Law of Sums of the Squares of Areas, Volumes and Hyper-Volumes of Regular Polytopes from Clifford Algebras

Inspired by the recent sums of the squares law obtained by [1] we derive the law of the sums of the squares of the areas, volumes and hyper-volumes associated with the faces, cells and hyper-cells of regular polytopes in diverse dimensions by using Clifford algebraic methods [5].     

Concentration and velocity field measurements by magnetic resonance imaging in aperiodic heterogeneous porous media.

Magnetic resonance imaging (MRI) techniques were investigated as a means to obtain concentration and velocity field measurements for the verification of a stochastic model for conservative chemical transport. MRI techniques were successfully applied to obtain one-dimensional breakthrough images and two-dimensional velocity images along the length of an aperiodic heterogeneous porous medium. Experimental moment data showed the concentration field in the experimental model to be slightly positively skewed. Velocity images showed the velocity field to be relatively uniform with no channeling or preferential flow behavior. Measured covariance functions showed evidence of negative correlation in the velocity field. The detailed spatial information provided by these imaging experiments has demonstrated that MRI is a valuable tool for obtaining experimental data for the verification of existing theoretical models.     

Testing Lorentz invariance and CPT conservation with NuMI neutrinos in the MINOS near detector

A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).     

Binding of nontarget microorganisms from food washes to anti-<Emphasis Type="Italic">Salmonella</Emphasis> and anti-<Emphasis Type="Italic">E. coli</Emphasis> O157 immunomagnetic beads: most probable composition of background Eubacteria

We present herein the composition of bacterial communities occurring in ground chicken and the changes which arise in these populations based upon nonselective partitioning by commercially-available Dynal anti-Salmonella and anti-E. coli O157 immunomagnetic beads (IMB). Our enumeration and colony selection protocol was based upon a 6 × 6 drop plate method (n = 18 for each 25-g sub-sampling) using a dilution which resulted in ca. 4–8 colonies per drop. An average of 82 ± 13 colonies were selected from three 25-g ground chicken subsamplings per batch, each of which was repeated seasonally for one year. DNA was extracted from each colony and the composition of Eubacteria in each of these harvests was determined by sequence-based identification of 16S rDNA amplicons. The Gram-positive bacteria Brochothrix thermosphacta and Carnobacterium maltaromticum were the most commonly found organisms in both the total chicken wash (PBS) and in the IMB-bound (PBS-washed) fractions. The remaining background organisms which also adhered to varying degrees to commercial IMBs were: Pseudomonas oleovorans, Acinetobacter lwoffi, Serratia spp., and one Rahnella spp. A large number of the organisms were also cladistically evaluated based on rDNA basepair disparities: all Brochothrices were monophyletic; twelve different Pseudomonads were found along with eight Carnobacteria, seven Acinetobacteres, four Serratiae, and two Rahnellae. Carnobacterium alone showed an IMB-based concentration enhancement (ca. two to sixfold). Any reference to a brand or firm name does not constitute endorsement of the US Department of Agriculture over others of a similar nature not mentioned     

Quantitative study of interactions between oxygen lone pair and aromatic rings: substituent effect and the importance of closeness of contact

Current models describe aromatic rings as polar groups based on the fact that benzene and hexafluorobenzene are known to have large and permanent quadrupole moments. This report describes a quantitative study of the interactions between oxygen lone pair and aromatic rings. We found that even electron-rich aromatic rings and oxygen lone pairs exhibit attractive interactions. Free energies of interactions are determined using the triptycene scaffold and the equilibrium constants were determined by low-temperature 1H NMR spectroscopy. An X-ray structure analysis for one of the model compounds confirms the close proximity between the oxygen and the center of the aromatic ring. Theoretical calculations at the MP2/aug-cc-pVTZ level corroborate the experimental results. The origin of attractive interactions was explored by using aromatic rings with a wide range of substituents. The interactions between an oxygen lone pair and an aromatic ring are attractive at van der Waals' distance even with electron-donating substituents. Electron-withdrawing groups increase the strength of the attractive interactions. The results from this study can be only partly rationalized by using the current models of aromatic system. Electrostatic-based models are consistent with the fact that stronger electron-withdrawing groups lead to stronger attractions, but fail to predict or rationalize the fact that weak attractions even exist between electron-rich arenes and oxygen lone pairs. The conclusion from this study is that aromatic rings cannot be treated as a simple quadrupolar functional group at van der Waals' distance. Dispersion forces and local dipole should also be considered.     

Iridium(III) Complexes Bearing Pyrene‐Functionalized 1,10‐Phenanthroline Ligands as Highly Efficient Sensitizers for Triplet–Triplet Annihilation Upconversion

“Chemistry‐on‐the‐complex” synthetic methods have allowed the selective addition of 1‐ethynylpyrene appendages to the 3‐, 5‐, 3,8‐ and 5,6‐positions of Ir^III‐coordinated 1,10‐phenanthroline via Sonogashira cross‐coupling. The resulting suite of complexes has given rise to the first rationalization of their absorption and emission properties as a function of the number and position of the pyrene moieties. Strong absorption in the visible region (e.g. 3,8‐substituted Ir‐3 : λ_abs=481 nm, ?=52 400 m ^?1 cm^?1) and long‐lived triplet excited states (e.g. 5‐substituted Ir‐2 : τ_T=367.7 μs) were observed for the complexes in deaerated CH₂Cl₂. On testing the series as triplet sensitizers for triplet–triplet annihilation upconversion, those Ir^III complexes bearing pyrenyl appendages at the 3‐ and 3,8‐positions ( Ir‐1 , Ir‐3 ) were found to give optimal upconversion quantum yields (30.2 % and 31.6 % respectively).     

Vibrational spectra, DFT calculations, unusual structure, anomalous CH2 wagging and twisting modes, and phase-dependent conformation of 1,3-disilacyclobutane

Our previously published infrared and Raman spectra of 1,3-disilacyclobutane (13DSCB) and its 1,1,3,3-d4 isotopomer have been reexamined and partially reassigned on the basis of DFT and ab initio calculations. The calculations confirm previous microwave work that the CSiC angles in the ring are unexpectedly larger than the SiCSi angles. This may arise from the partial charges on the ring atoms. The calculations are in excellent agreement with the observed spectra in both frequency and intensity. They also demonstrate that this molecule has CH2 wagging and twisting vibrations with frequencies below 1000 cm-1, about 200 cm-1 lower than expected. These unprecedented low values can be explained by the decreased slope in the potential energy curves for these vibrations as the sideways motions of the CH2 groups result in attractive forces between the positively charged hydrogens on the carbon atoms and the negatively charged hydrogens on the silicon atoms. The theoretical calculations also confirm the previous conclusions that the individual molecules (vapor) have C2v symmetry whereas in the solid the molecules become planar with D2h symmetry. The vibrational coupling between the ring-angle bending mode and the SiH2 in-phase rocking, which is present for the C2v structure, is forbidden for D2h and hence disappears.     

Precise mass measurement of a double-stranded 500 base-pair (309 kDa) polymerase chain reaction product by negative ion electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd.