logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm....

{1}{\sqrt {m}}}\|A\|_{1}\leq \|A\|_{2}\leq {\sqrt {n}}\|A\|_{1}.} Dual norm Logarithmic norm The condition only applies when the product is defined, such as...

Richter scale of earthquake intensity. Logarithmic magnitudes can be negative. In the natural sciences, a logarithmic magnitude is typically referred to as...

P(\rho )} is an arbitrary LOCC operation over ρ {\displaystyle \rho } The logarithmic negativity is an entanglement measure which is easily computable and...

Hörmander as his advisors. As part of this work he introduced the logarithmic norm (also introduced by Russian mathematician Sergei Lozinskii the same...

Stochastic Gronwall inequality Logarithmic norm, for a version of Gronwall's lemma that gives upper and lower bounds to the norm of the state transition matrix...

In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient ∇ f {\displaystyle...

usually marked with an "A" for logarithmic taper or a "B" for linear taper; "C" for the rarely seen reverse logarithmic taper. Others, particularly those...

f ( x ^ ) = 0 {\displaystyle f({\hat {x}})=0} . If there exists a logarithmic norm μ {\displaystyle \mu } such that the Jacobian J ( x ) = D x f {\displaystyle...

other more complex definitions of strain are required, such as stretch, logarithmic strain, Green strain, and Almansi strain. Engineering strain, also known...

measure on the real numbers under the logarithm: it is the length on the logarithmic scale. In fact, it is an invariant measure with respect to multiplication...

of the logarithmic derivative of f {\displaystyle f} , which is ( log ⁡ f ) ′ = f ′ / f {\displaystyle (\log f)'=f'/f} , and the logarithmic derivative...

arithmetic to the geometric composition of angles. Marking the line with logarithmically spaced graduations associates multiplication and division with geometric...

Logarithmic chart of the hearing ranges of some animals...

of norms in finite dimensions, a topologically equivalent metric is obtained if N is the taxicab norm, a p-norm, the maximum norm, or any other norm which...

({\hat {x}}).} Korevaar, J.; Meyers, J. L. H. (1994), "Logarithmic convexity for supremum norms of harmonic functions", Bull. London Math. Soc., 26 (4):...

associated with a norm called the Euclidean norm, defined as the distance of each vector from the origin. One of the important properties of this norm, relative...

property above, x = ƒ(t). The order of growth of Dirichlet's kernel is logarithmic, i.e. ∫ | D N ( t ) | d t = 4 π 2 log ⁡ N + O ( 1 ) . {\displaystyle...

there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding...

removed. This 2-norm in logarithmic space can be generalized to p-norm in logarithmic space. The drawback of this 2-norm in logarithmic space is that it...

comparison to the reference level of 1 pPa (= 10−12 pascals). It is a logarithmic measure of the ratio of two sound energy densities. The unit of the sound...

precise estimate may be given in terms of the logarithmic integral function. The number of prime ideals of norm ≤ X is L i ( X ) + O K ( X exp ⁡ ( − c K log...

When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so...

n=2} the term bidisc is sometimes used. A polydisc is an example of logarithmically convex Reinhardt domain. Poincare, H, Les fonctions analytiques de...

expected frequency: points that fall more than 3 standard deviations from the norm are likely outliers (unless the sample size is significantly large, by which...

right-most child's index, used to guide the search), taking the time logarithmic in the list's size, but as long as it doesn't change much will provide...

of the coordinates (e.g. 7 for the coordinates (3/7, 1/2)), but in a logarithmic scale. Height functions allow mathematicians to count objects, such as...

mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a...

security) (see survey of Goldwasser [4] 1990 Introduced the first poly-logarithmic Oblivious RAM (ORAM) scheme. 1993 Proved (with A. Wigderson) equivalence...

semitones play a part in communicative situations". Note that, given the logarithmic characteristics of Hz, for both music and speech perception results should...