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Number Theory and its Applications最新文献

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Euler's Generalization and ϕ-function 欧拉泛化与ϕ-函数
Number Theory and its Applications Pub Date : 2021-11-24 DOI: 10.1201/9781003275947-7
S. Kundu, Sypriyo Mazumder
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引用次数: 0
Primitive Roots 原始的根
Number Theory and its Applications Pub Date : 2021-11-24 DOI: 10.1201/9781003275947-8
S. Kundu, Sypriyo Mazumder
{"title":"Primitive Roots","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-8","DOIUrl":"https://doi.org/10.1201/9781003275947-8","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127930480","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
Certain Applications on Number Theory 数论的某些应用
Number Theory and its Applications Pub Date : 2021-11-24 DOI: 10.1201/9781003275947-14
S. Kundu, Sypriyo Mazumder
{"title":"Certain Applications on \u0000Number Theory","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-14","DOIUrl":"https://doi.org/10.1201/9781003275947-14","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117001948","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
I–Convergence of Arithmetical Functions 算术函数的收敛性
Number Theory and its Applications Pub Date : 2020-11-04 DOI: 10.5772/intechopen.91932
V. Baláž, T. Visnyai
{"title":"I–Convergence of Arithmetical Functions","authors":"V. Baláž, T. Visnyai","doi":"10.5772/intechopen.91932","DOIUrl":"https://doi.org/10.5772/intechopen.91932","url":null,"abstract":"Let n > 1 be an integer with its canonical representation, n = p 1 α 1 p 2 α 2 ⋯ p k α k . Put H n = max α 1 … α k , h n = min α 1 … α k , ω n = k , Ω n = α 1 + ⋯ + α k , f n = ∏ d ∣ n d and f ∗ n = f n n . Many authors deal with the statistical convergence of these arithmetical functions. For instance, the notion of normal order is defined by means of statistical convergence. The statistical convergence is equivalent with I d –convergence, where I d is the ideal of all subsets of positive integers having the asymptotic density zero. In this part, we will study I –convergence of the well-known arithmetical functions, where I = I c q = A ⊂ N : ∑ a ∈ A a − q < + ∞ is an admissible ideal on N such that for q ∈ 0 1 we have I c q ⊊ I d , thus I c q –convergence is stronger than the statistical convergence ( I d –convergence).","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126151584","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: 4
Modular Sumset Labelling of Graphs 图的模Sumset标记
Number Theory and its Applications Pub Date : 2020-08-08 DOI: 10.5772/intechopen.92701
S. Naduvath
{"title":"Modular Sumset Labelling of Graphs","authors":"S. Naduvath","doi":"10.5772/intechopen.92701","DOIUrl":"https://doi.org/10.5772/intechopen.92701","url":null,"abstract":"Graph labelling is an assignment of labels or weights to the vertices and/or edges of a graph. For a ground set X of integers, a sumset labelling of a graph is an injective map f:VG→PX such that the induced function f⊕:EG→PX is defined by f+uv=fu+fv, for all uv∈EG, where fu+fv is the sumset of the set-label, the vertices u and v. In this chapter, we discuss a special type of sumset labelling of a graph, called modular sumset labelling and its variations. We also discuss some interesting characteristics and structural properties of the graphs which admit these new types of graph labellings.","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125505642","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
The Borel-Cantelli Lemmas, and Their Relationship to Limit Superior and Limit Inferior of Sets (or, Can a Monkey Really Type Hamlet?) Borel-Cantelli引理及其与集合极上极下的关系(或者，猴子真的能成为哈姆雷特吗?)
Number Theory and its Applications Pub Date : 2020-07-09 DOI: 10.5772/intechopen.93121
A. Godbole
{"title":"The Borel-Cantelli Lemmas, and Their Relationship to Limit Superior and Limit Inferior of Sets (or, Can a Monkey Really Type Hamlet?)","authors":"A. Godbole","doi":"10.5772/intechopen.93121","DOIUrl":"https://doi.org/10.5772/intechopen.93121","url":null,"abstract":"The purpose of this chapter is to show that if a monkey types infinitely, Shakespeare’s Hamlet and any other works one may wish to add to the list will each be typed, not once, not twice, but infinitely often with a probability of 1. This dramatic fact is a simple consequence of the Borel-Cantelli lemma and will come as no surprise to anyone who has taken a graduate-level course in Probability. The proof of this result, however, is quite accessible to anyone who has but a rudimentary understanding of the concept of independence, together with the notion of limit superior and limit inferior of a sequence of sets.","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126755415","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 Identities Involving 2-Variable Modified Degenerate Hermite Polynomials Arising from Differential Equations and Distribution of Their Zeros 微分方程中涉及2变量修正退化埃尔米特多项式的恒等式及其零点的分布
Number Theory and its Applications Pub Date : 2020-05-30 DOI: 10.5772/intechopen.92687
C. Ryoo
{"title":"Some Identities Involving 2-Variable Modified Degenerate Hermite Polynomials Arising from Differential Equations and Distribution of Their Zeros","authors":"C. Ryoo","doi":"10.5772/intechopen.92687","DOIUrl":"https://doi.org/10.5772/intechopen.92687","url":null,"abstract":"In this chapter, we introduce the 2-variable modified degenerate Hermite polynomials and obtain some new symmetric identities for 2-variable modified degenerate Hermite polynomials. In order to give explicit identities for 2-variable modified degenerate Hermite polynomials, differential equations arising from the generating functions of 2-variable modified degenerate Hermite polynomials are studied. Finally, we investigate the structure and symmetry of the zeros of the 2-variable modified degenerate Hermite equations.","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123095748","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: 2
Identification of Eigen-Frequencies and Mode-Shapes of Beams with Continuous Distribution of Mass and Elasticity and for Various Conditions at Supports 具有连续质量和弹性分布和不同支承条件的梁的本征频率和模态振型识别
Number Theory and its Applications Pub Date : 2020-05-04 DOI: 10.5772/intechopen.92185
T. Makarios
{"title":"Identification of Eigen-Frequencies and Mode-Shapes of Beams with Continuous Distribution of Mass and Elasticity and for Various Conditions at Supports","authors":"T. Makarios","doi":"10.5772/intechopen.92185","DOIUrl":"https://doi.org/10.5772/intechopen.92185","url":null,"abstract":"In the present article, an equivalent three degrees of freedom (DoF) system of two different cases of inverted pendulums is presented for each separated case. The first case of inverted pendulum refers to an amphi-hinge pendulum that possesses distributed mass and stiffness along its height, while the second case of inverted pendulum refers to an inverted pendulum with distributed mass and stiffness along its height. These vertical pendulums have infinity number of degree of freedoms. Based on the free vibration of the above-mentioned pendulums according to partial differential equation, a mathematically equivalent three-degree of freedom system is given for each case, where its equivalent mass matrix is analytically formulated with reference on specific mass locations along the pendulum height. Using the three DoF model, the first three fundamental frequencies of the real pendulum can be identified with very good accuracy. Furthermore, taking account the 3 × 3 mass matrix, it is possible to estimate the possible pendulum damages using a known technique of identification mode-shapes via records of response accelerations. Moreover, the way of instrumentation with a local network by three accelerometers is given via the above-mentioned three degrees of freedom.","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"130 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114090514","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: 1
Moments of Catalan Triangle Numbers 加泰罗尼亚三角数的矩
Number Theory and its Applications Pub Date : 2020-04-22 DOI: 10.5772/intechopen.92046
Pedro J. Miana, Natalia Romero
{"title":"Moments of Catalan Triangle Numbers","authors":"Pedro J. Miana, Natalia Romero","doi":"10.5772/intechopen.92046","DOIUrl":"https://doi.org/10.5772/intechopen.92046","url":null,"abstract":"In this chapter, we consider the Catalan numbers, C n = 1 n + 1 2 n n , and two of their generalizations, Catalan triangle numbers, B n , k and A n , k , for n , k ∈ N . They are combinatorial numbers and present interesting properties as recursive formulae, generating functions and combinatorial interpretations. We treat the moments of these Catalan triangle numbers, i.e., with the following sums: ∑ k = 1 n k m B n , k j , ∑ k = 1 n + 1 2 k − 1 m A n , k j , for j , n ∈ N and m ∈ N ∪ 0 . We present their closed expressions for some values of m and j . Alternating sums are also considered for particular powers. Other famous integer sequences are studied in Section 3, and its connection with Catalan triangle numbers are given in Section 4. Finally we conjecture some properties of divisibility of moments and alternating sums of powers in the last section.","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126898970","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: 2
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