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The characterizations when two natural upper bounds of the set of copulas with a given diagonal section are copulas have been well studied in the literature. Given a curvilinear section, however, there is only a partial result concerning the characterization when a natural upper bound of the set of copulas is a copula. In this paper, we completely solve the characterization problem for this natural upper bound to be a copula in the curvilinear case.

Lifecycle assessment of wind turbines is essential to improve their design and to optimum maintenance plans for preventing failures during the design life. A critical element of wind turbines is the composite blade due to uncertain cyclic wind loads with relatively high frequency and amplitude in offshore environments. It is critical to detect the wind fatigue damage evolution in composite blades before they fail catastrophically and destroy the entire wind turbines. This study presents a methodology for analysing the fatigue failure probability of a wind turbine composite blade by using monitoring stochastic deterioration modelling. On the basis of 5 minutes mean wind speed measurements, the internal stresses can be accurately obtained from finite element analysis, and failure probabilities are predicted by stochastic gamma process fatigue damage model in design service life. A numerical example of a wind turbine composite blade is investigated to show the applicability of the proposed model. The results show that the stochastic fatigue damage model can give reliable results for time-dependent reliability analysis for composite blades of wind turbines.

Whether astrophysical black holes (BHs) can have charge is a question to be addressed by observations. In the era of gravitational wave (GW) astronomy, one can constrain the charge of a merged BH remnant using the merger-ringdown signal of the GW data. Extending earlier studies, we analyze five GW events in GWTC-3, assuming Kerr-Newman BHs. Our results show no strong evidence for a charged BH, and give a limit on the charge-to-mass-ratio $Q<0.37$ at $90\%$ credible level (CL). Due to the charge-spin degeneracy in the waveform and the limited signal-to-noise ratios (SNRs), it is challenging for LIGO/Virgo/KAGRA observations to provide better constraints. We further simulate data for the Einstein Telescope (ET), where SNRs can be as large as $\sim270$ in the ringdown signal. These simulated events allow us to consider the 220, 221, and 330 ringdown modes altogether, which can help break the charge-spin degeneracy. The analysis of a simulated GW150914-like signal shows that ET can improve the constraints on the charge-to-mass-ratio to $Q \lesssim 0.2$ at $90\%$ CL with one ringdown signal., Comment: 13 pages, 7 figures; accepted by PRD

Superelastic NiTi tubes are promising candidates for eco-friendly elastocaloric cooling, but their cyclic stability suffers severely from functional degradation. Herein, we investigate the functional degradation of nanocrystalline NiTi tubes via in-depth analysis and find out that it is beneficial to elastocaloric cooling performance. The results show that the functional degradation accompanies with progressive accumulation of residual strain and significant reduction in both hysteresis loop area (D) and forward transformation stress. The accumulation of residual strain arises from phase-transition-induced dislocations and dislocation-pinned residual martensite. The former separates the original austenite grains to much smaller nanodomains (equivalent to grain size effect) and contributes to the strain hardening during phase transition, leading to the significant reduction of D. The latter induces compressive residual stress in the austenite phase and thus gives rise to the evolutive reduction of forward transformation stress. Consequently, the material coefficient of performance (COPmater) was self-enhanced for 40~104 %. The beneficial effect is mainly because of the cyclically-decreased D. The study might provide a processing route to tailor COPmater and stabilize the mechanical response of NiTi by cyclic compression., Comment: 48 pages, 11 figures, 12 supporting figures.To be submitted to Acta Materialia

The ordinal sum construction provides a very effective way to generate a new triangular norm on the real unit interval from existing ones. One of the most prominent theorems concerning the ordinal sum of triangular norms on the real unit interval states that a triangular norm is continuous if and only if it is uniquely representable as an ordinal sum of continuous Archimedean triangular norms. However, the ordinal sum of triangular norms on subintervals of a bounded lattice is not always a triangular norm (even if only one summand is involved), if one just extends the ordinal sum construction to a bounded lattice in a na\"{\i}ve way. In the present paper, appropriately dealing with those elements that are incomparable with the endpoints of the given subintervals, we propose an alternative definition of ordinal sum of countably many (finite or countably infinite) triangular norms on subintervals of a complete lattice, where the endpoints of the subintervals constitute a chain. The completeness requirement for the lattice is not needed when considering finitely many triangular norms. The newly proposed ordinal sum is shown to be always a triangular norm. Several illustrative examples are given.

Synchrotron radiation with the characteristic of high brilliance, high level of polarization, high collimation, low emittance and wide tunability in energy has been used as a standard source in metrology(1, 2). For a decade, lots of calibration work have been done on 4B7A in Beijing Synchrotron Radiation Facility (BSRF) (3, 4). For the calibration process, a high-precision online monitor is indispensable. To control the uncertainty under 0.1%, we studied different sizes parallel ion chambers with rare-gas and used different collecting methods to monitor the x-ray intensity of the beamline. Two methods to collect the signal of the ion chambers: reading the current directly with electrometer or signal amplification to collect the counts were compared., Comment: 7 pages

We present a vacuum ultraviolet (VUV) band-pass photon detector for inverse photoemission spectroscopy. A SrF2 window is used due to its high-energy cutoff of the optical transmission being 9.7eV, and acetone is selected as filling gas with the photoionization threshold also being 9.7eV. The structure of the detector described in detail is based on a Geiger-M\"uller type counter with an MgF2 window and argon as amplification gas. Its energy resolution can be tuned continuously from 46meV with a normal temperature situation to 105meV at 215K. Meanwhile, the signal intensity of the detector is adjusted accordingly to find an optimal operation program for our inverse photoemission system which is being constructed. The ratio of acetone vapor and argon is varied carefully. Background signals and the response of time are analyzed. The detector is normalized by deuterium lamp in combination with a grating monochromator., Comment: This paper has been withdrawn by the author due to the confusing layout in the whole article