Abstract We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost are of the form $$P(\Omega )T^q(\Omega )|\Omega |^{-2q-1/2}$$ P ( Ω ) T...

We report measurements on the ageing dynamics of a colloid–polymer mixture with a large polymer– colloid size ratio of 0.62. Quenched into a two-phase region the system gels and forms a network with a characteristic radius Rc. We find three distinct regimes in the time evolution of Rc(t), reminiscent of the linear, late and gravity-dominated regimes of coarsening seen in classical spinodal deco...

Let Ω ⊂ R, n > 1 be a bounded domain with smooth boundary. Consider utt −4xu + q(x)u = 0 in Ω× [0, T ] u(x, 0) = 0, ut(x, 0) = 0 if x ∈ Ω u(x, t) = f(x, t) on ∂Ω× [0, T ] Define the Dirichlet to Neumann map Λq : H (∂Ω× [0, T ] ) −→ L(∂Ω× [0, T ] ) f(x, t) 7−→ ∂u ∂n where ~n is the unit outward normal to ∂Ω. If T > diam(Ω), we express q(x) in terms of Λq, and show that if q(x) is piecewise const...

the radial trace transform was introduced by the stanford exploration project many years ago (ottolini, 1979 and claerbout, 1983), primarily for use in migration and imaging applications. it has been shown subsequently, because of its particular geometry, to be very useful for wavefield separation (claerbout, 1983) and coherent noise attenuation (henley, 1999). the radial trace transform, unlik...

Empirical evidence for scale-invariant distributions in financial data has attracted the research interest of physicists. While the power-law tails of the distribution of stock returns P{R>x} approximately x;{-zeta_{R}} are becoming increasingly well documented, less understood are the statistics of other closely related microstructural variables such as q_{i} , the number of shares exchanged i...

Abstract. We start with a (q, t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is the order of a finite field. These (q, t)-binomial coefficients and their interpretations generalize further in two directions, one relating to col...

Let T be the unit circle, f be an α-Hölder continuous function on T, α > 1/2, and A be the algebra of continuous function in the closed unit disk D that are holomorphic in D. Then f extends to a meromorphic function in D with at most m poles if and only if the winding number of f + h on T is bigger or equal to −m for any h ∈A such that f + h 6= 0 on T. 1. MAIN RESULTS Let g be a non-vanishing c...