The bacterial activity in rapid high heat methods breaks down the material to the extent that pathogens and seeds are destroyed, and the original feedstock is unrecognizable.

They originally experimented with the possibility of increasing the life of metal tools to anywhere between 200 %- 400 % of the original life expectancy using cryogenic tempering instead of heat treating.

Suggested locations for backups are a fireproof, waterproof, and heat proof safe, or in a separate, offsite location than that in which the original files are contained.

* Bacteria would not survive the immense heat and forces of an impact on Earth, also of the impact that launched them into space from their original habitat.

Annotated color version of the original 1824 Carnot heat engine showing the hot body ( boiler ), working body ( system, steam ), and cold body ( water ), the letters labeled according to the stopping points in Carnot cycle.

That is to say, the material must be able to be heated and cooled indefinitely often by the same increment and decrement of heat, and still return to its original pressure and volume and temperature every time.

( Fourier's law of conduction ) ( This definition of heat flux fits Maxwell's original definition.

As, sometimes, a tube or another mechanical part has to cross a wall or floor that has special fire insulation material or that have special fire insulation resistance, it is needed to recover the original level of security of the fire system in case of maintenance, or to reach the designed level of security, so to avoid or delay the propagation of flame, smoke and heat accordingly.

The original rock ( protolith ) is subjected to heat and pressure, ( temperatures greater than 150 to 200 ° C and pressures of 1500 bars ) causing profound physical and / or chemical change.

For example, if the wire and the base material get too close, the current will rapidly increase, which in turn causes the heat to increase and the tip of the wire to melt, returning it to its original separation distance.

Its original use as a vulgarism, documented to the fourteenth century, suggested high sexual desire in a woman, comparable to a dog in heat.

Its original use as an insult was based on a comparison of a woman to a dog in heat.

Although the original motivation was to solve the heat equation, it later became obvious that the same techniques could be applied to a wide array of mathematical and physical problems, and especially those involving linear differential equations with constant coefficients, for which the eigensolutions are sinusoids.

The next facelift in 1997 brought in the new exterior design cabin TerrNo1 with all new interior with better sound and heat insulation however the cabin design is based on the original so it can actually be retrofitted to all T815 built since 1993.

A Föhn wind results from precipitation on the windward side of a mountain range which releases latent heat into the atmosphere which is then warmer on the leeward side ( e. g. the Chinook or the original Föhn ).

They explained that, by the time they had raised enough money to purchase the original, only a few frames were still intact, the rest having been degraded beyond the point of usability by heat and humidity.

The heat setting step prevents the film from shrinking back to its original unstretched shape and locks in the molecular orientation in the film plane.

In some places, mixtures of older intrusive rocks and the original oceanic rocks have been distorted and warped under intense heat, weight and stress to create unusual swirled patters known as migmatite, appearing to have been nearly melted in the procedure.

The original process for " cracking " monazite so as to extract the thorium and lanthanide content, was to heat it with concentrated sulfuric acid to temperatures between 120 and 150 ° C for several hours.

The original rock ( protolith ) is subjected to heat and pressure, ( temperatures greater than 150 to 200 ° C and pressures of 1500 bars ) causing profound physical and / or chemical change.

The original two Porters ' performance was degraded by heat and height robbing power from engine performance.

It was destroyed after it crashed into an oil refinery and it was melted into its original gold compound by the intense heat.

A firestorm is created as a result of the stack effect as the heat of the original fire draws in more and more of the surrounding air.

The other, whom at that time I did not so much spare as since I wish I had, for that, as I have moderated the heat of living writers and might have used my own discretion ( especially in such a case, the author being dead ), that I did not I am as sorry as if the original fault had been my fault, because myself have seen his demeanor no less civil than he excellent in the quality he professes.

Developed original resolution and unification based first order theorem proving, co-editor of the " Handbook of Automated Reasoning ", recipient of the Herbrand Award 1996

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

The original form of the theorem, contained in a third-century AD book The Mathematical Classic of Sun Zi ( 孫子算經 ) by Chinese mathematician Sun Tzu and later generalized with a complete solution called Da yan shu ( 大衍术 ) in a 1247 book by Qin Jiushao, the Shushu Jiuzhang ( 數書九章 Mathematical Treatise in Nine Sections ) is a statement about simultaneous congruences ( see modular arithmetic ).

In Euclid's original approach, the Pythagorean theorem follows from Euclid's axioms.

Although flawed, Kempe's original purported proof of the four color theorem provided some of the basic tools later used to prove it.

Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics.

Baudhayana ( c. 8th century BCE ) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as:,,,, and as well as a statement of the Pythagorean theorem for the sides of a square: " The rope which is stretched across the diagonal of a square produces an area double the size of the original square.

Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument.

In modern logic texts, Gödel's completeness theorem is usually proved with Henkin's proof, rather than with Gödel's original proof.

The separation theorem is derived from the original form of the theorem.

Historical remark: In its original form by F. Riesz ( 1909 ) the theorem states that every continuous linear functional A over the space C ( 1 ) of continuous functions in the interval can be represented in the form

Since there is a one-to-one correspondence between Borel regular measures in the interval and functions of bounded variation ( that assigns to each function of bounded variation the corresponding Lebesgue-Stieltjes measure, and the integral with respect to the Lebesgue-Stieltjes measure agrees with the Riemann-Stieltjes integral for continuous functions ), the above stated theorem generalizes the original statement of F. Riesz.

A different generalization of Weierstrass ' original theorem is Mergelyan's theorem, which generalizes it to functions defined on certain subsets of the complex plane.

The virial theorem can be obtained directly from Lagrange's Identity as applied in classical gravitational dynamics, the original form of which was included in Lagrange's " Essay on the Problem of Three Bodies " published in 1772.

In essence, the theorem shows that a bandlimited analog signal can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2B samples per second, where B is the highest frequency of the original signal.

The theorem also leads to a formula for reconstruction of the original signal.

and the samples of x ( t ) are denoted by x ( nT ) for integer values of n. The sampling theorem leads to a procedure for reconstructing the original x ( t ) from the samples and states sufficient conditions for such a reconstruction to be exact.

The theorem describes two processes in signal processing: a sampling process, in which a continuous time signal is converted to a discrete time signal, and a reconstruction process, in which the original continuous signal is recovered from the discrete time signal.

According to the theorem, the reconstructed signal will match the original signal provided that the original signal contains no frequencies at or above this limit.

* If the highest frequency B in the original signal is known, the theorem gives the lower bound on the sampling frequency for which perfect reconstruction can be assured.

A distribution being " smoothed out " by summation, showing original Probability density function | density of distribution and three subsequent summations ; see Illustration of the central limit theorem for further details.