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Translation ambiguity occurs when a word in one language has multiple translations into another language, resulting in slower and less accurate language processing and production. We collected number-of-translation norms for 562 English words into Japanese, of which 70% were translation-ambiguous. When compared with previous norming studies with the same English words, our sample had the highest proportion of ambiguity. We then had a separate group of participants back-translate the correct Japanese translations into English and found that 54% were translation-ambiguous. We further analyzed types of errors in our sample, finding omission errors (i.e., no translation given) to be the most common in both translation directions. Errors made during translation were related to proficiency, wherein higher L2 proficiency was significantly positively correlated with making more semantic-type errors (i.e., providing a semantic associate instead of the correct translation), specifically in the Japanese to English direction. These norms provide information on how translation-ambiguous and translation-unambiguous words are produced in both directions of translation and can be used in future research examining translation ambiguity.
This note is the natural continuation of what was started in [I. Birindelli, A. Briani, and H. Ishii, Test Function Approach to Fully Nonlinear Equations in Thin Domains, arxiv:2404.19577, 2024], i.e., the extension to fully nonlinear operators of the well-known result on thin domains of Hale and Raugel [J. Math. Pures Appl. (9), 71 (1992), pp. 33--95]. Here we consider oblique boundary conditions and find some new phenomena, in particular the limit equations contain ``new terms"" in the second and first order terms which don't have an equivalent in the Neumann case.
In this paper, we introduce a new equivalence relation, named R-equivalence relation, on the set of colorings of an oriented knot diagram by a quandle. We determine the R-equivalence classes of colorings of a diagram of a torus knot by a quandle, called Rot E-2, under a certain condition.
The structural contribution of entasis, the subtle curvature observed in classical columns such as those in the Parthenon (ancient Greece) and Horyu-ji Temple (Japan), was investigated. The study employed a two-segment-width beam model for both traditional buckling analysis based on the bending beam theory and physical experimentation to determine its effect on column strength. The results indicated that, when the two-segment-width beam was treated as a two-dimensional experiment of entasis, it was confirmed that the buckling load increased. This increase was observed under specific conditions when compared against straight beams of uniform width and two-segment-width beams sharing the same projected area. The investigation reconfirms that the traditional architectural style of entasis in columns provides a verifiable structural strengthening benefit.
In this short note, we construct an explicit Hamiltonian cycle in the state graph of the 5-puzzle on a cylindrical 2 x 3 grid, a graph with 720 vertices. The cycle is described by a short symbolic sequence of 48 moves over the alphabet {L, R, V}, repeated 15 times, which can be verified directly. We also find a shorter 24-move sequence whose repetition yields a 2-cycle cover, which can be spliced into a Hamiltonian path. These constructions arise naturally from a general method: lifting Hamiltonian cycles from a quotient graph under the action of the puzzle's symmetry group. The method produces compact, human-readable cycle encoding. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
