We consider the Cucker？Smale model with a regular communication rate and nonlinear velocity couplings, which can be understood as the parabolic equations for the discrete p-Laplacian (p ≥ 1) with nonlinear weights involving a parameter β( > 0).

GW170817 is the very first observation of gravitational waves originating from the coalescence of two compact objects in the mass range of neutron stars, accompanied by electromagnetic counterparts, and offers an opportunity to directly probe the internal structure of neutron stars.

On 2019 April 25, the LIGO Livingston detector observed a compact binary coalescence with signal-to-noise ratio 12.9. The Virgo detector was also taking data that did not contribute to detection due to a low signal-to-noise ratio, but were used for subsequent parameter estimation.

Modern ground-based gravitational wave (GW) detectors require a complex interferometer configuration with multiple coupled optical cavities. Since achieving the resonances of the arm cavities is the most challenging among the lock acquisition processes, the scheme called arm length stabilization (ALS) had been employed for lock acquisition of the arm cavities.

The LIGO Scientific Collaboration and the Virgo Collaboration have cataloged eleven confidently detected gravitational-wave events during the first two observing runs of the advanced detector era.

We propose a Lohe matrix model in a random environment where each oscillator can be regarded as an element of a general matrix Lie group G

Given a real projective plane S embedded in a 4？manifold X4 with Euler number 2 or ？？2, the Price twist is a surgery operation on .S/ yielding (up to) three different 4？manifolds: X4 , S.X4/ and ？S.X4/. This is of particular interest when X4 D S4 ,as then ？S.X4/ is a homotopy 4？sphere which is not obviously diffeomorphic to S4 . Here we show how to produce a trisection deion of each Price twist on S  X4 by producing a relative trisection of X4 n .S/. Moreover, we show how to produce a trisection deion of general surface complements in 4？manifolds.

More than 98% of all microprocessors sold worldwide are used in embedded devices, and will continue to accelerate due to the emerging applications in Internet of Things (IoT).

A public-key cryptographic algorithm based on multivariate quadratic equations is one of promising post-quantum alternatives for current public-key cryptography. The security of multivariate quadratic schemes has been sufficiently analyzed mathematically, but few works have been devoted to implementation attacks. In this paper, we present algebraic fault analysis of two well-known multivariate quadratic schemes, UOV and Rainbow, which combines fault attacks with key recovery attacks using good keys. We focus on fault attacks which cause faults on random Vinegar values used in signing.