We consider dynamics of an oscillatory mechanical system with 1.5 degrees of freedom. The system consists of two linear subsystems, a leader and a follower, which are coupled via a kinetic friction interface, and additionally driven by a proportional control term. The kinetic friction model accounts for the Coulomb friction and the Stribeck effect (as negative damping) at the passage from zero to nonzero relative velocity. The equations of motion are equivalent to a Lur'e system with a single sign nonlinearity. We show that at a critical value of the parameter the zero steady state blows up into an attracting continuum (segment) of equilibrium states. Moreover, two antipodal smallamplitude periodic orbits bifurcate from the end points of the segment of equilibrium states, creating stick-slip vibrations. We consider other possible attractors consisting of stick-slip solutions of the Lur'e system such as a Z2-symmetric stick-slip periodic orbit and an attractor composed of a continuum of heteroclinic loops representing stick-slip motions towards a steady state.
In this paper, we investigate the spectral stability of two biharmonic Steklov problems under domain perturbation. We provide optimal conditions on the boundary perturbations ensuring the stability of both eigenvalues and eigenfunctions. To highlight the optimality of those conditions, we present alternative assumptions on the boundary perturbations that lead to either a degeneration of the spectrum or to the appearance of a strange term in the limiting problem. In particular, these phenomena are discussed for a boundary homogenization problem exhibiting a trichotomy in the asymptotic behaviour.
Deep learning has become a cornerstone in numerous applications, such as robotics, augmented reality, and autonomous systems, where accurate 6D pose estimation-determining an object's position and orientation in 3D space-is critical. Despite its success, designing optimal neural architectures and tuning hyperparameters remain computationally expensive and challenging, especially in high-variance and data-intensive domains like 6D pose estimation. To address this, we investigate the application of a Neural Architecture Search (NAS) technique guided by classical Machine Learning-based performance predictors. As these predictors estimate final model performance using early-stage training data, we demonstrate that leveraging such a strategy allows for efficient exploration of the hyperparameter space, significantly reducing the computational burden of exhaustive search while still achieving improved performance. Building on an existing NAS method, we introduce a novel modification that enhances the efficiency of the search process, further accelerating convergence by nearly 71% without sacrificing accuracy. Through extensive experimentation on the LineMOD dataset, we demonstrate that our method consistently discovers high-performing configurations of an Augmented Autoencoder for 6D pose estimation, outperforming benchmark models by almost 15% in pose accuracy and 42% in reconstruction loss. These results underscore the potential of predictor-based NAS as a powerful and computationally efficient tool for neural architecture optimization in complex, real-world tasks.
This paper investigates lump waves in a generalized (2+1)-dimensional Bogoyavlensky-Konopelchenko model with spatially balanced derivatives. Using a sum-of-squares ansatz, symbolic computation in Maple is employed to construct lump wave solutions of the nonlinear model from positive quadratic functions. The interplay of four sets of nonlinear terms and five dispersion terms gives rise to the resulting lump waves. The critical points of these quadratic functions are determined, and they travel at constant velocities along a straight line in the spatial plane. Along this characteristic line, the constructed lump waves remain invariant. Concluding remarks are provided in the final section.
This paper studies the far field refraction problem in negative refractive index material with loss of energy, which is a remaining problem in E. Stachura, Nonlinear Anal. 2017;157:76-103. The analysis is divided into two cases according to the relative refractive index kappa, that is, kappa < -1 and-1 < kappa < 0. For each case, we use the Minkowski method to establish the existence of the weak solution when the target measure is either discrete or a finite Radon measure. Eventually, the inequality involving a Monge-Ampe`re type operator satisfied by the solution of the problem is derived, which is useful to understand this complex optical phenomenon.
