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This is a pedagogical article cited in the foregoing research note, quant-ph/9911050

Quantum Physics · Physics 2020-02-12 S. A. Fulling

Recently, word enhancement has become very popular for Chinese Named Entity Recognition (NER), reducing segmentation errors and increasing the semantic and boundary information of Chinese words. However, these methods tend to ignore the…

Computation and Language · Computer Science 2021-07-13 Shuang Wu , Xiaoning Song , Zhenhua Feng

A simple and popular childhood game, `LOVES' or the `Love Calculator', involves an iterated rule applied to a string of digits and gives rise to surprisingly rich behaviour. Traditionally, players' names are used to set the initial…

History and Overview · Mathematics 2016-02-12 Iain G. Johnston

Let $S$ be a string of $l$ decimal digits. We give an explicit upper bound on some prime $p$ whose decimal representation contains the string $S$. We also show, as a corollary of the Green-Tao theorem, that there are arbitrarily long…

Number Theory · Mathematics 2014-07-31 Adrian Dudek

Hangeul was created as a phonetic alphabet and is known to have the best 1:1 correspondence between letters and pronunciation among existing alphabets. In this paper, we examine the possibility of modifying the basic form of Hangeul and…

Computation and Language · Computer Science 2024-12-24 Wonchan Kim , Michelle Meehyun Kim

The Chinese abacus is the resource presented in this paper, to teach and learn number sense and place-value system at primary level. The Chinese abacus can be material, virtual (software) or drawn on a worksheet. We present three tasks and…

History and Overview · Mathematics 2017-12-25 Caroline Poisard

This article contains ideas and their elaboration for quantifiers, which appeared after checking in practice the experimental language of the formal knowledge representation YAFOLL [1]: - looking at for_all and exists quantifiers as…

Logic in Computer Science · Computer Science 2019-08-30 Alex Shkotin

Idioms are an important language phenomenon in Chinese, but idiom translation is notoriously hard. Current machine translation models perform poorly on idiom translation, while idioms are sparse in many translation datasets. We present…

Computation and Language · Computer Science 2022-02-22 Kenan Tang

A class of powerful $q$-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $q$-ary block codes that encode $k$…

Information Theory · Computer Science 2016-04-18 Martianus Frederic Ezerman , Somphong Jitman , Patrick Solé

The origin of the numerals that we inherited from the arabo-Islamic civilization remained one enigma. The hypothesis of the Indian origin remained, with controversies, without serious rival. It was the dominant hypothesis since more of one…

History and Overview · Mathematics 2007-07-24 Ahmed Boucenna

Speakers often face choices as to how to structure their intended message into an utterance. Here we investigate the influence of contextual predictability on the encoding of linguistic content manifested by speaker choice in a classifier…

Computation and Language · Computer Science 2019-05-20 Meilin Zhan , Roger Levy

Unlike English, which uses distinct forms (e.g., had, has, will have) to mark the perfect aspect across tenses, Chinese and Japanese lack separate grammatical forms for tense within the perfect aspect, which complicates Natural Language…

Computation and Language · Computer Science 2025-08-19 Jie Lu , Du Jin , Hitomi Yanaka

A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…

Dynamical Systems · Mathematics 2012-07-03 Valerii Salov

Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…

Data Structures and Algorithms · Computer Science 2012-04-03 Youssef Bassil , Aziz Barbar

We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…

Number Theory · Mathematics 2016-12-30 Tommy Hofmann , Claus Fieker

Contemporary scientific exchanges are international, yet language continues to be a persistent barrier to scientific communication, particularly for non-native English-speaking scholars. Since the ability to absorb knowledge has a strong…

Digital Libraries · Computer Science 2019-08-22 Kaile Gong , Juan Xie , Ying Cheng , Vincent Larivière , Cassidy R. Sugimoto

Using the theory of metaplectic forms,we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estimates on average over arithmetic progressions are…

Number Theory · Mathematics 2011-11-03 Benoit Louvel

The article continues an analysis of the genetic 8-dimensional Yin-Yang-algebra. This algebra was revealed in a course of matrix researches of structures of the genetic code and it was described in the author's articles arXiv:0803.3330 and…

Genomics · Quantitative Biology 2008-09-17 Sergey V. Petoukhov

A four index notation (e.g. (10-11) is often used to denote reciprocal lattice vectors or crystal faces of hexagonal crystals. The purposes of this notation have never been fully explained. This note clarifies the underlying mathematics of…

Other Condensed Matter · Physics 2010-06-16 Philip B. Allen

Chinese Spelling Correction (CSC) stands as a foundational Natural Language Processing (NLP) task, which primarily focuses on the correction of erroneous characters in Chinese texts. Certain existing methodologies opt to disentangle the…

Computation and Language · Computer Science 2024-09-09 Xiangke Zeng , Zuchao Li , Lefei Zhang , Ping Wang , Hongqiu Wu , Hai Zhao