scholarly journals Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

6-D MoM Reaction Integrals Evaluated via the Divergence Theorem

2021 ◽  
Author(s):  
J. Rivero ◽  
F. Vipiana ◽  
D. R. Wilton ◽  
W. A. Johnson
Keyword(s):  
Divergence Theorem

scholarly journals The divergence theorem

1996 ◽  
Vol 121 (4) ◽  
pp. 349-356
Author(s):  
Josef Král
Keyword(s):  
Divergence Theorem

scholarly journals Numerically stable form factor of any polygon and polyhedron

2021 ◽  
Vol 54 (2) ◽  
pp. 580-587
Author(s):  
Joachim Wuttke
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Form Factors ◽  
Small Angle Scattering ◽  
Important Application ◽  
Divergence Theorem ◽  
Series Expansions ◽  
Stable Form ◽  
Application Domain ◽  
Angle Scattering

Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals.

The Evaluation of Moments of Regions With Piecewise-Linearly Approximated Boundaries via Line Integration

1989 ◽  
Author(s):  
J. Angeles ◽  
M. J. Al-Daccak
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Inertia Tensor ◽  
Divergence Theorem ◽  
Dimensional Euclidean Space ◽  
Repeated Application ◽  
The Subject ◽  
First Moment

Abstract The subject of this paper is the computation of the first three moments of bounded regions imbedded in the three-dimensional Euclidean space. The method adopted here is based upon a repeated application of Gauss’s Divergence Theorem to reduce the computation of the said moments — volume, vector first moment and inertia tensor — to line integration. Explicit, readily implementable formulae are developed to evaluate the said moments for arbitrary solids, given their piecewise-linearly approximated boundary. An example is included that illustrates the applicability of the formulae.

The Divergence Theorem

1929 ◽  
pp. 84-121 ◽  
Author(s):  
Oliver Dimon Kellogg
Keyword(s):  
Divergence Theorem

scholarly journals The patchwork divergence theorem

1994 ◽  
Vol 35 (11) ◽  
pp. 5922-5929 ◽  
Author(s):  
Tevian Dray ◽  
Charles Hellaby
Keyword(s):  
Divergence Theorem
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