Results 231 to 240 of about 9,965 (268)

The Adjoint of Differentiation

Experimental Mathematics, 2014
Let n be any nonnegative integer. Let V = Pn be the vector space of polynomials of degree at most n, equipped with the inner product ⟨f, g⟩ = ∫10f(x)g(x) dx. Let D: V → V be the differentiation operator, D(f) = f′. Then D has an adjoint D*. We have closed-form expressions for D*, which were conjectured by computing D* for small values of n and finding ...
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Left Adjoint for Booleanization

Applied Categorical Structures, 1998
A frame is a complete distributive lattice \(L\) in which \(a\wedge\bigvee_{b\in B}b=\bigvee_{b\in B}(a\wedge b)\) for each \(a\in L\) and \(B\subseteq L\). Boolean frames are precisely complete Boolean lattices. If \(L\) is a frame then the set \({\mathcal B}(L)=\{a\in L/a=a^{**}\}\) (where \(a^*\) is the pseudocomplement of a) of all skeletal ...
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Adjoints and self-adjointness for a differential operator with a varying structure

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1982
SynopsisIn this paper the adjoint operator is derived for a multi-point differential operator with a varying structure in a suitably chosen Hilbert space. The formal differential operator is given by different differential expressions in the adjoining intervals. This form of adjoint operator is used to characterize self-adjointness.
Das, P. C., Prasad, Uma Shanker
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Adjoint Process Duality

Mathematics of Operations Research, 1983
We study convex processes between topological vector spaces with particular emphasis on their adjoints. This study is then applied to produce general duality results for classes of convex programs involving processes. The use of processes allows one to exploit the symmetry of linear programming and to obtain significantly broader and stronger results.
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The Adjoint Representation and the Adjoint Action

2002
The purpose of this article is to study in detail the actions of a semisimple Lie or algebraic group on its Lie algebra by the adjoint representation and on itself by the adjoint action. We will focus primarily on orbits through nilpotent elements in the Lie algebra; these are called nilpotent orbits for short.
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Adjoints of oriented matroids

Combinatorica, 1986
An adjoint of a geometric lattice G is a geometric lattice \(\tilde G\) of the same rank into which there is an embedding e mapping the copoints of G onto the points of \(\tilde G.\) In this paper we introduce oriented adjoints and prove that they can be embedded into the extension lattice of oriented matroids.
Achim Bachem, Walter Kern
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ADJOINT FUNCTIONS AND INTEGRALS

Mathematics of the USSR-Izvestiya, 1972
In this paper it is proved that A-integrals and B-integrals are inconsistent with the Denjoy-Hincin integral of functions which are adjoint to a summable function. Furthermore, the paper establishes nonadditivity of the B-integrals on an interval.
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Adjoint, Symmetric, and Self-adjoint Linear Operators

2019
Here we first recall the definition of the adjoint of a linear operator and discuss some related results. Then we shall address the case of compact operators A : H → H, where H is a Hilbert space, and present the Fredholm theorem as an application. The last section is devoted to symmetric operators and self-adjoint operators.
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On the Method of Adjoints

auto, 1973
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A tutorial on the adjoint method for inverse problems

Computer Methods in Applied Mechanics and Engineering, 2021

exaly