Amila J. Maldeniya, N. Ganegoda, Kaushika De Silva, S. Boralugoda
In this paper, we present some properties of integrable distributions which are continuous linear functional on the space of test function . Here, it uses two-dimensional Henstock–Kurzweil integral. We discuss integrable distributional solution for Poisson’s equation in the upper half space with Dirichlet boundary condition.
{"title":"Solving Poisson Equation by Distributional HK-Integral: Prospects and Limitations","authors":"Amila J. Maldeniya, N. Ganegoda, Kaushika De Silva, S. Boralugoda","doi":"10.1155/2021/5511283","DOIUrl":"https://doi.org/10.1155/2021/5511283","url":null,"abstract":"<jats:p>In this paper, we present some properties of integrable distributions which are continuous linear functional on the space of test function <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi mathvariant=\"script\">D</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>. Here, it uses two-dimensional Henstock–Kurzweil integral. We discuss integrable distributional solution for Poisson’s equation in the upper half space <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msubsup>\u0000 <mi>ℝ</mi>\u0000 <mo>+</mo>\u0000 <mn>3</mn>\u0000 </msubsup>\u0000 </math>\u0000 </jats:inline-formula> with Dirichlet boundary condition.</jats:p>","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128619126","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}
This paper mainly focuses on building the fuzzy prime ideal theorem of residuated lattices. Firstly, we introduce the notion of fuzzy ideal generated by a fuzzy subset of a residuated lattice and we give a characterization. Also, we introduce different types of fuzzy prime ideals and establish existing relationships between them. We prove that any fuzzy maximal ideal is a fuzzy prime ideal in residuated lattice. Finally, we give and prove the fuzzy prime ideal theorem in residuated lattice.
{"title":"Fuzzy Prime Ideal Theorem in Residuated Lattices","authors":"Pierre Carole Kengne, B. B. K. Njionou, C. Lélé","doi":"10.1155/2021/5569981","DOIUrl":"https://doi.org/10.1155/2021/5569981","url":null,"abstract":"This paper mainly focuses on building the fuzzy prime ideal theorem of residuated lattices. Firstly, we introduce the notion of fuzzy ideal generated by a fuzzy subset of a residuated lattice and we give a characterization. Also, we introduce different types of fuzzy prime ideals and establish existing relationships between them. We prove that any fuzzy maximal ideal is a fuzzy prime ideal in residuated lattice. Finally, we give and prove the fuzzy prime ideal theorem in residuated lattice.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"667 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134390201","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}
The aim of this study is to determine the necessary and sufficient condition for any AH subset to be a full ideal in a neutrosophic ring R(I) and to be a nil ideal too. Also, this work shows the equivalence between Kothe’s conjecture in classical rings and corresponding neutrosophic rings, i.e., it proves that Kothe’s conjecture is true in the neutrosophic ring R(I) if and only if it is true in the corresponding classical ring R.
{"title":"A Study of Nil Ideals and Kothe's Conjecture in Neutrosophic Rings","authors":"Mohammad Abobala","doi":"10.1155/2021/9999707","DOIUrl":"https://doi.org/10.1155/2021/9999707","url":null,"abstract":"The aim of this study is to determine the necessary and sufficient condition for any AH subset to be a full ideal in a neutrosophic ring R(I) and to be a nil ideal too. Also, this work shows the equivalence between Kothe’s conjecture in classical rings and corresponding neutrosophic rings, i.e., it proves that Kothe’s conjecture is true in the neutrosophic ring R(I) if and only if it is true in the corresponding classical ring R.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123541458","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}
We extend the well-known characterizations of convergence in the spaces l p ( 1 ≤ p < ∞ ) of p -summable sequences and c 0 of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant corollaries characterizations of convergence in an infinite-dimensional separable Hilbert space and the space c of convergent sequences.“The method in the present paper is abstract and is phrased in terms of Banach spaces, linear operators, and so on. This has the advantage of greater simplicity in proof and greater generality in applications.” Jacob T. Schwartz
{"title":"On a Characterization of Convergence in Banach Spaces with a Schauder Basis","authors":"M. V. Markin, Olivia B. Soghomonian","doi":"10.1155/2021/1640183","DOIUrl":"https://doi.org/10.1155/2021/1640183","url":null,"abstract":"We extend the well-known characterizations of convergence in the spaces \u0000 \u0000 \u0000 \u0000 l\u0000 \u0000 \u0000 p\u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 1\u0000 ≤\u0000 p\u0000 <\u0000 ∞\u0000 \u0000 ) of \u0000 \u0000 p\u0000 \u0000 -summable sequences and \u0000 \u0000 \u0000 \u0000 c\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant corollaries characterizations of convergence in an infinite-dimensional separable Hilbert space and the space \u0000 \u0000 c\u0000 \u0000 of convergent sequences.“The method in the present paper is abstract and is phrased in terms of Banach spaces, linear operators, and so on. This has the advantage of greater simplicity in proof and greater generality in applications.” Jacob T. Schwartz","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127468386","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}
In this paper, we introduce a new three-parameter distribution defined on the unit interval. The density function of the distribution exhibits different kinds of shapes such as decreasing, increasing, left skewed, right skewed, and approximately symmetric. The failure rate function shows increasing, bathtub, and modified upside-down bathtub shapes. Six different frequentist estimation procedures were proposed for estimating the parameters of the distribution and their performance assessed via Monte Carlo simulations. Applications of the distribution were illustrated by analyzing two datasets and its fit compared to that of other distributions defined on the unit interval. Finally, we developed a regression model for a response variable that follows the new distribution.
{"title":"Bounded Odd Inverse Pareto Exponential Distribution: Properties, Estimation, and Regression","authors":"Suleman Nasiru, A. Abubakari, I. Angbing","doi":"10.1155/2021/9955657","DOIUrl":"https://doi.org/10.1155/2021/9955657","url":null,"abstract":"In this paper, we introduce a new three-parameter distribution defined on the unit interval. The density function of the distribution exhibits different kinds of shapes such as decreasing, increasing, left skewed, right skewed, and approximately symmetric. The failure rate function shows increasing, bathtub, and modified upside-down bathtub shapes. Six different frequentist estimation procedures were proposed for estimating the parameters of the distribution and their performance assessed via Monte Carlo simulations. Applications of the distribution were illustrated by analyzing two datasets and its fit compared to that of other distributions defined on the unit interval. Finally, we developed a regression model for a response variable that follows the new distribution.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125061987","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}
Non-self-adjoint operators have many applications, including quantum and heat equations. On the other hand, the study of these types of operators is more difficult than that of self-adjoint operators. In this paper, our aim is to study the resolvent and the spectral properties of a class of non-self-adjoint differential operators. So we consider a special non-self-adjoint elliptic differential operator (Au)(x) acting on Hilbert space and first investigate the spectral properties of space . Then, as the application of this new result, the resolvent of the considered operator in -dimensional space Hilbert
非自伴随算子有许多应用，包括量子方程和热方程。另一方面，研究这类算子比研究自伴随算子更为困难。本文的目的是研究一类非自伴随微分算子的解析和谱性质。因此，我们考虑了作用于Hilbert空间上的一个特殊的非自伴随椭圆微分算子(Au)(x)，并首先研究了空间h1 =的谱性质L 2 Ω 1。然后，作为这个新结果的应用，考虑算子在l维空间中的解析，Hilbert H =L 2 Ω L是利用一些解析技术和可对角化方法得到的。
{"title":"Investigation of the Spectral Properties of a Non-Self-Adjoint Elliptic Differential Operator","authors":"Arezoo Ghaedrahmati, A. Sameripour","doi":"10.1155/2021/5564552","DOIUrl":"https://doi.org/10.1155/2021/5564552","url":null,"abstract":"<jats:p>Non-self-adjoint operators have many applications, including quantum and heat equations. On the other hand, the study of these types of operators is more difficult than that of self-adjoint operators. In this paper, our aim is to study the resolvent and the spectral properties of a class of non-self-adjoint differential operators. So we consider a special non-self-adjoint elliptic differential operator (Au)(x) acting on Hilbert space and first investigate the spectral properties of space <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <msup>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi mathvariant=\"normal\">Ω</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>. Then, as the application of this new result, the resolvent of the considered operator in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>ℓ</mi>\u0000 </math>\u0000 </jats:inline-formula>-dimensional space Hilbert <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <msup>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 ","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125702130","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}
Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial with complex coefficients has a complex root. However, no analogous result holds for guaranteeing that a real root exists to if we restrict the coefficients to be real. Let and be the vector space of all polynomials of degree or less with real coefficients. In this article, we give explicit forms of polynomials in such that all of their roots are real. Furthermore, we present explicit forms of linear transformations on which preserve real roots of polynomials in a certain subset of
多项式可以用来表示现实世界的情况，当它们是实数时，它们的根具有现实世界的意义。代数基本定理告诉我们，每一个复数系数的非常数多项式p都有一个复根。然而，如果我们将系数限制为实数，则没有类似的结果可以保证p存在实数根。设n≥1,pn为所有次多项式的向量空间系数小于等于N。在这篇文章中，我们给出了np中多项式的显式形式，使得它们的所有根都是实数。此外,我们给出了pn上的线性变换的显式形式，这些变换在一定的子集中保持多项式的实根P n .;
{"title":"Real Root Polynomials and Real Root Preserving Transformations","authors":"Suchada Pongprasert, Kanyarat Chaengsisai, Wuttichai Kaewleamthong, Puttarawadee Sriphrom","doi":"10.1155/2021/5585480","DOIUrl":"https://doi.org/10.1155/2021/5585480","url":null,"abstract":"<jats:p>Polynomials can be used to represent real-world situations, and their roots have real-world meanings when they are real numbers. The fundamental theorem of algebra tells us that every nonconstant polynomial <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>p</mi>\u0000 </math>\u0000 </jats:inline-formula> with complex coefficients has a complex root. However, no analogous result holds for guaranteeing that a real root exists to <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>p</mi>\u0000 </math>\u0000 </jats:inline-formula> if we restrict the coefficients to be real. Let <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>1</mn>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> be the vector space of all polynomials of degree <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>n</mi>\u0000 </math>\u0000 </jats:inline-formula> or less with real coefficients. In this article, we give explicit forms of polynomials in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> such that all of their roots are real. Furthermore, we present explicit forms of linear transformations on <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> which preserve real roots of polynomials in a certain subset of <jats:inline-formula>\u0000 ","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133817132","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}
For parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems inverse in time. It linearly combines the meaning of the solution at the initial and some intermediate points in time. The conditions for the correct solvability of this problem are clarified and the formula for its solution is found. Using the results obtained, the corresponding problems with impulse action were solved.
{"title":"Modified Cauchy Problem with Impulse Action for Parabolic Shilov Equations","authors":"G. Unguryan","doi":"10.1155/2021/5539676","DOIUrl":"https://doi.org/10.1155/2021/5539676","url":null,"abstract":"For parabolic Shilov equations with continuous coefficients, the problem of finding classical solutions that satisfy a modified initial condition with generalized data such as the Gelfand and Shilov distributions is considered. This condition arises in the approximate solution of parabolic problems inverse in time. It linearly combines the meaning of the solution at the initial and some intermediate points in time. The conditions for the correct solvability of this problem are clarified and the formula for its solution is found. Using the results obtained, the corresponding problems with impulse action were solved.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132047736","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}
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.
{"title":"Novel Theorems and Algorithms Relating to the Collatz Conjecture","authors":"Michael R. Schwob, P. Shiue, R. Venkat","doi":"10.1155/2021/5754439","DOIUrl":"https://doi.org/10.1155/2021/5754439","url":null,"abstract":"Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128289872","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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