Photophysical aspects of single-molecule detection by two-photon excitation with consideration of sequential pulsed illumination.

An important goal in single molecule fluorescence correlation spectroscopy is the theoretical simulation of the fluorescence signal stemming from individual molecules and its autocorrelation function. The simulation approaches developed up to now are based exclusively on continuous-wave (cw) illumination and consequently on cw-excitation. However, this approximation is no longer valid in the case of two-photon excitation, for which pulsed illumination is usually employed. We present a novel theoretical model for the simulation of the fluorescence signal of single molecules and its autocorrelation function with consideration of the time dependence of the excitation flux and thus of all illumination-dependent photoprocesses: two-photon excitation, induced emission and photobleaching. Further important characteristics of our approach are the consideration of the dependence of the photobleaching rate on illumination and the low intersystem-crossing rates of the studied coumarins. Moreover, using our approach, we can predict quantitatively the effect of the laser pulse width on the fluorescence signal of a molecule, that is, the contributions of the photobleaching and saturation effects, and thus we can calculate the optimal laser pulse width. The theoretical autocorrelation functions were fitted to the experimental data, and we could ascertain a good agreement between the resulting and the expected parameters. The most important parameter is the photobleaching constant sigma, the cross section of the transition Sn<--S1, which characterises the photostability of the molecules independent of the experimental conditions. Its value is 1.7 x 10(-23) cm2 for coumarin 153 and 5 x 10(-23) cm2 for coumarin 314.     

Advanced kinetic tools for the evaluation of decomposition reactions

Summary An advanced kinetic study on the thermal behaviour of pyrotechnic ignition mixtures has been carried out by differential scanning calorimetry using different B/KNO3 mixtures (50:50, 30:70, 20:80) as a model reaction. The experimental conditions applied (isochoric conditions/closed crucibles and isobaric conditions/open crucibles) as well as the composition of the mixtures noticeably influences the relative thermal stabilities of the energetic materials. The kinetic study focused on the prediction of the thermal stability of the different mixtures both in extended temperature ranges and under temperature conditions at which ordinary investigation would be very difficult. Using advanced numerical tools [1], thermal ageing and influence of the complex thermal environment on the heat accumulation conditions were computed. This can be done for any surrounding temperature profile such as isothermal, non-isothermal, stepwise, modulated, shock, adiabatic conditions and additionally for temperature profiles reflecting real atmospheric temperature changes (yearly temperature profiles of different climates with daily minimal and maximal fluctuations). Applications of accurate decomposition kinetics enabled the determination of the time to maximum rate under adiabatic conditions (TMR_ad) with a precision given by the confidence interval of the predictions. This analysis can then be applied for the examination of the effects of the surrounding temperature for safe storage or transportation conditions (e.g. determination of the safe transport or storage temperatures).     

Surface transient effects in ultralow‐energy Cs+ sputtering of Si

This study examines the dependence of the sputter rate and the transient width (z_tr) as a function of Cs⁺ primary ion energy (impact energy (E_p) = 320 eV, 500 eV and 1 keV) and incident angles between 0 and 70° . The instrument used was the ATOMIKA 4500 SIMS depth profiler and the sample was Si with ten delta layers of Si_0.7 Ge_0.3. We observed the narrowest transient widths of between 1.4 and 2.0 nm apparent depth. This was achieved at incident angles (θ) of 30–50° . An extended transient effect was observed when profiled at θ > 50° . Below this incident angle, the transient width is less than twice the penetration depth (z_tr < 2R_norm). At minimum z_tr, z_tr ≈ R_norm. The detection sensitivity is best achieved at θ ≈ 30° for all energies investigated. The sputter rate is lowest at normal incidence, rising gradually to a maximum at θ ≈ 50–60° . This is similar to that observed with ultralow‐energy O₂⁺ primary ion beams. 1 At ultralow energies, reducing E_p does not have a significant effect in reducing z_tr. We conclude that for E_p < 1 keV, the optimum condition to achieve minimum z_tr while maintaining good sensitivity and high sputter rate is at θ ≈ 30° . Copyright © 2007 John Wiley & Sons, Ltd.     

Traveling waves for a four-compartment lattice epidemic system with exposed class and standard incidence

This paper is considering the problem of traveling wave solutions (TWS) for a susceptible-exposed-infectious-recovered (SEIR) epidemic model with discrete diffusion. The threshold condition for the existence and nonexistence of TWS is obtained. More specifically, such kind of solutions are governed by the threshold number ?₀. We can find a critical wave speed c^? if ?₀ > 1, by employing the Schauder's fixed point theorem, limiting argument and two-sided Laplace transform, we confirm that there exists TWS for c > c^?, while there exists no TWS for c < c^?. We also obtain the nonexistence of TWS for ?₀ ≤ 1. At last, we give some biological explanations from the epidemiological perspective.     

?*-extensions of tori, higher chow groups and applications to incidence equivalence relations for algebraic cycles

LetX be a smooth projective variety over an algebraically closed fieldk. We repeat Bloch's construction of aG _m -biextension (torseur)E over CH _hom ^p (X)×CH _hom ^q (X) forp+q=dim(X)+1. First we show that in characteristic zeroE comes via pullback from the Poincaré biextension over the corresponding product of intermediate Jacobians which has been conjectured by Bloch and Murre. Then the relations betweenE and various equivalence relations for algebraic cycles are studied. In particular we reprove Murre's theorem stating that Griffiths' conjecture holds for codimension 2 cycles, i.e. every 2-codimensional cycle which is algebraically and incidence equivalent to zero has torsion Abel-Jacobi invariant.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

An Arithmetic Reduction of Finite Rank 3 Geometries with Linear Spaces as Plane Residues and with Dual Linear Spaces as Point Residues

Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons.