Simulated granular packings with different particle friction coefficient mu are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P(f) are computed and compared with existing experimental data. Here f identical with F/(-)F is the contact force F normalized by the average value (-)F. P(f) exhibits exponential-like decay at large forces, a ...

We show here that the limit mapping f of a weakly convergent sequence of mappings fν with finite distortion also has finite distortion and give several dimension free estimates for the dilatation of f . Our arguments are based on the weak continuity of the Jacobian determinants and the concept of polyconvexity.

Abstract In the paper we will focus on weakly Światkowski functions. We say that f satisfies weak Świa̧tkowski condition (or is a function) if for all $$x_1, x_2$$ x 1 , 2 with $$f(x_1)&lt; f(x_2)$$ f</mml:...

We show that if two 3-manifolds with toroidal boundary are glued via a “sufficiently complicated” map then every Heegaard splitting of the resulting 3-manifold is weakly reducible. Additionally, suppose X∪F Y is a manifold obtained by gluing X and Y , two connected small manifolds with incompressible boundary, along a closed surface F . Then the following inequality on genera is obtained:

A selective and sensitive turn-on fluorescent NIR probe for cysteine has been developed. Cleavage of 2,4-dinitrobenzenesulfonyl (DNBS) with thiols switches the weakly fluorescent aza-BODIPY dye (λ(em) = 734 nm, Φ(f) = 0.03) to a strongly fluorescent species in the NIR region (λ(em) = 755 nm, Φ(f) = 0.14).

Let (T; T) be an arbitrary measurable space, X a Banach space whose dual X is strongly separable and f an integrand deened on T X. If f is normal in the sense of Rockafellar 18], then the conjugate integrand f is normal. Moreover the subdiierential multifunction is EEros (or weakly) measurable. These results extend those of Rockafellar 18] and of Hess 6], and provide an alternate approach to th...

The goal of the following is to use (infinitedimensional) linear systems theory to approach the H∞functional calculus. This extends recent work by the authors using the notion of admissible observation operators to define f (A) where f is bounded, analytic in the left half-plane and A generates an exponentially stable strongly continuous semigroup. Among other things it is shown that f (A) is a...

We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ ⊂ R, we construct a sparsely-connected depth-4 neural network and bound its error in approximating f . The size of the network depends on dimension and curvature of the manifold Γ, the complexity of f , in terms of its wavelet description, and only weakly on the ambient dimension m. Es...