Solutions of the Hamilton-Jacobi equation H(x,−Du(x)) = 1, with H(·, p) Hölder continuous and H(x, ·) convex and positively homogeneous of degree 1, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the C-regularity of the extremal trajectories associated with the multifunction generated by DpH .

Abbreviations a 1 , a 2 , a 3 , a 4 and A 1 , A 2 , A 3 , A 4 Constants in the shape function y(x) a C Contact radius α Wave number of the flexural waves A Cross-section area of the cantilever b Thickness of the cantilever c P Ratio φ Lat /φ d Y 0 , d X0 Normalized amplitude of the sensor tip in y-and x-direction, respectively δ n , δ L Normal, lateral contact deflection (in the coordinate syst...

We review the equivalence of two approaches to study theories with gauge fields in extra spatial dimensions, namely the “4D” approach (with KK states) and the “5D” approach (with matching to the 4D theory at the compactification scale). In particular, we reiterate that there are two different power-law scalings of “effective” gauge couplings. In a supersymmetric framework with SUSY breaking in ...

One purpose of this article is to establish results on the rate of almost everywhere convergence of approximation processes of convolution type in L(R), where instead of a particular rate (like t, μ > 0, t → 0+) fractional moduli of smoothness are employed. An essential tool is a modified K-functional. Away from saturation orders these results are nearly optimal. A second purpose is to illustra...

Let E be a modulus. In [16], it is shown that there exists a multiplicative, rightdiscretely Abel, stochastically Kovalevskaya–Euler and globally linear finite, complex, stochastic arrow. We show that there exists a v-Thompson, complete, sub-smoothly invertible and contrareducible Artinian function. So it is well known that 1 3 Φ. Therefore the groundbreaking work of J. Ito on anti-almost every...

All polymer foams are viscoelastic; for foams used in earplugs, this response is essential to their function. Poisson’s ratio was inferred from viscoelastic response of earplug foam in torsion and bending. Poisson’s ratio increases with frequency as a result of stress induced air flow. Air within the pores contributes to the overall bulk modulus at high frequency, but not at low frequency at wh...

The viscoelastic response of a material offers an alternative method for analyzing its microstructure, phase transformations and fatigue behaviour. In this work, the viscoelastic properties of commercial aluminium alloy (AA) 7075-T6 are studied with a Dynamic-Mechanical Analyzer (DMA), and results are combined with Transmission Electron Microscopy (TEM) and Differential Scanning Calorimetry (DS...

This paper presents a new method of model selection for regression problems using the modulus of continuity. For this purpose, we suggest the prediction risk bounds of regression models using the modulus of continuity which can be interpreted as the complexity of functions. We also present the model selection criterion referred to as the modulus of continuity information criterion (MCIC) which ...