On a Hardy operator inequality

The famous Hardy inequality asserts that if f is a non-negative p-integrable \((p>1)\) function on \((0,\infty )\), then

$$\begin{aligned} \int _{0}^{\infty }\left( \frac{1}{x}\int _{0}^{x}f(t)dt\right) ^pdx\le \left( \frac{p}{p-1}\right) ^p\int _{0}^{\infty }f(x)^pdx. \end{aligned}$$

We present an external form of the Hardy inequality for Hilbert space operators. Moreover, utilizing the operator log-convex functions, a refinement of the operator Hardy inequality is also given.

     

Molecular dynamics simulations on the inhibition of Cyclin-Dependent Kinases 2 and 5 in the presence of activators

Interests in CDK2 and CDK5 have stemmed mainly from their association with cancer and neuronal migration or differentiation related diseases and the need to design selective inhibitors for these kinases. Molecular dynamics (MD) simulations have not only become a viable approach to drug design because of advances in computer technology but are increasingly an integral part of drug discovery processes. It is common in MD simulations of inhibitor/CDK complexes to exclude the activator of the CDKs in the structural models to keep computational time tractable. In this paper, we present simulation results of CDK2 and CDK5 with roscovitine using models with and without their activators (cyclinA and p25). While p25 was found to induce slight changes in CDK5, the calculations support that cyclinA leads to significant conformational changes near the active site of CDK2. This suggests that detailed and structure-based inhibitor design targeted at these CDKs should employ activator-included models of the kinases. Comparisons between P/CDK2/cyclinA/roscovitine and CDK5/p25/roscovitine complexes reveal differences in the conformations of the glutamine around the active sites, which may be exploited to find highly selective inhibitors with respect to CDK2 and CDK5.     

Melatonin Induces Autophagy via Reactive Oxygen Species-Mediated Endoplasmic Reticulum Stress Pathway in Colorectal Cancer Cells

Even though an increasing number of anticancer treatments have been discovered, the mortality rates of colorectal cancer (CRC) have still been high in the past few years. It has been discovered that melatonin has pro-apoptotic properties and counteracts inflammation, proliferation, angiogenesis, cell invasion, and cell migration. In previous studies, melatonin has been shown to have an anticancer effect in multiple tumors, including CRC, but the underlying mechanisms of melatonin action on CRC have not been fully explored. Thus, in this study, we investigated the role of autophagy pathways in CRC cells treated with melatonin. In vitro CRC cell models, HT-29, SW48, and Caco-2, were treated with melatonin. CRC cell death, oxidative stress, and autophagic vacuoles formation were induced by melatonin in a dose-dependent manner. Several autophagy pathways were examined, including the endoplasmic reticulum (ER) stress, 5′–adenosine monophosphate-activated protein kinase (AMPK), phosphoinositide 3-kinase (PI3K), serine/threonine-specific protein kinase (Akt), and mammalian target of rapamycin (mTOR) signaling pathways. Our results showed that melatonin significantly induced autophagy via the ER stress pathway in CRC cells. In conclusion, melatonin demonstrated a potential as an anticancer drug for CRC.     

Intermediacy of an N-heterocyclic carbene complex in the catalytic C-H activation of a substituted benzimidazole

An N-heterocyclic carbene complex was found to be the active catalyst in the Rh(I)-catalyzed intramolecular coupling of an alkenyl group to a C-H bond of a substituted benzimidazole. Kinetic studies demonstrated that the catalytic cyclization is zero-order in substrate and first-order in catalyst. Furthermore, DFT calculations with a model system suggest that the rate-limiting step involves insertion of the alkenyl double bond into the rhodium-carbene bond.     

Determining bounds for the first conjugate point

Summary The purpose of this paper is to provide relatively simple methods for the determination of useful upper and lower bounds for the first zero greater than a of solutions of systems y″+p(x)y=0, y(a)=0, where p(x) is positive and continuous on an interval [a, b] and is either convex or concave there. On occasion, p(x) is required to be of class C′ or of class C″. This will acknowledge the partial support of the authors by the U.S. Army Research Office (Durham) under Grant numbered DA-ARO-D-31-124-G1007. Entrata in Redazione il 4 novembre 1969.     

Optimizing biosensing properties on undecylenic Acid-functionalized diamond

The optimization of biosensing efficiency on a diamond platform depends on the successful coupling of biomolecules on the surface, and also on effective signal transduction in the biorecognition events. In terms of biofunctionalization of diamond surfaces, surface electrochemical studies of diamond modified with undecylenic acid (UA), with and without headgroup protection, were performed. The direct photochemical coupling method employing UA was found to impart a higher density of carboxylic acid groups on the diamond surface compared to that using trifluoroethyl undecenoate (TFEU) as the protecting group during the coupling process. Non-faradic impedimetric DNA sensing revealed that lightly doped diamond gives better signal transduction sensitivity compared to highly doped diamond.     

Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide

ABSTRACT

We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with homogeneous initial and Dirichlet data.     

Oxygenation of zinc dialkyldithiocarbamate complexes: isolation, characterization, and reactivity of the stoichiometric oxygenates

S-oxygenation of dithiocarbamate (DTC) complexes has been implicated in their function as industrial anti-oxidants, as well as in their use as pesticides and most recently in their cumulative toxicity, but little is known of the species generated. Several S-oxygenated derivatives of N,N-disubstituted DTCs have been synthesized, characterized by a variety of methods, and their structure and reactivity examined. Low-temperature reaction of bis(N,N-diethyldithiocarbamato)zinc(II), Zn(deDTC)2 1, with oxygenating reagents (hydrogen peroxide, m-chloroperbenzoic acid, urea hydrogen peroxide) yields mono-oxygenated DTC complexes (N,N-peroxydiethyldithiocarbamato)(N,N-diethyldithiocarbamato)zin(II), Zn(O-deDTC)(deDTC), 2 and bis(N,N-peroxydiethyldithiocarbamato)zinc(II), Zn(O-deDTC)2, 3. The tetraoxygenated derivative bis(N,N-diethylthiocarbamoylsulfinato)zinc(II), Zn(O(2)-deDTC)2, 4, was cleanly obtained by initial reaction of the DTC salts with stoichiometric oxidant prior to complexation with Zn(II). X-ray crystallographic analysis of 2, 3, and 4 show that the peroxydithiocarbamate ligands are S,O-bound. Similar derivatives were obtained from the homoleptic dimethyl and pyrollidine DTC Zn complexes. These oxygenated species display unique 1H and 13C NMR variable-temperature spectra, as the symmetry of DTC ligand is broken upon oxygenation; total line shape analysis (TLSA) was used to compare the energetic parameters for rotation about the C-N bond in several derivatives. Compounds 2, 3, and 4 were deoxygenated by alkyl phosphine, regenerating the parent dithiocarbamate 1. The peroxydithiocarbamate complexes were susceptible to base-catalyzed hydrolytic decomposition, giving ligand-based products indicative of S-oxidation and S-extrusion.