Zimbabwe. The Advanced National Seismic System (ANSS), the Northern California Earthquake Data Centre website, and UC Berkeley in the United States provided the data used for this study. The natural earthquakes with Mb ≥ 4.0 that occurred in the study area between January 1, 1901 and December 31, 2001 (a period of 100 years) with a focal depth ranging from 0 to 700 km made up the selected data. The study area is between 150S - 220S and 250E -340E in coordinates. A total of 81 events were used in the investigation. According to the results, there is a 100% chance that earthquakes with a magnitude between 4.5 and 5.5 will occur during the time interval of approximately 1 to 14 years and a 9.5% chance that within the next 100 years, there will be an earthquake with a magnitude of Mb = 6.0 or higher. For magnitudes Mb = 6.0 and above, the return period is relatively long - roughly 50 – 701 years. This suggests that there is little chance that Zimbabwe will experience earthquakes larger than magnitude 6.0. Despite being low, it is impossible to forecast with certainty because earthquake forecasting and prediction is still a complex topic.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"52 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139151134","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}

引用次数: 0

Some Fixed Point Techniques using (psi)-contraction Mapping on the (mathit{C}^*)-algebra Valued Metric Space 使用 (mathit{C}^*)-algebra Valued Metric Space 上 (psi)-contraction Mapping 的一些定点技术

Asian Research Journal of Mathematics Pub Date : 2023-12-23 DOI: 10.9734/arjom/2023/v19i12769

Alshaimaa Awad, Saleh Omran

引用次数: 0

On Suborbits and Graphs Associated with Action of Alternating Groups on Cartesian Product of Two Sets 论交替群对两个集合的笛卡尔积的作用相关的子轨道和图形

Asian Research Journal of Mathematics Pub Date : 2023-11-28 DOI: 10.9734/arjom/2023/v19i11763

Stephen Kadedesya, L. Nyaga, J. Rimberia

引用次数: 0