Area integral estimates for solutions and normalized adjoint solutions to nondivergence form elliptic equations

We show that theL ^p norms, 0<p<∞, of the nontangenital maximal function and area integral of solutions and normalized adjoint solutions to second order nondivergence form elliptic equations, are comparable when integrated on the boundary of a Lipschitz domain with respect to measures, which are respectivelyA _∞ with respect to the corresponding harmonic measure or normalized harmonic measure. Both authors are supported by NSF     

The correlation dimension of rat hearts in an experimentally controlled environment

The electric response of several isolated rat hearts in a controlled environment was studied experimentally. The correlation dimension D(2) was estimated and was found to be between 4 and 6.5 when the response was nearly periodic. The variation of D(2) with the concentration of calcium was studied and a general trend of its increase with increasing concentration was found. Two types of ventricular fibrillation (VF) were observed, one that corresponds to a stochastic signal where D(2) is unbounded and the other to a low dimensional dynamical system with 3.5相似文献   

Properties of blends containing two liquid crystalline polymers

Blends containing two, wholly aromatic, naphthalene-based liquid crystalline polymers (LCPs) are studied. Experimental results show that the viscosities of the resulting blends are lower than the parent LCPs over the entire shear-rate range investigated. The orientation development following capillary flow demonstrates, that over a defined blend composition range, some blends have higher orientability than the constituent polymers. This is further manifested in the tensile and flexural properties of injection-molded specimens. A detailed analysis indicates that in the composition range where synergistic effects are observed in orientation development as well as in mechanical properties, only one glass transition temperature is detected. This suggests that “miscibility” is desirable for obtaining maximum properties in these blend systems.     

Unconventional model of neutrino masses

Gelmini and Roncadelli have proposed a model of neutrino masses in which B?L symmetry is spontaneously broken by a small vacuum expectation value of a Higgs triplet. We give an exegesis of this model. We show that the massive neutrinos in this model cannot be cosmologically relevant today and that conflicting analyses of double beta decay experiments can be reconciled.     

On fibering four- and five-manifolds

This paper studies the question of which manifolds fiber over the circle in dimensions four and five. Partially supported by an NSF Postdoctoral Fellowship.     

Optimal iterative processes for root-finding

Letf ₀(x) be a function of one variable with a simple zero atr ₀. An iteration scheme is said to be locally convergent if, for some initial approximationsx ₁, ...,x _s nearr ₀ and all functionsf which are sufficiently close (in a certain sense) tof ₀, the scheme generates a sequence {x _k} which lies nearr ₀ and converges to a zeror off. The order of convergence of the scheme is the infimum of the order of convergence of {x _k} for all such functionsf. We study iteration schemes which are locally convergent and use only evaluations off,f, ...,f ^[d] atx ₁, ...,x _k–1 to determinex _k, and we show that no such scheme has order greater thand+2. This bound is the best possible, for it is attained by certain schemes based on polynomial interpolation.This work was supported (in part) by the Office of Naval Research under contract numbers N0014-69-C-0023 and N0014-71-C-0112.