Sentence examples for double contraction from inspiring English sources

is the single contraction and : the double contraction of two tensors.

A is a fourth-order tensor, (underline{underline{a}}) is a second-order tensor, and (overrightarrow {x}) is a vector, while the symbol ":" defines an inner product of two second-order tensors ((underline{underline{a}}!:!underline{underline{b}}= {a_{ij}}{b_{ij}})) or a double contraction of adjacent indices of tensors of rank two or higher [(A:a) ij  = A ijkl a kl ].

where H ̄ ∈ ℂ I × M is a channel matrix obtained from a double contraction of the end-to-end channel tensor ℋ ∈ ℂ F × F × M r × M t such as [ H ̄ ] i, m = [ H ̄ ] ( f − 1 ) M r + m r = h ( f − 1 ) M t + m r = h f, f, m r, m t.

He predicted revenue would fall 12percentt, or $62 billion, in 2009 — double its contraction after the Sept. 11, 2001, attacks.

At a time when the global economy is entering its deepest recession in decades, the immediate impact on the tiny island nation will be especially brutal, with a double-digit contraction in economy activity expected in 2009.

Keep your eyes out for double letters, contractions, and short words.

Finland continued its terrible run with a 0.4% contraction, double the 0.2% contraction earlier this year.

In those countries where GDP relies so heavily on migrants sending money back home, a prolonged currency crisis throughout 2015 would, all other factors remaining the same, potentially even lead to double-digit economic contraction.

Over the course of dorsal closure, the tissue solidifies and effective stiffness doubles as net contraction of the tissue commences.

For the liquid lithium flow target of International Fusion Materials Irradiation Facility (IFMIF), the double reducer (two-step contraction) nozzle with a high-contraction ratio of 10 which generated high-speed uniform jet flows up to 20 m/s was proposed.

Contraction and double twinning are the dominant twinning mechanisms in uniaxial tension, while extension twinning prevails in uniaxial compression and ring hoop tension testing.