Finite quotients of the automorphism group of a free group

The automorphism group AutF_n of a free group F_n of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutF_nto a permutation group. We determine this antihomomorphic image of AutF_n when G is the semidirect product Z_p x Z_q     

Stable Anticancer Gold(III)–Porphyrin Complexes: Effects of Porphyrin Structure

In the design of physiologically stable anticancer gold(III) complexes, we have employed strongly chelating porphyrinato ligands to stabilize a gold(III) ion [Chem. Commun. 2003 , 1718; Coord. Chem. Rev. 2009 , 253, 1682]. In this work, a family of gold(III) tetraarylporphyrins with porphyrinato ligands containing different peripheral substituents on the meso‐aryl rings were prepared, and these complexes were used to study the structure–bioactivity relationship. The cytotoxic IC₅₀ values of [Au(Por)]⁺ (Por=porphyrinato ligand), which range from 0.033 to >100 μM , correlate with their lipophilicity and cellular uptake. Some of them induce apoptosis and display preferential cytotoxicity toward cancer cells than to normal noncancerous cells. A new gold(III)–porphyrin with saccharide conjugation [Au(4‐glucosyl‐TPP)]Cl ( 2 a ; H₂(4‐glucosyl‐TPP)=meso‐tetrakis(4‐β‐D ‐glucosylphenyl)porphyrin) exhibits significant cytostatic activity to cancer cells (IC₅₀=1.2–9.0 μM ) without causing cell death and is much less toxic to lung fibroblast cells (IC₅₀>100 μM ). The gold(III)–porphyrin complexes induce S‐phase cell‐cycle arrest of cancer cells as indicated by flow cytometric analysis, suggesting that the anticancer activity may be, in part, due to termination of DNA replication. The gold(III)–porphyrin complexes can bind to DNA in vitro with binding constants in the range of 4.9×10⁵ to 4.1×10⁶ dm³ mol^?1 as determined by absorption titration. Complexes 2 a and [Au(TMPyP)]Cl₅ ( 4 a ; [H₂TMPyP]⁴⁺=meso‐tetrakis(N‐methylpyridinium‐4‐yl)porphyrin) interact with DNA in a manner similar to the DNA intercalator ethidium bromide as revealed by gel mobility shift assays and viscosity measurements. Both of them also inhibited the topoisomerase I induced relaxation of supercoiled DNA. Complex 4 a , a gold(III) derivative of the known G‐quadruplex‐interactive porphyrin [H₂TMPyP]⁴⁺, can similarly inhibit the amplification of a DNA substrate containing G‐quadruplex structures in a polymerase chain reaction stop assay. In contrast to these reported complexes, complex 2 a and the parental gold(III)–porphyrin 1 a do not display a significant inhibitory effect (<10 %) on telomerase. Based on the results of protein expression analysis and computational docking experiments, the anti‐apoptotic bcl‐2 protein is a potential target for those gold(III)–porphyrin complexes with apoptosis‐inducing properties. Complex 2 a also displays prominent anti‐angiogenic properties in vitro. Taken together, the enhanced stabilization of the gold(III) ion and the ease of structural modification render porphyrins an attractive ligand system in the development of physiologically stable gold(III) complexes with anticancer and anti‐angiogenic activities.     

Synthesis and characterization of coordination compounds of organotin(IV) with nitrogen and sulfur donor ligands

The reactions of dimethyltin dichloride with nitrogen and sulfur donor ligands derived by condensation of S‐benzyldithiocarbazate with indol‐3‐carboxylaldehyde, thiophene‐2‐aldehyde and furfuraldehyde have been investigated in 1:1 and 1:2 molar ratios in anhydrous alcohol. These ligands act as mononegatively charged bidentate species and coordinate to the central tin(IV) atom through the thiosulfur by proton exchange with the azomethine nitrogen. The newly synthesized complexes have been characterized by elemental analysis, conductance measurements and molecular weight determinations. The mode of bonding and the geometry of the complexes have been suggested on the basis of infrared, electronic and ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy, and probable structures have been assigned to these complexes. A few representative ligands and their tin(IV) complexes have also been screened for their antifungal and antibacterial activities and found to be quite active in this respect. Copyright © 2001 John Wiley & Sons, Ltd.     

Three-component Heck–Diels–Alder cascade processes involving alkylallenes, aryl iodides and dienophiles

A wide variety of aryl/heteroaryl iodides undergo an intermolecular Heck reaction with alkylallenes to furnish 1,3-dienes. These subsequently react in situ with various dienophiles to give Diels–Alder adducts. The chemistry has been extended to incorporate cyclisation-anion capture methodology and the stereochemistry of the products has been determined.     

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation

We propose the backward phase flow method to implement the Fourier–Bros–Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.     

LED-activated pheophorbide a in ovarian cancer cells: Cytotoxicity and apoptosis induction

Pheophorbide a (Pa) from Chinese herbal medicine Scutellaria Barbata and Silkworm excreta has been proved to be potential photosensitizer. The present study investigated the cytotoxicity of ovarian cancer cells induced by LED-activated Pa using light microscopy with the SRB staining. We further investigated the apoptosis of the cells 6 h after LED-activated Pa using of the flow cytometer with PI staining and nuclear staining. The results showed that LED-activated Pa remarkably caused cell death of ovarian cancer cells. The condensation of chromatin, nuclear fragmentations, and 12.3% of cells containing subdiploid levels of DNA were found in the ovarian cancer cells after the treatment of LED-activated Pa. These data demonstrated that LED-activated Pa could cause significant cytotoxicity and apoptosis of ovarian cancer cells.