Derrick's theorem is an argument by physicist G. H. Derrick which shows that stationary localized solutions to a nonlinear wave equation or nonlinear...

I. Pokhozhaev and is similar to the virial theorem. This relation is also known as G.H. Derrick's theorem. Similar identities can be derived for other...

Derrick's theorem Equipartition theorem Ehrenfest theorem Pokhozhaev's identity Statistical mechanics Clausius, RJE (1870). "On a Mechanical Theorem Applicable...

generalized to Hamiltonian systems with a more general symmetry group. Derrick's theorem Linear stability Lyapunov stability Nonlinear Schrödinger equation...

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices...

Last Theorem", PNAS, 40 (1): 25–33, Bibcode:1954PNAS...40...25L, doi:10.1073/pnas.40.1.25, PMC 527932, PMID 16589420 Brillhart, J. (1992). "Derrick Henry...

In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of...

than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...

1073/pnas.11.1.97. PMC 1085844. PMID 16586982. Lehmer, D. N. (1927). "A theorem on factorization". Bull. Amer. Math. Soc. 33 (1): 35–36. doi:10...

{\displaystyle N-1} . The basic version of the test relies on the Pocklington theorem (or Pocklington criterion) which is formulated as follows: Let N > 1 {\displaystyle...

which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole...

together they proved the Green–Tao theorem, which is well known among both amateur and professional mathematicians. This theorem states that there are arbitrarily...

mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after...

{\displaystyle {\bar {x}}} is assumed to be normal. By the central limit theorem, if the observations are independent and the second moment exists, then...

Sun proved a theorem about what are now known as the Wall–Sun–Sun primes that guided the search for counterexamples to Fermat's Last Theorem. Wall was born...

of California, Berkeley (PhD) Known for Stark conjectures Stark–Heegner theorem Awards American Academy of Arts and Sciences United States National Academy...

the outer loop. Knuth, The Art of Computer Programming vol 2 "Seminumerical algorithms", chapter 4.5.3 Theorem E. Kapil Paranjape, Lehmer's Algorithm...

\infty }{\frac {\pi (x)}{x/\log x}}=1.} This statement is the prime number theorem. An equivalent statement is lim x → ∞ π ( x ) li ⁡ ( x ) = 1 {\displaystyle...

dystopian satire trilogy it forms with 1995's 12 Monkeys and 2013's The Zero Theorem (although he later denied having said this). Gilliam has stated that Brazil...

defensible approximation to an interval scale, in which case the central limit theorem allows treatment of the data as interval data measuring a latent variable...

Henrik Abel, Norwegian mathematician – Abelian group, Abel's theorem, Abel–Ruffini theorem Helmut Abt, German-born American astrophysicist - Abt's star...

p + q ) n . {\displaystyle 1=1^{n}=(p+q)^{n}.} Using Newton's binomial theorem, this can equally be written as: ( p + q ) n = ∑ k = 0 ∞ ( n k ) p k q...

Probability and Statistics. Springer. pp. 234–238. ISBN 1-85233-896-2. Derrick, Ben; Green, Elizabeth; Ritchie, Felix; White, Paul (September 2022). "The...

{3}}\\&=6-\sigma ,\end{aligned}}} where the first equality uses the Binomial Theorem in a finite field, which is ( x + y ) M p ≡ x M p + y M p ( mod M p ) {\displaystyle...

doi:10.1080/00031305.2014.917055, PMC 4321753, PMID 25678714 Joanes, Derrick N.; Gill, Christine A. (1998), "Comparing measures of sample skewness and...

Deconstruction Dedekind cut Deduction Deduction and induction Deduction theorem Deductive Deductive-nomological model Deductive closure Deductive closure...

the Graham–Rothschild theorem in the Ramsey theory of parameter words and Graham's number derived from it, the Graham–Pollak theorem and Graham's pebbling...

divisible by 4. These three requirements are referred to as the Hull–Dobell Theorem. This form may be used with any m, but only works well for m with many...

1884 John Henry Poynting defined the Poynting vector and gave Poynting's theorem, which describe the flow of power across an area within electromagnetic...

by proving “challenge” theorems concerning properties that the specification is expected to exhibit. If correct, these theorems reinforce the specifier's...