Here the first sum is taken over the finite set of orbits of SL2(Z) on the set QD of all positive definite binary quadratic forms of discriminant −D, z is the (orbit of the) unique root in the upper half plane, and u(z) is half the order of the stabilizer. The internal sum in the second expression is over the primitive positive definite binary quadratic forms of discriminant −d and zd is a root...

The present paper deals with the mixed mode fracture analysis of a weakened orthotropic half-plane with multiple cracks propagation. The orthotropic half-plane contains Volterra type glide and climb edge dislocations. It is assumed that the medium is under in-plane loading conditions. The distributed dislocation technique is used to obtain integral equations for the dynamic problem of multiple ...

The classical Loewner’s theorem states that operator monotone functions on real intervals are described by holomorphic the upper half-plane. We characterize local order isomorphisms domains biholomorphic automorphisms of generalized half-plane, which is collection all operators with positive invertible imaginary part. describe such maps in an explicit manner, and examine properties maximal isom...

We obtain inverse formulas for the Fourier coefficients of functions in space just meromorphic upper half-plane complex variable. Both and direct can be interpreted as generalizations known Carleman formula.

Let Π = {z ∈ C : Imz > 0} be the upper half-plane in the complex plane. This paper characterizes the bounded products of differentiation operator and composition operator acting from the weighted Bergman space Aα(Π) to the weighted-type space A∞(Π) and the Bloch-type space B∞(Π). Mathematics Subject Classification: Primary 47B38; Secondary 47B33, 47B37

The plane strain deformation of an isotropic, homogeneous, poroelastic medium caused by an inclined line-load is studied using the Biot linearized theory for fluid saturated porous materials. The analytical expressions for the displacements and stresses in the medium are obtained by applying suitable boundary conditions. The solutions are obtained analytically for the limiting case of undrained...

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n ≥ 2. To this end, we first generalize the Carleman’s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna’s representation for harmonic functions in the half s...

Abstract We study the watermelon probabilities in uniform spanning forests on two-dimensional semi-infinite square lattice near either open or closed boundary to which can cannot be rooted, respectively. derive universal power laws describing asymptotic decay of these with distance between reference points growing infinity, as well their non-universal constant prefactors. The obtained exponents...