Let k ≥ 2 and let f be meromorphic in the unit disc ∆, such that f(z)f (k)(z) 6= 0 for all z ∈ ∆ and the poles of f in ∆ have bounded multiplicities. Then f has asymptotic values on a dense subset of ∂∆. MSC: 30D40, 30D35.

The known concepts of Lyapunov exponent, moment Lyapunov exponents, and stability index for stationary points of stochastic systems are carried over for invariant orbits with nonvanishing di usion. The obtained general results are applied to investigating stochastic stability and stabilization of orbits on the plane.

We consider the family B̃ of bounded nonvanishing analytic functions f(z) = a0 + a1 z + a2 z 2 + · · · in the unit disk. The coefficient problem had been extensively investigated (see e. g. [2], [13], [14], [16], [17], [18], [20]), and it is known that |an| ≤ 2 e for n = 1, 2, 3, and 4. That this inequality may hold for n ∈ IN, is known as the Krzyż conjecture. It turns out that for f ∈ B̃ with a...

We prove that for any partition (λ1, . . . , λd2) of size dm there exists k ≥ 1 such that the tensor square of the irreducible representation of the symmetric group Skdm with respect to the rectangular partition (km, . . . , km) contains the irreducible representation corresponding to the stretched partition (kλ1, . . . , kλd2). We also prove a related approximate version of this statement in w...

By using the grand canonical Monte Carlo simulations on spherical surfaces with two fixed vertices separated by the distance L, we find that the second-order phase transition changes to the first-order one when L is sufficiently large. We find that string tension σ 6= 0 in the smooth phase while σ → 0 in the wrinkled phase.

We prove a non-vanishing theorem of the cohomology H0 of the adjoint divisor KX + dLe where dLe is the round up of a nef and big Q-divisor L.

In [Ja-Sh], Jacquet and Shalika use the spectral theory of Eisenstein series to establish a new result concerning the nonvanishing of L-functions on <(s) = 1. Specifically they show that the standard L-function L(s, π) of an automorphic cusp form π on GLm is nonzero for <(s) = 1. We analyze this method, make it effective and also compare it with the more standard methods. This note is based on ...

We consider an internal space of two discrete points in the fifth dimension of the Kaluza-Klein theory by using the formalism of noncommutative geometry developed in a previous paper [1] of a spacetime supplemented by two discrete points. With the nonvanishing internal torsion 2-form there are no constraints implied on the vielbeins. The theory contains a pair of tensor, a pair of vector and a ...