Measurement of the positive muon anomalous magnetic moment to 0.7 ppm

A higher precision measurement of the anomalous g value, a(mu)=(g-2)/2, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron, based on data collected in the year 2000. The result a(mu(+))=11 659 204(7)(5)x10(-10) (0.7 ppm) is in good agreement with previous measurements and has an error about one-half that of the combined previous data. The present world average experimental value is a(mu)(expt)=11 659 203(8)x10(-10) (0.7 ppm).     

The NC-proximal average for multiple functions

The NC-proximal average is a parametrized function used to continuously transform one proper, lsc, prox-bounded function into another. Until now it has been defined for two functions. The purpose of this article is to redefine it so that any finite number of functions may be used. The layout generally follows that of Hare (SIAM J Optim 20(2):650–666, 2009), extending those results to the more general case and in some instances giving alternate proofs by using techniques developed after the publication of that paper. We conclude with an example examining the discontinuity of the minimizers of the NC-proximal average.     

On cycles for the doubling map which are disjoint from an interval

Let \(T:[0,1]\rightarrow [0,1]\) be the doubling map and let \(0 . We say that an integer \(n\ge 3\) is bad for \((a,b)\) if all \(n\) -cycles for \(T\) intersect \((a,b)\) . Let \(B(a,b)\) denote the set of all \(n\) which are bad for \((a,b)\) . In this paper we completely describe the sets: $$\begin{aligned} D_2=\{(a,b) : B(a,b)\,\text {is finite}\} \end{aligned}$$ and $$\begin{aligned} D_3=\{(a,b) : B(a,b)=\varnothing \}. \end{aligned}$$ In particular, we show that if \(b-a<\frac{1}{6}\) , then \((a,b)\in D_2\) , and if \(b-a\le \frac{2}{15}\) , then \((a,b)\in D_3\) , both constants being sharp.     

Beta-expansions for infinite families of Pisot and Salem numbers

This paper continues the study of beta-expansions of 1 where β is a Pisot or Salem number. Special attention is given to regular Pisot numbers, and the Salem numbers that approach these Pisot numbers.     

A classification of (some) Pisot-Cyclotomic numbers

A complete classification of degree 2, 3 and degree 4 Pisot-Cyclotomic numbers is given. Some examples of higher degrees are also given. Pisot-Cyclotomic numbers have applications to quasicrystals and quasilattices.     

The Size of Max(p) Sets and Density Bases

In this article we use a generalization of the classical Perron tree construction to derive newthinness conditions which must be satisfied by directions of rectangles which differentiate characteristic functions or define L^pL^p bounded maximal operators. For example, we prove that such sets of directions must be of Hausdorff dimension less than one and have thickness zero.     

On the cardinality of positively linearly independent sets

Positive bases, which play a key role in understanding derivative free optimization methods that use a direct search framework, are positive spanning sets that are positively linearly independent. The cardinality of a positive basis in \(\mathbb {R}^n\) has been established to be between \(n+1\) and 2n (with both extremes existing). The lower bound is immediate from being a positive spanning set, while the upper bound uses both positive spanning and positively linearly independent. In this note, we provide details proving that a positively linearly independent set in \(\mathbb {R}^n\) for \(n \in \{1, 2\}\) has at most 2n elements, but a positively linearly independent set in \(\mathbb {R}^n\) for \(n\ge 3\) can have an arbitrary number of elements.     

Hydrated electron extinction coefficient revisited

The extinction coefficient of the hydrated electron (e(-))aq generated by pulse radiolysis is evaluated relative to the methyl viologen radical cation (*)MV(+), whose extinction coefficient at 605 nm has been carefully measured in the past. We find that the room temperature (e(-))aq extinction coefficients reported in the literature are underestimated by 10-20%. We obtain = 22,700 M(-1) cm(-1) for the 20 degrees C hydrated electron at 720 nm, assuming the (*)MV(+) extinction is 13,700 M(-1) cm(-1) at 605 nm. This has implications both for second-order reaction rate measurements of (e(-))aq and for the estimate of its integrated oscillator strength.     

Individually addressable microelectrode array for monitoring oxygen and nitric oxide release

We have fabricated a six individual addressable gold working electrode microarray. The device is wirebonded to an eight-pin DIL package that can be easily interconnected to an external multi-channel potentiostat. A polyion complex film coating on the electrode surface provides a suitable coating for the growth of cells. The responses of oxygen and nitric oxide were assessed on uncoated and coated devices using electroanalytical methods. The film coating reduced the diffusion current by approximately 20% in both cases. No changes in the electrochemical mechanism were observed. Simultaneous recordings were obtained for 2 h in the presence of the cells, thus the device is stable for the duration of the bioanalytical measurements. Measurements were conducted to study the simultaneous changes in oxygen and nitric oxide levels in cultured fibroblast cells in the presence of growth hormones that cause cell proliferation. Increases in oxygen consumption of the cells were coupled with increases in nitric oxide levels when in the presence of the growth hormones. Use of a biological detergent to cause an oxidative burst resulted in a large increase in the current for potentials set to detect nitric oxide and oxygen.