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Page "Laplace–Beltrami operator" ¶ 23
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for and all
`` We've been looking for work, but all the ranchers have turned us down ''.
`` You mean you dragged your wife all over hell's half-acre looking for work ''??
He knew who was riding after him -- the men he had known all his life, the men who had worked for him, sworn their loyalty to him.
They blame us for all their troubles.
It poured out of him like an electric current, a feeling that the muscles and nerves of his fine-drawn body were coiling for action, and that that action would be all that he anticipated.
It is possible, although highly doubtful, that he killed none at all but merely let his reputation work for him by privately claiming every unsolved murder in the state.
`` Soon as we send them on their way and make camp, let's you and me go for a walk down by the Snake -- all by ourselves ''.
Seeing them waiting there at the foot of Emigrant Rock was so overwhelming that, for a good minute after they rounded the bend and started down the grade leading toward them, Matilda could not speak at all.
There were no less than six or seven saloons in Ganado, not counting the lower class dives, all vying for the trade of celebrating miners and teamsters.
It was fun for me, all right.
this is not so, for education offers all kinds of dividends, including how to pull the wool over a husband's eyes while you are having an affair with his wife.
Packing a small suitcase, informing her husband whom she found in Harry's Bar that she was taking a train to Germany to get away for a while, patting his arm, refusing a drink, getting on the train -- all this had only taken her two hours.
Perhaps her eyes were larger and more of a summer blue for all they had seen and wept that day.
`` I guess he spent the morning getting himself all organized, then headed for home.
`` You think I got you and Artie and Herr Schaffner all the way out here just for the boat ride??
I will make him distributor for all of Florida -- a big market.
Once and for all he'd finish this marine who would not die.
`` If Blue Throat has his way he'll keep us all cooped up in here for days '', he said.
At the same time, all suggestions that some sort of societal responsibility existed for the welfare of the people within the territorial state was strongly resisted.
For better or for worse, we all now live in welfare states, the organizing principle of which is collective responsibility for individual well-being.
Alternate locations exist for all key command centers.
These songs ( practically all Persian music, for that matter ) are limited to a range of two octaves.
First of all, to Italy for a short vacation -- Forte Dei Marmi, a place he loves.
`` As an independent American I considered all who were not for us, and you amongst the rest, as against us, yet be assured that John Jay never ceased to be the friend of Peter Van Schaack ''.

for and compactly
On larger kites, clever hinges and latches allow the kite to be disassembled and compactly folded for storage or transport.
The Lorentz transform for a boost in one of the above directions can be compactly written as a single matrix equation:
Very commonly, these values are powers of 10 ; so for instance, if / stands for one,for ten and + for 100, then the number 304 can be compactly represented as < tt >+++ ////</ tt > and the number 123 as < tt >+ − − ///</ tt > without any need for zero.
He compactly expressed the basis for a cultural recapitulation theory of education in the following claim, published in 1861, five years before Haeckel first published on the subject:
for all continuous compactly supported functions ƒ.
Clothes are folded to allow them to be stored compactly, to prevent creasing, to preserve creases or to present them in a more pleasing manner, for instance when they are put on sale in stores.
In America, the term is not used for this purpose because the bands are metal compactly sewn, while ' lace ' seems to imply cloth sewn into patterns with holes in them.
This construct displays a person's genealogy compactly, without the need for a diagram such as a family tree.
The transformation rules for polar vectors and pseudovectors can be compactly stated as
The one-dimensional Schrödinger operator with the potential, defined initially on smooth compactly supported functions, is essentially self-adjoint ( that is, has a self-adjoint closure ) for < math > 0 <
Let U be an open set in R < sup > n </ sup > and φ: U → R < sup > n </ sup > an injective differentiable function with continuous partial derivatives, the Jacobian of which is nonzero for every x in U. Then for any real-valued, compactly supported, continuous function f, with support contained in φ ( U ),
: Variational definition: A surface M ⊂ R < sup > 3 </ sup > is minimal if and only if it is a critical point of the area functional for all compactly supported variations.
: Energy definition: A conformal immersion X: M → R < sup > 3 </ sup > is minimal if and only if it is a critical point of the Dirichlet energy for all compactly supported variations, or equivalently if any point p ∈ M has a neighbourhood with least energy relative to its boundary.
One can prove directly from the Fourier slice theorem and change of variables for integration that for a compactly supported continuous function ƒ of two variables
Sadval campaigned for the redrawing of the Russian – Azerbaijani border to allow for the creation of a single Lezgin state encompassing areas in Russia and Azerbaijan where Lezgins were compactly settled.
To complete the buildup of measure theory for locally compact spaces from the functional-analytic viewpoint, it is necessary to extend measure ( integral ) from compactly supported continuous functions.
# Definition of the upper integral μ *( g ) of a lower semicontinuous positive ( real-valued ) function g as the supremum ( possibly infinite ) of the positive numbers μ ( h ) for compactly supported continuous functions h ≤ g
This property is interesting in the case of locally compact topological groups, since locally compact compactly generated topological groups can be approximated by locally compact, separable metric factor groups of G. More precisely, for a sequence

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