Measurement of unstable burning velocities of iso-octane–air mixtures at high pressure and the derivation of laminar burning velocities

A new technique is reported for measuring burning velocities at high pressures in the final stages of two inwardly propagating flame kernels in an explosion bomb. The flames were initiated at diametrically opposite spark electrodes, close to the wall, in quiescent mixtures. Measurements of pressure and flame kernel propagation speeds by high-speed photography showed the burning velocities to be elevated above the corresponding laminar burning velocities as a result of the developing flame instabilities. The enhancement increased with increase in pressure and decreased with increase in Markstein number. When the Markstein number was negative, instabilities could be appreciable, as could the enhancement. For the iso-octane–air mixtures investigated, where the mixtures had well-characterised Markstein numbers or critical Peclet numbers at the relevant pressures and temperatures, it was possible to explain the enhancement quantitatively by the spherical explosion flame instability theory of Bechtold and Matalon, provided the critical Peclet number was that observed experimentally, and allowance was made for the changing pressure. With this theoretical procedure, it was possible to derive values of laminar burning velocity from the measured values of burning velocity over a wide range of equivalence ratios, pressures, and temperatures. The values became less reliable at the higher temperatures and pressures as the data on Markstein and critical Peclet numbers became less certain. It was found that with iso-octane as the fuel the laminar burning velocity decreased during isentropic compression.     

Nuclear orientation below 1 mK: Development and applications

The Oxford top-loading PrNi₅ nuclear demagnetisation stage /1/ has been further developed to reach temperatures below 1 mK. The hyperfine field for⁷¹As in nickel has been measured by low temperature nuclear orientation as 14.61(36)T. Measurements on transitions in⁷¹Ge yield spin values 3/2 (1299 kev and 1139 kev) and 5/2 (1027 kev) and 5 E2/M1 mixing ratios are given.     

A stationary,pairwise independent,absolutely regular sequence for which the central limit theorem fails

Summary A strictly stationary finite-state non-degenerate random sequence is constructed which satisfies pairwise independence and absolute regularity but fails to satisfy a central limit theorem. The mixing rate for absolute regularity is only slightly slower than that in a corresponding central limit theorem of Ibragimov.This work was partially supported by NSF grant DMS 86-00399     

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.     

2,3,7,8,12,13‐Hexaaryltruxenes: An ortho‐Substituted Multiarm Design and Microwave‐Accelerated Synthesis toward Starburst Macromolecular Materials with Well‐Defined π Delocalization

We present herein a novel design and the efficient synthesis towards a “homogeneous” starburst fluorene system based on the novel 2,3,7,8,12,13‐hexaaryltruxene scaffold. Controlled microwave heating provides a facile and powerful approach for each step in the synthesis of these bulky materials with large steric hindrance, suggesting an avenue to access structurally well‐defined complex organic semiconductors (OSCs) rapidly and conveniently with high yield and purity. The resulting materials exhibited good thermal stability and an excellent glassy structure as revealed by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) as well as wide‐angle X‐ray diffraction (WAXD) studies. Moreover, compared with their corresponding three‐arm‐substituted counterparts T1 – T4 , the introduction of the ortho substituents around the truxene core in Tr1 – Tr4 results in significant blueshifts (of 7–24 nm) of the absorption maxima λ_max and higher energy optical gaps (E_g). Comparative studies with corresponding linear, rod‐shaped oligofluorene counterparts (OFX) have revealed that the longest para‐conjugated segment in the TrX (X=1–4) structures plays the dominant role in determining their electronic properties. UV/Vis data and cyclic voltammetry (CV) investigations have indicated that there is little electronic interaction between the arms, even for the shortest armed oligomer Tr1 . A clear linear relationship of both 1/λ_max and E_g with the inverse of (n+1) for these branched systems was found. Our findings highlight a novel molecular design comprising an ortho‐substituted, multiarmed architecture that would allow the introduction of isotropic physical and/or mechanical properties, while at the same time maintaining most of the important electronic properties of the rod‐shaped constituents of a fully conjugated system.     

On the Tutte–Krushkal–Renardy polynomial for cell complexes

Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte–Krushkal–Renardy polynomial evaluated at the origin gives a weighted count of cellular spanning trees, and therefore its free term can be calculated by the cellular matrix-tree theorem of Duval et al. In the case of cell decompositions of a sphere, this modified polynomial satisfies the same duality identity as the original polynomial. We find that evaluating the Tutte–Krushkal–Renardy along a certain line gives the Bott polynomial. Finally we prove skein relations for the Tutte–Krushkal–Renardy polynomial.     

Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications

Given a simply connected nilpotent Lie group having unitary irreducible representations that are square-integrable modulo the center, we use operator-valued periodization to give a range-function type characterization of shift-invariant spaces of function on the group. We then give characterizations of frame and Riesz families for shift-invariant spaces.     

Symbolical Algebra as a Foundation for Calculus: D. F. Gregory's Contribution

Duncan Farquharson Gregory (1813–1844) was a mathematician and founder of the Cambridge Mathematical Journal. His 1841 Examples of the Processes of the Differential and Integral Calculus was an extensive revision of Peacock's 1820 textbook of a similar title. Among the new material in Gregory's version is an exposition of symbolical algebra, prominently featuring the method of “separation of symbols.” We examine Gregory's career; the mathematicians he influenced; and Servois and Murphy, who influenced him. We consider Gregory's use of separation of symbols in the Examples and consider whether he believed these techniques to be capable of providing an adequate foundation for calculus. © 2002 Elsevier Science (USA).Le mathématicien Duncan Farquharson Gregory (1813–1844) fut également fondateur du Cambridge Mathematical Journal. Son ouvrage publié en 1841, Examples of the Processes of the Differential and Integral Calculus, constitue une révision substantielle du livre de Peacock au titre similaire. L'un des apports du livre de Gregory est un exposé de l'algèbre symbolique, et en particulier de la méthode de séparation des symboles. Dans cet article nous passons en revue la carrière de Gregory et nous parlons des mathématiciens qu'il a influencés, ainsi que de l'influence que Servois et Murphy ont eu sur ses travaux. Nous considérons son usage de la séparation des symboles dans ses Examples, et nous examinons si Gregory croyait que ses techniques pouvaient constituer un fondement pour le calcul différentiel. © 2002 Elsevier Science (USA).MSC 1991 subject classifications: 01A55, 01A70, 01A50, 26-03, 26A03, 34-03, 34A30.