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a constant. The value given corresponds to the
Gregorian calendar year (a = 365.2425 d).
Y yield, Y Y Y (in biotechnology) Ratio express-

ing the efficiency of a mass conversion process.
The yield coefficient is defined as the amount
of cell mass (kg) or product formed (kg, mol)
Yang-Mills theory A nonabelian gauge the- related to the consumed substrate (carbon or
ory. For a fixed compact Lie group G with Lie nitrogen source or oxygen in kg or moles) or to
algebra g, the field in this theory is vector poten- the intracellular ATP production (moles).
tialA, i.e., aconnection1-formonsomeprincipal
G bundle. Let F be the curvature 2-form of the
A
0
0
connection A. The fundamental Lagrangian in yield stress The shear stress σ or τ at
which yielding starts abruptly. Its value depends
pure gauge theory is
on the criterion used to determine when yielding
1 n occurs.
L(A) = |F ||d x|,
A
2
where |F | denotes the norm in the Lie algebra. Young’s inequality Let p, q, r ≥ 1 and
A
n
p
From the variational principle we get the equa- 1/p + 1/q + 1/r = 2. Let f ∈ L (R ), g ∈
n
q
n
r
tions of motion, the Yang-Mills equations L (R ), h ∈ L (R ). Then
, ,
, ,
d ∗ F = 0,
A A , f (x)(g ∗ h)(x)dx ,
, n ,
where d is the covariant derivative with respect R
A ≤ C f g h .
to A and ∗ is the Hodge star operator. For any A p,q,r,n p q r
we also have the Bianchi identity d F = 0. In
A A Yukawa-Tsunoequation Amultiparameter
local coordinates we have:
extension of the Hammett equation to quan-
F µν = ∂ A − ∂ A + i[A ,A ], and tify the role of enhanced resonance effects on
ν
ν
µ
ν
ν
µ
L = Tr(F F µν ). the reactivity of meta- and para-substituted
µν
benezene derivatives, e.g.,
Then the Yang-Mills equations become +
lg k = lg k + ρ[σ + r(σ − σ)].
0
µ
µ
∂ F µν + i[A ,F ] = 0.
µν
The parameter r gives the enhanced resonance
year Unit of time, a = 31 556 952 s. The effect on the scale (σ − σ) or (σ − σ), respec-
+
year is not commensurable with the day and not tively.

© 2003 by CRC Press LLC