检索结果-内蒙古大学图书馆

26th International Symposium on Mathematical Theory of Networks and Systems (MTNS)

作者： Verriest, Erik, I Dirr, Gunther Gray, W. Steven Georgia Inst Technol Atlanta GA 30332 USA Julius Maximilians Univ D-9707 Wurzburg Germany Old Dominion Univ Norfolk VA 23529 USA

We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in R by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra to allow for products of generalized functions. This is important in the study of (smooth) nonlinear systems driven by impulsive inputs, and hybrid system theory. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Algebraic Systems Theory Nonlinear Systems and Control Operator Theoretic Methods in Systems Theory generalized functions Impulsive Systems Laplace Transform

来源：评论

学校读者我要写书评

暂无评论

Analytical solutions for strain-driven Timoshenko nanobeam bending using generalized functions

引用

MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES 2025年第4期53卷 3010-3043页

作者： Khanra, Gaurab Kumar Krishna, I. R. Praveen Raveendranath, P. Indian Inst Space Sci & Technol Dept Aerosp Engn Thiruvananthapuram Kerala India

Static nanobeam bending problems have yielded conflicting results from many researchers. Methods suggested by numerous researchers have shown inconsistencies in capturing size effects and satisfying essential and natural boundary conditions for nanobeam configurations when subjected to different types of loading. This work proposes an alternative approach using Eringen's strain-driven integral nonlocal elasticity to arrive at analytical solutions. The theory of generalized functions and the Dirac-delta identity are used to revisit Timoshenko nanobeam modeling aspects, focusing on nanobeam elastostatics. Proposed analytical solutions for fundamental and derived quantities based on the strain-driven nonlocal model have been compared with the results of existing approaches. A crucial drawback with the strain-driven models of Eringen in both integral and differential form is its inability to satisfy equilibrium equations, which is addressed extensively in this work.

关键词： Nonlocal elasticity strain-driven model Dirac-delta identity generalized functions

来源：评论

学校读者我要写书评

暂无评论

A Multifractal Detrended Fluctuation Analysis approach using generalized functions

引用

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2024年 637卷

作者： Mendonca, Suzielli M. Cabella, Brenno C. T. Martinez, Alexandre S. Univ Sao Paulo Fac Philosophy Sci & Letters Ribeirao Preto Ave Bandeirantes 3900 BR-14040901 Ribeirao Preto SP Brazil Univ Estadual Paulista Inst Theoret Phys R Dr Bento Teobaldo Ferraz271 Bloco 2 BR-01140070 Sao Paulo SP Brazil

Detrended Fluctuation Analysis (DFA) and its generalization for multifractal signals, Multifractal Detrend Fluctuation Analysis (MFDFA), are widely used techniques to investigate the fractal properties of time series by estimating their Hurst exponent (H). These methods involve calculating the fluctuation functions, which represent the square root of the mean square deviation from the detrended cumulative curve of a given time series. However, in the multifractal variant of the method, a particular case arises when the multifractal index vanishes. Consequently, it becomes necessary to define the fluctuation function differently for this specific case. In this paper, we propose an approach that eliminates the need for a piecewise definition of the fluctuation function, thereby enabling a unified formulation and interpretation in both DFA and MFDFA methodologies. Our formulation provides a more compact algorithm applicable to mono and multifractal time series. To achieve this, we express the fluctuation functions as generalized means, using the generalized logarithm and exponential functions from the context of the non -extensive statistical mechanics. We identified that the generalized formulation is the Box-Cox transformation of the dataset;hence we established a relationship between statistics parametrization and multifractality. Furthermore, this equivalence is related to the entropic index of the generalized functions and the multifractal index of the MFDFA method. To validate our formulation, we assess the efficacy of our method in estimating the (generalized) Hurst exponents H using commonly used signals such as the fractional Ornstein-Uhlenbeck (fOU) process, the symmetric Levy distribution, pink, white, and Brownian noises. In addition, we apply our proposed method to a real -world dataset, further demonstrating its effectiveness in estimating the exponents H and uncovering the fractal nature of the data.

关键词： Multifractal detrended fluctuation analysis Hurst exponent generalized functions Power-law correlations generalized fluctuation function

来源：评论

学校读者我要写书评

暂无评论

Iteration of the Laplace transform over generalized functions and a Post-Widder inversion formula over distributions of compact support

引用

INTEGRAL TRANSFORMS AND SPECIAL functions 2023年第11期34卷 835-848页

作者： Gonzalez, B. J. Negrin, E. R. Univ La Laguna ULL Fac Ciencias Dept Anal Matemat ES-38271 San Cristobal la Laguna Tenerife Spain Inst Matemat & Aplicac IMAULL Campus Anchieta ES-38271 San Cristobal la Laguna Tenerife Spain

In this paper, we deal with the iteration of the Laplace transform over certain spaces of generalized functions. As a consequence we prove a new Post-Widder-type inversion formula for this transform over distributions... 详细信息

关键词： Laplace transform Stieltjes transform generalized functions iteration distributions of compact support Post-Widder inversion formula

来源：评论

学校读者我要写书评

暂无评论

General shells and generalized functions

引用

CLASSICAL AND QUANTUM GRAVITY 2025年第9期42卷 095014-095014页

作者： Huber, Albert UAS Tech Wien Hochstadt pl 6 A-1200 Vienna Austria Karl Franzens Univ Graz Schubert str 51 Graz Austria

In this work, standard methods of the mixed thin-shell formalism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular regularizations of the Heaviside step function and the delta distribution, instead of working directly with the corresponding Schwartz distributions. Based on this change of method, the resulting extended thin shell formalism is shown to offer a decisive advantage over traditional approaches to the subject: it avoids dealing with ill-defined products of distributions in the calculation of nonlinear curvature expressions, thereby allowing for the treatment of problems that prove intractable with the 'conventional' thin-shell formalism. This includes, in particular, the problem of matching singular spacetimes with distributional metrics (containing a delta distribution term) across a joint boundary hypersurface in spacetime, the problem of setting up the dominant energy condition for thin shells, and the problem of defining reasonably rigorously nonlinear distribution-valued curvature invariants needed in higher-derivative theories of gravity. Eventually, as a further application, close links to Penrose's cut-and-paste method are established by proving that results of said method can be re-derived using the generalized formalism presented.

关键词： Colombeau algebras generalized functions thin shell formalism gluing methods

来源：评论

学校读者我要写书评

暂无评论

generalized functions in the Study of Signals and Systems

引用

IFAC-PapersOnLine 2024年第17期58卷 380-385页

作者： Erik I. Verriest Gunther Dirr W. Steven Gray

We collect three instances where the theory of generalized functions may still make contributions to the study of signals and systems. In the first, a purely algebraic approach is presented for LTI-ODE's, in terms of two operators, D and T, respectively the differentiation operator and the multiplication-by-the-independent-variable operator. This formalism adds simplicity, a duality theory, and nicely generalizes to other classes of operator equations and their solutions. In the second part we extend the classical bilateral Laplace transform to include Bohl functions with support in ℝ by invoking Sato's hyperfunctions. Finally, in the third case we use the Colombeau algebra to allow for products of generalized functions. This is important in the study of (smooth) nonlinear systems driven by impulsive inputs, and hybrid system theory.

关键词： Algebraic Systems Theory Nonlinear Systems and Control Operator Theoretic Methods in Systems Theory generalized functions Impulsive Systems Laplace Transform

来源：评论

学校读者我要写书评

暂无评论

Superoscillating Sequences and Supershifts for Families of generalized functions

引用

COMPLEX ANALYSIS AND OPERATOR THEORY 2022年第3期16卷 1-37页

作者： Colombo, F. Sabadini, I. Struppa, D. C. Yger, A. Politecn Milan Dipartimento Matemat Via E Bonardi 9 I-20133 Milan Italy Chapman Univ Donald Bren Presidential Chair Math Orange CA USA Univ Bordeaux IMB F-33405 Talence France

We construct a large class of superoscillating sequences, more generally of F-supershifts, where F is a family of smooth functions in (t, x) (resp. distributions in (t, x), or hyperfunctions in x depending on the parameter t) indexed by lambda is an element of R. The frame in which we introduce such families is that of the evolution through Schrodinger equation (i partial derivative/partial derivative t - H (x))(psi) = 0 (H(x) = - (partial derivative(2)/partial derivative x(2))/2+V (x)), V being a suitable potential). If F = {(t, x) bar right arrow phi(lambda)(t, x);lambda is an element of R}, where phi(lambda) is evolved from the initial datum x bar right arrow e(i lambda x), F-supershifis will be of the form {Sigma(N)(j=0) C-j (N, a)phi(1-2j/N)}(N >= 1) for a is an element of R\[-1, 1], taking C-j (N, a) = ((N)j)(1 + a)( N-j) (1 - a)(j) /2(N). Our results rely on the fact that integral operators of the Presnel type govern, as in optical diffraction, the evolution through the Schrodinger equation, such operators acting continuously on the weighted algebra of entire functions Exp(C). Analyzing in particular the quantum harmonic oscillator case forces us, in order to take into account singularities of the evolved datum that occur when the stationary phasis in the Fresnel operator vanishes, to enlarge the notion of F-supershift, F being a family of C-infinity functions or distributions in (t, x), to that where F is a family of hyperfunctions in x, depending on t as a parameter.

关键词： Superoscillations Infinite order differential operators Schrodinger equation generalized functions

来源：评论

学校读者我要写书评

暂无评论

An Improved Setting for generalized functions: Fine Ultrafunctions

引用

MILAN JOURNAL OF MATHEMATICS 2022年第2期90卷 575-646页

作者： Benci, Vieri Univ Pisa Dipartimento Matemat Via F Buonarroti 1-C Pisa Italy

Ultrafunctions are a particular class of functions defined on a Non Archimedean field E superset of R. They have been introduced and studied in some previous works (Benci, in Adv Nonlinear Stud 13:461-486, 2013;Benci and Luperi Baglini, in Electron J Differ Equ Conf 21:11-21, 2014;Benci et al., in Adv Nonlinear Anal 10. https: //doi . org/10.1515/anona-2017-0225. 2;Benci et al., in Adv. Nonlinear Anal 9, 2018). In this paper we develop the notion of fine ultrafunctions which improves the older definitions in many crucial points. Some applications are given to show how ultrafunctions can be applied in studing Partial Differential Equations. In particular, it is possible to prove the existence of ultrafunction solutions to ill posed evolution poblems.

关键词： Partial differential equations generalized functions Distributions Non archimedean mathematics Non standard analysis Ill posed problems

来源：评论

学校读者我要写书评

暂无评论

Abelian theorems for Laplace, Mellin and Stieltjes transforms over distributions of compact support and generalized functions

引用

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO 2023年第3期72卷 2213-2229页

作者： Maan, Jeetendrasingh Negrin, E. R. Indian Inst Technol Indian Sch Mines Dept Math & Comp Dhanbad 826004 Bihar India Univ La Laguna Dept Anal Matemat San Cristobal la Laguna Spain

Our goal in this article is to derive Abelian theorems for the two-sided Laplace transform, Mellin transform, one-sided real Laplace transform and Stieltjes transform over distributions of compact support and over cer... 详细信息

关键词： Two-sided Laplace transform Mellin transform One-sided real Laplace transform Stieltjes transform Distributions of compact support generalized functions Abelian theorems

来源：评论

学校读者我要写书评

暂无评论

Asymptotic Behaviours of Laplace Transforms of generalized functions

引用

NATIONAL ACADEMY SCIENCE LETTERS-INDIA 2025年 1-7页

作者： Negrin, E. R. Gonzalez, B. J. Maan, Jeetendrasingh Univ La Laguna ULL Dept Anal Matemat San Cristobal la Laguna 38271 Tenerife Spain Natl Inst Technol Dept Math & Sci Comp Hamirpur 177005 India

This paper derives asymptotic behaviours of Laplace transforms of generalized functions. The results demonstrate how distribution theory contributes to the depth of mathematical analysis.

关键词： Asymptotic behaviours generalized functions Two-sided Laplace transform One-sided Laplace transform n-dimensional Laplace transform

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：