Zhenwei Guo

Understanding the process of language learning and quantifying interlingual relationships are central challenges in linguistics, cognitive science, and language education. In this paper, we propose a novel framework that models second language acquisition as a diffusion process within a structured, multidimensional space of languages. We introduce a formal measure of interlingual distance, grounded in linguistic features, to quantify structural and functional differences between languages. Building on Barenblatt-type nonlinear diffusion models, we represent language learning as a multicontinua diffusion process, where distinct components of language – such as phonetics, grammar, vocabulary, and pragmatics – are treated as separate, interacting continua. Each continuum evolves independently according to its own diffusion dynamics, capturing the heterogeneous difficulty and pace of learning across linguistic subsystems. The interaction between these continua reflects the coupling between linguistic competencies in real-world acquisition. We can validate this model with empirical data on second language learning rates across various language pairs, demonstrating that diffusion distances in each continuum correlate with observed learning difficulties in the corresponding language domain. This approach not only offers a new theoretical lens on language learning but also provides a predictive framework for curriculum design, learner modeling, and applications in multilingual NLP and AI systems.

The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical forms of a split quaternion matrix and derives algebraic techniques for finding the canonical forms of a split quaternion matrix. This paper also gives two applications for the right eigenvalue and diagonalization in split quaternionic mechanics.

A nectarine was introduced in 2014 by Bernd Schmeikal in the form of , , and , in which are real numbers. This paper studies the problems of right eigenvalues and eigenvectors of a nectarine matrix by means of a real representation matrix of the nectarine matrix and derives algebraic techniques for the right eigenvalues and eigenvectors of the nectarine matrix.