Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

A comparison of T2*-weighted magnitude and phase imaging for measuring the arterial input function in the rat aorta following intravenous injection of gadolinium contrast agent

The arterial input function (AIF) is important for quantitative MR imaging perfusion experiments employing Gd contrast agents. This study compared the accuracy of T(2)*-weighted magnitude and phase imaging for noninvasive measurement of the AIF in the rat aorta. Twenty-eight in vivo experiments were performed involving simultaneous arterial blood sampling and MR imaging following Gd injection. In vitro experiments were also performed to confirm the in vivo results. At 1.89 T and TE=3 ms, the relationship between changes in 1/T(2)* in blood (estimated from MR signal magnitude) and Gd concentration ([Gd]) was measured to be approximately 19 s(-1) mM(-1), while that between phase and [Gd] was approximately 0.19 rad mM(-1). Both of these values are consistent with previously published results. The in vivo phase data had approximately half as much scatter with respect to [Gd] than the in vivo magnitude data (r(2)=.34 vs. r(2)=.17, respectively). This is likely due to the fact that the estimated change in 1/T(2)* is more sensitive than the phase to a variety of factors such as partial volume effects and T(1) weighting. Therefore, this study indicates that phase imaging may be a preferred method for measuring the AIF in the rat aorta compared to T(2)*-weighted magnitude imaging.     

Controlled Reduction of Carboxamides to Alcohols or Amines by Zinc Hydrides

New protocols for controlled reduction of carboxamides to either alcohols or amines were established using a combination of sodium hydride (NaH) and zinc halides (ZnX₂). Use of a different halide on ZnX₂ dictates the selectivity, wherein the NaH‐ZnI₂ system delivers alcohols and NaH‐ZnCl₂ gives amines. Extensive mechanistic studies by experimental and theoretical approaches imply that polymeric zinc hydride (ZnH₂)_∞ is responsible for alcohol formation, whereas dimeric zinc chloride hydride (H?Zn?Cl)₂ is the key species for the production of amines.     

Nickel(II) and cobalt(II) complexes with 4,5-dichloro-isothiazole-3-carboxylic acid and 1,10-phenanthroline: synthesis,crystal structures and cytotoxicity

Transition Metal Chemistry - In this study, Ni(II) and Co(II) complexes [Co(H2O)2L2] (1), [Ni(H2O)2L2] (2), [Co(phen)L2] (3), [Ni(phen)L2]·2H2O·EtOH (4·2H2O), and...     

Sialoside analogue arrays for rapid identification of high affinity siglec ligands

The siglec family of sialic acid binding proteins participates in diverse cell surface biology that includes regulation of immune cell signaling and the interaction of neuronal cells with glial cells. The weak intrinsic affinity of the natural sialoside ligands has hampered the development of synthetic ligand based probes needed to elucidate their roles in siglec function. In this report, we describe a glycan microarray comprising a library of 9-acyl-substituted sialic acids incorporated into sialosides containing the Neu5Acalpha2-3Gal and Neu5Acalpha-6Gal linkages commonly recognized by the siglecs. The array is demonstrated to exhibit utility for detecting 9-acyl substituents that increase the affinity of siglecs for their ligands. Substituents that increase affinity are anticipated to be useful for the design of high affinity ligand based probes of siglec function.