The complex Busemann-Petty problem for arbitrary measures

The complex Busemann-Petty problem asks whether origin symmetric convex bodies in with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if and negative if . In this article we show that the answer remains the same if the volume is replaced by an “almost” arbitrary measure. This result is the complex analogue of Zvavitch’s generalization to arbitrary measures of the original real Busemann-Petty problem. Received: 6 May 2008     

Why is copper locally etched by scanning electrochemical microscopy?

The etching of thin copper films by scanning electrochemical microscopy (SECM) was investigated. It is not trivial that locally injected charge by an oxidized mediator will lead to dissolution of copper as the charge can easily be dissipated by lateral charge propagation. We studied the effect of different parameters, such as thickness of the Cu film and concentration of the mediator, on the efficiency of etching. The feedback current is the sum of three charge transfer contributions: diffusion of mediator species, chemical reaction on the surface and lateral charge propagation across the copper film. We have introduced an approach for isolating the lateral contribution and studied the parameters affecting the fate of the locally injected charge. We found that etching becomes effective once the lateral contribution cannot dissipate the locally injected charge. This occurs as the concentration of the etchant increases or the film thickness decreases. Measuring the steady-state current above Cu films with different thickness, allowed estimating the potential difference across the Cu area underneath the tip. We conclude that driving local processes, such as etching, depends on creating a mechanism which maintains the injected charge focused.     

Synthesis of epi-oxetin via a serine-derived 2-methyleneoxetane

The unique reactivity of 2-methyleneoxetanes and 1,5-dioxaspiro[3.2]hexanes has been exploited for the synthesis of epi-oxetin (26), an oxetane-containing beta-amino acid. While the preparation of the natural product oxetin (1) was the original goal, the unexpected diastereoselectivity of an precedented reduction provided the epi-oxetin framework. The methodology described herein should be amenable for the preparation of oxetin with a change in nitrogen protection.     

Mechanistic study of asymmetric oxidative biaryl coupling: evidence for self-processing of the copper catalyst to achieve control of oxidase vs oxygenase activity

Copper(I) and copper(II) 1,5-diaza-cis-decalin complexes [(N2)Cu] are effective precatalysts for aerobic oxidative coupling of naphthol substrates. Mechanistic studies, however, reveal that these complexes are not the reactive form of the catalyst under steady-state conditions. Rather, the active catalyst forms in a presteady-state self-processing step that involves oxygenation of the naphthol substrate. The oxygenated substrate, NapHOX, serves as a cofactor that combines with the (N2)Cu complexes to achieve highly selective, steady-state oxidase reactivity (aerobic oxidative biaryl coupling).     

Catalytic enantioselective Meerwein-Eschenmoser Claisen rearrangement: asymmetric synthesis of allyl oxindoles

The first catalytic, enantioselective Meerwein-Eschenmoser Claisen rearrangement has been achieved. Palladium(II) BINAP or phosphinooxazoline catalysts were employed to generate oxindole products with 100% conversion and up to 92% ee.     

Continuous monitoring of ascorbate transport through neuroblastoma cells with a ruthenium oxide hexacyanoferrate modified microelectrode

The uptake of ascorbate by neuroblastoma cells using a ruthenium oxide hexacyanoferrate (RuOHCF)-modified carbon fiber disc (CFD) microelectrode (r = 14.5 microm) was investigated. By use of the proposed electrochemical sensor the amperometric determination of ascorbate was performed at 0.0 V in minimum essential medium (MEM, pH = 7.2) with a limit of detection of 25 micromol L(-1). Under the optimum experimental conditions, no interference from MEM constituents and reduced glutathione (used to prevent the oxidation of ascorbate during the experiments) was noticed. The stability of the RuOHCF-modified electrode response was studied by measuring the sensitivity over an extended period of time (120 h), a decrease of around 10% being noticed at the end of the experiment. The rate of ascorbate uptake by control human neuroblastoma SH-SY5Y cells, and cells transfected with wild-type Cu,Zn-superoxide dismutase (SOD WT) or with a mutant typical of familial amyotrophic lateral sclerosis (SOD G93A), was in agreement with the level of oxidative stress in these cells. The usefulness of the RuOHCF-modified microelectrode for in vivo monitoring of ascorbate inside neuroblastoma cells was also demonstrated.     

Laplacian Flow of Closed G$$_$$-Structures Inducing Nilsolitons

We study the existence of left invariant closed \(G_2\)-structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these \(G_2\)-structures, we show long time existence and uniqueness of solution for the Laplacian flow on the noncompact manifold. Moreover, considering the Laplacian flow on the associated Lie algebra as a bracket flow on \({\mathbb {R}}^7\) in a similar way as in Lauret (Commun Anal Geom 19(5):831–854, 2011) we prove that the underlying metrics \(g(t)\) of the solution converge smoothly, up to pull-back by time-dependent diffeomorphisms, to a flat metric, uniformly on compact sets in the nilpotent Lie group, as \(t\) goes to infinity.     

On Models of Directed Path Graphs Non Rooted Directed Path Graphs

A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted directed path graph is the intersection graph of a family of directed subpaths of a rooted tree. Clearly, rooted directed path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted directed path graphs. With the purpose of proving knowledge in this direction, we show in this paper properties of directed path models that can not be rooted for chordal graphs with any leafage and with leafage four. Therefore, we prove that for leafage four directed path graphs minimally non rooted directed path graphs have a unique asteroidal quadruple, and can be characterized by the presence of certain type of asteroidal quadruples.     

Dissociation enthalpies of synthesized multicomponent gas hydrates with respect to the guest composition and cage occupancy

This study presents the influences of additional guest molecules such as C2H6, C3H8, and CO2 on methane hydrates regarding their thermal behavior. For this purpose, the onset temperatures of decomposition as well as the enthalpies of dissociation were determined for synthesized multicomponent gas hydrates in the range of 173-290 K at atmospheric pressure using a Calvet heat-flow calorimeter. Furthermore, the structures and the compositions of the hydrates were obtained using X-ray diffraction and Raman spectroscopy as well as hydrate prediction program calculations. It is shown that the onset temperature of decomposition of both sI and sII hydrates tends to increase with an increasing number of larger guest molecules than methane occupying the large cavities. The results of the calorimetric measurements also indicate that the molar dissociation enthalpy depends on the guest-to-cavity size ratio and the actual concentration of the guest occupying the large cavities of the hydrate. To our knowledge, this is the first study that observes this behavior using calorimetrical measurements on mixed gas hydrates at these temperature and pressure conditions.     

Polyphenolic Flavonoid Compound Quercetin Effects in the Treatment of Acute Myeloid Leukemia and Myelodysplastic Syndromes

Flavonoids are ubiquitous groups of polyphenolic compounds present in most natural products and plants. These substances have been shown to have promising chemopreventive and chemotherapeutic properties with multiple target interactions and multiple pathway regulations against various human cancers. Polyphenolic flavonoid compounds can block the initiation or reverse the promotion stage of multistep carcinogenesis. Quercetin is one of the most abundant flavonoids found in fruits and vegetables and has been shown to have multiple properties capable of reducing cell growth in cancer cells. Acute myeloid leukemia (AML) and myelodysplastic syndromes (MDS) therapy remains a challenge for hematologists worldwide, and the outcomes for patients with both disorders continue to be poor. This scenario indicates the increasing demand for innovative drugs and rational combinative therapies. Herein, we discuss the multitarget effects of the flavonoid quercetin, a naturally occurring flavonol, on AML and MDS.