In this paper we study the L-convergence of the Riesz means S R(f) for the sublaplacian on the sphere S in the complex n-dimensional space C. We show that S R(f) converges to f in L (S) when δ > δ(p) := (2n− 1)| 2 − 1 p |. The index δ(p) improves the one found by Alexopoulos and Lohoué [AL], 2n| 1 2 − 1 p |, and it coincides with the one found by Mauceri [Ma] and, with different methods, by Mül...

We study the existence of extremal Kähler metrics on Kähler manifolds. After introducing a notion of relative K-stability for Kähler manifolds, we prove that Kähler manifolds admitting extremal Kähler metrics are relatively K-stable. Along the way, we prove a general Lp lower bound on the Calabi functional involving test configurations and their associated numerical invariants, answering a ques...

Often landscape metrics are not thoroughly evaluated with respect to remote sensing data characteristics, such as their behavior in relation to variation in spatial and temporal resolution, number of land cover classes or dominant land cover categories. In such circumstances, it may be difficult to ascertain whether a change in a metric is due to landscape pattern change or due to the inherent ...

Distance measures like the Euclidean distance are used to measure similarity between images in content-based image retrieval. Such geometric measures implicitly assign more weighting to features with large ranges than those with small ranges. This paper discusses the effects of five feature normalization methods on retrieval performance. We also describe two likelihood ratio-based similarity me...

A converse theorem of approximation in various metrics for 2π periodic functions of several variables was proved in [5]. We prove the theorem of representation for the derivative of a function, and then the analogous converse theorem for nonperiodic functions defined on the space R. In this way we generalize and improve the results from [4, 6.4]. As usually we say that f(x1, . . . , xn) ∈ Lp(R ...

The wide-range used distance measurement in digital image processing is the Euclidean norm nowadays. This is defined over the set of the real numbers that is why it does not suit the digital approach, perfectly. The use of neighborhood sequences is an alternative to the Lp metrics and because they are based on the set of integers it is more suitable for digital thinking. In this paper we summar...

We prove that a Banach space X is not super-reflexive if and only if the hyperbolic infinite tree embeds metrically into X. We improve one implication of J.Bourgain’s result who gave a metrical characterization of super-reflexivity in Banach spaces in terms of uniforms embeddings of the finite trees. A characterization of the linear type for Banach spaces is given using the embedding of the inf...

Despite the remarkable performance of graph neural networks (GNNs) in semi-supervised learning, it is criticized for not making full use unlabeled data and suffering from over-fitting. Recently, augmentation, used to improve both accuracy generalization GNNs, has received considerable attentions. However, one fundamental question how evaluate quality augmentations principle? In this paper, we p...

Bias Temperature Instability (BTI) has led to more vulnerable ICs with the continuous downscaling of CMOS technologies. This paper presents the impact of BTI for two different SRAM sense amplifiers which target two applications, i.e., low power (LP), and high performance (HP). The evaluation metrics, the sensing delay (SD) and energy, are analyzed for three workloads. In contrast to earlier wor...

Die Verwendung von ID/LP-Grammatiken und komplexen Symbolen ist bei Flektionsreichen und in der Wortstellung flexiblen Sprachen wie dem Deutschen erfolgversprechender als der Rückgriff auf kontextfreie Grammatiken (cfg). Dieser Artikel beschreibt in einem ersten Schritt die dafür notwendigen Veränderungen des TomitaAlgorithmus und dessen Tabellengenerators. In einem zweiten Schritt werden wir a...