Results 11 to 20 of about 360,754 (261)
Existence and computation of Riemann-Stieltjes integrals through Riemann integrals [PDF]
arXiv, 2011 We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we present a new generalization to the well-known formula for continuous integrands and continuously differentiable ...
Rodrigo López Pouso
arxiv +5 more sources
A Generalization of the Riemann Integral [PDF]
Proceedings of the American Mathematical Society, 1952 By considering certain kinds of sets as exceptional in the definition of the Riemann integral, a variety of possible generalizations of the integral concept for bounded functions is obtained, one of which is the Lebesgue integral. Such an extension has been discussed by E. H.
Casper Goffman
openalex +2 more sources
Theta and Riemann xi function representations from harmonic oscillator eigensolutions [PDF]
, 2006 From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical zeta function. A key result provides a basis for generalizing the important Riemann-Siegel integral formula.
Abramowitz +25 more
arxiv +3 more sources
Pattern Integration with Improper Riemann Integrals [PDF]
Proceedings of the American Mathematical Society, 1951 2. The improper integral defined as the limit of a sum. We first consider the case where ak = 1 (k =1, 2, 3, * * * ). A fundamental difficulty not encountered in the previous paper is apparent from the definition of .fof(x)dx. Bromwich and Hardy have considered this problem [2]. As they point out, the ordinary definition of this improper integral is by
R. E. Carr
openalex +3 more sources
The Lebesgue integral as a Riemann integral [PDF]
International Journal of Mathematics and Mathematical Sciences, 1987 The object of this paper is to develop a very direct theory of the Lebesgue integral that is easily accessible to any audience familiar with the Riemann integral.
Enrique A. Gonzalez-Velasco
doaj +3 more sources
ON THE POSITIVITY OF RIEMANN–STIELTJES INTEGRALS [PDF]
Bulletin of the Australian Mathematical Society, 2012 AbstractWe study the question whether a Riemann–Stieltjes integral of a positive continuous function with respect to a nonnegative function of bounded variation is positive.
Jani Lukkarinen, Mikko S. Pakkanen
openalex +7 more sources
Kajian Intgeral Henstock [PDF]
, 2022 A study of the properties of Henstock integral has been carried out. Henstock integral is an extension of Riemann integral. This is because the Henstock integral is built on the concept of Riemann integral, using the Riemann sum over the partition on the
Dethan, Nugraha K. F.
core +2 more sources
Connection between the Riemann integrability of a multi-valued function and of its convex hull [PDF]
Journal of Mathematical Analysis and Applications, Available
online 8 September 2021, 125652, 2021 For a Banach space $X$ we demonstrate the equivalence of the following two properties: (1) $X$ is B-convex (that is, possesses a nontrivial infratype), and (2) if ${F: [0,1] \to 2^{X} \setminus \{\varnothing\}}$ is a {multifunction}, $\mathrm{conv} F$ denotes the mapping $t \mapsto \mathrm{conv} F(t)$, then the Riemann integrability of $\mathrm ...
arxiv +1 more source
Modelling interactions between waves and diffused interfaces
International Journal for Numerical Methods in Fluids, Volume 95, Issue 2, Page 215-241, February 2023., 2023 When simulating multiphase compressible flows using the diffuse‐interface methods, important issues arise during the interaction of waves with diffused interfaces. A solution is to use a pressure‐disequilibrium model with finite, instead of infinite, pressure‐relaxation rate.
Kevin Schmidmayer +4 more
wiley +1 more source
International Journal for Numerical Methods in Fluids, Volume 95, Issue 1, Page 107-142, January 2023., 2023 In this article, a novel mass and momentum conservative semi‐implicit finite volume scheme is developed for the coupled solution of hydrostatic shallow water flow and the movement of one or more floating rigid bodies. The coupling is achieved via a nonlinear volume function in the mass conservation equation that depends on the coordinates of the ...
Cristian Brutto, Michael Dumbser
wiley +1 more source