Some characterizations of space-forms

Integral conditions on the traceless Ricci tensor are used to characterize Euclidean and hyperbolic spaces among complete, locally conformally flat manifolds of constant scalar curvature. The main tools are vanishing-type results for -solutions of a large class of differential inequalities. Further applications of the technique are also given.

     

Some characterizations ofL-regular points

Bernstein-Walsh type estimates of polynomials and their relation to compact subsets of ⁿ are discussed.     

Some characterizations of domination

We show that a cocycle has a dominated splitting if and only if there is a uniform exponential gap between singular values of its iterates. Then we consider sets Σ in with the property that any cocycle with values in Σ has a dominated splitting. We characterize these sets in terms of existence of invariant multicones, thus extending a two-dimensional result by Avila, Bochi, and Yoccoz. We give an example showing how these multicones can fail to have convexity properties. J. Bochi and N. Gourmelon were partially supported by CNPq (Brazil). An erratum to this article can be found at     

Some characterizations of partial algebras

Partial algebras arise frequently in applications, especially in quantum theory where observables are represented by unbounded linear maps that are often not conformable for multiplication. In this paper, we introduce a certain class of partial algebras and prove, among other results, that every partial algebra belonging to the class may be identified with a partial subalgebra of some algebra. This furnishes a means of studying the members of the class by exploiting known results about algebras.     

Some characterizations of discrete unimodality

Let F be a discrete distribution function on $\text{|Z}$. This paper gives a characterization of discrete unimodal distribution functions (Theorem 5.1) and a representation theorem for those distribution functions (Theorem 6.3), both in terms of their Lévy concentration functions.     

Some algebraic characterizations of F-frames

In pointfree topology, F-frames have been defined by Ball and Walters-Wayland by means of a frame-theoretic translation of the topological characterization of F-spaces as those whose cozero-sets are C*-embedded. This is a departure from the way in which F-spaces were defined by Gillman and Henriksen as those spaces X for which the ring C(X) is Bézout, meaning that every finitely generated ideal is principal. In this note, we show that, as in the case of spaces, a frame L is an F-frame precisely when the ring ${\mathcal{R}L}$ of continuous real-valued functions on L is Bézout. A commutative ring with identity is called almost weak Baer if the annihilator of each element is generated by idempotents. We establish that ${\mathcal{R}L}$ is almost weak Baer iff L is a strongly zero-dimensional F-frame.     

Some characterizations of BLO space

For , a real‐valued function belongs to space if In this paper, we establish a version of John–Nirenberg inequality suitable for the space with . As a corollary, it is proved that spaces are independent of the scale in sense of norm. Also, we characterize the space through weighted Lebesgue spaces and variable Lebesgue spaces, respectively.     

Some characterizations of unique extremality

In this paper, it is shown that some necessary characteristic conditions for unique extremality obtained by Zhu and Chen are also sufficient and some sufficient ones by them actually imply that the uniquely extremal Beltrami differentials have a constant modulus. In addition, some local properties of uniquely extremal Beltrami differentials are given.     

Some characterizations of Krull domains

In this paper, we define the v-finiteness for a length function L_v on the set of all v-ideals of an integral domain R and show that R is a Krull domain if and only if every proper integral v-ideal of R has v-finite length and L_v((AB)_v)=L_v(A)+L_v(B) for every pair of proper integral v-ideals A and B in R. We also give Euclidean-like characterizations of factorial, Krull, and π-domains. Finally we define the notion of quasi-∗-invertibility and show that if every proper prime t-ideal of an integral domain R is quasi-t-invertible, then R is a Krull domain.