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for all smooth functions f on M and all smooth sections σ of E. It follows that the difference ∇< sub > 1 </ sub > − ∇< sub > 2 </ sub > is induced by a one-form on M with values in the endomorphism bundle End ( E ) = EE *:
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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.
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.
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.
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.
These songs ( practically all Persian music, for that matter ) are limited to a range of two octaves.
`` 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 smooth
Make slight, smooth grooves rather than cuts for the texture ( cuts could cause air pockets under the glaze creating pinholes or craters in the glaze during firing ).
special equipment required for registering respiration and for recording the contraction of smooth muscles under various conditions was developed by the Instruments Section ( Victor Jackman, W. C. Barnes, J. F. Reiss ) ; ;
In general, pottery was used for cooking or storage in the region was unpainted gray, either smooth or textured.
He who gives in charity and fears Allah And in all sincerity testifies to the Truth ; We shall indeed make smooth for him the path of Bliss
Although used for similar purposes, transparent colors and image masks do not permit the smooth blending of the superimposed image pixels with those of the background ( only whole image pixels or whole background pixels allowed ).
Aortic pressure is highest at the aorta and becomes less pulsatile and lower pressure as blood vessels divide into arteries, arterioles, and capillaries such that flow is slow and smooth for gases and nutrient exchange.
" After a string quartet ," Martin explains, " I do not think there is a satisfactory sound for strings until one has at least three players on each line ... as a rule two stringed instruments together create a slight " beat " which does not give a smooth sound.
The primary benefits over rifled barrels is reduced barrel wear, longer ranges that can be achieved ( due to the reduced loss of energy to friction and gas escaping around the projectile via the rifling ) and larger explosive cores for a given caliber artillery due to less metal needing to be used to form the case of the projectile because of less force applied to the shell from the non-rifled sides of the barrel of smooth bore guns.
These paints are good for watercolor techniques, airbrush application, or when smooth coverage is desired.
This class of device was used for smooth control of large motors, primarily for elevators and naval guns.
This tissue gives bones their smooth, white, and solid appearance, and accounts for 80 % of the total bone mass of an adult skeleton.
Although α and − α produce the same differential equation, it is conventional to define different Bessel functions for these two orders ( e. g., so that the Bessel functions are mostly smooth functions of α ).
The material is valued by watchmakers for its light weight, scratch resistance, durability and smooth touch.
Bristol board and even heavier acid-free boards, frequently with smooth finishes, are used for drawing fine detail and do not distort when wet media ( ink, washes ) are applied.
A piece of chamois is useful for creating smooth textures, and for removing material to lighten the tone.
Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).
The Center for American Progress issued a report in March 2010 that said a smooth implementation of an end to DADT required eight specified changes to the military's internal regulations.
A dynamical system is a manifold M called the phase ( or state ) space endowed with a family of smooth evolution functions Φ < sup > t </ sup > that for any element of t ∈ T, the time, map a point of the phase space back into the phase space.
In chemistry, the letter H as symbol of enthalpy sometimes is said to be a Greek eta, but since enthalpy comes from ἐνθάλπος, which begins in a smooth breathing and epsilon, it is more likely a Latin H for ' heat '.
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