Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and the converse holds under mild assumptions. A natural question is for what singular rings these invariants are closest to one. For Hilbert–Kunz multiplicity this question was first considered by the last two authors and attracted significant attention. In this paper, we study this question, i.e., an upper bound, for F-signature and revisit lower bounds on Hilbert–Kunz multiplicity.

Let $(A,\mathfrak m)$ be an excellent two-dimensional normal local domain. In this paper, we study the elliptic and the strongly elliptic ideals of A with the aim to characterize elliptic and strongly elliptic singularities, according to the definitions given by Wagreich and Yau. In analogy with the rational singularities, in the main result, we characterize a strongly elliptic singularity in terms of the normal Hilbert coefficients of the integrally closed $\mathfrak m$ -primary ideals of A. Unlike $p_g$ -ideals, elliptic ideals and strongly elliptic ideals are not necessarily normal and necessary, and sufficient conditions for being normal are given. In the last section, we discuss the existence (and the effective construction) of strongly elliptic ideals in any two-dimensional normal local ring.

Little is known about predictors of decline in vitamin D status (vitamin D decline) over time. We aimed to determine demographic and lifestyle variables associated with vitamin D decline by sufficiently controlling for seasonal effects of vitamin D uptake in a middle-aged to elderly population. Using a longitudinal study design within the larger framework of the Murakami Cohort Study, we examined 1044 individuals aged between 40 and 74 years, who provided blood samples at baseline and at 5-year follow-up, the latter of which were taken on a date near the baseline examination (±14 d). Blood 25-hydroxyvitamin D (25(OH)D) concentrations were determined with the Liaison® 25OH Vitamin D Total Assay. A self-administered questionnaire collected demographic, body size and lifestyle information. Vitamin D decline was defined as the lowest tertile of 5-year changes in blood 25(OH)D (Δ25(OH)D) concentration (<6·7 nmol/l). Proportions of those with vitamin D decline were 182/438 (41·6 %) in men and 166/606 (27·4 %) in women (P < 0·0001). In men, risk of vitamin D decline was significantly lower in those with an outdoor occupation (P = 0·0099) and those with the highest quartile of metabolic equivalent score (OR 0·34; 95 % CI 0·14, 0·83), and higher in those with ‘university or higher’ levels of education (OR 2·92; 95 % CI 1·04, 8·19). In women, risk of vitamin D decline tended to be lower with higher levels of vitamin D intake (Pfor trend = 0·0651) and green tea consumption (Pfor trend = 0·0025). Predictors of vitamin D decline differ by sex, suggesting that a sex-dependent intervention may help to maintain long-term vitamin D levels.

Although dietary Ca, vitamin D and vitamin K are nutritional factors associated with osteoporosis, little is known about their effects on incident osteoporotic fractures in East Asian populations. This study aimed to determine whether intakes of these nutrients predict incident osteoporotic fractures. We adopted a cohort study design with a 5-year follow-up. Subjects were 12 794 community-dwelling individuals (6301 men and 6493 women) aged 40–74 years. Dietary intakes of Ca, vitamin D and vitamin K were assessed with a validated FFQ. Covariates were demographic and lifestyle factors. All incident cases of major osteoporotic limb fractures, including those of the distal forearm, neck of humerus, neck or trochanter of femur and lumbar or thoracic spine were collected. Hazard ratios (HR) for energy-adjusted Ca, vitamin D and vitamin K were calculated with the residual method. Mean age was 58·8 (sd 9·3) years. Lower energy-adjusted intakes of Ca and vitamin K in women were associated with higher adjusted HR of total fractures (Pfor trend = 0·005 and 0·08, respectively). When vertebral fracture was the outcome, Pfor trend values for Ca and vitamin K were 0·03 and 0·006, respectively, and HR of the lowest and highest (reference) intake groups were 2·03 (95 % CI 1·08, 3·82) and 2·26 (95 % CI 1·19, 4·26), respectively. In men, there were null associations between incident fractures and each of the three nutrient intakes. Lower intakes of dietary Ca and vitamin K were independent lifestyle-related risk factors for osteoporotic fracture in women but not men. These associations were robust for vertebral fractures, but not for limb fractures.

The main aim of this paper is to classify Ulrich ideals and Ulrich modules over two-dimensional Gorenstein rational singularities (rational double points) from a geometric point of view. To achieve this purpose, we introduce the notion of (weakly) special Cohen–Macaulay modules with respect to ideals, and study the relationship between those modules and Ulrich modules with respect to good ideals.

In this paper we study Ulrich ideals of and Ulrich modules over Cohen--Macaulay local rings from various points of view. We determine the structure of minimal free resolutions of Ulrich modules and their associated graded modules, and classify Ulrich ideals of numerical semigroup rings and rings of finite CM-representation type.

Strategies to manipulate the gut microbiota have been explored for preventing allergy development. We previously showed that dietary supplementation with fructo-oligosaccharide (FOS) reduced 2, 4-dinitrofluorobenzene (DNFB)-induced contact hypersensitivity (CHS) in BALB/c mice. Because the CHS response was negatively correlated with the number of faecal bifidobacteria, particularly Bifidobacterium pseudolongum, the present study aimed to examine whether oral administration of B. pseudolongum affects CHS response. Viable B. pseudolongum was successfully isolated from mouse faeces. Female BALB/c mice were fed a synthetic diet with or without FOS supplementation, and B. pseudolongum (2 × 107 cells) was administered daily throughout the experimental period. Two weeks after starting the test diets, mice received DNFB on the ear auricle twice at 7-d intervals. Conventional cultivation and molecular biological analyses based on 16S rRNA gene sequences showed that administration of FOS and B. pseudolongum resulted in higher excretion of viable bifidobacteria, mainly B. pseudolongum. Although dietary FOS reduced the CHS response as demonstrated by ear swelling, B. pseudolongum administration resulted in a reduction in the initial phase only of the CHS response. B. pseudolongum administration increased hapten-specific IgG1, while dietary FOS decreased IgG2a in sera. Administration of FOS and B. pseudolongum decreased interferon-γ production and increased IL-10 production in cervical lymph node cells restimulated with hapten in vitro. We conclude that B. pseudolongum proliferation in the intestinal tract is partially responsible for the reduction in DNFB-induced CHS response by dietary supplementation with FOS in mice, which may be mediated by the modulation of antigen-induced cytokine production.

Strategies to manipulate the gut microbiota in infancy have been considered to prevent the development of allergic diseases later in life. We aimed to elucidate the effects of maternal dietary supplementation with a prebiotic oligosaccharide on gut microbiota and spontaneously developing atopic dermatitis-like skin lesions in the offspring of NC/Nga mice. Female NC/Nga mice were fed diets either with or without fructo-oligosaccharide supplementation during pregnancy and lactation. After weaning, offspring were fed the diets supplemented with or without fructo-oligosaccharide for 11 weeks in an air-uncontrolled conventional room. Changes in gut microbiota were assessed by denaturing gradient gel electrophoresis of the PCR-amplified 16S rRNA gene. Skin lesions were evaluated by a clinical score and scratching behaviour. Serum antibody levels were measured by ELISA, and expression levels of cytokines and chemokines in lesional tissue were evaluated by quantitative RT-PCR. Maternal supplementation with fructo-oligosaccharide modulated the gut microbiota in sucklings. Although maternal supplementation with fructo-oligosaccharide suppressed the increase in clinical skin severity score and scratching behaviour in offspring, dietary fructo-oligosaccharide after weaning was less effective. The diminution of skin lesions was accompanied by lower serum concentrations of total IgG1 and lower expression levels of TNF-α in the lesional tissue. These data suggest that maternal consumption of fructo-oligosaccharide diminishes the severity of atopic dermatitis-like skin lesions in the offspring of NC/Nga mice.

Our preliminary clinical trial showed that consumption of cooked rice of a Japanese common cultivar Yukihikari improved atopic dermatitis associated with a suspected rice allergy, although the underlying mechanisms remain unclear. We hypothesised that the ameliorating effect of Yukihikari on atopic dermatitis is associated with the gut microbiota. BALB/c mice were fed a synthetic diet supplemented with uncooked and polished white rice powder prepared from one of four different cultivars: Yukihikari, rice A (common rice), rice B (brewery rice) and rice C (waxy rice). Denaturing gradient gel electrophoresis of PCR-amplified 16S rRNA gene fragments showed that the composition of faecal microbiota was different between mice fed Yukihikari and those fed rice A. Analysis of the 16S rRNA clone library and species-specific real-time PCR showed that the abundance of Akkermansia muciniphila, a mucin degrader, tended to be lower in mice fed Yukihikari. The incidence of allergic diarrhoea induced by oral administration of ovalbumin in systemically immunised mice was lower in mice fed Yukihikari, albeit with no difference in serum antibodies specific to ovalbumin. In a separate experiment, serum antibody levels specific to orally administered ovalbumin were lower in mice fed Yukihikari. Additionally, the translocation of horseradish peroxidase in isolated segments of ileum and colon tended to be lower in mice fed Yukihikari, suggesting a reduction in gut permeability in mice fed Yukihikari. These data indicate that changes in the gut microbiota of mice fed Yukihikari could be advantageous in the prevention of food allergy.

Strategies to manipulate the intestinal microbiota have been considered to promote immune health. The aim of the present study was to examine whether fructo-oligosaccharide, a typical prebiotic, could suppress antigen-specific skin inflammation by favourably changing the population of intestinal microbiota. Female BALB/c mice were fed a synthetic diet with or without fructo-oligosaccharide supplementation for 3 weeks and were then epicutaneously immunised with 2,4-dinitrofluorobenzene. Afterwards, mice continued to receive their respective diets. At 5 d after immunisation, the mice were ear challenged with the hapten. Ear swelling after the challenge was significantly reduced in the mice fed the diet supplemented with fructo-oligosaccharide than in mice fed the control diet. To characterise the change in the intestinal microbiota, DNA samples isolated from fresh faeces were subjected to PCR–denaturing gradient gel electrophoresis and real-time PCR based on 16S rDNA gene sequences. Dietary fructo-oligosaccharide altered the composition of intestinal microbiota. The numbers of bifidobacteria, but not lactobacilli, were significantly higher in mice fed the fructo-oligosaccharide-supplemented diet than in mice fed the control diet. Ear swelling was negatively correlated with the numbers of bifidobacteria in the faeces. Sequence analysis revealed that Bifidobacterium pseudolongum was the most predominant bifidobacteria in the intestine of mice fed the fructo-oligosaccharide-supplemented diet. These results suggest that consumption of fructo-oligosaccharide reduces contact hypersensitivity, which is associated with proliferation of B. pseudolongum in the intestinal tract of mice.

The present study introduced a molecular biological approach to demonstrate changes in the composition of intestinal microbiota in neonatal mice. Female BALB/c mice were fed either a control diet or a diet supplemented with fructo-oligosaccharide (FOS) at 50 g/kg diet, and then mated to male mice. A cultivation-independent approach, denaturing gradient gel electrophoresis (DGGE) of the PCR-amplified 16S rRNA gene, was performed to characterise changes in intestinal microbial populations in pups at 0, 7, 14 and 21 d old and their dams. Comparisons of DGGE profiles were performed using the Dice similarity coefficient and the unweighted pair group method with arithmetic mean (UPGMA) cluster analysis based on numbers, positions and intensities of bands. DGGE profiles differed between dams fed control and FOS-supplemented diets. Although profiles in pups on the day of birth showed a high similarity with dams, profiles in 7-d-old pups differed from dams and showed high similarity to littermates. In 14- and 21-d-old pups, profiles again showed high similarity with dams. DGGE profiles in pups were divided into two large clusters of control and FOS-supplemented diet groups in the range of 0- to 21-d-old, suggesting modulation of intestinal microbiota in infants by manipulation of microbiota in dams. The present study shows a useful technique for demonstrating changes in intestinal microbiota and provides a mouse model for modulation of intestinal microbiota in neonatal life.

In this paper, we investigate the lower bound sHK(p, d) of Hilbert-Kunz multiplicities for non-regular unmixed local rings of Krull dimension d containing a field of characteristic p > 0. Especially, we focus on three-dimensional local rings. In fact, as a main result, we will prove that sHK (p, 3) = 4/3 and that a three-dimensional complete local ring of Hilbert-Kunz multiplicity 4/3 is isomorphic to the non-degenerate quadric hypersurface k[[X, Y, Z,W]]/(X2 + Y2 + Z2 + W2) under mild conditions.

Furthermore, we pose a generalization of the main theorem to the case of dim A ≥ 4 as a conjecture, and show that it is also true in case dim A = 4 using the similar method as in the proof of the main theorem.

Oral administration of raffinose, a naturally occurring indigestible oligosaccharide, has reportedly ameliorated atopic dermatitis in human subjects although the mechanism is unknown. The present study investigated the effect of dietary raffinose on allergen-induced airway eosinophilia in ovalbumin-sensitised Brown Norway rats as an atopic disease model. Brown Norway rats were immunised by subcutaneous injection with ovalbumin on day 0 and fed either a control diet or the diet supplemented with raffinose (50 g/kg diet). The rats were exposed to aerosolised ovalbumin on day 20, and broncho-alveolar lavage fluid was obtained on the next day. The number of eosinophils in the fluid was significantly lower in the rats fed the raffinose diet than in those fed the control diet. Dietary raffinose significantly reduced IL-4 and IL-5 mRNA levels in lung tissue and tended to lower ovalbumin-specific Ig E levels. Suppression of eosinophilia by dietary raffinose was still observed in caecectomised and neomycin-administered rats, suggesting little contribution by the colonic bacteria to the effect of raffinose. Intraperitoneal administration of raffinose also suppressed eosinophilia. Significant concentrations of raffinose were detected in portal venous and abdominal arterial plasma after the intragastric administration of raffinose. Overall, the findings suggest that dietary raffinose ameliorates allergic airway eosinophilia at least partly via post-absorptive mechanisms in Brown Norway rats.

We have constructed an advanced electric probing system, which is a triple-probe atomic force microscope (T-AFM). The T-AFM consists of “Nanotweezers” and an AFM with a carbon nanotube probe. Using this system, we fabricated a single-walled carbon nanotubes (SWNTs)/deoxyribonucleic acid (DNA) three-terminal device and measured the current-voltage (I-V) curves of this device. In this three-terminal device, DNA strands were entangled with the SWNT bundle, and behaved as a gate-insulator-layer. This three-terminal device worked as a metal-insulator-semiconductor field effect transistor (MIS-FET) with depletion switching behavior.

For measuring molecular device, we developed a dual-probe scanning tunneling microscope (D-STM) composed of two STM systems in which a carbon nanotube (NT) was used for STM tip. Using D-STM, we fabricated a NT ring device. The NT ring device showed a switching behavior with applying gate bias. Furthermore, in STM imaging for various gate biases, we could observe directly hole injection into the NT ring.

We have constructed an advanced electric probing system, which is a triple-probe atomic force microscope (T-AFM). The T-AFM consists of “Nanotweezers” and an AFM with a carbon nanotube probe. Using this system, we fabricated a single-walled carbon nanotubes (SWNTs)/deoxyribonucleic acid (DNA) three-terminal device and measured the current-voltage (I-V) curves of this device. In this three-terminal device, DNA strands were entangled with the SWNT bundle, and behaved as a gate-insulator-layer. This three-terminal device worked as a metal-insulator-semiconductor field effect transistor (MIS-FET) with depletion switching behavior.

For measuring molecular device, we developed a dual-probe scanning tunneling microscope (D-STM) composed of two STM systems in which a carbon nanotube (NT) was used for STM tip. Using D-STM, we fabricated a NT ring device. The NT ring device showed a switching behavior with applying gate bias. Furthermore, in STM imaging for various gate biases, we could observe directly hole injection into the NT ring.

We study the behavior of Hilbert-Kunz multiplicity for powers of an ideal, especially the case of stable ideals and ideals in local rings of dimension 2. We can characterize regular local rings by certain equality between Hilbert-Kunz multiplicity and usual multiplicity.

We show that rings with “minimal” Hilbert-Kunz multiplicity relative to usual multiplicity are “Veronese subrings” in dimension 2.

Photoluminescence (PL) of SiO2 films co-doped with Si nanocrystals (nc-Si) and Er was studied. The average size of nc-Si was changed in a wide range in order to tune the exciton energy of nc-Si to the energy separations between the discrete electronic states of Er3+. PL from exciton recombination in nc-Si and the intra-4f shell transition of Er3+ were observed simultaneously. At low temperatures, periodic features were observed in the PL spectrum of nc-Si. The period agreed well with the optical phonon energy of Si. The appearance of the phonon structures implies that nc-Si which satisfy the energy conservation rule during the energy transfer process can resonantly excite Er3+. The effects of the quantum confinement of excitons in nc-Si on the energy transfer process are discussed.

We investigated the hydride structures at the step edges on Si( 111) surfaces after removing surface oxide by HF solution, followed by immersion in boiling water, by using polarized infrared attenuated total-reflection spectroscopy. Vicinal (111) surfaces misoriented toward the [112] direction at angles of 0°, 2°, and 4° were used to know the hydride structures at the steps. We assigned absorption peaks as monohydride chains at the step edges along the [110] direction, vertical dihydride (whose three atoms make a surface vertical to [111]) at the kinks, and monohydride on the terraces. We determined that the silicon monohydride chain forms an atomically straight step edge along the [110] direction with a small amount of vertical dihydride kinks after 5-min immersion in boiling water. Only the monohydrides on the terraces and the mohydride chains are stable on vicinal (111) surface in pure water.