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QUADRATURE FORMULAS FOR SOME CLASSES OF CURVILINEAR INTEGRALS
Baku Mathematical Journal, 2022Quadrature formulas for simple-layer and double-layer potentials are established, and error estimates for these quadrature formulas are obtained.
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Multitime Dynamic Programming for Curvilinear Integral Actions
Journal of Optimization Theory and Applications, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Udrişte, C., Ţevy, I.
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On an Approximate Solution of a Class of Systems of Curvilinear Integral Equations
Differential Equations, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Examining Oriented Curvilinear Integrals
2020In the present chapter, the question of the so-called “oriented integrals” over surfaces is undertaken. The first notion to be introduced is that of the orientation. It will be explained in detail when solving particular problems and the formal definition is as follows. Given a linear k-dimensional space over \(\mathbb R\) and its basis e = (e1, e2, …,
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Random Curvilinear Integrals and Their Applications
Theory of Probability & Its Applications, 1991The paper considers a measurable space of curves (sequences of states) ― equivalence classes in Skorokhod space which are invariant under change of time. We define on each class, which can be characterized by a linear ordering on a subset of the metric state space, integrals of functions with respect to additive functionals.
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An integral equation with curvilinear convolutions on a closed contour
Ukrainian Mathematical Journal, 1985The authors consider an integral equation with curvilinear convolutions in the space \(L_ p(\Gamma ...
Peschanskij, A. I., Cherskij, Yu. I.
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Path integrals in curvilinear coordinates
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1970Abstract The problem of summation over Feynman histories in curvilinear coordinates is discussed. Ordinary rules of calculus are used in conjunction with a Hamiltonian approach to the summation over histories. The procedure is illustrated by considering the propagator for dynamical systems in spherical polar coordinates.
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Analytic formulation of Cauchy integrals for boundaries with curvilinear geometry
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007A general framework for analytic evaluation of singular integral equations with a Cauchy kernel is developed for higher order line elements of curvilinear geometry. This extends existing theory which relies on numerical integration of Cauchy integrals since analytic evaluation is currently published only for straight lines, and circular and hyperbolic ...
Steward, David R. +3 more
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(Complex) Derivative and (Curvilinear) Integrals
1979This short chapter is comprised of very basic and very easy material, probably familiar to most readers in one form or other. Even the reader with only modest experience can probably supply his own proofs for most of these results as quickly as he can read mine! We record them here for later reference and to fix notation and terminology.
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The Numerical Evaluation of Curvilinear Integrals and Areas
The Aeronautical Journal, 1968We envisage here that it is desired to evaluate (using a digital computer) the integral of a function f (x, y) with respect to x (say), along a curve γ in the xy-plane; the value of the function and of the co-ordinates of the curve being known only at discrete, and possibly irregularly spaced, points of γ.
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