It is proved that the operator of a boundary value problem of heat conductivity in an infinite angular domain in a class of growing functions is Noetherian with an index which is equal to minus one.
The results show that both in human and in Arabidopsis, there is a limited but statistically highly significant, positive correlation between the rate differences of domains in the two classes of domain pairs.
Let D be a bounded homogeneous domain in ℂ n, H (D) the class of all holomorphic functions on D. For φ, a holomorphic self-map of D, the linear operator defined by C φ ( f ) = f ∘ φ, f ∈ H ( D ), is called the composition operator with symbol φ.
Let D be an arbitrary domain in R n and A a denote the class of nonnegative radial potentials a ( P ), i.e. 0 ≤ a ( P ) = a ( r ), P = ( r, Θ ) ∈ D, such that a ∈ L loc b ( D ) with some b > n / 2 if n ≥ 4 and with b = 2 if n = 2 or n = 3.
Let C n be an arbitrary domain in R n and A a denote the class of nonnegative radial potentials a ( P ), i.e. 0 ≤ a ( P ) = a ( r ), P = ( r, Θ ) ∈ C n , such that a ∈ L loc b ( C n with some b > n / 2 if n ≥ 4 and with b = 2 if n = 2 or n = 3.
Let D be an arbitrary domain in R n and A a denote the class of non-negative radial potentials a ( P ), i.e. 0 ≤ a ( P ) = a ( r ), P = ( r, Θ ) ∈ D, such that a ∈ L loc b ( D ) with some b > n / 2 if n ≥ 4 and with b = 2 if n = 2 or n = 3 (see [[1], p.354] and [2]).
For an arbitrary domain D in R n, A D denotes the class of non-negative radial potentials a ( P ) (i.e., 0 ≤ a ( P ) = a ( r ) for P = ( r, Θ ) ∈ D ) such that a ∈ L loc b ( D ) with some b > n / 2 if n ≥ 4 and with b = 2 if n = 2 or n = 3.
Sequencing of fc1 showed a deletion generating a premature stop codon, such that the predicted polypeptide product lacked the domain implicated in the DNA binding activity of the class of transcriptional regulators to which tb1 belongs.
If CIA is the class of domains,, that are convex in the direction of the imaginary axis and that admit a mapping so that and satisfies the normalization (1.1), then we have the following result.
Our result holds for the class of uniformly perfect bounded domains, in fact we can allow that a portion of the boundary is thin in the sense of capacity.
