We show how to express a conformal map Φ of a general two connected domain in the plane such that neither boundary component is a point to a representative domain of the form Ar = {z : |z + 1/z| < 2r}, where r > 1 is a constant. The domain Ar has the virtue of having an explicit algebraic Bergman kernel function, and we shall explain why it is the best analogue of the unit disc in the two conne...

The palindromization map ψ in a free monoid A was introduced in 1997 by the first author in the case of a binary alphabet A, and later extended by other authors to arbitrary alphabets. Acting on infinite words, ψ generates the class of standard episturmian words, including standard ArnouxRauzy words. In this paper we generalize the palindromization map, starting with a given code X over A. The ...

Let X →֒ PN be a smooth complex projective variety of dimension n. Let λ be an algebraic one parameter subgroup ofG := SL(N+1,C). Let 0 ≤ l ≤ n+1. We associate to the coefficients Fl(λ) of the normalized weight of λ on the mth Hilbert point of X new energies Fω,l(φ). The (logarithmic) asymptotics of Fω,l(φ) along the potential deduced from λ is the weight Fl(λ). Fω,l(φ) reduces to the Aubin ener...

A natural L∞ functional calculus for an absolutely continuous contraction is investigated. It is harmonic in the sense that for such a contraction and any bounded measurable function φ on the circle, the image can rightly be considered as φ̂(T ), where φ̂ is the solution of the Dirichlet problem for the disk with boundary values φ. The main result shows that if the functional calculus is isometri...

This study determined whether muscle contraction causes an increase in extracellular levels of serotonin (5-HT) in the rostral (rVLM) or caudal ventrolateral medulla (cVLM) in anesthetized rats. Muscle contraction, evoked by tibial nerve stimulation, increased mean arterial blood pressure (MAP) by 27 ± 4 mmHg ( n = 8). In addition, 5-HT levels in the rVLM were elevated by 65 ± 9% during the con...

Very recently, Fang (Fuzzy Sets Syst. 267:86-99, 2015) gave some fixed point theorems for probabilistic φ-contractions in Menger spaces. Fang’s results improve the one of Jachymski (Nonlinear Anal. 73:2199-2203, 2010) by relaxing the restriction on the gauge function φ . In this paper, inspired by the results of Fang, we prove a new fixed point theorem for a probabilistic φ-contraction in Menge...

Let (X, d) be a compact metric space, f : X 7→ X be a continuous map with the specification property, and φ : X 7→ R a continuous function. We consider the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set for φ) and show that this set is either empty or carries full topological pressure (in the sense of Pesin and Pitskel). We formulate various eq...

For a positive integer n, let Mn be the set of n×n complex matrices. Suppose m,n ≥ 2 are positive integers and k ∈ {1, . . . ,mn− 1}. Denote by Wk(X) the k-numerical range of a matrix X ∈Mmn. It is shown that a linear map φ : Mmn →Mmn satisfies Wk(φ(A⊗B)) = Wk(A⊗B) for all A ∈Mm and B ∈Mn if and only if there is a unitary U ∈Mmn such that one of the following holds. (i) For all A ∈Mm, B ∈Mn, φ(...

In this paper we study the birational rigidity problem for smooth Mori fibrations on del Pezzo surfaces of degree 1 and 2. For degree 1 we obtain a complete description of rigid and non-rigid cases. 1. Notions and results. Due to progress in the Minimal Model Program, the classification problem in the modern birational geometry for varieties of negative Kodaira dimension can be formulated as fo...

In 2011, Gabeleh and Akhar [3] introduced semi-cyclic-contraction and considered the existence and convergence results of best proximity points in Banach spaces. In this paper, the author introduces a cone semicyclic φ-contraction pair in cone metric spaces and considers best proximity points for the pair in cone metric spaces. His results generalize the corresponding results in [1–5]..