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# The scalar multiplication ·: K × V → V, where K is the underlying scalar field of V, is jointly continuous.
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# and scalar
# Given u in W and a scalar c in R, if u = ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, 0 ) again, then cu = ( cu < sub > 1 </ sub >, cu < sub > 2 </ sub >, c0 ) = ( cu < sub > 1 </ sub >, cu < sub > 2 </ sub >, 0 ).
# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) be an element of W, that is, a point in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub >, and let c be a scalar in R. Then cp = ( cp < sub > 1 </ sub >, cp < sub > 2 </ sub >); since p < sub > 1 </ sub > = p < sub > 2 </ sub >, then cp < sub > 1 </ sub > = cp < sub > 2 </ sub >, so cp is an element of W.
# There exists a non-zero scalar function h ( t ) and a non-decreasing scalar function f ( t ) such that X ( t ) = h ( t ) W ( f ( t )), where W ( t ) is the standard Wiener process.
# If the injectivity radius of a compact n-dimensional Riemannian manifold is ≥ π then the average scalar curvature is at most n ( n-1 ).
# You cannot cleanly define what may mean, due to the fact the O notation is about growth of functions, but to the left hand and the right hand side of the relation, there are scalar values, and you cannot decide whether the relation holds if you look at particular function values.
# The Einstein tensor must match the stress-energy tensor for the scalar field, which in the simplest case, a minimally coupled massless scalar field, can be written
# and multiplication
However, if only # is B-smooth for some divisor of, the product might not be ( 0: 1: 0 ) because addition and multiplication are not well-defined if is not prime.
# proved that if E is a curve over a number field F with complex multiplication by an imaginary quadratic field K of class number 1, F = K or Q, and L ( E, 1 ) is not 0 then E ( F ) is a finite group.
# showed that for elliptic curves defined over an imaginary quadratic field K with complex multiplication by K, if the L-series of the elliptic curve was not zero at s = 1, then the p-part of the Tate – Shafarevich group had the order predicted by the Birch and Swinnerton-Dyer conjecture, for all primes p > 7.
where is the number of ways to distribute cards between hands of two cards each .< ref name =" prod " group =" Note "> See " Capital Pi notation for multiplication " for a description of the ( capital π or pi ) symbol .</ ref > is the factorial # Double factorial | double factorial operator: ( 2n-1 )!!
# R is a principal ideal domain with a unique irreducible element ( up to multiplication by units ).
# R is a unique factorization domain with a unique irreducible element ( up to multiplication by units ).
# the severity of the infection: less serious infection ( contained multiplication of microbes ) or possibly life-threatening sepsis ( uncontrolled and uncontained multiplication of microbes throughout the blood stream ).
# and ·
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