Largeness of the set of finite products in a semigroup

We investigate when the set of finite products of distinct terms of a sequence 〈x _n 〉 _n=1^∞ in a semigroup (S,⋅) is large in any of several standard notions of largeness. These include piecewise syndetic, central, syndetic, central*, and IP*. In the case of a “nice” sequence in (S,⋅)=(ℕ,+) one has that FS(〈x _n 〉 _n=1^∞) has any or all of the first three properties if and only if {x _n+1−∑ _t=1 ⁿ x _t :n∈ℕ} is bounded from above. N. Hindman acknowledges support received from the National Science Foundation via Grant DMS-0554803.     

Semiconductor Research Needs in the Nanoscale Physical Sciences: A Semiconductor Research Corporation Working Paper

The purpose of this paper is to identify areas in the basic physical sciences where additional research is needed to sustain the extraordinary progress in electronics that has now extended for several decades. Also, it is argued that basic research will provide the foundation for the discovery of new generations of nanoelectronic devices that will continue the experimental rate of reduction in cost per function. Some of the fundamental areas requiring further research are the chemistry and physics of material interfaces, conductivity at small dimensions, deterministic doping effects, and nanomagnetics. Discovery research also is needed in the functional synergy of nanoelectronic materials and non-traditional fabrication methods.     

Influence of Molecular Conformation on the Constitutive Response of Polyethylene: A Comparison of HDPE, UHMWPE, and PEX

The current work presents the characterization and comparison of the mechanical response of three different industrial forms of polyethylene. Specifically, high-density polyethylene (HDPE), ultra high molecular weight polyethylene (UHMWPE), and cross-linked polyethylene (PEX) were tested in compression as a function of temperature (−75 to 100°C) and strain-rate (10⁻⁴ to 2,600 s⁻¹). The responses of UHMWPE and PEX are very similar, whereas HDPE exhibits some differences. The HDPE samples display a significantly higher yield stress followed by a flat flow behavior. Conversely UHMWPE and PEX both exhibit significant strain hardening after yield. The temperature and strain-rate dependence are captured by simple linear and logarithmic fits over the full range of conditions investigated. The yield behavior is presented in terms of an empirical mapping function that is extended to analytically solve for the mapping constant. The power-law dependence on strain-rate observed in some polymers is explained using this mapping function.     

Two new eudesmane derivatives from Verbesina virginica

<正>Two new eudesmane derivatives were isolated from the leaves and flowers of Verbesina virginica,along with the known 6-O-β-E -p-coumaroyl-4α-hydroxyeudesmane(1).Their structures were determined as 6-O-β-Z-p-coumaroyl-4α-hydroxyeudesmane(2) and 6-O-α-E-p-coumaroyl-1β-4α-dihydroxyeudesmane(3) by spectroscopic methods.     

Binuclear cyclopentadienylcobalt sulfur and phosphinidene complexes Cp2Co2E2 (E = S, PX): Comparison with their Iron carbonyl analogues

Density functional theory studies on a series of Cp₂Co₂E₂ derivatives (E = S and PX; X = H, Cl, OH, OMe, NH₂, NMe₂) predict global minimum butterfly structures with one Co-Co bond for the “body” of the butterfly and four Co-E bonds at the edges of the “wings” of the butterfly. Tetrahedrane structures with both Co-Co and E-E bonds are higher in energy for Cp₂Co₂S₂ and Cp₂Co₂(PH)₂ and are not found in the other systems. This differs from the corresponding Fe₂(CO)₆S₂ and Fe₂(CO)₆(PX)₂ derivatives where tetrahedrane structures are predicted to be the lowest energy structures for all cases except X = NR₂ and OH and such a tetrahedrane structure is found experimentally for Fe₂(CO)₆S₂. The butterfly structures for the Cp₂Co₂E₂ derivatives are of two types. For Cp₂Co₂(PX)₂ (X = H, OH, OMe, NH₂, NMe₂) the lowest energy structures are unsymmetrical butterflies Cp₂Co₂(P)(PX₂) with two X groups on one phosphorus atom and a lone pair on the other (naked) phosphorus atom. Related low-energy unsymmetrical butterfly Fe₂(CO)₆(P)(PX₂) structures, not observed in previous theoretical studies, are now found for the corresponding Fe₂(CO)₆(PX)₂ derivatives. Symmetrical butterfly singlet diradical structures with one X group on each phosphorus atom in relative cis or trans positions are also found for the Cp₂Co₂(PX)₂ derivatives and are the global minima for Cp₂Co₂(PCl)₂ as well as Cp₂Co₂S₂. In all cases the cis structures are of lower energy than the corresponding trans structures. Rhombus structures having neither Co-Co nor E-E bonds are also found for all of the Cp₂Co₂(PX)₂ derivatives but always at higher energies than the butterfly structures, ranging from 17 to 29 kcal/mol above the global minima.     

Detection of heteroplasmy in individual mitochondrial particles

Mitochondrial DNA (mtDNA) mutations have been associated with disease and aging. Since each cell has thousands of mtDNA copies, clustered into nucleoids of five to ten mtDNA molecules each, determining the effects of a given mtDNA mutation and their connection with disease phenotype is not straightforward. It has been postulated that heteroplasmy (coexistence of mutated and wild-type DNA) follows simple probability rules dictated by the random distribution of mtDNA molecules at the nucleoid level. This model has been used to explain how mutation levels correlate with the onset of disease phenotype and loss of cellular function. Nonetheless, experimental evidence of heteroplasmy at the nucleoid level is scarce. Here, we report a new method to determine heteroplasmy of individual mitochondrial particles containing one or more nucleoids. The method uses capillary cytometry with laser-induced fluorescence detection to detect individual mitochondrial particles stained with PicoGreen, which makes it possible to quantify the mtDNA copy number of each particle. After detection, one or more particles are collected into polymerase chain reaction (PCR) wells and then subjected to real-time multiplexed PCR amplification. This PCR strategy is suitable to obtain the relative abundance of mutated and wild-type mtDNA. The results obtained here indicate that individual mitochondrial particles and nucleoids contained within these particles are not heteroplasmic. The results presented here suggest that current models of mtDNA segregation and distribution (i.e., heteroplasmic nucleoids) need further consideration.     

Determination of methylamines and trimethylamine-N-oxide in particulate matter by non-suppressed ion chromatography

An ion chromatography method with non-suppressed conductivity detection was developed for the simultaneous determination of methylamines (methylamine, dimethylamine, trimethylamine) and trimethylamine-N-oxide in particulate matter air samples. The analytes were well separated by means of cation-exchange chromatography using a 3 mM nitric acid/3.5% acetonitrile (v/v) eluent solution and a Metrosep C 2 250 (250 mm × 4 mm i.d.) separation column. The effects of the different chromatographic parameters on the separation were also investigated. Detection limits of methylamine, dimethylamine, trimethylamine, and trimethylamine-N-oxide were 43, 46, 76 and 72 μg/L, respectively. The relative standard deviations of the retention times were between 0.42% and 1.14% while the recoveries were between 78.8% and 88.3%. The method is suitable for determining if methylamines and trimethylamine-N-oxide are a significant component of organic nitrogen aerosol in areas with high concentration of these species.