‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

Given a finite point set P ⊂ R, we call a multiset A a one-sided weak ε-approximant for P (with respect to convex sets), if |P ∩ C|/|P | − |A ∩C|/|A| ≤ ε for every convex set C. We show that, in contrast with the usual (two-sided) weak ε-approximants, for every set P ⊂ R there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.

We extend the Larson–Sweedler theorem for weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We establish the autonomous monoidal category of the modules of a weak Hopf algebra A and show the semisimplicity of the unit and the invertible modules of A. We also reveal the connection of these modules to lef...

In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [5, 8, 9]. The fractional weak discrepancy wdF (P ) of a poset P = (V,≺) is the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a)− f(b)| ≤ k. We formulate the fractional weak...

In this article we study nonparametric estimation of regression function by using the weighted Nadaraya-Watson approach. We establish the asymptotic normality and weak consistency of the resulting estimator for-mixing time series at both boundary and interior points, and we show that the estimator preserves the bias, variance, and more importantly, automatic good boundary behavior properties of...

QuiSci is incredible fast, faster than most other ciphers. On modern CPUs it needs only arround 1 clock cycle per byte, so it is 10 times fast than most other well-known algorithm. On the website of QuiSci [1] it is claimed that this algorithm is secure. With this paper I like to show a key recovery attack on QuiSci, exploiting the weak key setup. When you are able to guess the beginning of the...

This paper considers a class of semiparametric models being the sum of a nonparametric trend function g and a FARIMA-GARCH error process. Estimation of g( ), the th derivative of g, by local polynomial tting is investigated. The focus is on the derivation of the asymptotic normality of ĝ( ). At rst a central limit theorem based on martingale theory is developed and asymptotic normality of the s...

Given a sample from a discretely observed compound Poisson process we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. Asymptotic expansions of the bias and variance of the estimator are given and pointwise weak consistency and asymptotic normality are established. We also derive the minimax conve...

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic. In the papers concerning quan...