Geometric relative Hardy inequalities and the discrete spectrum of Schrödinger operators on manifolds

The classical Hardy inequality for the Laplacian Δ on ${\mathbb{R}^n}$ shows the borderline-behavior of a potential V for the following question: whether the Schrödinger operator ?Δ + V has a finite or infinite number of the discrete spectrum. In this paper, we will give a sharp generalization of this inequality on ${\mathbb{R}^n}$ to a relative version of that on large classes of complete noncompact manifolds. Replacing ${\mathbb{R}^n}$ by some specific classes of complete noncompact manifolds, including hyperbolic spaces, we also establish some sharp criteria for the above-type question.     

Differences in dual-task performance and prefrontal cortex activation between younger and older adults

Background

The purpose of this study was to examine task-related changes in prefrontal cortex (PFC) activity during a dual-task in both healthy young and older adults and compare patterns of activation between the age groups. We also sought to determine whether brain activation during a dual-task relates to executive/attentional function and how measured factors associated with both of these functions vary between older and younger adults.

Results

Thirty-five healthy volunteers (20 young and 15 elderly) participated in this study. Near-infrared spectroscopy (NIRS) was employed to measure PFC activation during a single-task (performing calculations or stepping) and dual-task (performing both single-tasks at once). Cognitive function was assessed in the older patients with the Trail-making test part B (TMT-B). Major outcomes were task performance, brain activation during task (oxygenated haemoglobin: Oxy-Hb) measured by NIRS, and TMT-B score. Mixed ANOVAs were used to compare task factors and age groups in task performance. Mixed ANOVAs also compared task factors, age group and time factors in task-induced changes in measured Oxy-Hb. Among the older participants, correlations between the TMT-B score and Oxy-Hb values measured in each single-task and in the dual-task were examined using a Pearson correlation coefficient. Oxy-Hb values were significantly increased in both the calculation task and the dual-task within patients in both age groups. However, the Oxy-Hb values associated with there were higher in the older group during the post-task period for the dual-task. Also, there were significant negative correlations between both task-performance accuracy and Oxy-Hb values during the dual-task and participant TMT-B scores.

Conclusions

Older adults demonstrated age-specific PFC activation in response to dual-task challenge. There was also a significant negative correlation between PFC activation during dual-task and executive/attentional function. These findings suggest that the high cognitive load induced by dual-task activity generates increased PFC activity in older adults. However, this relationship appeared to be strongest in participants with better baseline attention and executive functions.     

First enantioselective synthesis of salinipostin A,a marine cyclic enol-phosphotriester isolated from Salinispora sp

Salinipostins are cyclic enol-phosphotriesters isolated from a marine-derived Salinispora sp. as antimalarial compounds. Herein, the first enantioselective synthesis of salinipostin A was achieved. Organocatalyst-mediated asymmetric cyclopropanation and regioselective cyclopropane ring opening were the key steps.     

Isotopically selective infrared multiphoton dissociation of 2,3-dihydropyran

Oxygen isotopic selectivity on infrared multiphoton dissociation of 2,3-dihydropyran has been studied by the examination of the effects of excitation frequency, laser fluence, and gas pressure on the dissociation probability of 2,3-dihydropyran and isotopic composition of products. Oxygen-18 was enriched in a dissociation product: 2-propenal. The enrichment factor of 18O and the dissociation probability were measured at a laser frequency between 1033.5 and 1057.3 cm-1, the laser fluence of 2.2-2.3 J/cm2, and the 2,3-dihydropyran pressure of 0.27 kPa. The dissociation probability decreases as the laser frequency being detuned from the absorption peak of 2,3-dihydropyran around 1081 cm-1. On the other hand, the enrichment factor increases with detuning the frequency. The enrichment factor of 18O increases with increasing the 2,3-dihydropyran pressure at the laser fluence of 2.7 J/cm2 or less and the laser frequency of 1033.5 cm-1, whereas the yield of 2-propenal decreases with increasing the pressure. A very high enrichment factor of 751 was obtained by the irradiation of 0.53 kPa of 2,3-dihydropyran at 2.1 J/cm2. Collisional effect of vibrationally excited molecules with ambient molecules on isotopic selectivity is discussed on the basis of a rate equation model including a collisional vibrational de-excitation process.     

Facile cell patterning on an albumin-coated surface

Fabrication of micropatterned surfaces to organize and control cell adhesion and proliferation is an indispensable technique for cell-based technologies. Although several successful strategies for creating cellular micropatterns on substrates have been demonstrated, a complex multistep process and requirements for special and expensive equipment or materials limit their prevalence as a general experimental tool. To circumvent these problems, we describe here a novel facile fabrication method for a micropatterned surface for cell patterning by utilizing the UV-induced conversion of the cell adhesive property of albumin, which is the most abundant protein in blood plasma. An albumin-coated surface was prepared by cross-linking albumin with ethylene glycol diglycidyl ether and subsequent casting of the cross-linked albumin solution on the cell culture dish. While cells did not attach to the albumin surface prepared in this way, UV exposure renders the surface cell-adhesive. Thus, surface micropatterning was achieved simply by exposing the albumin-coated surface to UV light through a mask with the desired pattern. Mouse fibroblast L929 cells were inoculated on the patterned albumin substrates, and cells attached and spread in a highly selective manner according to the UV-irradiated pattern. Although detailed investigation of the molecular-level mechanism concerning the change in cell adhesiveness of the albumin-coated surface is required, the present results would give a novel facile method for the fabrication of cell micropatterned surfaces.     

Comparative study on the structural, optical, and electrochemical properties of bithiophene-fused benzo[c]phospholes

Three types of bithiophene-fused benzo[c]phospholes were successfully prepared by Ti(II)-mediated cyclization of the corresponding dialkynylated bithiophene derivatives as a key step. Each sigma(3)-phosphorus center of the benzo[c]phosphole subunits was readily transformed into sigma(4)-phosphorus center by Au coordination or oxygenation. In addition, the bithiophene subunit was functionalized at the alpha,alpha'-carbon atoms by Pd-catalyzed cross-coupling reactions with heteroarylmetals and by an S(N)Ar reaction with hexafluorobenzene. The experimentally observed results (NMR spectroscopy, X-ray analysis, UV/Vis absorption/fluorescence spectroscopy, and cyclic/differential-pulse voltammetry) have revealed that the structural, optical, and electrochemical properties of the bithiophene-fused benzo[c]phospholes vary considerably depending on the pi-conjugation modes at the bithiophene subunits and the substituents of the heterocyclopentadiene components. The appropriately ring-annulated sigma(3)-P derivatives and sigma(4)-P-AuCl complexes were found to emit fluorescence in the orange-red region, and the sigma(4)-P-oxo derivatives proved to undergo reversible one-electron reduction at -1.4 to -1.8 V (vs ferrocene/ferrocenium). These results indicate that the bithiophene-fused benzo[c]phospholes possess narrow HOMO-LUMO gaps and low-lying LUMOs, which was confirmed by density functional theory calculations of their model compounds. The time-of-flight measurement of an ITO/benzo[c]phosphole/Al device showed that the electron mobility in the P-oxo derivative is one-order higher than that in Alq(3) at low electric fields. The present study demonstrates that the arene-fused benzo[c]phosphole skeleton could be a highly promising platform for the construction of a new class of phosphole-based optoelectrochemical materials.     

Oxidative Annulation of Arenecarboxylic and Acrylic Acids with Alkynes under Ambient Conditions Catalyzed by an Electron‐Deficient Rhodium(III) Complex

It has been established that an electron‐deficient Cp^E rhodium(III) complex catalyzes the oxidative [4+2] annulation of substituted arenecarboxylic and acrylic acids with alkynes under ambient conditions (at RT–40 °C, under air) without using excess amounts of substrates to produce the corresponding substituted isocoumarins and α‐pyrones in high yields. Minor modification of reaction conditions depending on the coordination ability of alkynes realized the high efficiency.     

Preferential solvation in urea solutions at different concentrations: properties from simulation studies

We performed molecular dynamics simulations of urea solutions at different concentrations with two urea models (OPLS and KBFF) to examine the structures responsible for the thermodynamic solution properties. Our simulation results showed that hydrogen-bonding properties such as the average number of hydrogen bonds and their lifetime distributions were nearly constant at all concentrations between infinite dilution and the solubility limit. This implies that the characterization of urea-water solutions in the molarity concentration scale as nearly ideal is a result of facile local hydrogen bonding rather than a global property. Thus, urea concentration does not influence the local propensity for hydrogen bonds, only how they are satisfied. By comparison, the KBFF model of urea donated fewer hydrogen bonds than OPLS. We found that the KBFF urea model in TIP3P water better reproduced the experimental density and diffusion constant data. Preferential solvation analysis showed that there were weak urea-urea and water-water associations in OPLS solution at short distances, but there were no strong associations. We divided urea molecules into large, medium, and small clusters to examine fluctuation properties and found that any particular urea molecule did not stay in the same cluster for a long time. We found neither persistent nor large clusters.