Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

Some new domains with complete Kähler metrics of negative curvature

We add to the known examples of complete Kähler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ?ⁿ, intersections of complex-ellipsoidal domains in ?², and intersections of fractional linear transforms of the unit ball in ?². In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ?², the sum of the Bergman metrics is a Kähler metric with negative curvature operator.     

PDMS-based microfluidic device with multi-height structures fabricated by single-step photolithography using printed circuit board as masters

We have developed a method for fabricating microfluidic devices with multi-height structures using single step photolithography. The whole fabrication process is executed by conventional printed circuit board (PCB) technology without the need of having access to clean room facilities. Specifically designed "windows" and "rims" architectures were printed on films that were used as photomasks. Different levels of protruding features on the PCB master were produced by exposing a photomask followed by chemical wet etching. Poly(dimethylsiloxane) (PDMS) was then moulded against the positive relief master to generate microfluidic structures. In this report, we described the fabrication of a microfluidic device featured with a multi-height "sandbag" structure for particle entrapment and peripheral microchannels. Controlled immobilization of biological cells and immunocytochemcial staining assays were performed to demonstrate the applicability of the microfluidic device for cellular analysis. The integrity of the microdevice remained stable under applied pressure, indicating the robustness of the elastic PDMS structures for analytical operation. The simple microfabrication process requires only low-cost materials and minimal specialized equipment and can reproducibly produce mask lines of about 20 microm in width, which is sufficient for most microfluidic applications.     

Total Synthesis of (+)‐β‐Himachalene

An enantioselective synthesis of (+)‐β‐himachalene ( 2 ) was accomplished starting from (1S,2R)‐1,2‐epoxy‐p‐menth‐8‐ene ( 3 ) in 15 or 16 steps with an overall yield of ca. 6% (Schemes 3, 5, and 6). Key transformations include an Ireland–Claisen rearrangement, a Corey oxidative cyclization, and a ring expansion.     

Reactivity of dioxoruthenium(VI) porphyrins toward amines. Synthesis and characterization of bis(arylamine)ruthenium(II), bis(arylamido)- and bis(diphenylamido)ruthenium(IV), and oxo(tert-butylimido)ruthenium(VI) porphyrins

Reactions of dioxoruthenium(VI) porphyrins, [Ru(VI)O2(Por)], with p-chloroaniline, trimethylamine, tert-butylamine, p-nitroaniline, and diphenylamine afforded bis(amine)ruthenium(II) porphyrins, [Ru(II)(Por)(L)2] (L-p-ClC6H4NH2, Me3N, Por=TTP, 4-Cl-TPP; L=tBuNH2, Por = TPP, 3,4,5-MeO-TPP, TTP, 4-Cl-TPP, 3,5-Cl-TPP) and bis(amido)ruthenium(IV) porphyrins, [Ru(IV)(Por)(X)2] (X=p-NO2C6H4NH, Por=TTP, 4-Cl-TPP; X = Ph2N, Por = 3,4,5-MeO-TPP, 3,5-Cl-TPP), respectively. Oxidative deprotonation of [Ru(II)(Por)(NH2-p-C6H4Cl)2] in chloroform by air generated bis(arylamido)ruthenium(IV) porphyrins, [RuIV(Por)(NH-p-C6H4Cl)2] (Por=TTP. 4-Cl-TPP). Oxidation of [RuII(Por)-(NH2tBu)2] by bromine in dichloromethane in the presence of tert-butylamine and traces of water produced oxo(imido)ruthenium(VI) porphyrins, [RuVI-O(Por)(NtBu)] (Por=TPP, 3,4,5-MeO-TPP, TTP, 4-Cl-TPP, 3,5-Cl-TPP). These new classes of ruthenium complexes were characterized by 1H NMR, IR, and UV/visible spectroscopy, mass spectrometry, and elemental analysis. The structure of [Ru(IV)(TTP)(NH-p-C6H4Cl)2 . CH2Cl2 was determined by X-ray crystallography. The Ru-N bond length and the Ru-N-C angle of the Ru-NHAr moiety are 1.956(7) A and 135.8(6) degrees, respectively.     

Near-infrared laser spectroscopy of NiI

Laser-induced fluorescence spectrum of NiI in the near infrared region of 714-770 nm has been recorded. Seven bands belonging to three electronic transition systems were observed and analyzed: the (0,0), (1,0), and (2,0) bands of [13.3] (2)Sigma(+)-A (2)Pi(3/2) system; the (1,1) and (0,1) bands of [13.9] (2)Pi(3/2)-X (2)Delta(5/2) system; and the (0,0) and (1,0) bands of [13.9] (2)Pi(3/2)-A (2)Pi(3/2) system. Spectra of isotopic molecules confirmed the vibrational quantum number assignment of the observed bands. Least-squares fit of rotationally resolved transition lines yielded accurate molecular constants for the v=0-2 levels of the [13.3] (2)Sigma(+) state, the v=0 level of the A (2)Pi(3/2), and the v=1 level of the X (2)Delta(5/2) state. The vibrational separation, DeltaG(1/2), of the ground state was measured to be 276.674 cm(-1). With the observation of the [13.9] (2)Pi(3/2)-A (2)Pi(3/2) and [13.9] (2)Pi(3/2)-X (2)Delta(5/2) transitions, we accurately determined the energy separation between the A (2)Pi(3/2) and the X (2)Delta(5/2) to be 163.847 cm(-1). This confirms that the order of the A (2)Pi(3/2) and X (2)Delta(5/2) states in NiI is reversed when compared with other nickel monohalides.     

Bis axial ligation of simple imine and methyleneamido groups by ruthenium porphyrins

Bis(N-ethylideneethanamine)ruthenium(ii) porphyrins, [Ru11(Por)(N(Et)=CHMe)2] (Por=TTP, 4-Cl-TPP), were prepared by the reaction of dioxoruthenium(VI) porphyrins with triethylamine in approximately 85% yields. The reaction between dioxoruthenium(VI) porphyrins and benzophenone imine afforded bis(diphenylmethyleneamido)ruthenium(IV) porphyrins, [Ru(IV)(Por)(N=CPh2)2] (Por=TTP, 3,4,5-MeO-TPP), in approximately 65% yields. These new classes of metalloporphyrins were characterized by 1H NMR, UV/Vis, and IR spectroscopy as well as by mass spectrometry and elemental analysis. The X-ray crystallographic structures of [Ru(II)(TTP)(N(Et)=CHMe)2] and [Ru(IV)(3,4,5-MeO-TPP)(N=CPh2)2] revealed an axial Ru-N bond length of 2.115(6) A for the imine complex and 1.896(8) A for the methyleneamido complex. Each of the N=CPh2 axial groups in [Ru(IV)(3,4,5-MeO-TPP)(N=CPh2)2] adopts a linear coordination mode with a corresponding Ru-N-C angle of 175.9(9)degrees. Spectral and structural studies revealed essentially single bonding character for the bis(imine) complexes but a multiple bonding character for the bis(methyleneamido) complexes with respect to their axial Ru-N bonds.     

Bis‐clickable Mesoporous Silica Nanoparticles: Straightforward Preparation of Light‐Actuated Nanomachines for Controlled Drug Delivery with Active Targeting

Bis(clickable) mesoporous silica nanospheres (ca. 100 nm) were obtained by the co‐condensation of TEOS with variable amounts (2–5 % each) of two clickable organosilanes in the presence of CTAB. Such nanoparticles could be easily functionalized with two independent functions using the copper‐catalyzed alkyne‐azide cycloaddition (CuAAC) reaction to transform them into nanomachines bearing cancer cell targeting ligands with the ability to deliver drugs on‐demand. The active targeting was made possible after anchoring folic acid by CuAAC click reaction, whereas the controlled delivery was performed by clicked azobenzene fragments. Indeed, the azobenzene groups are able to obstruct the pores of the nanoparticles in the dark whereas upon irradiation in the UV or in the blue range, their trans‐to‐cis photoisomerization provokes disorder in the pores, enabling the delivery of the cargo molecules. The on‐command delivery was proven in solution by dye release experiments, and in vitro by doxorubicin delivery. The added value of the folic acid ligand was clearly evidenced by the difference of cell killing induced by doxorubicin‐loaded nanoparticles under blue irradiation, depending on whether the particles featured the clicked folic acid ligand or not.