for all z0 ∈ D(A). Here T (t) is the C0-semigroup generated by A. A system (1) that satisfies the above conditions will be denoted by Σ(A,C). The admissibility of C, eqn. (2), implies that we can extend the mapping z0 → CT (·)z0 to a bounded linear mapping from Z to L2(0,∞). We denote this mapping by C. Thus we have that for any initial condition z0 the solution of (1) is given by z(t) = T (t)z...

A result of Hinchliffe 2003 is extended to transcendental entire function, and an alternative proof is given in this paper. Our main result is as follows: let α z be an analytic function, F a family of analytic functions in a domain D, and H z a transcendental entire function. If H ◦ f z and H ◦ g z share α z IM for each pair f z , g z ∈ F, and one of the following conditions holds: 1 H z −α z0...

Let U be an open neighborhood of the origin in C and let f : (U ,0) → (C, 0) be complex analytic. Let z0 be a generic linear form on C. If the relative polar curve Γ1f,z0 at the origin is irreducible and the intersection number ( Γ f,z0 · V (f))0 is prime, then there are severe restrictions on the possible degree n cohomology of the Milnor fiber at the origin. We also obtain some interesting, w...

Realistic specifications of the roughness length and zero-plane displacement are crucial in the boundarylayer parametrisation that plays an important role in numerical mesoscale models (Abdella and Mcfarlane 1996). Martano (2000) proposed a method for estimating the surface roughness length (z0) and the displacement height (d) from single-level sonic anemometer data. This method reduces the pro...

Pulmonary diffusion capacity for carbon monoxide (DLCO), regional electrical impedance (Z0), and the distribution of technetium-99m-labeled erythrocytes together with concentration of plasma atrial natriuretic peptide (ANP) were determined before and after a 6-min "all-out" row in nine oarsmen and in six control subjects. Two and one-half hours after exercise in the upright seated position, DLC...

Wind erosion in agricultural soils is dependent, in part, on the aerodynamic roughness length (z0) produced by tillage ridges. Although previous studies have related z0 to ridge characteristics (ridge height (RH) and spacing (RS)), these relationships have not been tested for tillage ridges observed in the North African agricultural fields. In these regions, due to climate and soil conditions, ...

In [20] and [9] we analyzed the second variation of the Robin function associated to a smooth variation of domains in C for n ≥ 2; i.e., D = ∪t∈B(t, D(t)) ⊂ B×Cn is a variation of domains D(t) in C each containing a fixed point z0 and with ∂D(t) of class C ∞ for t ∈ B := {t ∈ C : |t| < ρ}. For such t and for z ∈ D(t) we let g(t, z) be the R-Green function for the domain D(t) with pole at z0; i....

A standard isosurface extraction algorithm for a 3D image is the Marching Cubes algorithm [4]. The image is assumed to be defined on a regular lattice of size N0×N1×N2 with integer points (x, y, z) where 0 ≤ x < N0, 0 ≤ y < N1, and 0 ≤ z < N2. The image values themselves are F (x, y, z). An isosurface is of the form F (x, y, z) = c for some specified level value c where x, y, and z are treated ...

and Applied Analysis 3 Remark 1.5. In Theorem 1.2 setting α z constant zero and P z,w a polynomial in variable w that vanishes exactly on a finite set of holomorphic functions S, we obtain Corollary 1.6 which generalizes the famous Montel’s criterion that a holomorphic family omitting 2 or more values is normal. Corollary 1.6. Let F be a family of holomorphic functions on a domain D. Let S be a...

Abstract: Firstly, we construct kernels for integral relations among solutions of the confluent Heun equation (CHE). Additional kernels are systematically generated by applying substitutions of variables. Secondly, we establish integral relations between known solutions of the CHE that are power series and solutions that are series of special functions. Thirdly, by using one of the integral rel...