The Green's function of the discrete Sch & ouml;dinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting the appropriate potentials. We show two ways of the expression for the Green's function by using graph structures. The first way is based on the factor of the graph by subtrees which have uni-self-loops; the second way is based on that by odd unicycle graphs. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Given a graph F, a hypergraph is called a Berge-F if it can be obtained by expanding each edge of F into a hyperedge containing it. Let Mk denote the matching of size k. Kang, Ni, and Shan [12] determined the Turán number of Berge-Mk. Our main result shows that if an r-uniform hypergraph H on n vertices has nearly as many edges as the extremal in their theorem without containing Berge-Mk, then H must be structurally close to certain well-specified graphs. Meanwhile, our result also implies several stability results, such as the stability version of the well-known Erdős-Gallai theorem (Erdős and Gallai, 1959 [5]).
This article reports the measurement of the neutron background flux accidentally induced by the neutrino beam at the J-PARC facility in Japan. In particular, neutrino-nucleus neutral-current quasi-elastic (NCQE) scattering events, ν(ν̄)+N→ν(ν̄)+N′, can be obscured by a massive background of neutron-nucleus scattering events. The neutrons are produced within the materials (such as sand and concrete) located between the beam dump and the experimental area where the detectors are placed. We measured the accidental neutron events at the J-PARC neutrino facility using BGO and liquid scintillation detectors, with a plastic scintillation detector serving as an active veto counter. Based on a neutrino-mode data set of 2.972×1020 POT, we observed 88 neutron-induced recoil proton events within an electron-equivalent recoil energy range of 0.98–11.60 MeVee, selected via pulse-shape discrimination in the liquid scintillation detector. Accounting for the detection efficiency and resolution, and through comparison with simulations, the neutron flux was determined to be[1.45−0.24+0.22(stat.)±0.55(sys.)]×10−7cm−2s−1POT−1, assuming an exponential neutron energy spectrum. This result will contribute to the evaluation of neutron backgrounds for neutrino experiments at the J-PARC facility.
Post-installed shear reinforcements (PHSRs) are widely used to strengthen underground reinforced concrete (RC) members where single-sided access limits conventional retrofit. While prior studies have examined PHSRs retrofitted onto already-damaged members, the behavior of sound members retrofitted with PHSRs that subsequently experience damage and water exposure has not been systematically investigated. This study experimentally examines the reversed cyclic response of four RC beams, three retrofitted with PHSRs and one with plain round bars to investigate the role of mechanical anchorage. The beams were subjected to controlled static pre-damage at pre-peak or peak levels, followed by reversed cyclic loading at successive amplitudes from ±1 mm to ±6 mm under partial water submersion. Residual load-carrying capacity, secant stiffness degradation, residual displacement, strain evolution, cumulative energy absorption, and the evolution of arch and beam action contributions were examined. Peak-damaged beam tested in water showed consistently lower residual capacity and cumulative energy absorption than the air-tested beam, with accelerated transition from arch-dominated to beam-dominated shear behavior. At 2 and 3 mm, the pre-peak damaged beam retained residual loads at or slightly exceeding the static pre-peak capacity (ηP= 1.004 and 1.04, respectively). Water exposure altered the shear-transfer response in beam with peak damage, with Varch/Vbeam reaching 0.67 compared with 0.80 in air at 6 mm, while the beam with plain round bars exhibited a substantially lower ratio of 0.10 in water. The outcomes highlight the critical effect of pre-damage severity, water exposure, and the condition of mechanical anchorage on cyclic shear performance of PHSR-retrofitted RC members.
Reliable identification of localized reflection events is essential for diagnosing optical fiber links in high-capacity communication networks. Optical correlation-domain reflectometry (OCDR) enables distributed reflectivity measurements with high spatial selectivity; however, closely spaced reflection points can be difficult to distinguish when their reflection peaks overlap because of insufficient effective spatial resolution or surrounding noise. Here, we propose and experimentally demonstrate a polarization-state-control method for identifying closely spaced reflection points in OCDR. The method exploits the polarization dependence of the beat-signal waveform and selectively enhances the contribution from each reflection point by adjusting the polarization state of the reference light. Experiments were performed using two reflection points with separations of 5.0, 3.0, and 1.3 cm in three OCDR configurations: sinusoidal-modulation OCDR with an acousto-optic modulator (AOM), sinusoidalmodulation OCDR without an AOM, and periodic pseudo-random modulation OCDR. Under polarizationscrambled conditions, the two reflection contributions appeared as a single overlapped response in all configurations. In contrast, reference-polarization adjustment produced states that selectively enhanced either reflection point, enabling their contributions to be identified down to the smallest tested separation of 1.3 cm. For the 5.0-cm condition, the apparent 3-dB peak widths ranged from 8.2 to 12.3 cm and exceeded the physical separation, confirming that the identification did not result from conventional peak-width-limited spatial resolution. The proposed method therefore provides an additional degree of freedom for identifying overlapping reflection events, provided that they exhibit sufficiently distinguishable effective polarization responses.
