Simple synthesis of 2-acetyl-5,8-dimethoxy-3,4-dihydronaphthalene,a key intermediate for the synthesis of optically active anthracycliones

2-Acetyl-5,8-dimethoxy-3,4-dihydronaphthalene is synthesised easily·starting from 2-acetyl-5,8-dimethoxytetralone.     

Slow magnetohydrodynamic flow past a circular cylinder

Oseen’ approximations are used to study the slow motion of a viscous, incompressible, electrically conducting fluid past a circular cylinder in the presence of a uniform aligned magnetic field. Using series truncation method, the analytical solutions for the first three terms in the Fourier sine series expansion of the stream function are obtained. Numerical values of the tangential drag for different values of magnetic interaction parameter and viscous Reynolds number are calculated.     

On a conjecture of S. Chowla and of S. Chowla and H. Walum,II

In 1965, Chowla and Walum conjectured that, $\text{G}{}_{\mathrm{a,k}}\text{(x):=}\text{Σ}{}_{\mathrm{n\; \le \; \surd x}}\text{n}{}^{\mathrm{a}}\text{P}{}_{\mathrm{k}}\text{(}\text{x}\text{n}\text{) = O(x}{}^{\mathrm{<mtext>a</mtext><mtext>2</mtext><mtext>\; +\; </mtext><mtext>1</mtext><mtext>4</mtext><mtext>\; +\; \epsilon </mtext>}}\text{)}$ holds for each ε > 0 and x → ∞, where integers a ≥ 0 and k ≥ 1 are given and P_k is the periodic Bernoulli function of order k. Recently, the authors established this conjecture in case k ≥ 2 and $\text{a >}\text{1}\text{2}$ with ε = 0 while if $\text{a =}\text{1}\text{2}$, with a log factor. In this paper, it is proven that the conjecture, in case $\text{|a| <}\text{1}\text{2}$, k = 2, is true “on average”.     

Change of variable formulas for non-anticipative functionals on path space

We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits. The functionals are only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Itô formula for a large class of stochastic processes, including semimartingales and Dirichlet processes. In particular, we show the stability of the class of semimartingales under certain functional transformations.     

On the Asymptotic Stability of the Intrinsic and Fractional Bayes Factors for Testing Some Diffusion Models

Random processes, from which a single sample path data are available on a fine time scale, abound in many areas including finance and genetics. An effective way to model such data is to consider a suitable continuous-time-scale analog, X _t say, for the underlying process. We consider three diffusion models for the process X _t and address model selection under improper priors. Specifically, fractional and intrinsic Bayes factors (FBF and IBF) for model selection are considered. Here, we focus on the asymptotic stability of the IBF's and FBF's for comparing these models. Specifically, we propose to employ certain novel transformations of the data in order to ensure the asymptotic stability of the IBF's. While we use different transformations for pairwise comparisons of the models, we also show that a single common transformation can be used when simultaneously comparing all three models. We then demonstrate that, when FBF's are used to compare these models, we may have to employ different, model-specific training fractions in order to achieve asymptotic stability of the FBF's.     

A novel transformation of 2-dichloracetamido-1-methyl-5-nitroimidazole to 5-dichloroacetylimino-tetrahydroimidazo (4,5-c) pyrazoles.

2-Dichloracetamido-1-methyl-5-nitroimidazole undergoes novel cycloaddition with diazomethane to form 5-dichloracetylimino-tetrahydroimidazopyrazoles via 2-dichloracetylimino-1,3-dimethyl-5-nitroimidazoline.     

Testing Hypotheses About the Power Law Process Under Failure Truncation Using Intrinsic Bayes Factors

Conventional Bayes factors for hypotheses testing cannot typically accommodate the use of standard noninformative priors, as such priors are defined only up to arbitrary constants which affect the values of the Bayes factors. To circumvent this problem, Berger and Pericchi (1996, J. Amer. Statist. Assoc., 19, 109-122) introduced a new criterion called the Intrinsic Bayes Factor (IBF). In this paper, we use their methodology to test several hypotheses regarding the shape parameter of the power law process. Assuming that we have data from the process according to the failure-truncation sampling scheme, we derive the arithmetic and geometric IBF's using the reference priors. We deduce a set of intrinsic priors that correspond to these IBF's, as the observed number of failures tends to infinity. We then use these results to analyze an actual data set on the failures of an aircraft generator.     

Systemic Administration of Polymer‐Coated Nano‐Graphene to Deliver Drugs to Glioblastoma

Graphene—2D carbon—has received significant attention thanks to its electronic, thermal, and mechanical properties. Recently, nano‐graphene (nGr) has been investigated as a possible platform for biomedical applications. Here, a polymer‐coated nGr to deliver drugs to glioblastoma after systemic administration is reported. A biodegradable, biocompatible poly(lactide) (PLA) coating enables encapsulation and controlled release of the hydrophobic anticancer drug paclitaxel (PTX), and a hydrophilic poly(ethylene glycol) (PEG) shell increases the solubility of the nGr drug delivery system. Importantly, the polymer coating mediates the interaction of nGr with U‐138 glioblastoma cells and decreases cytotoxicity compared with pristine untreated nGr. PLA‐PEG‐coated nGr is also able to encapsulate PTX at 4.15 wt% and sustains prolonged PTX release for at least 19 d. PTX‐loaded nGr‐PLA‐PEGs are shown to kill up to 20% of U‐138 glioblastoma cells in vitro. Furthermore, nGr‐PLA‐PEG and CNT‐PLA‐PEG, two carbon nanomaterials with different shapes, are able to kill U‐138 in vitro as well as free PTX at significantly lower doses of drug. Finally, in vivo biodistribution of nGr‐PLA‐PEG shows accumulation of nGr in intracranial U‐138 glioblastoma xenografts and organs of the reticuloendothelial system.