Let P = PtP2 + 2 be a linear partial differential operator on R^ with Pt and P2, of orders mx and ra2, respectively, strictly hyperbolic with respect to the first variable and Q of order ml + m2 2. Although the characteristic variety of P may have self-intersections, the hyperbolicity of Px and P2 implies local solvability for Pu = ƒ; indeed the Cauchy problem for P is locally solvable. In this...

We establish universality limits for measures on a subarc of the unit circle. Assume that μ is a regular measure on such an arc, in the sense of Stahl, Totik, and Ullmann, and is absolutely continuous in an open arc containing some point z0 = e0 . Assume, moreover, that μ′ is positive and continuous at z0. Then universality for μ holds at z0, in the sense that the reproducing kernel Kn (z, t) f...

We prove that for ??(0,8), if (?1,?2) is a 2-SLE?pair in simply connected domain D with an analytic boundary point z0, then as r?0+, P[dist(z0,?j)0, which called the two-curve Green’s function. The exponent ? equals 12 ??1 or 2(12 ??1) depending on whether z0 one of endpoints ?1 ?2. also find convergence rate and exact formula function up multiplica...

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....