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The generalized Riemann-Stieltjes integral [PDF]
Real Analysis Exchange, 1995 A Stieltjes type integral \(\int_Af \,dG\) of a function \(f\) with respect to a charge \(G\) in the bounded \(BV\) set \(A\subset \mathbb R^m\) is defined in the paper via Riemann type integral sums and the concept of the indefinite integral. Some specific results concerning the concept are presented.
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On the fractional Laplacian of a function with respect to another function
Mathematical Methods in the Applied Sciences, Volume 47, Issue 18, Page 14079-14110, December 2024.The theories of fractional Laplacians and of fractional calculus with respect to functions are combined to produce, for the first time, the concept of a fractional Laplacian with respect to a bijective function. The theory is developed both in the 1‐dimensional setting and in the general n$$ n $$‐dimensional setting.
Arran Fernandez +2 more
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A Formal Proof Of The Riesz Representation Theorem
Journal of Formalized Reasoning, 2011 This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral.
Anthony Narkawicz
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Fractional integrals, derivatives and integral equations with weighted Takagi–Landsberg functions
Nonlinear Analysis, 2020 In this paper, we find fractional Riemann–Liouville derivatives for the Takagi–Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi–Landsberg functions, which have arbitrary bounded coefficients in the expansion under ...
Vitalii Makogin, Yuliya Mishura
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Inequalities for Riemann - Stieltjes integral
International Journal of Emerging Multidisciplinaries: Mathematics, 2022 Two new inequalities for Riemann--Stieltjes integral are introduced for functions of bounded $p$-variation and H\"{o}lder continuous integrators.
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An inequality for the Riemann-Stieltjes integral [PDF]
Proceedings of the American Mathematical Society, 1970 Let g g and h h be real valued and continuous on the interval [ a , b ] [a,b] , and suppose that the variation, V [ h ] V[h] , of h h on [ a , b ] [a,b]
Darst, Richard, Pollard, Harry
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Welding defect detection with image processing on a custom small dataset: A comparative study
IET Collaborative Intelligent Manufacturing, Volume 6, Issue 4, December 2024.This work focuses on detecting defects in welding seams using the most advanced You Only Look Once (YOLO) algorithms and transfer learning. To this end, the authors prepared a small dataset of images using manual welding and compared the performance of the YOLO v5, v6, v7, and v8 methods after two‐step training.
József Szőlősi +5 more
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Journal of Inequalities and Applications, 2021 In this paper, we are concerned with a kind of tempered fractional differential equation Riemann–Stieltjes integral boundary value problems with p-Laplacian operators.
Bibo Zhou, Lingling Zhang
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Φ V[h] and Riemann-Stieltjes integration [PDF]
Colloquium Mathematicum, 1990 The authors introduce and consider the class of functions of generalized (in some sense) variation and find some connections of that class with Fourier series. At the end they consider the problem of Riemann-Stieltjes integration (the existence of \(\int f dg)\) by strengthening the requirements of \(f\) and weakening those on \(g\).
Schembari, N. Paul, Schramm, Michael
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Mathematical Methods in the Applied Sciences, Volume 47, Issue 12, Page 9493-9523, August 2024.This paper deals with the probabilistic analysis of a class of compartmental models formulated via a system of linear differential equations with time‐dependent non‐homogeneous terms. For the sake of generality, we assume that initial conditions and rates between compartments are random variables with arbitrary distributions while the source terms ...
Vicente J. Bevia +3 more
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