A class of relations among multiple zeta values

We prove a new class of relations among multiple zeta values (MZV's) which contains Ohno's relation. We also give the formula for the maximal number of independent MZV's of fixed weight, under our new relations. To derive our formula for MZV's we consider the Newton series whose values at non-negative integers are finite multiple harmonic sums.Comment: 36 pages, presentation improved, to appear in Journal of Number Theor

A generalization of the duality for multiple harmonic sums

The duality is a fundamental property of the finite multiple harmonic sums (MHS). In this paper, we prove a duality result for certain generalizations of MHS which appear naturally as the differences of MHS. We also prove a formula for the differences of these generalized MHS.Comment: 12 pages; minor corrections; to appear in Journal of Number Theor

Cyclic sum formula for multiple L-values

AbstractThe cyclic sum formula for multiple L-values, which can be viewed as a generalization of the cyclic sum formula for multiple zeta values proved by Hoffman and Ohno (or Ohno and Wakabayashi), is shown. An algebraic formulation of the cyclic sum formula is also presented

A Boy with Non-Herpes Simplex Acute Limbic Encephalitis and Antiglutamate Receptor Antibodies

This report concerns a 12-year-old male with intractable seizures over a long period. The case fulfilled the diagnostic criteria for nonherpetic acute limbic encephalitis. He had frequent convulsions starting with a partial seizure at the left angle of the mouth and progressing to secondary generalized seizures. He was treated with several anticonvulsants, combined with methylprednisolone and γ-globulin under mechanical ventilation. However, his convulsions reappeared after tapering of the barbiturate. His magnetic resonance imaging showed a high intensity area in the hippocampus by FLAIR and diffusion. After five months he recovered without serious sequelae. Virological studies, including for herpes simplex virus, were all negative. He was transiently positive for antiglutamate receptor antibodies in cerebrospinal fluid and serum

Geographic disparity of pathophysiological coronary artery disease characteristics: Insights from ASET trials

The geographical disparity in the pathophysiological pattern of coronary artery disease (CAD) among patients undergoing percutaneous coronary intervention (PCI) is unknown. To elucidate the geographical variance in the pathophysiological characteristics of CAD. Physiological indices derived from angiography-based fractional flow reserve pullbacks from patients with chronic coronary syndrome enrolled in the ASET Japan (n = 206) and ASET Brazil (n = 201) studies, which shared the same eligibility criteria, were analysed. The pathophysiological patterns of CAD were characterised using Murray law-based quantitative flow ratio (μQFR)-derived indices acquired from pre-PCI angiograms. The diffuseness of CAD was defined by the μQFR pullback pressure gradient index. Significant functional stenoses pre-PCI (μQFR ≤0.80) were more frequent in ASET Japan compared to ASET Brazil (89.9% vs. 67.5%, p < 0.001), as were rates of a post-PCI μQFR <0.91 (22.1% vs. 12.9%, p = 0.013). In the multivariable analysis, pre-procedural μQFR and diffuse disease were independent factors for predicting a post-PCI μQFR <0.91, which contributed to the different rates of post-PCI μQFR ≥0.91 between the studies. Among vessels with a post-PCI μQFR <0.91, a consistent diffuse pattern of CAD pre- and post-PCI occurred in 78.3% and 76.7% of patients in ASET Japan and Brazil, respectively; only 6.3% (Japan) and 10.0% (Brazil) of vessels had a major residual gradient. Independent risk factors for diffuse disease were diabetes mellitus in ASET Japan, and age and male gender in Brazil. There was geographic disparity in pre-procedural angiography-based pathophysiological characteristics. The combined pre-procedural physiological assessment of vessel μQFR and diffuseness of CAD may potentially identify patients who will benefit most from PCI. [Abstract copyright: Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.