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If the list of binary numbers is read by upward-sloping diagonals, the resulting ``sloping binary numbers'' 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) have some surprising properties. We give formulae for the n-th…

Number Theory · Mathematics 2016-08-16 David Applegate , Benoit Cloitre , Philippe Deléham , N. J. A. Sloane

The definition generation task aims to generate a word's definition within a specific context automatically. However, owing to the lack of datasets for different complexities, the definitions produced by models tend to keep the same…

Computation and Language · Computer Science 2022-09-30 Jiaxin Yuan , Cunliang Kong , Chenhui Xie , Liner Yang , Erhong Yang

Chinese parsing has traditionally been solved by three pipeline systems including word-segmentation, part-of-speech tagging and dependency parsing modules. In this paper, we propose an end-to-end Chinese parsing model based on character…

Computation and Language · Computer Science 2020-12-09 Yuan Zhang , Zhiyang Teng , Yue Zhang

Tang (618-907 AD) and Song (960-1279) dynasties are two very important periods in the development of Chinese literary. The most influential forms of the poetry in Tang and Song were Shi and Ci, respectively. Tang Shi and Song Ci established…

Computation and Language · Computer Science 2016-08-30 Chao-Lin Liu

The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have…

Differential Geometry · Mathematics 2018-05-15 Bang-Yen Chen

In this paper we consider integers in base 10 like $abc$, where $a$, $b$, $c$ are digits of the integer, such that $abc^2 - (abc \cdot cba) \; = \; \pm n^2$, where $n$ is a positive integer, as well as equations $abc^2 - (abc \cdot cba) \;…

Number Theory · Mathematics 2016-02-23 Geoffrey B. Campbell , Aleksander Zujev

We introduce two new classes of integers. The first class consists of numbers $N$ for which there exists at least one nonnegative integer $A$, such that the sum of $A$ and the sum of digits of $N$, added to the reversal of the sum, gives…

Number Theory · Mathematics 2019-08-05 Viorel Nitica , Andrei Török

As handwriting input becomes more prevalent, the large symbol inventory required to support Chinese handwriting recognition poses unique challenges. This paper describes how the Apple deep learning recognition system can accurately handle…

Computer Vision and Pattern Recognition · Computer Science 2020-05-19 Youssouf Chherawala , Hans J. G. A. Dolfing , Ryan S. Dixon , Jerome R. Bellegarda

The Chinese language poses challenges for natural language processing based on the unit of a word even for formal uses of the Chinese language, social media only makes word segmentation in Chinese even more difficult. In this document we…

Information Retrieval · Computer Science 2012-06-22 Peiyou Song , Anhei Shu , Anyu Zhou , Dan Wallach , Jedidiah R. Crandall

The Chinese character riddle is a unique form of cultural entertainment specific to the Chinese language. It typically comprises two parts: the riddle description and the solution. The solution to the riddle is a single character, while the…

Computation and Language · Computer Science 2023-09-26 Fan Xu , Yunxiang Zhang , Xiaojun Wan

Chinese word segmentation and part-of-speech tagging are necessary tasks in terms of computational linguistics and application of natural language processing. Many re-searchers still debate the demand for Chinese word segmentation and…

Computation and Language · Computer Science 2021-12-20 Duc-Vu Nguyen , Linh-Bao Vo , Ngoc-Linh Tran , Kiet Van Nguyen , Ngan Luu-Thuy Nguyen

To analyse the significance of the digits used for interval bounds, we clarify the philosophical presuppositions of various interval notations. We use information theory to determine the information content of the last digit of the numeral…

Numerical Analysis · Mathematics 2025-10-20 M. H. van Emden

The average number of primitive quadratic Dirichlet characters of modulus n tends to a constant as n->infty. The same is true for primitive cubic characters. It is therefore surprising that, as n->infty, the average number of primitive…

Number Theory · Mathematics 2016-03-28 Steven Finch

In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…

Data Structures and Algorithms · Computer Science 2012-09-24 A. Emre Cetin

Idioms, whose figurative meanings usually differ from their literal interpretations, are common in everyday language, especially in Chinese, where they often contain historical references and follow specific structural patterns. Despite…

Computation and Language · Computer Science 2025-08-15 Cai Yang , Yao Dou , David Heineman , Xiaofeng Wu , Wei Xu

Chinese font generation aims to create a new Chinese font library based on some reference samples. It is a topic of great concern to many font designers and typographers. Over the past years, with the rapid development of deep learning…

Computer Vision and Pattern Recognition · Computer Science 2025-08-12 Weiran Chen , Guiqian Zhu , Ying Li , Yi Ji , Chunping Liu

Over the past thirty years, there has been significant progress in developing general-purpose, language-based approaches to incremental computation, which aims to efficiently update the result of a computation when an input is changed. A…

Programming Languages · Computer Science 2021-03-24 Matthew A. Hammer , Jana Dunfield , Kyle Headley , Nicholas Labich , Jeffrey S. Foster , Michael Hicks , David Van Horn

Harmonic numbers have been studied since antiquity, while hyperharmonic numbers were intoduced by Conway and Guy in 1996. The degenerate harmonic numbers and degenerate hyperharmonic numbers are their respective degenerate versions. The aim…

Number Theory · Mathematics 2023-01-10 Hye Kyung Kim , Dae San Kim , Taekyun Kim

Given the advantage and recent success of English character-level and subword-unit models in several NLP tasks, we consider the equivalent modeling problem for Chinese. Chinese script is logographic and many Chinese logograms are composed…

Computation and Language · Computer Science 2018-09-11 Falcon Z. Dai , Zheng Cai

The renowned proverb, Numbers do not lie, underscores the reliability and insight that lie beneath numbers, a concept of undisputed importance, especially in economics and finance etc. Despite the prosperity of Benford's Law in the first…

Computation and Language · Computer Science 2023-09-12 Fuqian Zhang , Zhenhua Wang
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