On the best constant in a Wente‐type inequality for the fractional Laplace operator

In this paper, we consider the solution to Wente's problem with the fractional Laplace operator (?Δ)^α/2, where 0 < α < 2. We derive a Wente‐type inequality for this problem. Next, we compute the optimal constant in such inequality. Copyright © 2015 John Wiley & Sons, Ltd.     

An Optimal L∞–error Estimate for an Approximation of a Parabolic Variational Inequality

In this article, an optimal error estimate for parabolic variational inequalities is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L^∞-asymptotic behavior in uniform norm is proved using the semi-implicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolutions.     

Quadratic differentials (A(z − a)(z − b)/(z − c)2) dz2 and algebraic Cauchy transform

We discuss the representability almost everywhere (a.e.) in C of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials A(z ? a)(z ? b)×(z ? c)^?2 dz². More precisely, we give a necessary and sufficient condition on the complex numbers a and b for these quadratic differentials to have finite critical trajectories. We also discuss all possible configurations of critical graphs.     

Synthesis, NMR conformational analysis and pharmacological evaluation of 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole analogues as melatonin receptor ligands

A structure for the self-condensation product of 2-(1H-indol-2-yl)ethyl tosylate 2a, previously proposed as 6,7,14,15-tetrahydro-15aH-azocino[1,2-a:6,5-b]diindole 3a, was revised based on the (13)C-2D-INADEQUATE experiment, and proved to be 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole 4a. A mechanism for the unexpected formation of this novel hexacyclic heterocycle was proposed and its NMR solution structure was elucidated. Five derivatives of the title ring skeleton 12-16 designed as melatonin receptor ligands were synthesized and their affinities for the human MT(1) and MT(2) receptors were determined. Both butyramides 13 and 15, as well as the non-methoxy acetamide 12 exhibited micromolar binding affinities for both receptors being slightly MT(2) selective. The methoxy acetamide 14 showed the best pharmacological profile exhibiting a five times higher affinity for MT(1) (K(i) = 49 nM) than for MT(2) (K(i) = 246 nM) receptor.     

A domino-based approach toward stereodefined heavily functionalized cyclohexanes: synthesis of iridal's core structure

A stereoselective synthesis of heavily functionalized six-membered ring subunits, which possess functionality at sites appropriate for further elaboration, is described. The cyclopentanone moiety of hydrindenediol is required to achieve total facial selectivity during the pre-domino installation of the second quaternary center, while oxidative cleavage is responsible for the ring-expanding rearrangement. A microwave-assisted version of the key domino transformation and a test of concept approach toward the iridal core structure are also presented.     

Synthesis,crystal structures and spectra of Hg(II)-1,2-bis(diphenylphosphino)ethane monoxide complexes: Monomer and polymer formation

The reaction of mercury(II) halides with 1,2-bis(diphenylphosphino)ethane monoxide (dppeO) in 1:1 molar ratio yielded P,O-coordinated polymers having the empirical formula [HgX₂(dppeO)]_n [X = Cl (1), Br (2), I (3)]. In contrast, the reaction between the same reactants in a 1:2 molar ratio yielded the P, P-coordinated monomeric complexes, HgX₂(dppeO)₂[X = Cl (4), Br (5), I (6)]. The structures of 2, 3, 4 and 5 have been characterized crystallographically. The results indicate that the geometry around the mercury atom in each of these molecules is tetrahedral with considerable distortion. The ³¹P NMR spectra of the 1:1 complexes indicate the dissociation of the Hg–O bond in solution.     

Lanthanide-containing polymer nanoparticles for biological tagging applications: nonspecific endocytosis and cell adhesion

We describe the synthesis and characterization of element-encoded polystyrene nanoparticles with diameters on the order of 100 nm and a narrow size distribution. Individual particles contain ca. 10(3) chelated lanthanide ions, of either a single element or a mixture of elements. These particles were effectively internalized by nonspecific endocytosis into three cell lines associated with human leukemia. Using an assay based upon ICP-MS detection, we could monitor quantitatively cell adhesion induced by cell differentiation of THP-1 cells in response to phorbol ester stimulation (PMA) in single cell type or mixed cultures.     

Vibrational spectra, DFT calculations, unusual structure, anomalous CH2 wagging and twisting modes, and phase-dependent conformation of 1,3-disilacyclobutane

Our previously published infrared and Raman spectra of 1,3-disilacyclobutane (13DSCB) and its 1,1,3,3-d4 isotopomer have been reexamined and partially reassigned on the basis of DFT and ab initio calculations. The calculations confirm previous microwave work that the CSiC angles in the ring are unexpectedly larger than the SiCSi angles. This may arise from the partial charges on the ring atoms. The calculations are in excellent agreement with the observed spectra in both frequency and intensity. They also demonstrate that this molecule has CH2 wagging and twisting vibrations with frequencies below 1000 cm-1, about 200 cm-1 lower than expected. These unprecedented low values can be explained by the decreased slope in the potential energy curves for these vibrations as the sideways motions of the CH2 groups result in attractive forces between the positively charged hydrogens on the carbon atoms and the negatively charged hydrogens on the silicon atoms. The theoretical calculations also confirm the previous conclusions that the individual molecules (vapor) have C2v symmetry whereas in the solid the molecules become planar with D2h symmetry. The vibrational coupling between the ring-angle bending mode and the SiH2 in-phase rocking, which is present for the C2v structure, is forbidden for D2h and hence disappears.     

Prolonged charge-separated states of starburst tetra(diphenylaminofluoreno)[60]fullerene adducts upon photoexcitation

Construction of starburst C60(>DPAF-C9)4 pentads was coupled with the use of highly fluorescent diphenylaminofluorene-C9 (DPAF-C9) addends as donor components in conjunction with the fullerene acceptor during single-photon excitation processes. High quantum yields (PhiCS) of charge-separation processes in the range 0.83-0.90 for C60(>DPAF-C9)n (n = 1, 2, or 4) were obtained in the formation of C60*-(>DPAF*+-C9)(>DPAF-C9)n-1 transient states. The lifetime of the radical ion-pairs (tauRIP) was found to be 900 ns for starburst C60(>DPAF-C9)4 (3) samples, which is 6-fold longer than that of the linear analogue C60(>DPAF-C9) (1), with a ca. 2 times increase of the charge-separation rate (kCS) compared to that of 1. These data implied the important role of sterically hindered DPAF-C9 pendants arranged in a starburst-like environment that encapsulates the central C60 core on extending the tauRIP. We interpreted the phenomena by the occurrence of intramolecular migration or exchange of electron or positive charge among multiple DPAF-C9 pendants of C60*-(>DPAF*+-C9)(>DPAF-C9)n-1, which gives an increased rate in charge generation and delayed charge recombination.     

Silicon-phthalocyanine-cored fullerene dendrimers: synthesis and prolonged charge-separated states with dendrimer generations

Silicon-phthalocyanine-cored fullerodendrimers with up to eight fullerene substituents (SiPc-n C(60); n=2, 4, and 8) have been synthesized. Photophysical properties of newly synthesized SiPc-n C(60) have been investigated by time-resolved fluorescence and transient absorption analysis with pulsed laser light. Laser photolysis measurements suggest the occurrence of a charge-separation process from (1)SiPc* to the C(60) subunits. The nanosecond transient absorption spectra in the near-IR region indicate that the lifetimes of the formed radical ion pairs are prolonged on the order of SiPc-8 C(60)>SiPc-4 C(60)>SiPc-2 C(60), which may be related to the electron migration among the C(60) subunits. The usefulness of SiPc-n C(60) as light-harvesting systems, evaluated as a ratio of the rates of charge recombination to those of charge separation, increases markedly with the dendrimer generation.