From the viewpoint of rational homotopy theory, we introduce an iterated cyclic homology of connected commutative differential graded algebras over the rational number field, which is regarded as a generalization of the ordinary cyclic homology. Let T be the circle group and $\mathscr F$ (T^l, X) denote the function space of continuous maps from the l-dimensional torus T^l to an l-connected space X. It is also shown that the iterated cyclic homology of the differential graded algebra of polynomial forms on X is isomorphic to the rational cohomology algebra of the Borel space ET × _T $\mathscr F$ (T^l, X), where the T-action on $\mathscr F$ (T^l, X) is induced by the diagonal action of T on the source space T^l.

We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. We obtain a generalization of results obtained by Ünal in [9, Acta Appl. Math. 40(1995)] and E. García-Río and D. N. Kupeli in [4, Proceeding of the Third World Congress of Nonlinear Analysts, Part 5 (Catania, 2000). Nonlinear Anal. 47 (5) 2995-3004, 2001].

As a tool, we use an induced volume form on the degenerate boundary by introducing a star like operator.

A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained.

In this paper, by using Ahlfors' theory of covering surface, we study singular direction of meromorphic functions and their derivatives, which is a continuous research of Yang Lo in J. London Math. Soc. 25 (1982) 2: 288-296.

The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study a transcendental entire function f (z) that shares a non-zero polynomial a (z) with f′(z), together with its linear differential polynomials of the form: L[f] = a₂(z)f″(z) + a₃ (z)f′′′(z) + … + a_m (z)f^(m) (z) (a_m (z) $\not\equiv$ 0), where the coefficients a_k (z) (k = 2, 3, ..., m) are rational functions.

Let K be a nonempty closed convex subset of a real Banach space E,T : K → K a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {k_n}_{n ≥ 0} $\subset$ [1, ∞), lim_{n → ∞} k_n = 1 such that p $\in$ F(T) = {x $\in$ K : Tx = x}. Let {α_n}_{n ≥ 0} $\subset$ [0,1] be such that ∑_{n ≥ 0} α_n = ∞ and lim_{n → ∞} α_n = 0. For arbitrary x₀ $\in$ K and {v_n}_{n ≥ 0} in K let {x_n}_{n ≥ 0} be iteratively defined by

x_{n + 1} = (1 - α_n)x_n + α_n Tⁿv_n, n ≥ 0,

satisfying lim_{n → ∞} ||v_n - x_n|| = 0. Suppose there exists a strictly increasing function φ : [0, ∞) → [0, ∞), φ (0) = 0 such that

<Tⁿx - p, j (x - p)> ≤ k_n ||x - p||² - φ (||x - p||), ∀x $\in$ K.

Then {x_n}_{n ≥ 0} converges strongly to p $\in$ F (T).

The remark at the end is important.

For a closed subset E of the Riemann sphere, its Teichmüller space T (E) is a universal parameter space for holomorphic motions of E over a simply connected complex Banach manifold. In this paper, we study some new applications of this universal property.

In this paper, we prove that for algebroid functions of order ρ satisfying that 0 < ρ < +∞, there exists a Borel direction of the largest type dealing with multiple values and there is a sequence of filling disks in this direction.

We show that the degeneration locus of the Kobayashi pseudodistance on a complex manifold is always a pseudoconcave set of order 1. We give some results cocerning the degeneration locus of the Kobayashi pseudodistance. Next we prove a generalization of the little Picard theorem relevantly. Finally, we consider the case N = Δ_N.

This paper studies the problem of the uniqueness of meromorphic functions sharing three values. The results in this paper improve some theorems given by H. Ueda, H. X. Yi and other authors.

Kutbi and Protas showed that if the zeros {a_k} of a given Blaschke product B satisfy Σ_k (1 - |a_k|)^α < ∞ for some α $\in$ (0, 1), then the integral means of its derivative B⁽ⁿ⁾ satisfies certain estimate. In this paper, we extend their result.