fraction x is said to be restricted, or composed of restricted partial quotients, if the sequence of denominators of its partial quotients is bounded; that is...

surjective when restricted to its image, the term partial bijection denotes a partial function which is injective. An injective partial function may be...

number field Apotome (mathematics) Periodic continued fraction Restricted partial quotients Quadratic integer Jörn Steuding, Diophantine Analysis, (2005)...

In mathematics, a partial equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous...

or restricted Lorentz group, and is denoted by SO+(1, 3). The set of the four connected components can be given a group structure as the quotient group...

Mathematical constants by continued fraction representation Restricted partial quotients – Analytic series Stern–Brocot tree – Ordered binary tree of...

rootsPages displaying short descriptions of redirect targets Restricted partial quotients – Analytic series Continued fraction factorization Pettofrezzo...

compared to the single-vector one-by-one technique. Non-linear iterative partial least squares (NIPALS) is a variant the classical power iteration with...

to replace partial derivatives which are difficult to analytically evaluate, experimentally measure, or integrate with quotients of partial derivatives...

{\partial f_{1}}{\partial x}}&{\dfrac {\partial f_{1}}{\partial y}}\\[1em]{\dfrac {\partial f_{2}}{\partial x}}&{\dfrac {\partial f_{2}}{\partial...

dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other...

3-manifolds that have Riemannian metrics of positive Ricci curvature are the quotients of the 3-sphere by discrete subgroups of SO(4) that act properly discontinuously...

{\displaystyle \partial ^{\mu }\partial _{\mu }A=0} with the condition ⟨ χ | ∂ μ A μ | ψ ⟩ = 0 {\displaystyle \langle \chi |\partial ^{\mu }A_{\mu }|\psi...

I_{x}^{n}(M)} be the ideal of smooth functions which vanish up to the n-1th partial derivative at x. I x n ( M ) {\displaystyle I_{x}^{n}(M)} is invariant...

a + b. The atoms of this partial order are precisely the primitive idempotents. When the above partial order is restricted to the central idempotents...

circle defines y as an implicit function of x if −1 ≤ x ≤ 1, and y is restricted to nonnegative values. The implicit function theorem provides conditions...

_{i}{\frac {\partial H}{\partial q_{i}}}{\frac {\partial p_{\lambda }}{\partial p_{i}}}-{\frac {\partial H}{\partial p_{i}}}{\frac {\partial p_{\lambda...

{D}{dy}}V-{\frac {D}{dy}}{\frac {D}{dx}}V=R\left({\frac {\partial \sigma }{\partial x}},{\frac {\partial \sigma }{\partial y}}\right)V} where R is the curvature tensor...

extensive use of this special case of Taylor series in the 18th century. The partial sum formed by the first n + 1 terms of a Taylor series is a polynomial...

derivative of the delta function is the distributional limit of the difference quotients: δ ′ ( x ) = lim h → 0 δ ( x + h ) − δ ( x ) h . {\displaystyle \delta...

{1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}-{\frac {\partial ^{2}}{\partial x^{2}}}-{\frac {\partial ^{2}}{\partial y^{2}}}-{\frac {\partial ^{2}}{\partial z^{2}}}...

the normal bundle is in general a quotient of the tangent bundle of the ambient space M {\displaystyle M} restricted to the subspace N {\displaystyle N}...

a_{\alpha }\partial ^{\alpha }\right]=\left(\delta ^{h}(a_{\alpha })\circ R_{h}\right)\partial ^{\alpha }.} Hence the difference quotients δhw are uniformly...

finite products and coproducts. If one drops "pseudo", one cannot take quotients. Lawvere also gave an alternate definition of such spaces as enriched...

functions, linear functions and quadratic functions. Rational functions are quotients of two polynomial functions, and their domain is the real numbers with...

{\partial L}{\partial f}}\eta +{\frac {\partial L}{\partial f'}}\eta '\right)\,dx\\&=\int _{x_{1}}^{x_{2}}{\frac {\partial L}{\partial f}}\eta \...

the otherwise wide meaning of the general descriptors is interpreted as restricted to the same class, if any, of the preceding specific descriptors. eluceat...

_{\bar {\partial }}={\bar {\partial }}{\bar {\partial }}^{*}+{\bar {\partial }}^{*}{\bar {\partial }},\ \ \ \ \Delta _{\partial }=\partial \partial ^{*}+\partial...

cancel out because of the defining Fibonacci recurrence relation. The partial fraction decomposition is given by s ( z ) = 1 5 ( 1 1 − φ z − 1 1 − ψ...

{\displaystyle {\bar {\partial }}} -closed differential form is ∂ ¯ {\displaystyle {\bar {\partial }}} -exact is more restricted than for the Poincaré...