Monomer Concentrations in Simple Micellar Systems from NMR Relaxation Times and C‐13 Chemical Shifts

The monomer concentrations for some simple micelle forming surfactants, octylammonium bromide (OTAB), sodium decyl sulphate, SDecS, and dodecyltrimethylammonium bromide (DTAB) were determined from the NMR‐paramagnetic relaxation enhancement experiment (the NMR‐PRE) on the H‐1 spin lattice relaxation times for the surfactant protons as a function of the surfactant concentration above and below the critical micelle concentration (cmc region). The NMR relaxation times, determined from the inversion recovery method, decrease steadily as the concentration of the surfactant is increased above the cmc value. A second, simple method is proposed whereby the p‐value of the surfactant in the micelle is determined from the two‐site model via extrapolation of the observed relaxation rate data to high concentrations. The p‐values and the calculated monomer concentrations are compared to each other and to those obtained using the mass‐action and phase separation models. In most cases, the monomer concentrations appear to remain constant at concentrations up to 2–3 times the cmc value, and then begin to decrease thereafter. These results are compared to the trends in monomer concentrations obtained from other NMR experiments in other surfactant systems.     

Approximation of throughput in tandem queues with multiple servers and blocking

In this paper, we develop an approximation method for throughput in tandem queues with multiple independent reliable servers at each stage and finite buffers between service stations. We consider the blocking after service (BAS) blocking protocol of each service stage. The service time distribution of each server is exponential. The approximation is based on the decomposition of the system into a set of coupled subsystems which are modeled by two-stage tandem queue with two buffers and are analyzed by using the level dependent quasi-birth-and-death (LDQBD) process.     

Fourier Transform EPR Spectroscopy of Trityl Radicals for Multifunctional Assessment of Chemical Microenvironment

Pulse techniques in electron paramagnetic resonance (EPR) allow for a reduction in measurement times and increase in sensitivity but require the synthesis of paramagnetic probes with long relaxation times. Here it is shown that the recently synthesized phosphonated trityl radical possesses long relaxation times that are sensitive to probe the microenvironment, such as oxygenation and acidity of an aqueous solution. In principle, application of Fourier transform EPR (FT‐EPR) spectroscopy makes it possible to acquire the entire EPR spectrum of the trityl probe and assess these microenvironmental parameters within a few microseconds. The performed analysis of the FT‐EPR spectra takes into consideration oxygen‐, proton‐, buffer‐, and concentration‐induced contributions to the spectral shape, therefore enabling quantitative and discriminative assessment of pH, pO₂, and concentrations of the probe and inorganic phosphate.     

Fractional smoothness for the generalized local time of the indefinite Skorohod integral

Let be the indefinite Skorohod integral on Wiener space (Ω,H,P), and let Lt(x) be its the generalized local time introduced by Tudor in [C.A. Tudor, Martingale-type stochastic calculus for anticipating integral processes, Bernoulli 10 (2004) 313-325]. We prove that the generalized local time, as a nonlinear functional of ω, is in the fractional Sobolev spaces Dα,p ( and p>2) under some conditions imposed on the anticipating integrand u via the technique of Malliavin calculus and the K-method in the real interpolation theory. The result is optimal for the fractional Brownian motion with the Hurst parameter .     

Fluctuation Identities Applied to the Hitting Time of a Half-line in the Plane

We study asymptotic estimates that contain the hitting time and the hitting place of a half-line by a two-dimensional random walk. Fluctuation identities are used without resorting to pair annihilation but by interchanging summation and integration. The same method applies to the hitting of the half-space by a one-dimensional random walk. The author was supported by a grant (no. 18740053) of Japan Society for the Promotion of Science.     

Pricing double-barrier options under a flexible jump diffusion model

In this paper we present a Laplace transform-based analytical solution for pricing double-barrier options under a flexible hyper-exponential jump diffusion model (HEM). The major theoretical contribution is that we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution.     

The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach

In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.     

Sampling frequency,response times and embedded signal filtration in fast,high efficiency liquid chromatography: A tutorial

With increasingly efficient columns, eluite peaks are increasingly narrower. To take full advantage of this, choice of the detector response time and the data acquisition rate a.k.a. detector sampling frequency, have become increasingly important. In this work, we revisit the concept of data sampling from the theorem variously attributed to Whittaker, Nyquist, Kotelnikov, and Shannon. Focusing on time scales relevant to the current practice of high performance liquid chromatography (HPLC) and optical absorbance detection (the most commonly used method), even for very narrow simulated peaks Fourier transformation shows that theoretical minimum sampling frequency is still relatively low (<10 Hz). However, this consideration alone may not be adequate for real chromatograms when an appreciable amount of noise is present. Further, depending on the instrument, the manufacturer's choice of a particular data bunching/integration/response time condition may be integrally coupled to the sampling frequency. In any case, the exact nature of signal filtration often occurs in a manner neither transparent to nor controllable by the user. Using fast chromatography on a state-of-the-art column (38,000 plates), we evaluate the responses produced by different present generation instruments, each with their unique black box digital filters. We show that the common wisdom of sampling 20 points per peak can be inadequate for high efficiency columns and that the sampling frequency and response choices do affect the peak shape. If the sampling frequency is too low or response time is too large, the observed peak shapes will not remain as narrow as they really are – this is especially true for high efficiency and high speed separations. It is shown that both sampling frequency and digital filtering affect the retention time, noise amplitude, peak shape and width in a complex fashion. We show how a square-wave driven light emitting diode source can reveal the nature of the embedded filter. We discuss time uncertainties related to the choice of sampling frequency. Finally, we suggest steps to obtain optimum results from a given system.