Sentence examples for degree s from inspiring English sources
It follows from (16) and (10) that the (n - k) parity checks, h s, are vectors of degree (S - 1).
Delsarte, Goethals and Seidel showed that if X is a spherical t-design with degree s satisfying t⩾2s−2, X carries the structure of an association scheme.
Also Bannai and Bannai showed that the same conclusion holds if X is an antipodal spherical t-design with degree s satisfying t="2s−3.
Now let (P_{s} {(Phi_{alpha,gamma },0)} z,0)) be the Taylor polynomial of (Phi_{alpha,gamma } z,0)) at the origin of homogeneous degree s.
This suggests to describe the molecular dynamics in reduced dimensionality of just the most important degree(s) of freedom, e.g. the bond distance between the metal atom Mn and the photodissociated ligand CO, assuming Cs symmetry.
An extension of the existing theory is introduced so as to analyse the nature of the gained degree(s -of-freedom at a gain-type s -of-freedom
Recall that the function K : R + n → R is said to be homogeneous of degree −s, s > 0, if K ( t x ) = t − s K ( x ) for all t > 0. Furthermore, for a = ( a 1, a 2, …, a n ) ∈ R n, we define k i ( a ) = ∫ R n − 1 K ( u ˆ i ) ∏ j = 1, j ≠ i n u j a j d ˆ i u, i = 1, 2, …, n, (2.1).
Recall that a function K : R + × R + → R is said to be homogeneous of degree −s, s > 0, if K ( t x, t y ) = t − s K ( x, y ), for every x, y, t ∈ R +.
Theorem 3 Let p, q > 1 be conjugate parameters and K : R + × R + → R be a non-negative measurable homogeneous function of degree −s, s > 0. Further, let α 1 and α 2 be real parameters fulfilling condition (16) and β = − q α 1 ∈ ( m − 1, s − 1 ), s > m, where m is a fixed non-negative integer.
Degree Granting Institution(s): University of Illinois.
