Lifespan Theorem for simple constrained surface diffusion flows

We consider closed immersed hypersurfaces in R³ and R⁴ evolving by a special class of constrained surface diffusion flows. This class of constrained flows includes the classical surface diffusion flow. In this paper we present a Lifespan Theorem for these flows, which gives a positive lower bound on the time for which a smooth solution exists, and a small upper bound on the total curvature during this time. The hypothesis of the theorem is that the surface is not already singular in terms of concentration of curvature. This turns out to be a deep property of the initial manifold, as the lower bound on maximal time obtained depends precisely upon the concentration of curvature of the initial manifold in L² for M² immersed in R³ and additionally on the concentration in L³ for M³ immersed in R⁴. This is stronger than a previous result on a different class of constrained surface diffusion flows, as here we obtain an improved lower bound on maximal time, a better estimate during this period, and eliminate any assumption on the area of the evolving hypersurface.     

The chemistry and complexes of small cyano anions

The chemistry of the anions dicyanamide and tricyanomethanide (dca and tcm, respectively) has produced a plethora of discoveries over the past few decades, particularly in relation to transition-metal coordination polymers with magnetic coupling. Over recent years there have been an increasing number of reports of heterofunctionalised cyano-containing anions, typically derivatives of dicyanomethanide. Our own group has been particularly concerned with the amide- and nitroso-functionalised anions carbamoyldicyanomethanide (cdm) and dicyanonitrosomethanide (dcnm), respectively. This feature article examines the fascinating diversity of materials and complexes that can be obtained using small cyano anions, ranging from coordination polymers to heterometallic clusters and hydrogen bonding networks. In particular, we focus on results from our own laboratories in the past few years. The magnetic properties of these materials are briefly discussed.     

An Asynchronous Distributed Expectation Maximization Algorithm for Massive Data: The DEM Algorithm

The family of expectation--maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by proposing an asynchronous and distributed generalization of the EM called the distributed EM (DEM). Using DEM, existing EM-type algorithms are easily extended to massive data settings by exploiting the divide-and-conquer technique and widely available computing power, such as grid computing. The DEM algorithm reserves two groups of computing processes called workers and managers for performing the E step and the maximization step (M step), respectively. The samples are randomly partitioned into a large number of disjoint subsets and are stored on the worker processes. The E step of DEM algorithm is performed in parallel on all the workers, and every worker communicates its results to the managers at the end of local E step. The managers perform the M step after they have received results from a γ-fraction of the workers, where γ is a fixed constant in (0, 1]. The sequence of parameter estimates generated by the DEM algorithm retains the attractive properties of EM: convergence of the sequence of parameter estimates to a local mode and linear global rate of convergence. Across diverse simulations focused on linear mixed-effects models, the DEM algorithm is significantly faster than competing EM-type algorithms while having a similar accuracy. The DEM algorithm maintains its superior empirical performance on a movie ratings database consisting of 10 million ratings. Supplementary material for this article is available online.     

Least-Cost Rations and Optimal Livestock Feeding Policy

In evaluating feeding policy in livestock production, it is generally assumed that an optimal feeding policy will involve using least-cost rations throughout the production process. It is demonstrated that this assumption may not be valid when the supply of some of the feedstuffs used for livestock feeding is limited. A method for testing the validity of this assumption is presented for a linear programming model of an integrated crop and intensive beef production enterprise in which some of the crops may be used for livestock feeding, and an iterative solution procedure is proposed for cases where this assumption is not valid.     

Cation transport at 25°c from binary Tl+Mn+ and K+Mn+ nitrate mixtures in a H2OCHCl3H2O liquid membrane system containing a series of macrocyclic polyether carriers

Carrier-mediated cation fluxes were determined using a H₂OCHC1₃H₂O liquid merebrane system for TlNO₃ and for binary mixtures of either TlNO₃ or KNO₃ with alkali metal ions, alkaline earth metal ions, and Pb²⁺ (in the case of TlNO₃). Both macrocyclic polyether and cryptand ligands were used as carriers. In Tl⁺Mⁿ⁺ mixtures, selective transport of Tl⁺ was found over all cations studied, except in the cases of Ag⁺ by 2.2 and of Pb²⁺ by 18C6, DC18C6, ClDKP18C6, and 2.2. Generally, K⁺ was transported selectively from K⁺Mⁿ⁺ mixtures, except in the cases of K⁺Tl⁺ mixtures in which Tl⁺ was transported selectively in all cases. A model relating cation flux to log K(CH₃OH) for Mⁿ⁺—macrocycle interaction and to ion-partitioning between the organic and aqueous phases was successful in rationalizing selective cation transport in most of the systems studied.     

Stereospecific vinyl substitutions occurring by free radical addition-elimination

The free radical chain reaction between cyclohexyl-HgCl and ($\text{E}$) or ($\text{Z}$) MeO₂CCH=CHSnBu₃, MeO₂CCH=CHI, or ClCH=CHHgCl forms MeO₂CCH=CHC₆H₁₁ or ClCH=CHC₆H₁₁ in a stereospecific manner with retention of stereochemistry.     

Chromatic uniqueness and equivalence of K4 homeomorphs

We derive a new formula for the chromatic polynomial of any K₄ homeomorph. We obtain a large family of chromatically unique K₄ homeomorphs. We obtain seven infinite pairs of chromatically equivalent nonisomorphic K₄ homeomorphs.     

The determination of zinc,cadmium, lead and copper in human hair by differential pulse anodic stripping voltammetry at a hanging mercury drop electrode after nitrate fusion

Samples of hair are digested with nitric acid and fused with alkali metal nitrates, prior to the determination of Zn, Cd, Pb and Cu by differential pulse anodic stripping voltammetry at a hanging mercury drop electrode. Recoveries from spiked samples range from 91 to 101%. Relative standard deviations vary from 2.6 to 13%, depending on the metal and sample source. Some causes of poor reproducibility are discussed.