We consider a setup in a Hele-Shaw cell where a fluid of constant viscosity l occupying a near-half-plane pushes a fluid of constant viscosity l occupying a layer of length L which in turn pushes another fluid of constant viscosity r occupying the right half-plane. The fluid upstream has a velocity U. Careful analysis of the dispersion relation arising from linear stability of the three-layer H...

We prove Pólya’s conjecture of 1943: For a real entire function of order greater than 2 with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity as n → ∞ . We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.

We give two examples of algebraic fourfolds of general type with the same Betti numbers as the product of projective lines ( P )4 . Both examples are realized as quotients Γ\H of the product H of four copies of the upper half plane H by irreducible discrete groups of automorphisms. 2000 Mathematics Subject Classification 11F06, 22E40

We investigate a variant of the Beurling-Ahlfors extension quasisymmetric homeomorphisms real line that is given by convolution heat kernel, and prove complex dilatation such quasiconformal strongly symmetric homeomorphism (i.e. its derivative an ${\rm A}_\infty$-weight whose logarithm in VMO) induces vanishing Carleson measure on upper half-plane.

In this paper, we study the geometry of rectifying curves in 3-dimensional hyperbolic space $\mathbb H^{3}(-r)$. Further obtain distance function terms arc length when curve lying upper half plane. Then find and also give general equations curvature torsion helices $\mathbb{H}^3(-r)$.

We develop a new transmission scheme for additive white Gaussian noisy (AWGN) single-input single-output (SISO) channels without fading based on arithmetic Fuchsian groups. The properly discontinuous character of the action of these groups on the upper half-plane translates into fast decodability.

To the Farey tessellation of the upper half-plane we associate an AF algebra A encoding the cutting sequences that define vertical geodesics. The Effros-Shen AF algebras arise as quotients of A. Using the path algebra model for AF algebras we construct, for each τ ∈ (0, 1 4 ], projections (En) in A such that EnEn±1En ≤ τEn.

The class of objects we consider are algebraic relations between the four kinds of classical Jacobi theta functions θj(z|τ), j = 1, . . . , 4, and their derivatives. We present an algorithm to prove such relations automatically where the function argument z is zero, but where the parameter τ in the upper half complex plane is arbitrary.

is a weakly holomorphic modular form of integral or half-integral weight w2 on the congruence subgroup Γ1(N). By a weakly holomorphic modular form we mean a function f(z) which is holomorphic on the upper half-plane, meromorphic at the cusps, and which transforms in the usual way under the action of Γ1(N) on the upper half-plane (see, for example, [13] for generalities on modular forms of half-...