Overmodulation of projections as signal‐to‐noise enhancement method in EPR imaging

A study concerning the image quality in electron paramagnetic resonance imaging in two‐dimensional spatial experiments is presented. The aim of the measurements was to improve the signal‐to‐noise ratio (SNR) of the projections and the reconstructed image by applying modulation amplitude higher than the radical electron paramagnetic resonance linewidth. Data were gathered by applying four constant modulation amplitudes, where one was below 1/3 (A_mod = 0.04 mT) of the radical linewidth (ΔB_pp = 0.14 mT). Three other modulation amplitude values were used in this experiment, leading to undermodulated (A_mod < 1/3 ΔB_pp), partially overmodulated (A_mod ~ 1/3 ΔB_pp) and fully overmodulated (A_mod > > 1/3 ΔB_pp) projections. The advantages of an applied overmodulation condition were demonstrated in the study performed on a phantom containing four shapes of 1.25 mM water solution of 2, 2, 6, 6‐tetramethyl‐1‐piperidinyloxyl. It was shown that even when the overmodulated reference spectrum was used in the deconvolution procedure, as well as the projection itself, the phantom shapes reconstructed as images directly correspond to those obtained in undermodulation conditions. It was shown that the best SNR of the reconstructed images is expected for the modulation amplitude close to 1/3 of the projection linewidth, which is defined as the distance from the first maximum to the last minimum of the gradient‐broadened spectrum. For higher modulation amplitude, the SNR of the reconstructed image is decreased, even if the SNR of the measured projection is increased. Copyright © 2015 John Wiley & Sons, Ltd.     

A Lower Estimation of the Hausdorff Dimension for Attractors with Overlaps

We give a lower estimate of the Hausdorff dimension for attractors which can be obtained by an overlapping construction.     

A Note on Transient Gaussian Fluid Models

In this paper we study the distribution of the supremum over interval [0,T] of a centered Gaussian process with stationary increments with a general negative drift function. This problem is related to the distribution of the buffer content in a transient Gaussian fluid queue Q(T) at time T, provided that at time 0 the buffer is empty. The general theory is illustrated by detailed considerations of different cases for the integrated Gaussian process and the fractional Brownian motion. We give asymptotic results for P(Q(T)>x) and P(sup _0tT Q(t)>x) as x.     

Self‐Intersection Local Time for 𝒮′(ℝd)‐Ornstein‐Uhlenbeck Processes Arising from Immigration Systems

Fluctuation limits of an immigration branching particle system and an immigration branching measure‐valued process yield different types of 𝒮′(ℝ^d)‐valued Ornstein‐Uhlenbeck processes whose covariances are given in terms of an excessive measure for the underlying motion in Rd, which is taken to be a symmetric α‐stable process. In this paper we prove existence and path continuity results for the self‐intersection local time of these Ornstein‐Uhlenbeck processes. The results depend on relationships between the dimension d and the parameter α.     

On the mixed problem for hyperbolic partial differential-functional equations of the first order

We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order where is a function defined by z _(x,y)(t, s) = z(x + t, y + s), (t, s) [–, 0] × [0, h]. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.     

Column Chromatography and Preparative TLC for Isolation and Purification of Coumarins from Peucedanum verticillare L. Koch ex DC

JPC – Journal of Planar Chromatography – Modern TLC - Preparative separation and isolation of coumarins from petroleum ether and methanol extracts of the fruits and roots of Peucedanum...     

Diffusion in a Weakly Random Hamiltonian Flow

We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves undergoes a spatial diffusion.     

On commutators of equivariant homeomorphisms

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a G-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case of diffeomorphisms. The theorem is a starting point for computing H₁(HG(M)) for more complicated G-manifolds.     

Stationarity of Lagrangian Velocity¶in Compressible Environments

We study the transport of a passive tracer particle by a random d-dimensional, Gaussian, compressible velocity field. It is well known, since the work of Lumley, see [13], and Port and Stone, see [20], that the observations of the velocity field from the moving particle, the so-called Lagrangian velocity process, are statistically stationary when the field itself is incompressible. In this paper we study the question of stationarity of Lagrangian observations in compressible environments. We show that, given sufficient temporal decorrelation of the velocity statistics, there exists a transformation of the original probability measure, under which the Lagrangian velocity process is time stationary. The transformed probability is equivalent to the original measure. As an application of this result we prove the law of large numbers for the particle trajectory. Received: 1 May 2001 / Accepted: 4 December 2001