An extension of J\'{o}nsson-Tarski representation and model existence in predicate non-normal modal logics

In this paper, we give an extension of the J\'{o}nsson-Tarski representation theorem for both normal and non-normal modal algebras so that it preserves countably many infinitary meets and joins. To extend the J\'{o}nsson-Tarski representation to non-normal modal algebras we consider neighborhood frames, instead of Kripke frames, and to deal with infinite meets and joins, we make use of Q-filters, instead of prime filters. Then, we show that every predicate modal logic, whether it is normal or non-normal, has a model defined on a neighborhood frame with constant domains, and give completeness theorem for some predicate modal logics. We also show the same results for infinitary modal logics

A non-compact deduction rule for the logic of provability and its algebraic models

In this paper, we introduce a proof system with a non-compact deduction rule, that is, a deduction rule with countably many premises, to axiomatize the logic $\mathbf{GL}$ of provability, and show its Kripke completeness in an algebraic manner. As $\mathbf{GL}$ is not canonical, a standard proof of Kripke completeness for $\mathbf{GL}$ is given by a Kripke model which is obtained by changing the binary relation of the canonical model, while our proof is given by a submodel of the canonical model of $\mathbf{GL}$ which is obtained by making use of an infinitary extension of the J\'{o}nsson-Tarski representation. We also show the three classes of algebras defined by $\Box x\leq\Box\Box x$ and one of the following three conditions, $\bigwedge_{n\in\omega}\Diamond^{n}1=0$, the non-compact deduction rule and the L\"{o}b formula, are mutually different, while all of them define $\mathbf{GL}$

Duality for κ\kappa-additive complete atomic modal algebras

In this paper, we give a duality theorem between the category of $\kappa$-additive complete atomic modal algebras and the category of $\kappa$-downward directed multi-relational Kripke frames, for any cardinal number $\kappa$. Multi-relational Kripke frames are not Kripke frames for multi-modal logic, but frames for monomodal logics in which the modal operator $\Diamond$ does not distribute over (possibly infinite) disjunction, in general. We first define homomorphisms of multi-relational Kripke frames, and then show the equivalence between the category of $\kappa$-downward directed multi-relational Kripke frames and the category $\kappa$-complete neighborhood frames, from which the duality theorem follows. We also present another direct proof of this duality based on the technique given by Minari

Study of Auroral VLF Hiss Observed at Syowa Station, Antarctica

Observations of polarization, incident angle and arriving direction of auroral hiss were carried out at Syowa Station during the period of 1967 to 1970. The present paper consists of two parts. In Part I, we describe the equipment used for the measurement of polarization, incident and azimuthal angles and show the obtained results. The direction finding (DE) system used is based on the analysis of Lissajous\u27 figures of electric and magnetic fields displayed on cathode ray tubes. The individual polarization of the received signal is also measured. Moreover, auroral hiss is decomposed into right-and left-handed polarized components, and these two components are continuously recorded. From the discussion of the observed results, it is found that auroral hiss has propagated downward in the azimuthal direction from a not so broad range around the magnetic meridian plane and its incident angle is also not so large. Additionally, in most cases, auroral hiss is known to consist of wave components downcoming from multiple directions in the azimuthal and incident planes. The DF system used was found to be effective in a few cases of isolated and sharp auroral hiss. However, this system should be re-examined because it is, strictly speaking, useful only for monochromatic waves, while the auroral hiss seems to have a noise-like nature. Therefore, a new DF system applying the correlation method is being planned to study, with more accuracy, the azimuthal and incident angles of noisy signals such as auroral hiss. The polarization of auroral hiss received on the ground seems to be almost right-handed circular, at VLF and LF, which is theoretically confirmed by the full wave calculation of the polarization using the realistic model of the auroral ionosphere. On the other hand, the observed polarization of ELF hiss is slightly right-handed circular, which can be reasonably accepted, taking into consideration the result of the full, wave calculation. In Part II, the morphological characteristics of auroral hiss are discussed in comparison with those of low-latitude hiss using the VLF data observed at Syowa Station and at Moshiri in Japan. Auroral hiss, considered to be a manifestation of polar substorms, is a local phenomenon and its frequency extends from a few kHz to more than 100 kHz. Low-latitude hiss, however, is closely correlated with worldwide geomagnetic storms and it is a narrow band VLF phenomenon. Together with other differences between them, it is concluded that auroral hiss is completely different from low-latitude hiss. Although the morphological features of auroral hiss have been well known, a complete understanding of its generation mechanism has not yet been obtained. There are unsolved problems such as about two orders shortening of the calculated intensity below the observations and the existence of the threshold low-energy electron flux below which VLF hiss is not observed. These facts may suggest that a coherent plasma instability mechanism is partially involved in the generation of auroral hiss. Therefore, the investigation of the coherency of auroral hiss being planned by us may give a better understanding of the generation processes of auroral hiss

IL-36受容体アンタゴニスト欠損は、皮膚虚血再灌流障害における創傷治癒を悪化させる。

藤田医科大

Development of microstructures in rapidly-quenched Mg85Y9Zn6 alloy ribbons during heating at a constant speed examined by simultaneous small- and wide angle scattering measurements

Developments of microstructures during heating Mg85Y9Zn6 amorphous ribbons have been examined by in-situ synchrotron radiation small- and wide-angle scattering measurements. The samples show sharp crystallization peak in a DSC measurement at 450 K for a heating rate of 10 K/min. During and just after crystallization, clustering occurred first within supersaturated hcp crystallites, with concomitant hcp grain growth. Above 550 K, the spatial arrangements of the cluster became anisotropic, eventually lead to 18R LPSO structures accompanied by introduction of stacking faults

hzAnalyzer: detection, quantification, and visualization of contiguous homozygosity in high-density genotyping datasets

The analysis of contiguous homozygosity (runs of homozygous loci) in human genotyping datasets is critical in the search for causal disease variants in monogenic disorders, studies of population history and the identification of targets of natural selection. Here, we report methods for extracting homozygous segments from high-density genotyping datasets, quantifying their local genomic structure, identifying outstanding regions within the genome and visualizing results for comparative analysis between population samples

Diversity of preferred nucleotide sequences around the translation initiation codon in eukaryote genomes

Understanding regulatory mechanisms of protein synthesis in eukaryotes is essential for the accurate annotation of genome sequences. Kozak reported that the nucleotide sequence GCCGCC(A/G)CCAUGG (AUG is the initiation codon) was frequently observed in vertebrate genes and that this ‘consensus’ sequence enhanced translation initiation. However, later studies using invertebrate, fungal and plant genes reported different ‘consensus’ sequences. In this study, we conducted extensive comparative analyses of nucleotide sequences around the initiation codon by using genomic data from 47 eukaryote species including animals, fungi, plants and protists. The analyses revealed that preferred nucleotide sequences are quite diverse among different species, but differences between patterns of nucleotide bias roughly reflect the evolutionary relationships of the species. We also found strong biases of A/G at position −3, A/C at position −2 and C at position +5 that were commonly observed in all species examined. Genes with higher expression levels showed stronger signals, suggesting that these nucleotides are responsible for the regulation of translation initiation. The diversity of preferred nucleotide sequences around the initiation codon might be explained by differences in relative contributions from two distinct patterns, GCCGCCAUG and AAAAAAAUG, which implies the presence of multiple molecular mechanisms for controlling translation initiation