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The purpose of this paper is to develop a unified a posteriori method for verifying the positivity of solutions of elliptic boundary value problems by assuming neither $H^2$-regularity nor $ L^{\infty} $-error estimation, but only $ H^1_0 $-error estimation. In [J. Comput. Appl. Math, Vol. 370, (2020) 112647], we proposed two approaches to verify the positivity of solutions of several semilinear elliptic boundary value problems. However, some cases require $ L^{\infty} $-error estimation and, therefore, narrow applicability. In this paper, we extend one of the approaches and combine it with a priori error bounds for Laplacian eigenvalues to obtain a unified method that has wide application. We describe how to evaluate some constants required to verify the positivity of desired solutions. We apply our method to several problems, including those to which the previous method is not applicable., 28 pages, 7 figures

Apple bitter rot caused by Colletotrichum acutatum sensu lato results in fruit decay before and after harvest. We investigated the epidemiology of the disease in terms of conidial formation and dispersal as well as the change in susceptibility of fruits in Iwate, Japan. Conidia of C. acutatum were detected in rainwater collected from inside the tree canopy from May to August with peaks in production in mid-May to early June and mid- to late July. The first peak corresponded to the most conidia being produced on fruit scars, but the second peak was due to conidiation on mummified fruitlets and peduncles collected in July. Inoculation experiments revealed that fruits were susceptible to the pathogen between 20 and 90 days after petal fall and that immature fruits infected as early as 20 days after petal fall frequently developed lesions on the lower fruit half as growth progressed. These results suggest that C. acutatum sporulates on infested fruit scars to infect immature fruits, resulting in bitter rot and that the fungus also colonizes mummified fruitlets and peduncles, contributing to survival of the pathogen on fruit scars. Thus, infested fruit scars represent the primary source of inoculum.

Dictyosporiaceae fam. nov. is introduced to accommodate a holomorphic group of Dothideomycetes that are saprobes on decaying wood and plant debris in terrestrial and freshwater habitats. The sexual morph comprises Dictyosporium meiosporum, D. sexualis, Gregarithecium curvisporum, Pseudocoleophoma calamagrostidis and P. polygonicola. The sexual morphs are characterized by immersed to erumpent, superficial, globose to subglobose, dark brown to black ascomata, bitunicate asci, and septate, hyaline, sheathed ascospores. The asexual morphs are hyphomycetous with brown, multi-septate, cheirosporous conidia, produced from holoblastic conidiogenous cells, on micronematous conidiophores. Phylogenetic analyses of LSU, SSU and TEF1 sequence data place the genera with cheirospores in a monophyletic clade in the order Pleosporales. Phylogenetic analyses based on ITS sequence data show the family to comprise 44 distinct lineages that correspond to ten genera and an undetermined genus. Four new genera Dictyocheirospora, Dictyopalmispora, Jalapriya and Vikalpa, and eight new species Dictyocheirospora bannica, D. rotunda, D. vinaya, Dictyopalmispora palmae, Dictyosporium olivaceosporum, D. sexualis, Jalapriya pulchra, and Vikalpa lignicola, are introduced in the family.

This paper provides recommendations of one name for use among pleomorphic genera in Dothideomycetes by the Working Group on Dothideomycetes established under the auspices of the International Commission on the Taxonomy of Fungi (ICTF). A number of these generic names are proposed for protection because they do not have priority and/or the generic name selected for use is asexually typified. These include: Acrogenospora over Farlowiella; Alternaria over Allewia, Lewia, and Crivellia; Botryosphaeria over Fusicoccum; Camarosporula over Anthracostroma; Capnodium over Polychaeton; Cladosporium over Davidiella; Corynespora over Corynesporasca; Curvularia over Pseudocochliobolus; Elsinoë over Sphaceloma; Excipulariopsis over Kentingia; Exosporiella over Anomalemma; Exserohilum over Setosphaeria; Gemmamyces over Megaloseptoria; Kellermania over Planistromella; Kirschsteiniothelia over Dendryphiopsis; Lecanosticta over Eruptio; Paranectriella over Araneomyces; Phaeosphaeria over Phaeoseptoria; Phyllosticta over Guignardia; Podonectria over Tetracrium; Polythrincium over Cymadothea; Prosthemium over Pleomassaria; Ramularia over Mycosphaerella; Sphaerellopsis over Eudarluca; Sphaeropsis over Phaeobotryosphaeria; Stemphylium over Pleospora; Teratosphaeria over Kirramyces and Colletogloeopsis; Tetraploa over Tetraplosphaeria; Venturia over Fusicladium and Pollaccia; and Zeloasperisporium over Neomicrothyrium. Twenty new combinations are made: Acrogenospora carmichaeliana (Berk.) Rossman & Crous, Alternaria scrophulariae (Desm.) Rossman & Crous, Pyrenophora catenaria (Drechsler) Rossman & K.D. Hyde, P. dematioidea (Bubák & Wróbl.) Rossman & K.D. Hyde, P. fugax (Wallr.) Rossman & K.D. Hyde, P. nobleae (McKenzie & D. Matthews) Rossman & K.D. Hyde, P. triseptata (Drechsler) Rossman & K.D. Hyde, Schizothyrium cryptogamum (Batzer & Crous) Crous & Batzer, S. cylindricum (G.Y. Sun et al.) Crous & Batzer, S. emperorae (G.Y. Sun & L. Gao) Crous & Batzer, S. inaequale (G.Y. Sun & L. Gao) Crous & Batzer, S. musae (G.Y. Sun & L. Gao) Crous & Batzer, S. qianense (G.Y. Sun & Y.Q. Ma) Crous & Batzer, S. tardecrescens (Batzer & Crous) Crous & Batzer, S. wisconsinense (Batzer & Crous) Crous & Batzer, Teratosphaeria epicoccoides (Cooke & Massee) Rossman & W.C. Allen, Venturia catenospora (Butin) Rossman & Crous, V. convolvularum (Ondrej) Rossman & Crous, V. oleaginea (Castagne) Rossman & Crous, and V. phillyreae (Nicolas & Aggéry) Rossman & Crous, combs. nov. Three replacement names are also proposed: Pyrenophora grahamii Rossman & K.D. Hyde, Schizothyrium sunii Crous & Batzer, and Venturia barriae Rossman & Crous noms. nov.

This paper is concerned with an explicit value of the embedding constant from $W^{1,q}(\Omega)$ to $L^{p}(\Omega)$ for a bounded domain $\Omega\subset\mathbb{R}^N~(N\in\mathbb{N})$, where $1\leq q\leq p\leq \infty$. To obtain this value, we previously proposed a formula for estimating the embedding constant on bounded and unbounded Lipschitz domains by estimating the norm of Stein's extension operator, in the article (K. Tanaka, K. Sekine, M. Mizuguchi, and S. Oishi, Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator, Journal of Inequalities and Applications, Vol. 389, pp. 1-23, 2015). This formula is also applicable to a domain that can be divided into Lipschitz domains. However, the values computed by the previous formula are very large. In this paper, we propose several sharper estimations of the embedding constant on a bounded domain that can be divided into convex domains., Comment: 18 pages, 7 figures

Astrosphaeriella sensu lato is a common genus occurring on bamboo, palms and stout grasses. Species of Astrosphaeriella have been collected from various countries in tropical, subtropical or temperate regions. In Asia, species have been collected in Brunei, China, Indonesia, Japan, Philippines and Vietnam. There have been several morphological studies on Astrosphaeriella, but molecular work and phylogenetic analyses are generally lacking. Taxa included in Astrosphaeriella were characterized in three main groups 1) typical Astrosphaeriella species (sensu stricto) having carbonaceous, erumpent, conical ascostromata 2) atypical Astrosphaeriella species (sensu lato) having immersed, coriaceous ascostromata with short to long papilla and 3) lophiostoma-like species having immersed ascostromata with slit-like openings. Some of the latter Astrosphaeriella species, having slit-like openings, have been transferred to Fissuroma and Rimora in Aigialaceae. In this study five type specimens of Astrosphaeriella were loaned from herbaria worldwide and re-examined and are re-described and illustrated. Collections of Astrosphaeriella were also made in Thailand and morphologically examined. Pure cultures were obtained from single spores and used in molecular studies. The asexual morph was induced on sterile bamboo pieces placed on water agar. Phylogenetic analyses of combined LSU, SSU and TEF1 sequence data of astrosphaeriella-like species using Bayesian, Maximum parsimony (MP) and Randomized Accelerated Maximum Likelihood (RAxML) analyses were carried out. Phylogenetic analyses show that species of Astrosphaeriella can be distinguished in at least three families. Species of Astrosphaeriella sensu stricto with erumpent, carbonaceous ascostromata, form a strongly supported clade with Pteridiospora species and a new family, Astrosphaeriellaceae, is introduced to accommodate these taxa. The genera are revised and Astrosphaeriella bambusae, A. neofusispora, A. neostellata, A. thailandica, A. thysanolaenae and Pteridiospora chiangraiensis are introduced as new species. Astrosphaeriella exorrhiza is reported on a dead stem of Thysanolaena maxima and is the first record for Thailand. Reference specimens for A. fusispora and A. tornata are designated to stabilize the taxonomy of Astrosphaeriella. The coelomycetous asexual morph of A. bambusae is reported and forms hyaline, globose to subglobose, aseptate conidia. Species of Astrosphaeriella sensu lato with immersed, coriaceous ascostromata, with short to long papilla and striate ascospores, form a sister clade with Tetraplosphaeriaceae. The genus Pseudoastrosphaeriella is introduced to accommodate some of these taxa with three new species and three new combinations, viz. P. aequatoriensis, P. africana, P. bambusae, P. longicolla, P. papillata and P. thailandensis. A new family Pseudoastrosphaeriellaceae is introduced to accommodate this presently monotypic lineage comprising Pseudoastrosphaeriella. The asexual morph of P. thailandensis is described. Astrosphaeriella bakeriana forms a distinct clade basal to Aigialaceae. Astrosphaeriella bakeriana is excluded from Astrosphaeriella and a new genus Astrosphaeriellopsis, placed in Dothideomycetes genera incertae sedis, is introduced to accommodate this taxon. Fissuroma aggregata (Aigialaceae) is re-visited and is shown to be a cryptic species. Three new species of Fissuroma and a new combination are introduced based on morphology and phylogeny viz. F. bambusae, F. fissuristoma, F. neoaggregata and F. thailandicum.

The genera Lophiostoma, Misturatosphaeria and several other allied taxa in Lophiostomataceae are revisited. Accounts of these taxa, including their history, morphology, and family placement, based on molecular phylogeny, are provided. Type or representative specimens of Lophiostoma and Misturatosphaeria were examined and fresh specimens were obtained from Germany, Italy, Japan and Thailand. A multi-gene phylogenetic analysis of the lophiostomataceous genera Floricola, Lophiostoma, Misturatosphaeria and related taxa is provided. Sixteen genera including Lophiostoma, Lophiohelichrysum, Dimorphiopsis, Platystomum and Vaginatispora, plus eleven newly introduced genera Biappendiculispora, Alpestrisphaeria, Capulatispora, Coelodictyosporium, Guttulispora, Lophiopoacea, Neotrematosphaeria, Paucispora, Pseudolophiostoma, Pseudoplatystomum and Sigarispora are accepted in Lophiostomataceae based on morphology and phylogeny. Lophiostoma caulium, Lophiostoma arundinis and Lophiostoma caudatum are accommodated in Sigarispora. Lophiostoma winteri and Lophiostoma fuckelii are placed in the genera Lophiopoacea and Vaginatispora respectively. Three Curreya species and Misturatosphaeria claviformis are transferred to a new genus, Neocurreya. All other Misturatosphaeria species except Misturatosphaeria aurantiinotata and M. uniseptata are separated in the new genera Asymmetrispora, Aurantiascoma, Magnibotryascoma, Pseudoaurantiascoma and Pseudomisturatosphaeria based on their morphological and phylogenetic affinities. Another new genus, Ramusculicola is introduced for a new collection from Thailand. These seven new genera are accommodated in a new family Floricolaceae, together with Floricola and Misturatosphaeria. Several massarina-like species clustered as a sister clade to Amorosia littoralis and are accommodated in a new genus Angustimassarina. A new family Amorosiaceae is proposed to accommodate the genera Amorosia and Angustimassarina. The putatively named species Decaisnella formosa and Thyridaria macrostomoides form a separate clade together with a new genus Lignosphaeria which is placed in Dothideomycetes, genera incertae sedis.

This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of estimation is important for verified computations of solutions to elliptic boundary value problems. The proposed method uses a generalized eigenvalue problem to derive the norm estimation. This method has several advantages. Namely, it can be applied to two types of boundary conditions: the Dirichlet type and the Neumann type. It also provides a way of numerically evaluating lower and upper bounds of target eigenvalues. Numerical examples are presented to show that the proposed method provides effective estimations in most cases.

The ascomycetous families, Didymosphaeriaceae and Montagnulaceae, have been treated in Pleosporales, Dothideomycetes, and both include saprobes, endophytes and pathogens associated with a wide variety of substrates worldwide. Didymosphaeriaceae was characterized by 1-septate ascospores and trabeculate pseudoparaphyses, mainly anastomosing above the asci, while species in Montagnulaceae had 1 to multi-septate ascospores and generally cellular pseudoparaphyses. In recent treatments, Bimuria, Didymocrea, Kalmusia, Karstenula, Montagnula, Paraphaeosphaeria, Paraconiothyrium and Letendraea were placed in Montagnulaceae, while only Didymosphaeria has been placed in Didymosphaeriaceae. New morphological and molecular data from recent collections have become available and thus the understanding of the families can be improved. Based on analyses of concatenated internal transcribed spacer (ITS) with LSU, SSU and beta-tubulin gene sequences, the taxonomy of the genera classified in these families are re-assessed. Our phylogenetic analyses conclude that, the recently introduced Didymosphaeria rubi-ulmifolii with Paraconiothyrium brasiliense species complex, Alloconiothyrium, Bimuria, Deniquelata, Didymocrea, Kalmusia, Karstenula, Letendraea, Montagnula, Neokalmusia, Paraconiothyrium, Paraphaeosphaeria, Phaeodothis and Tremateia, forms a robust clade named here Didymosphaeriaceae. We therefore synonymize Montagnulaceae under Didymosphaeriaceae which is the oldest name and has priority and provide a update account of the family. Didymosphaeria is represented by Didymosphaeria rubi-ulmifolii. A new genus, Neokalmusia, is introduced in the family to accommodate the bambusicolous taxa Kalmusia brevispora and K. scabrispora. This introduction is based on molecular data coupled with morphology. One new species, Paraconiothyrium magnoliae and the sexual morph of Paraconiothyrium fuckelii, is also introduced. Julella and Barria are assigned to the family based on morphological similarity with Didymosphaeriaceae. Wilmia (previously referred to the Phaeosphaeriaceae) is synonymized under Letendraea (Didymosphaeriaceae). Furthermore, a new species, Letendraea cordylinicola, is introduced and placed in Didymosphaeriaceae based on phylogeny and morphology. The paraphyletic nature of Paraconiothyrium is partially resolved, but further sampling with fresh collections and molecular data of species in this genus are needed to obtain a natural classification.

Dothideomycetes comprise a highly diverse range of fungi characterized mainly by asci with two wall layers (bitunicate asci) and often with fissitunicate dehiscence. Many species are saprobes, with many asexual states comprising important plant pathogens. They are also endophytes, epiphytes, fungicolous, lichenized, or lichenicolous fungi. They occur in terrestrial, freshwater and marine habitats in almost every part of the world. We accept 105 families in Dothideomycetes with the new families Anteagloniaceae, Bambusicolaceae, Biatriosporaceae, Lichenoconiaceae, Muyocopronaceae, Paranectriellaceae, Roussoellaceae, Salsugineaceae, Seynesiopeltidaceae and Thyridariaceae introduced in this paper. Each family is provided with a description and notes, including asexual and asexual states, and if more than one genus is included, the type genus is also characterized. Each family is provided with at least one figure-plate, usually illustrating the type genus, a list of accepted genera, including asexual genera, and a key to these genera. A phylogenetic tree based on four gene combined analysis add support for 64 of the families and 22 orders, including the novel orders, Dyfrolomycetales, Lichenoconiales, Lichenotheliales, Monoblastiales, Natipusillales, Phaeotrichales and Strigulales. The paper is expected to provide a working document on Dothideomycetes which can be modified as new data comes to light. It is hoped that by illustrating types we provide stimulation and interest so that more work is carried out in this remarkable group of fungi.

Species of Cryptocoryneum were taxonomically reassessed on the basis of morphological observations and the results of molecular phylogenetic analysis. Eighteen isolates of Cryptocoryneum species, namely two strains from Africa, three from Europe, and 13 from Japan, were phylogenetically analysed using sequences of nuclear rDNA internal transcribed spacers (ITS) and the partial sequence of the translation elongation factor 1α gene (TEF1). The phylogenetic analysis indicated that Cryptocoryneum species formed a monophyletic clade and were closely related to Lophiotrema (Lophiotremataceae) and Aquasubmersa (incertae sedis) in the Pleosporales (Dothideomycetes). We examined holotype specimens of C. fasciculatum, C. hysterioides, and Torula uniformis and concluded that these species are conspecific, with C. hysterioides having priority. Although C. hysterioides has long been regarded as a synonym of C. condensatum, we consider C. hysterioides to be a distinct species within the genus. We found several cryptic species that were morphologically similar to C. condensatum sensu lato, but that could be separated on the basis of conidial size and the number of conidial arms and conidial septa, characters that seem to be informative for species delimitation within Cryptocoryneum. A total of seven new species, namely C. akitaense, C. brevicondensatum, C. congregatum, C. japonicum, C. longicondensatum, C. paracondensatum, and C. pseudorilstonei, are described and illustrated. A key to species accepted in Cryptocoryneum is provided.

In July 2003, a new disease occurred on leaves of highbush blueberry (Vaccinium corymbossum L.) in Iwate, Japan. Leaves initially had brownish spots, which subsequently developed into large lesions with concentric rings, resulting in premature defoliation. Teardrop-shaped conidia infecting leaves were visible by the naked eye as small protuberances in the center of lesions. Star-shaped conidia were sporadically produced on large lesions. The causal fungus was identified as Valdensinia heterodoxa, based on cultural, morphological and genetic studies. Inoculation tests showed that the fungus reproduced lesions on detached young leaves of highbush blueberry. A field survey in 2009 indicated that symptoms initially appeared on the lower leaves of basal shoots in late May, and the disease rapidly progressed on leaves of basal shoots, eventually spreading to lateral shoots from late June to late July. Removal of all basal shoots in late June significantly reduced disease incidence on lateral shoots in late July.

In this paper, we propose a method for estimating the Sobolev-type embedding constant from $W^{1,q}(\Omega)$ to $L^{p}(\Omega)$ on a domain $\Omega\subset\mathbb{R}^{n}$ ( $n=2,3,\dots$ ) with minimally smooth boundary (also known as a Lipschitz domain), where $p\in(n/(n-1),\infty)$ and $q=np/(n+p)$ . We estimate the embedding constant by constructing an extension operator from $W^{1,q}(\Omega)$ to $W^{1,q}(\mathbb{R}^{n})$ and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.

However well we control a walking bipedal robot, the images obtained by a camera are tilted to the left or right, and have small irregularities. This complicates the recognition of an environment by using a camera in a walking robot when the robot cannot move smoothly. The reason for using a bipedal robot is to make the robot as similar as possible to a human in body shape and behavior in order to make collaboration easier. This is difficult to attain with other types of robot such as wheel-driven robots (Sato et al. AROB2008; Fujiwara et al. WMSCI2009). In an artificial environment which mainly consists of vertical and horizontal lines, the tilt angle of camera images must be corrected by using the Hough transformation, which detects lines which are nearly vertical (Okutomi et al. 2004; Forsyth and Ponce 2007). As a result, the robot can successfully recognize the environment with stereo vision using images obtained by correcting the tilted ones.

When the influence of host species, inoculum density, temperature, leaf wetness duration, and leaf position on the incidence of gentian brown leaf spot caused by Mycochaetophora gentianae, was examined, the fungus severely infected all seven Gentiana triflora cultivars, but failed to infect two cultivars of G. scabra and an interspecific hybrid cultivar. Inoculum density correlated closely with disease incidence, and a minimum of 102 conidia/mL was enough to cause infection. In an analysis of variance, temperature and leaf wetness duration had a significant effect upon disease incidence, which increased with higher temperature (15–25°C) and longer duration of leaf wetness (36–72 h). No disease developed at temperatures lower than 10°C or when leaf wetness lasted 50% of conidia germinated at temperatures >15°C after 24-h leaf wetness. More appressoria formed at higher temperatures (15–25°C) with extended duration of leaf wetness (24–72 h). At 48-h leaf wetness, appressorium formation was 0, 8, 26, and 73% at 10, 15, 20, and 25°C, respectively. These results suggest that temperature and leaf wetness duration were important factors for infection of gentian leaves.

A 303-nucleotide viroid was isolated from an apple tree (Malus × domestica, ‘Fuji’) cultivated in Japan. The viroid had 84.9% overall nucleotide sequence homology to Apple dimple fruit viroid (ADFVd), a member of Pospiviroidae, reported from Italy. This viroid differed from the Italian variant by 47 mutations (38 substitutions, six deletions and three insertions), and most of these mutations occurred on either side of the central conserved region. The leaves and branches of the infected trees did not have any disease symptoms, but the fruits were dimpled and yellow. The infected scions were top-grafted onto a healthy ‘Fuji’ apple tree, which tested positive for this viroid in a northern hybridization analysis, and yellow dimple fruits were produced in the second growing season. We propose that this viroid is a new variant of ADFVd and causes yellow dimple fruit formation in ‘Fuji’ apple trees.

Hyphodiscus hyaloscyphoides sp. nov. and its Catenulifera anamorph are described and illustrated. The teleomorph is morphologically most similar to H. hymeniophila but distinguished by dull white-colored apothecia. The anamorph is characterized by its minute conidiogenous structure with small subglobose conidia. The monophyly of Hyphodiscus was strongly supported in our molecular phylogenetic analyses using the D1–D2 region of large subunit of nuclear rDNA, but the phylogenetic relationships with other members of Hyaloscyphaceae were not strongly supported. In addition, Hyphodiscus hymeniophilus, one of the close relatives of H. hyaloscyphoides, turned out to be a heterogeneous assemblage based on the ITS region, which requires further research for taxonomic revision.

Six polymorphic sites of the bovine prion protein gene (PRNP) were genotyped in 569 animals of Asian native cattle, Japanese breeds, purebred mythun (Bos frontalis), and mythun x cattle composite animals. At the 23-bp indel site, a deletion (23-) allele was a major allele in all populations except mythun. At the 12-bp indel site, an insertion (12+) allele was a major allele in all populations. The 14-bp indel site was polymorphic in all Asian native cattle. In the octapeptide repeat region, a six-repeat allele was a major allele in all populations, and 5/5 and 4/6 genotypes were detected in Japanese Black and Mongolian cattle and in mythun, respectively. Two nonsynonymous single nucleotide polymorphisms (SNPs) (K3T and S154N) were detected in Asian native cattle and mythun. Haplotype analysis using the genotypes of the six sites estimated 33 different haplotypes. The haplotype 23- 12- K 6 S 14+ was found in all populations.

Apple fruit crinkle viroid (AFCVd) infects apples and hops. To analyze the genetic diversity of AFCVd, nine apple and six hop isolates were collected from several locations in Japan. In total, 76 independent cDNA clones were used for sequencing and phylogenetic analyses. Two major population clusters were identified. The first consisted of all four hop isolates from Akita and some from Yamagata. The second cluster consisted of some Yamagata hop and all apple isolates. On the basis of the polymorphism found in the nucleotide insertion between positions 142/143 of the AFCVd genome and the history of hop cultivation in the region, it appears likely that one of the AFCVd populations that pre-existed in the Yamagata hops served as a "founder" for the Akita hop cluster. In this scenario, a genetic bottleneck caused by vegetative propagation played an important role in the shaping of viroid populations in a cultivated crop.

Overwintering of the brown leaf spot fungus, Mycochaetophora gentianae, in infected gentian leaves was studied in Iwate, northern Japan. Sporophores were produced on overwintered, infected leaves when they were sampled from January to July, but not in August after incubation in high humidity at 15 °C. Symptoms developed on gentian plants grown in soil artificially infested with overwintered, infected leaves that were either left throughout the experiments or removed before planting. Few lesions developed when plants were grown in soil infested with conidia. These results indicate that M. gentianae can overwinter in infected leaves, which act as the primary inoculum source.