On the sum of digits of primes in imaginary quadratic fields

Let r≧2 be a fixed integer. Any positive integer n can be uniquely written in the form (1) n=Σ^k_f=1 afr^k-j=a1a2 ･･･ak, where each a is one of 0,1, ･･･, r-1 and ..

Multi-duplicated Characterization of Graph Structures using Information Gain Ratio for Graph Neural Networks

Various graph neural networks (GNNs) have been proposed to solve node classification tasks in machine learning for graph data. GNNs use the structural information of graph data by aggregating the features of neighboring nodes. However, they fail to directly characterize and leverage the structural information. In this paper, we propose multi-duplicated characterization of graph structures using information gain ratio (IGR) for GNNs (MSI-GNN), which enhances the performance of node classification by using an i-hop adjacency matrix as the structural information of the graph data. In MSI-GNN, the i-hop adjacency matrix is adaptively adjusted by two methods: (i) structural features in the matrix are selected based on the IGR, and (ii) the selected features in (i) for each node are duplicated and combined flexibly. In an experiment, we show that our MSI-GNN outperforms GCN, H2GCN, and GCNII in terms of average accuracies in benchmark graph datasets.Comment: 20pages, 8 figure

An Ontology Formalization of Relation Type Hierarchy in Conceptual Structure Theory

This paper presents an enhancement to ontology formalization, combining previous work in Conceptual Structure Theory and Order-Sorted Logic. In particular, the relation type hierarchy of the former theory is a subset of the predicate hierarchy of the latter. Most existing ontology formalisms place greater importance on concept types, but this paper focuses more on relation types, which are in essence predicates on concept types. New notions are introduced and new properties identified with the aim of completing missing arguments in relation types. The end result is a new ontology, that we call the closure of the original ontology, on which automated inference could be more easily produced (e.g., a query-answering system for legal knowledge)

Possible Superconductivity at 37 K in Graphite-Sulfur Composite

Sulfur intercalated graphite composites with diamagnetic transitions at 6.7 K and 37 K are prepared. The magnetization hysteresis loops (MHL), Xray diffraction patterns, and resistance were measured. From the MHL, a slight superconducting like penetration process is observed at 15 K in low field region. The XRD shows no big difference from the mixture of graphite and sulfur indicating that the volume of the superconducting phase (if any) is very small. The temperature dependence of resistance shows a typical semiconducting behavior with a saturation in low temperature region. This saturation is either induced by the de-localization of conducting electrons or by possible superconductivity in this system.Comment: CHIN. PHYS.LETT v18 1648 (2001

Computing top intersections in the tautological ring of MgM_g

We derive effective recursion formulae of top intersections in the tautological ring $R^*(M_g)$ of the moduli space of curves of genus $g\geq 2$. As an application, we prove a convolution-type tautological relation in $R^{g-2}(M_g)$.Comment: 18 page

Effect of high pressure homogenization (HPH) on the physical stability of tomato juice

AbstractHigh pressure homogenization (HPH) is a non-thermal technology that has been widely studied as a partial or total substitute for thermal food processing. Although the aspect of microbial inactivation has been widely studied, there are only a few works in the literature dealing with the physical–chemical changes in fruit products due to HPH, especially regarding its rheological properties. The present work evaluated the effect of HPH (up to 100MPa) on the physical stability of tomato juice. HPH changed the tomato juice particle size distribution (PSD), pulp sedimentation behavior, serum cloudiness (turbidity), color and microstructure, by disrupting the suspended pulp particles. It therefore increased juice stability to sedimentation and changed its color due to leakage of lycopene from the disrupted cells. The effect of homogenization pressure on the physical properties of the juice followed an asymptotic behavior. The results indicated that the HPH could be used as a valuable tool to promote desirable physical property changes in food products, such as increasing the consistency and reducing particle sedimentation and serum separation, hence improving sensory acceptance