Related papers: Chinese Names for Integers
The results of the computer hunt for the primes of the form $q = m^2+1$ up to $10^{20}$ are reported. The number of sign changes of the difference $\pi_q(x) - \frac{C_q}{2}\int_2^x{du \over \sqrt{u}\log(u)}$ and the error term for this…
A permutiple is a number which is an integer multiple of some permutation of its digits. A well-known example is 9801 since it is an integer multiple of its reversal, 1089. In this paper, we consider the permutiple problem in an entirely…
This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…
Automatic character generation is an appealing solution for new typeface design, especially for Chinese typefaces including over 3700 most commonly-used characters. This task has two main pain points: (i) handwritten characters are usually…
Conversion of Chinese graphemes to phonemes (G2P) is an essential component in Mandarin Chinese Text-To-Speech (TTS) systems. One of the biggest challenges in Chinese G2P conversion is how to disambiguate the pronunciation of polyphones -…
Encoder-only Transformers have advanced along three axes -- architecture, data, and systems -- yielding Pareto gains in accuracy, speed, and memory efficiency. Yet these improvements have not fully transferred to Chinese, where tokenization…
A wide variety of neural-network architectures have been proposed for the task of Chinese word segmentation. Surprisingly, we find that a bidirectional LSTM model, when combined with standard deep learning techniques and best practices, can…
Good integers introduced in 1997 form an interesting family of integers that has been continuously studied due to their rich number theoretical properties and wide applications. In this paper, we have focused on classes of $2^\beta$-good…
In this paper, we perform an arithmetization of well-formed parenthesis strings with zeros (Motzkin words) and of corresponding Motzkin paths. The transformations used are reminiscent of G\"odel numbering for mathematical objects of some…
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and…
The Fibonacci numbers are familiar to all of us. They appear unexpectedly often in mathematics, so much there is an entire journal and a sequence of conferences dedicated to their study. However, there is also another sequence of numbers…
An individual's identity in a human society is specified by his or her name. Differently from family names, usually inherited from fathers, a given name for a child is often chosen at the parents' disposal. However, their decision cannot be…
We consider the integers having the property of reversing when multiplied by a specific integer k. First, we proved that k should be either 1, 4 or 9. Second, we classify these integers as (10, 1)- reverse multiples, (10, 4)- reverse…
Unlike alphabetic languages, Chinese spelling and pronunciation are different. Both characters and pinyin take an important role in Chinese language understanding. In Chinese NLP tasks, we almost adopt characters or words as model input,…
A permutiple is a natural number that is a nontrivial multiple of a permutation of its digits in some base. Special cases of permutiples include cyclic numbers (multiples of cyclic permutations of their digits) and palintiple numbers…
Demographic change of human populations is one of the central questions for delving into the past of human beings. To identify major population expansions related to male lineages, we sequenced 78 East Asian Y chromosomes at 3.9 Mbp of the…
A class of good integers has been introduced by P. Moree in $1997$ together with the characterization of good odd integers. Such integers have shown to have nice number theoretical properties and wide applications. In this paper, a complete…
A look-and-say sequence is obtained iteratively by reading off the digits of the current value, grouping identical digits together: starting with 1, the sequence reads: 1, 11, 21, 1211, 111221, 312211, etc. (OEIS A005150). Starting with any…
A permutation $\pi$ is said to be {\em Dumont permutations of the first kind} if each even integer in $\pi$ must be followed by a smaller integer, and each odd integer is either followed by a larger integer or is the last element of $\pi$…
Chinese is one of the most widely used languages in the world, yet online handwritten Chinese character recognition (OLHCCR) remains challenging. To recognize Chinese characters, one popular choice is to adopt the 2D convolutional neural…