Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation ...

We demonstrate the (H, L) or (L, L) mapping properties of several rough operators. In all cases these estimates are sharp in the sense that the Lorentz exponent 2 cannot be replaced by any lower number.

We improve the upper bounds of disconnection exponents for planar Brownian motion that we derived in an earlier paper. We also give a plain proof of the lower bound 1/(2π) for the disconnection exponent for one path.

A number of results for reactions involving subdiffusive species, all with the same anomalous exponent , have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time in ordinary diffusion is replaced by tgamma. However, very few results are known for reactions involving different species characterized by different anomalous diffusion ex...

We show that if G is any p-group of class at most two and exponent p, then there exist groups G1 and G2 of class two and exponent p that contain G, neither of which can be expressed as a central product, and with G1 capable and G2 not capable. We provide upper bounds for rank(Gi ) in terms of rank(G) in each case.

We obtained the global persistence exponent for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent theta(g) by following the time evolution of probability P(t) that the order parameter of the model does not change its sign up to time t[P(t) approximately t(-theta(g)]. Afterwards, that exponent was...

We slightly inprove the upper bounds of disconnection exponents for planar Brownian motion that we derived in an earlier paper. We also give a plain proof of the lower bound 1=(2) for the disconnection exponent for one path.

We derive a lower bound for the subword complexity of the base-b expansion (b ≥ 2) of all real numbers whose irrationality exponent is equal to 2. This provides a generalization of a theorem due to Ferenczi and Mauduit. As a consequence, we obtain the first lower bound for the subword complexity of the number e and of some other transcendental exponential periods.

Which groups G contain difference sets with the parameters (v, k, A.)= (q 3 + 2q 2 , q2 + q, q), where q is a power of a prime p? Constructions of K. Takeuchi, R.L. McFarland, and J.F. Dillon together yield difference sets with these parameters if G contains an elementary abelian group of order q2 in its center. A result of R.J. Turyn implies that if G is abelian and p is self-conjugate modulo ...

Measurements of the aerosol optical depth (AOD) and the Ångström exponent were retrieved from level 1.5 data obtained by the CE318 sun photometer at Dalian monitoring station from April 2007 to April 2012 to characterize the aerosol spatial and temporal characteristics in this coastal region of Northeast China. The results suggest that the highest mean ̆ SD value for the AOD over Dalian occurre...