Piezoelectricity () is the charge that accumulates in certain solid materials ( notably crystals, certain ceramics, and biological matter such as bone, DNA and various proteins ) in response to applied mechanical stress.

Piezoelectricity is found in useful applications such as the production and detection of sound, generation of high voltages, electronic frequency generation, microbalances, and ultrafine focusing of optical assemblies.

Piezoelectricity is the combined effect of the electrical behavior of the material:

* Piezoelectricity is discovered by Pierre Curie and Jacques Curie.

Piezoelectricity was discovered in 1880 by French physicists Jacques and Pierre Curie.

Piezoelectricity may then manifest in a variation of the polarization strength, its direction or both, with the details depending on 1. the orientation of P within the crystal, 2. crystal symmetry and 3. the applied mechanical stress.

Piezoelectricity of single individual collagen fibrils was measured using piezoresponse force microscopy, and it was shown that collagen fibrils behave predominantly as shear piezoelectric materials.

Piezoelectricity was discovered by Jacques and Pierre Curie in 1880.

Even though in most cases the completion of the definitive editions of their writings is still years off, enough documentation has already been assembled to warrant drawing a new composite profile of the leadership which performed the heroic dual feats of winning American independence and founding a new nation.

When the grammatical dual form of Ajax is used in the Iliad, it was once believed that it indicated the lesser Ajax fighting side-by-side with Telamonian Ajax, but now it is generally thought that that usage refers to the Greater Ajax and his brother Teucer.

The system is a dual purpose test and interception facility in Alaska, and in 2006 was operational with a few interceptor missiles.

* there were no " half-open " connections ; once one end initiated a tear-down of the connection, the whole connection would be closed ( i. e., ADSP is full-duplex, not dual simplex ).

Changing the balance of serotonin and norepinephrine would help the brain cells send and receive messages, therefore boosting the mood, which also is the main reason why these types of medications are called dual reuptake inhibitors.

Since the reference model given for traffic policing in the network is the GCRA, this algorithm is normally used for shaping as well, and single and dual leaky bucket implementations may be used as appropriate.

It is unknown when dual wielding was first used in fiction, but it was likely from early western novels before spilling over into other works.

Alcoholism is called a " dual disease " since it includes both mental and physical components.

The town is served by junction seven of the M65 and is linked from the A680 and the A56 dual carriageway which briefly merge ; linking to the M66 motorway heading towards Manchester.

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

The spaceX * of all linear maps into K ( which is called the algebraic dual space to distinguish it from X ′) also induces a weak topology which is finer than that induced by the continuous dual since X ′ ⊆ X *.

There is a natural map F: X → X ′′ ( the dual of the dual

In mathematics terminology, the vector space of bras is the dual space to the vector space of kets, and corresponding bras and kets are related by the Riesz representation theorem.

Just as kets and bras can be transformed into each other ( making into ) the element from the dual space corresponding with is where A < sup >†</ sup > denotes the Hermitian conjugate ( or adjoint ) of the operator A.

Moreover ( and more embarrassingly, although this is essentially trivial ), mathematicians usually write the dual entity not at the first place, as the physicists do, but at the second one, and they don't use the *- symbol, but an overline ( which the physicists reserve to averages ) to denote conjugate-complex numbers, i. e. for scalar products mathematicians usually write

There is dual suspension:

`` This is a mighty empty country '', Morgan said.

This is the Rafter Aj.

Laurel is gone, my men are gone, Ed is dead -- and you come to me, to help me.

But California is where we're goin ''.

Clayton is with him, takin him out of the valley.

His wife had said to him: `` Nellie is in love with Clayton Roy.

California is too far, he thought.

`` The main bunch is outside, but there are some over there inside the wall ''.

`` No telling how good this horse is '', Mike panted.

My God, how long is he going to wait, I thought.

`` Gray Eyes is back,, Montero said.

`` This is Mitchell Barton.

That's really all he's got, all he is.

that is, to show no curiosity whatsoever.

`` But to take him and leave his mother behind is not good ''.

`` Exterminatin' cow thieves is just a business proposition with me '', he'd blandly announce.

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.

It is also possible, but equally doubtful, that he actually shot down the hundreds of men with which his legend credits him.

( The best evidence is that he received a monthly wage of about $125, very good money in an era when top hands worked for $30 and found.

He started toward the stairway, then turned to add, `` Tell her to come to Adams's room, that Adams is in trouble.

Even the knowledge that she was losing another boy, as a mother always does when a marriage is made, did not prevent her from having the first carefree, dreamless sleep that she had known since they dropped down the canyon and into Bear Valley, way, way back there when they were crossing those other mountains.

Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.

I seized the rack and made a western-style flying-mount just in time, one of my knees mercifully landing on my duffel bag -- and merely wrecking my camera, I was to discover later -- my other knee landing on the slivery truck floor boards and -- but this is no medical report.

One of my virtues or vices is a sort of three-dimensional imagination complete with sound effects and glorious living color.