* The Atiyah – Singer theorem applies to elliptic pseudodifferential operators in much the same way as for elliptic differential operators.

In general, Hodge theory applies to any elliptic complex over a compact manifold.

( The same remark applies to elliptic curves and elliptic functions ; and in fact to curves of genus > 1 and automorphic functions.

( The blue ' ionization | pre-ionisation ' curve applies to certain types of Nuclear weapon design | thermonuclear weapon, where gamma ray | gamma and x-ray s from the primary fission stage Ionization | ionise the atmosphere and make it electrically conductive before the main pulse from the thermonuclear stage.

For the youngest patients, whose thoracic insufficiency compromises their ability to breathe and applies significant cardiac pressure, ribcage implants that push the ribs apart on the concave side of the curve may be especially useful.

Specifically, he presented an explicit algebraic curve, and alleged that some of its local minima are missed when one applies the methods of infinitesimal calculus.

This relationship only applies in the elastic range and indicates that the slope of the stress vs. strain curve can be used to find Young's modulus.

For low light levels, the response of the human eye changes, and the scotopic curve applies.

* From the standard's component model, discover what thermal stress curve applies, and find the value of the temperature in operation for this component

* From the standard's component model, discover what, if any, part stress parameter is needed, what part stress curve applies, and find the value of that part stress parameter for this component in this application

At the first BloggerCon, Marks discussed the power curve as it applies to weblogs:

is based on curve fitting the viscosity dependence of many liquids ( refrigerants, hydrocarbons and lubricants ) versus temperature and applies over a large temperature and viscosity range:

However, the same difference applies with a drop D capo as with a regular capo ; namely, only the open tuning of the strings is affected, and thus, when used at the second fret, an E chord using the D shape will have the " Drop D sound " with a low E note.

Such statements, however, fall in the same category as statements such as " physics assumes that nature applies formulas such as Einstein's E = mc < sup > 2 </ sup > or Newton's F = ma " and " DST models assume that dynamic systems apply differential equations ".

In 1880, George E. Davis wrote in a letter to Chemical News ' A Chemical Engineer is a person who possesses chemical and mechanical knowledge, and who applies that knowledge to the utilisation, on a manufacturing scale, of chemical action.

Note that this result in particular applies to Euclidean spaces E < sup > n </ sup > and E < sup > m </ sup >, and it was in this form that Kirszbraun originally formulated and proved the theorem.

Oscar gives her f ( E ( x )), to which she applies a decoding D to obtain D ( f ( E ( x ))) = y.

( The same factor applies to other magnetic quantities such as H and M .) For example, in a planar light wave in vacuum, | E ( r, t )|=| B ( r, t )| in Gaussian units, while | E ( r, t )|= c | B ( r, t )| in SI units.

The equation E = m < sub > 0 </ sub > c < sup > 2 </ sup > applies only to isolated systems in their center of momentum frame.

1, 24 ( Bkrtcy. E. D. N. Y., 2006 ) (" Defendants ' argument that the sole actor rule applies, defeating the application of the adverse interest exception, must be rejected, at least on a motion to dismiss.

A similar problem, inverted, applies to subscriptions during the same period.

The problem of forum shopping also applies as between federal and state courts.

" And while the conjecture may one day be solved, the argument applies to similar unsolved problems ; to Brouwer, the law of the excluded middle was tantamount to assuming that every mathematical problem has a solution.

Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the McEliece cryptosystem based on a problem in coding theory.

However, if one of the deities has these properties the problem of evil applies.

The same applies to the event of typing a particular version of Hamlet followed by copies of itself ad infinitum ; or Hamlet immediately followed by all the digits of pi ; these specific strings are equally infinite, they are not prohibited by the terms of the thought problem, and they each have a prior probability of 0.

( For clarity, note that the problem just described can be improved by increasing the density of vertices in the object ( or perhaps increasing them just near the problem area ), but of course, this solution applies to any shading paradigm whatsoever-indeed, with an " incredibly large " number of vertices there would never be any need at all for shading concepts.

It can be said that a very small error applied over a very large number of individuals ( that is, those who are * not affected * by the condition in the general population during their lifetime ; for example, over 95 %) produces a relevant, non-negligible number of subjects who are incorrectly classified as having the condition or any other condition which is the object of a survey study: these subjects are the so-called false positives ; such reasoning applies to the ' false positive ' but not the ' false negative ' problem where we have an error applied over a relatively very small number of individuals to begin with ( that is, those who are * affected * by the condition in the general population ; for example, less than 5 %).

This may seem to be a problem if you wish to specify a proposition schema that applies only to functional predicates F ; how do you know ahead of time whether it satisfies that condition?

No oracle machine is capable of solving its own halting problem ( a variation of Turing's proof applies ).

Reprocessing has been politically controversial because of the potential to contribute to nuclear proliferation, the potential vulnerability to nuclear terrorism, the political challenges of repository siting ( a problem that applies equally to direct disposal of spent fuel ), and because of its high cost compared to the once-through fuel cycle.

* Economic calculation problem ( although mostly discussed in relation to command economies, it equally applies to firms )

The National Resident Matching Program applies graph matching methods to solve this problem for U. S. medical student job-seekers and hospital residency jobs.

Aristotle was particularly concerned with the problem of future contingents, where he could not accept that the principle of bivalence applies to statements about future events, i. e. that we can presently decide if a statement about a future event is true or false, such as " there will be a sea battle tomorrow ".

Enter the gargantuan Doctor Gideon Fell, who applies his substantial powers of deduction to the problem of how men can be indirectly murdered while they're inside locked, sealed and inaccessible rooms.

describe a technique involving limited backtracking for solving constraint satisfaction problems with binary variables and pairwise constraints ; they apply this technique to a problem of classroom scheduling, but they also observe that it applies to other problems including 2-SAT.

The idiomatic expression also applies to an obvious problem or risk no one wants to discuss.

Another limitation of the approach is that it applies only to optimization problems and not to " pure " decision problems like satisfiability, although it is often possible to conceive optimization versions of such problems, such as the maximum satisfiability problem ( Max SAT ).

The solution to this problem consists in XML file compression ( a solution that applies equally well to Flat Files ), which has nowadays gained EXI standards ( i. e., Efficient XML Interchange, which is often used by mobile devices ).

Fact checking began in the early 20th century: " Any bright girl who really applies herself to the handling of the checking problem can have a very pleasant time with it and fill the week with happy moments and memorable occasions "-Ed Kennedy, Time ( 1920s ).

The energy efficiency principal agent problem applies in many cases to rented buildings and apartments, but arises in other circumstances, most often involving relatively high up-front costs for energy-efficient technology.

Reagan used " sectarian religiosity to sell a political program "… the " evil empire " speech was " primitive "…" a mirror image of crude Soviet rhetoric "… " What is the world to think when the greatest of powers is led by a man who applies to the most difficult human problem a simplistic theology?

This fact can be used to prove existence and uniqueness of solutions to the Dirichlet problem for the Poisson equation in suitably regular domains, and for suitably well-behaved functions ƒ: one first applies a Newtonian potential to obtain a solution, and then adjusts by adding a harmonic function to get the correct boundary data.