This work investigates the existence of globally Lipschitz continuous solutions to a class of Cauchy problem of quasilinear wave equations. Applying Lax's method and generalized Glimm's method, we construct the approximate solutions of the corresponding perturbed Riemann problem and establish the global existence for the derivatives of solutions. Then, the existence of global Lipschitz continuous solutions can be carried out by showing the weak convergence of residuals for the source term of equation.

The silicon tracker of the AMS-02 detector measures the trajectory in three dimensions of electrons, protons and nuclei to high precision in a dipole magnetic field and thus measures their rigidity (momentum over charge) and the sign of their charge. In addition, it measures the specific energy loss of charged particles to determine the charge magnitude. Ladders from the AMS-02 tracker have been exposed to ion beams at CERN and GSI to study their response to nuclei from helium up to the iron group. The longest ladder, View the MathML source72×496mm2, verified in the tests contains 12 sensors. Good charge resolution is observed up to iro

Let K denote the contact Lie superalgebra K(m, n; t) over a field of characteristic p > 3, which has a finite Z-graded structure. Let T K be the canonical torus of K, which is an abelian subalgebra of K 0 and operates on K −1 by semisimple endomorphisms. Utilizing the weight space decomposition of K with respect to T K , we prove that each skew-symmetric super-biderivation of K is inner.

We present detections of stellar flares of Wolf 359, an M6.5 dwarf in the solar neighborhood (2.41 pc) known to be prone to flares due to surface magnetic activity. The observations were carried out from 2020 April 23 to 29 with a 1 m and a 0.5 m telescope separated by nearly 300 km in Xinjiang, China. In 27 hr of photometric monitoring, a total of 13 optical flares were detected, each with a total energy of ≳ 5 × 1029 erg. The measured event rate of about once every two hours is consistent with those reported previously in radio, X-ray, and optical wavelengths for this star. One such flare, detected by both telescopes on April 26, was an energetic event with a released energy of nearly 1033 erg. The two-telescope light curves of this major event sampled at different cadences and exposure timings enabled us to better estimate the intrinsic flare profile, which reached a peak of up to 1.6 times the stellar quiescent brightness, that otherwise would have been underestimated in the observed flare amplitudes of about 0.4 and 0.8, respectively, with single telescopes alone. The compromise between fast sampling so as to resolve a flare profile versus a longer integration time for a higher photometric signal-to-noise ratio provides a useful guidance in the experimental design of future flare observations.

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