Quadratic variation functionals and dilation equations

Here we present some distribution function inequalities between certain functionals defined relative to a convolution approximation procedure. Such inequalities are best known when the approximation is made using dilations of the Gaussian or Cauchy kernels. In these cases, classical differential equations, the heat equation or Laplace's equation, provide the basis for comparisons; in the latter case, the quadratic functional is known as the Lusin area integral. The kernels we consider are compactly supported, and satisfy a dilation equation, rather than a differential equation. For these kernels, there is an intrinsic quadratic variation, defined from the dilation structure. We obtain good lambda distribution function inequalities between a maximal function and the quadratic variation functional.     

Ester Carbonyl Vibration as a Sensitive Probe of Protein Local Electric Field

The ability to quantify the local electrostatic environment of proteins and protein/peptide assemblies is key to gaining a microscopic understanding of many biological interactions and processes. Herein, we show that the ester carbonyl stretching vibration of two non‐natural amino acids, L ‐aspartic acid 4‐methyl ester and L ‐glutamic acid 5‐methyl ester, is a convenient and sensitive probe in this regard, since its frequency correlates linearly with the local electrostatic field for both hydrogen‐bonding and non‐hydrogen‐bonding environments. We expect that the resultant frequency–electric‐field map will find use in various applications. Furthermore, we show that, when situated in a non‐hydrogen‐bonding environment, this probe can also be used to measure the local dielectric constant (ε). For example, its application to amyloid fibrils formed by Aβ_16–22 revealed that the interior of such β‐sheet assemblies has an ε value of approximately 5.6.     

NO reduction with C3H8 on Co/Al2O3 catalyst. effect of O2 concentration

The selective catalytic reduction (SCR) of NO by propane in excess oxygen-containing gas mixture was studied on Co/Al₂O₃ catalyst. The oxygen concentration is very important for the reaction. The NO conversion to N₂ without oxygen is 3% at 800 K and when the O₂ concentration is raised up to 8% the NO conversion reaches its maximum value of 60% at 800 K. Characterization results by TPR and UV-Vis spectroscopy show that in the catalyst, species strongly interacting with tetrahedral and octahedral Co²⁺ ions in the support are present. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Number of Embeddings of Minimally Rigid Graphs

Rigid frameworks in some Euclidean space are embedded graphs having a unique local realization (up to Euclidean motions) for the given edge lengths, although globally they may have several. We study the number of distinct planar embeddings of minimally rigid graphs with $n$ vertices. We show that, modulo planar rigid motions, this number is at most ${{2n-4}\choose {n-2}} \approx 4^n$. We also exhibit several families which realize lower bounds of the order of $2^n$, $2.21^n$ and $2.28^n$. For the upper bound we use techniques from complex algebraic geometry, based on the (projective) Cayley--Menger variety ${\it CM}^{2,n}(C)\subset P_{{{n}\choose {2}}-1}(C)$ over the complex numbers $C$. In this context, point configurations are represented by coordinates given by squared distances between all pairs of points. Sectioning the variety with $2n-4$ hyperplanes yields at most $deg({\it CM}^{2,n})$ zero-dimensional components, and one finds this degree to be $D^{2,n}=\frac{1}{2}{{2n-4}\choose {n-2}}$. The lower bounds are related to inductive constructions of minimally rigid graphs via Henneberg sequences. The same approach works in higher dimensions. In particular, we show that it leads to an upper bound of $2 D^{3,n}= {({2^{n-3}}/({n-2}})){{2n-6}\choose{n-3}}$ for the number of spatial embeddings with generic edge lengths of the $1$-skeleton of a simplicial polyhedron, up to rigid motions. Our technique can also be adapted to the non-Euclidean case.     

Enumerating Constrained Non-crossing Minimally Rigid Frameworks

In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints, which we call constrained non-crossing Laman frameworks, on a given set of n points in the plane. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph in O(n ⁴) time and O(n) space, or, with a slightly different implementation, in O(n ³) time and O(n ²) space. In particular, we obtain that the set of all the constrained non-crossing Laman frameworks on a given point set is connected by flips which preserve the Laman property. D. Avis’s research was supported by NSERC and FQRNT grants. N. Katoh’s, M. Ohsaki’s and S.-i. Tanigawa’s research was supported by NEXT Grant-in-Aid for Scientific Research on priority areas of New Horizons in Computing. I. Streinu’s research was supported by NSF grant CCF-0430990 and NSF-DARPA CARGO CCR-0310661.     

The calculation of the detection efficiency in the calibration of gross alpha–beta systems

This paper presents a method for efficiency calibration of a measuring alpha–beta system PROTEAN ORTEC, MPC-2000-DP, using standard radioactive sources. The system is used to measure gross alpha–beta activity concentrations in environmental samples. The calculated efficiencies of detection were subsequently introduced in the system for two working geometries: measuring geometry—gross alpha–beta $ \varepsilon_{\alpha }^{g} $  = 31,37 ± 0.25 (%)—the alpha efficiency and $ \varepsilon_{\beta }^{g} $  = 44.94 ± 0.69 (%)—the beta efficiency, where the spillover factor is $ X_{\text{talk}}^{g} $  = 25.59 ± 0.50 (%) and measuring geometry up alpha–beta $ \varepsilon_{\alpha }^{u} $  = 36.23 ± 0.29 (%)—the alpha efficiency and $ \varepsilon_{\beta }^{u} $  = 48.53 ± 0.74 (%)—the beta efficiency, where the spillover factor is $ X_{\text{talk}}^{u} $  = 31.08 ± 0.60 (%).     

Some particular aspects of the low-temperature oxidation of methane initiated by nitric acid

During methane oxidation initiated by nitric acid or nitrogen dioxide, it is possible to observe, under certain conditions of temperature, initiator content, and flow rates, the formation of an adiabatic “temperature peak.” Because the maximum temperature of the peak does not exceed the initial temperature of the reactor by more than 220°C, the recorded temperature-increase curves were used for a kinetic interpretation. The obtained kinetic parameters (overall n and E) agree with the values reported in the literature for isothermal methane oxidation and suggest that the overall mechanism does not change in the conditions of “temperature peak.”