关于态射的Drazin逆

给出了态射的Drazin逆存在的条件及显式表达式，改进并推广了[1]、[2]与[3]中的一些主要定理。     

泛代数的二次扩张

在本文中引入了泛代数的二次扩张的概念，解决了ＴＵ－ＥＣ（Ａ）和ＵＴ－ＥＣ（Ａ）的存在、真类和基数问题，范畴ＴＵ－ＥＣ（Ａ）（及ＵＴ－ＥＣ（Ａ）），并得到了有关二次扩张的几个同构定理，还对一点二次扩张作了讨论。     

Monoidal functors on the category of representations of a triangular Hopf algebra

Let (H,R) be a triangular Hopf algebra. The monoidal functors on the category of representations ofH is studied, and a universal quantum commutative algebraSeR(M) and a dual H°-comoduleM° for any H-moduleM with an integrale are constructed. Both constructions given here have tensor isomorphism properties. Project supported by the National Natural Science Foundation of China.     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Dimension Theory and Nonstable K 1

This article provides an introduction to A. Bak's theory of group-valued functors on categories with structure and dimension and applies this theory to the algebraic K-theory functors nonstable K ₁ and K ₂.     

Axiomatizing subcategories of Abelian categories

We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated.     

Generalized logic and the representation of rings

Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.     

A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .

     

A Novel Drinking Category Detection Method Based on Wireless Signals and Artificial Neural Network

With the continuous improvement of people’s health awareness and the continuous progress of scientific research, consumers have higher requirements for the quality of drinking. Compared with high-sugar-concentrated juice, consumers are more willing to accept healthy and original Not From Concentrated (NFC) juice and packaged drinking water. At the same time, drinking category detection can be used for vending machine self-checkout. However, the current drinking category systems rely on special equipment, which require professional operation, and also rely on signals that are not widely used, such as radar. This paper introduces a novel drinking category detection method based on wireless signals and artificial neural network (ANN). Unlike past work, our design relies on WiFi signals that are widely used in life. The intuition is that when the wireless signals propagate through the detected target, the signals arrive at the receiver through multiple paths and different drinking categories will result in distinct multipath propagation, which can be leveraged to detect the drinking category. We capture the WiFi signals of detected drinking using wireless devices; then, we calculate channel state information (CSI), perform noise removal and feature extraction, and apply ANN for drinking category detection. Results demonstrate that our design has high accuracy in detecting drinking category.