Polyadic Constacyclic Codes

For any given positive integer $m$, a necessary and sufficient condition for the existence of Type I $m$-adic constacyclic codes is given. Further, for any given integer $s$, a necessary and sufficient condition for $s$ to be a multiplier of a Type I polyadic constacyclic code is given. As an application, some optimal codes from Type I polyadic constacyclic codes, including generalized Reed-Solomon codes and alternant MDS codes, are constructed.Comment: We provide complete solutions on two basic questions on polyadic constacyclic cdes, and construct some optimal codes from the polyadic constacyclic cde

How Powerful Are Elements? An Evaluation of the Adequacy of Element Thory in Phonological Representations

In this dissertation, I resume the discussion of privative features as a notational device in segmental representation. I argue from both theoretical and empirical perspectives that element theory is a better theory of phonological representation than the binary-feature system. First, I argue that element theory is a more constrained and thus preferable theory since, with the proposal of single-valued features and a small element inventory, it is exempted from overgeneration of natural classes and phonological processes. Next, in case studies, I weigh the element-based representations of vowel shift, vowel harmony and consonantal lenition against the feature-based representations. The result of the evaluation shows that, compared to binary approaches, element theory is better in capturing the nature of various phonological processes. It generally provides non-arbitrary representations that can mirror how the processes occur, though it also has its limit in the characterization of Pasiego height harmony and consonantal affrication as well as providing a non-arbitrary account for occurrence of certain types of lenition in particular environments

2-[(2-Carboxy­phen­yl)sulfan­yl]acetic acid

The title compound, C9H8O4S, affords a zigzig chain in the crystal structure by inter­molecular O—H⋯O hydrogen bonds. The molecular geometry suggests that extensive but not uniform π-electron delocalization is present in the benzene ring and extends over the exocyclic C—S and C—C bonds

Action Recognition Using 3D Histograms of Texture and A Multi-Class Boosting Classifier

Human action recognition is an important yet challenging task. This paper presents a low-cost descriptor called 3D histograms of texture (3DHoTs) to extract discriminant features from a sequence of depth maps. 3DHoTs are derived from projecting depth frames onto three orthogonal Cartesian planes, i.e., the frontal, side, and top planes, and thus compactly characterize the salient information of a specific action, on which texture features are calculated to represent the action. Besides this fast feature descriptor, a new multi-class boosting classifier (MBC) is also proposed to efficiently exploit different kinds of features in a unified framework for action classification. Compared with the existing boosting frameworks, we add a new multi-class constraint into the objective function, which helps to maintain a better margin distribution by maximizing the mean of margin, whereas still minimizing the variance of margin. Experiments on the MSRAction3D, MSRGesture3D, MSRActivity3D, and UTD-MHAD data sets demonstrate that the proposed system combining 3DHoTs and MBC is superior to the state of the art

A finite theorem for Ahlfors' covering surface theory

Ahlfors' theory of covering surfaces is one of the major mathematical achievement of last century. The most important part of his theory is the Second Fundamental Theorem (SFT). We are interested in the relation of errors of Ahlfors' SFT with the same boundary curve. In this paper we will prove a result which is used to establish the best bound of the constant in Ahlfors' SFT (in \cite{Zh}). Precisely speaking, we will prove that for any surface $\Sigma\in\mathcal{F}_r(L,m)$, a new surface $\Sigma_1$ can be constructed based on it, such that $R(\Sigma_1)\ge R(\Sigma)$ and $L(\partial\Sigma_1)\le L(\partial\Sigma)$, where $R(\Sigma)$ is Ahlfors' error term and $L(\partial\Sigma)$ is the boundary length of the surface $\Sigma$, and the covering degree of $\Sigma_1$ has an upper bound independent of surfaces. Meanwhile, this conclusion suggests that the supremum of $H(\Sigma)=R(\Sigma)/L(\partial\Sigma)$ can be achieved by surfaces in the space $\mathcal{F}_r'(L,m)$