The purpose of this paper is to propose methods for verifying the positivity of a weak solution u of an elliptic problem assuming H01-error estimation ‖u−uˆ‖H01≤ρ given some numerical approximation ...uˆ and an explicit error bound ρ. We provide a sufficient condition for the solution to be positive and analyze the range of application of our method for elliptic problems with polynomial nonlinearities. We present numerical examples where our method is applied to some important problems.
We are glad that this special issue takes up the activities of The Resilience Research Council of Japan (RRCJ). Twelve years have passed since the founding of the RRCJ. In addition to regular ...meetings at which experts from various fields participate in disseminating information, one of the RRCJ’s main activities is holding study groups to delve deeply into specific aspects of disaster preparedness. To respond to the intensification and frequent occurrence of disasters in recent years, it is urgent to review existing measures against disasters and business continuity plans (BCPs). Furthermore, comprehensive and flexible strategies should be developed to enhance disaster resilience. Each study in this special issue provides new perspectives and clues on this problem. First, the existing BCPs lack concrete measures from the perspectives of individual corporate departments and employees. To tackle this problem, new procedures are proposed to formulate BCPs based on the questions “What if?” and “What when?” This is expected to increase the effectiveness of BCPs. Second and third, comprehensive methods for evaluating resilience are lacking. As a result of an examination of the 13 current indexes of “Resilient Organizations” and the “Organization Resilience Index” of the British Standards Institution, it is revealed that some important elements are absent from the evaluation of corporate resilience. By complementing the corporate resilience model with these elements, the model can be improved. Furthermore, local governments must implement effective disaster countermeasures for those with limited resources in their disaster management plans. The fourth study evaluates disaster management measures from the point of view of both local governments and residents, and proposes innovative solutions to collaborate and organize, adapt to the environment, and manage for the next generation. This reveals the problems faced by local governments and residents’ lack of knowledge, and provides a roadmap for future improvements. Overall, these studies indicate that creating a resilience strategy involving all stakeholders is an urgent matter, provide valuable insight into the limits of current strategies, and offer guidelines for strengthening the important aspects of resilience so that corporations and local governments can respond to disasters more effectively. We expect that the effectiveness of disaster measures will be enhanced through incorporating these proposals and methods into practical policies and actual works. We sincerely thank all the contributors for their contributions to this special issue and the reviewers for their valuable comments.
This paper proposes a method for rigorously analyzing the sign-change structure of solutions of elliptic partial differential equations subject to one of the three types of homogeneous boundary ...conditions: Dirichlet, Neumann, and mixed. Given explicitly estimated error bounds between an exact solution
u
and a numerically computed approximate solution
u
^
, we evaluate the number of sign-changes of
u
(the number of nodal domains) and determine the location of zero level-sets of
u
(the location of the nodal line). We apply this method to the Dirichlet problem of the Allen–Cahn equation. The nodal line of solutions of this equation represents the interface between two coexisting phases.
The Hénon equation, a generalized form of the Emden equation, admits symmetry-breaking bifurcation for a certain ratio of the transverse velocity to the radial velocity. Therefore, it has asymmetric ...solutions on a symmetric domain even though the Emden equation has no asymmetric unidirectional solution on such a domain. We discuss a numerical verification method for proving the existence of solutions of the Hénon equation on a bounded domain. By applying the method to a line-segment domain and a square domain, we numerically prove the existence of solutions of the Hénon equation for several parameters representing the ratio of transverse to radial velocity. As a result, we find a set of undiscovered solutions with three peaks on the square domain.
BACKGROUNDWhile pincer nails may be treated using overcurvature-correcting devices, it takes several months to achieve successful outcomes. Nail-softening drugs may reduce the treatment duration ...required. OBJECTIVETo evaluate the efficacy and safety of treatment with acetylcysteine (AC) gel added to an overcurvature-correcting device, and define the optimal AC concentration. METHODSIn this investigator-blinded study, 70 patients with hallux pincer nail were fitted with an overcurvature-correcting device for 7 days and were randomly assigned to receive a single 24-h administration of a gel containing 10%, 20% or 30% AC or vehicle. Nail improvement was objectively evaluated by calculating the distal narrowed nail width (dNNW) ratio. RESULTSAll three AC concentrations plus device showed earlier sustained improvement of pincer nails versus vehicle plus device. There was no observable correlation between AC concentration and effectiveness. No clinically problematic adverse events were observed at any AC concentration, and we recommended AC gel at a concentration of 10%. CONCLUSIONSBy adding AC gel application to an overcurvature-correcting device, early and sustained reductions in transverse curvature were produced compared with using a device alone (vehicle control). The dNNW ratio used in this study was an appropriate objective index for evaluating therapeutic effects.
Cyclopericodiol (1) and two new chlorinated melleins (2 and 3) were isolated from Periconia macrospinosa KT3863. The results of density functional theory (DFT)-based calculations while estimating the ...values of the 13C chemical shifts and the spin coupling constants allowed to determine the relative configurations of 1 and 2. The absolute configurations of these compounds were established by comparing the experimental electronic circular dichroism (ECD) spectra with those obtained while performing time-dependent DFT calculations. Interestingly, the methyl and hydroxy groups at C3 and C4, respectively, of 2 assume an 1,2-anti-diaxial conformation due to absence of 1,3-diaxial repulsion. This conclusion was supported by the observation that 2 afforded an ECD spectrum that was almost the mirror image of that of 3. Furthermore, the theoretical spin coupling constants 3JH-3/C1, 2JH-3/C4, 3JH-3/C4a, and 2JH-3/C9 were in agreement with the heteronuclear multiple-bond correlation (HMBC) intensities of H-3 with C1, C4, C4a, and C9.
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•Cyclopericodiol and two novel chlorinated melleins were isolated from P. macrospinosa KT3863.•DFT based 13C NMR chemical shifts and nJCH values were effective in configurational elucidation.•The 3-Me and 4-OH of 2 took pseudo 1,2-diaxial conformation due to absence of 1,3-diaxial repulsion.
This study investigates the phylogeny and taxonomy of Anthostomella-like fungi (Xylariales, Sordariomycetes) found in association with bamboo in Japan. Four new genera, Amphigermslita (including ...three new species, i.e., A. deformis, A. fusiformis, and A. pseudofusiformis), monotypic Crassipseudostroma (C. phyllostachydis) and Minuticlypeus (M. discosporus), and Pallidoperidium (two new species, P. exasperatum and P. paraexasperatum), and one known genus, Nigropunctata (one new species, N. complanata) are recognized and described. These five genera were found to constitute a distinct monophyletic lineage based on molecular phylogenetic analyses utilizing sequences of ITS and LSU nrDNA, rpb2, and tef1-α sequences. A new family, Pallidoperidiaceae, is proposed to accommodate these bambusicolous Anthostomella-like fungi. The identification of this lineage contributes to our understanding of the evolutionary relationships and classification of these bambusicolous fungi. It suggests that these five genera share a unique evolutionary history and possess shared morphological and ecological characteristics.
Peribysins O (1), P (3), and Q (4) were isolated from Periconia macrospinosa KT3863. The relative configuration of the 6,7-epoxide of 1 was elucidated by performing quantitative NOE experiments. The ...structure of 2, which is a tautomer of 1 present in CDCl3 solutions in 5% abundance, was also fully characterized by NMR analysis. Their absolute configurations were independently determined by the modified Mosher’s method (for 1 and 3), the electronic circular dichroism (ECD) exciton coupling theory after conversion into dibenzoate 9 (for 3), and theoretical ECD calculations (for 1, 3, and 4). The obtained relative structures 1, 3, and 4 were verified by calculating their 13C chemical shifts using density functional theory (DFT). Although the established (4S)-enantiomer for 1–4 is in accordance with that of other peribysins isolated from the related fungus Periconia byssoides OUPS-N133, Danishefsky’s total synthesis of peribysin E (5) led to the subsequent revision of the (2R,4S,5R,6S,7S,8R,10S)-enantiomer to the (2S,4R,5S,6R,7R,8S,10R)-enantiomer. This discordance led us to reinvestigate the configuration using time-dependent DFT-based ECD spectral calculations, which supported the original (4S)-enantiomer.
The genus
, previously known as a saprobic or hemibiotrophic ascomycete on various plants, was revised taxonomically and phylogenetically. Sequences of the following six regions, that is, the nuclear ...ribosomal internal transcribed spacer (ITS) region, the large subunit (LSU) of rDNA, the second largest RNA polymerase II subunit (
) gene, translation elongation factor 1-alpha (
) gene, the actin (
) gene, and the beta-tubulin (
) gene, were generated for molecular phylogenetic analyses of species of this genus.
, a genus encompassing medically important species, is synonymised with
based on molecular evidence and morphological similarities in their asexual characters. The generic concept for
is expanded to include species possessing both coelomycetous and hyphomycetous complex asexual morphs. In addition to type species of
,
, nine species were accepted in
upon morphological comparison and molecular phylogenetic analyses in this study. All seven species of
were treated as members of the genus
and new combinations were proposed. A bambusicolous fungus,
, was transferred to
, and an epitype is designated for this species. A new species,
, was described from
. The family Phialemoniopsidaceae, proposed as a familial placement for
, was regarded as a synonym of Thyridiaceae. A new order, Thyridiales, was established to accommodate Thyridiaceae; it forms a well-supported, monophyletic clade in Sordariomycetes.
5-Dehydrodecaspirones F (1) and H (2) were isolated from Phaeoseptum sp. KT4106 along with known structurally related compounds involving palmarumycins CP4a (3) and CP5 (4). Although these were ...reported to be pseudo-enantiomers, our chirality reinvestigation found that both possess (2S)-configuration.
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•Two decaspirons 5-dehydrodecaspirones F and H were isolated from P. sp. KT4106.•The structures were determined based on NMR spectral analysis.•DFT calculations verified the proposed structure.•Reinvestigation of palmarumycins CP4a and CP5 resulted in the chirality revision.
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