An attempt to interpret the Weil explicit formula from Beurling's spectral theory

AbstractA. Beurling introduced the celebrated problem of spectral synthesis. Roughly speaking, it is a problem whether functions belonging to a certain Banach space have a possibility to be approximated by trigonometric polynomials in the appropriate topology. For this problem Beurling introduced the concept of spectral sets whose elements are regarded as exponents of trigonometric polynomials. In the Weil explicit formula we can see a certain phenomenon which may be related to Beurling's spectral sets. The purpose of this paper is to study the phenomenon

Ratio of alpha2-macroglobulin levels in cerebrospinal fluid and serum: an expression of neuroinflammation in acute disseminated encephalomyelitis

博士（医学）福島県立医科大

Influence of deposition rate on magnetic properties of inverse-spinel NiCo2O4epitaxial thin films grown by pulsed laser deposition

We investigated the influence of the deposition rate on structural and magnetic properties of inverse-spinel ferrimagnet NiCo₂O₄ epitaxial films grown by pulsed laser deposition. While films' lattice constants are insensitive to the deposition rate, saturation magnetization, and perpendicular magnetic anisotropy for the film grown with a high deposition rate are reduced. These results imply that growing NiCo₂O₄ films with a high deposition rate leads to occupations of the tetrahedral site by Ni, although Ni ideally occupies only the octahedral site. Controlling the deposition rate and modulating the cation distribution is the key for tuning the magnetic properties in NiCo₂O₄ films

Regularity-Constrained Fast Sine Transforms

This letter proposes a fast implementation of the regularity-constrained discrete sine transform (R-DST). The original DST \textit{leaks} the lowest frequency (DC: direct current) components of signals into high frequency (AC: alternating current) subbands. This property is not desired in many applications, particularly image processing, since most of the frequency components in natural images concentrate in DC subband. The characteristic of filter banks whereby they do not leak DC components into the AC subbands is called \textit{regularity}. While an R-DST has been proposed, it has no fast implementation because of the singular value decomposition (SVD) in its internal algorithm. In contrast, the proposed regularity-constrained fast sine transform (R-FST) is obtained by just appending a regularity constraint matrix as a postprocessing of the original DST. When the DST size is $M\times M$ ($M=2^\ell$, $\ell\in\mathbb{N}_{\geq 1}$), the regularity constraint matrix is constructed from only $M/2-1$ rotation matrices with the angles derived from the output of the DST for the constant-valued signal (i.e., the DC signal). Since it does not require SVD, the computation is simpler and faster than the R-DST while keeping all of its beneficial properties. An image processing example shows that the R-FST has fine frequency selectivity with no DC leakage and higher coding gain than the original DST. Also, in the case of $M=8$, the R-FST saved approximately $0.126$ seconds in a 2-D transformation of $512\times 512$ signals compared with the R-DST because of fewer extra operations

Ternary maximal self-orthogonal codes of lengths 21,2221,22 and 2323

We give a classification of ternary maximal self-orthogonal codes of lengths $21,22$ and $23$. This completes a classification of ternary maximal self-orthogonal codes of lengths up to $24$

USING NEW MEASURES OF IMPLICIT L2 KNOWLEDGE TO STUDY THE INTERFACE OF EXPLICIT AND IMPLICIT KNOWLEDGE

Second language acquisition (SLA) becomes extremely difficult for late second language (L2) learners, who are assumed to have passed the sensitive or critical period for L2 learning. As one of the major accounts of the post-critical period L2 learning processes, a fundamental distinction between explicit and implicit learning and knowledge was proposed over three decades ago. The first goal of the current study was to develop fine-grained measures for implicit knowledge to distinguish it from automatized explicit knowledge. The second goal was to use these validated measures to explore the interface issue of explicit and implicit knowledge by correlating these measures with several cognitive aptitudes. One hundred advanced L2 Japanese speakers whose first language was Chinese were recruited; they were given tests for both automatized explicit knowledge and implicit knowledge, along with three cognitive aptitude measures. The present study developed three psycholinguistic tasks that can reliably assess implicit knowledge (the eye-tracking-while-listening task, the word-monitoring task, and the self-paced reading task) and compared them with the existing tasks that have been claimed to measure implicit knowledge (time-pressured form-focused tasks like grammaticality judgment tasks), but which we hypothesized tap into automatized explicit knowledge. The aptitude test battery consisted of LLAMA F, a measure of explicit learning aptitude, the Serial-Reaction Time (SRT) task, a measure of implicit learning aptitude, and the letter-span task, a measure of phonological short-term memory. In order to validate the measures for automatized explicit knowledge and implicit knowledge, a series of confirmatory factor analyses (CFA), multi-trait multi-method (MTMM) analyses, and structural equation model (SEM) analyses were conducted. Results confirmed that the existing tasks purported to measure implicit knowledge in fact tap into automatized explicit knowledge, whereas the new psycholinguistic measures tap into implicit knowledge. For the participants as a whole, the convergent validity for implicit knowledge measures was less than ideal. When the results were analyzed separately by length of residence, however, acceptable convergent validity for implicit knowledge was obtained for those with longer length of residence but not for those with shorter length of residence. In order to address the interface issue, SEM analyses were conducted to investigate the relationship between automatized explicit knowledge and implicit knowledge. Results showed that automatized explicit knowledge significantly predicted the acquisition of implicit knowledge. Furthermore, the aptitude for explicit learning was the only significant predictor of the acquisition of automatized explicit knowledge, not for the acquisition of implicit knowledge. The effects of implicit learning aptitude and phonological short-term memory on the acquisition of both types of linguistic knowledge were limited. In conclusion, the study demonstrated that the newer measures for implicit knowledge are more sensitive and opens up promising directions for developing additional fine-grained measures for implicit knowledge. The current findings provide the first empirical evidence at the latent construct level that automatized explicit knowledge, which develops through explicit learning mechanisms, impacts the acquisition of implicit knowledge