The classical Julia-Wolff-Carathéodory theorem gives a condition ensuring the existence of the non-tangential limit of both a bounded holomorphic function and its derivative at a given boundary point of the unit disk in the complex plane. This theorem has been generalized by Rudin to holomorphic maps between unit balls in C, and by the author to holomorphic maps between strongly (pseudo)convex ...

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

In the asymptotic theory of quantum hypothesis testing, the error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states, in an increasing way. This is well known as the direct part and strong converse of quantum Stein’s lemma. Here we look into the behavior of this sudden change and h...

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.

The BCD type system of intersection types has been introduced by Barendregt, Coppo and Dezani in [1]. It is derived from a filter lambda model in order to characterize exactly the strongly normalizing terms. Formally, intersection types over variables α ∈ V σ, τ, ρ ::= α | σ → τ | σ ∩ τ | ω are related by the least preorder ≤ closed under the rules σ ≤ ω, ω ≤ ω → ω, σ ∩ τ ≤ σ, σ ∩ τ ≤ τ, σ ≤ σ ...

We here provide additional proofs, definitions, lemmas and derivations omitted in the paper. Note that material contained in the latter are referred to by the captions used there (e.g. Theorem 1), whereas auxiliary statements contained exclusively in this supplement are preceded by a capital Roman letter (e.g. Theorem A.1). A Sub-Gaussian random variables and concentration inequalities A random...

In this supplementary file, we first present the parameter setting for ρ, and then present the proof of the lemmas and theorems appeared in the main paper. 1. Parameter Setting for ρ In the main paper, we present (14) as a simple and effective method to choose ρ, which is motivated by the thresholding strategy in StOMP for sparse signal recovery (Donoho et al., 2012). Specifically, let σ be the...

A map f : K → R of a simplicial complex is an almost embedding if f(σ) ∩ f(τ) = ∅ whenever σ, τ are disjoint simplices of K. Theorem. Fix integers d, k ≥ 2 such that d = 3k 2 + 1. (a) Assume that P 6= NP . Then there exists a finite k-dimensional complex K that does not admit an almost embedding in R but for which there exists an equivariant map K̃ → Sd−1. (b) The algorithmic problem of recognit...

] The primary purpose of the supplemental is to provide the theoretical arguments that our algorithm is correct. We first give the proof that our proposed tree metric is indeed tree additive. We then analyze the consistency of Algorithm 1. 1 Path Additivity We first prove that our proposed tree metric is path additive based on the proof technique in Song et al. (2011). Lemma 1. If Assumption 1 ...

Once massless quadratically divergent tadpole diagrams are discarded, because they contain no intrinsic scale, it is possible to convert other divergences into logarithmic form, using partial fraction identities; this includes the case of quadratic divergences, as has been applied to the linear sigma model. However the procedure must be carried out with due care, paying great attention to corre...