Unconditional ideals of finite rank operators

Let X be a Banach space. We give characterizations of when is a u-ideal in for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when is a u-ideal in for every Banach space Y, when is a u-ideal in for every Banach space Y, and when is a u-ideal in for every Banach space Y.     

Matrix-valued Schrödinger operators over local fields

We consider quantum systems that have as their configuration spaces finite dimensional vector spaces over local fields. The quantum Hilbert space is taken to be a space with complex coefficients and we include in our model particles with internal symmetry. The Hamiltonian operator is a pseudo-differential operator that is initially only formally defined. For a wide class of potentials we prove that this Hamiltonian is well-defined as an unbounded self-adjoint operator. The free part of the operator gives rise to ameasure on the Skorokhod space of paths,D[0,∞), and with respect to this measure there is a path integral representation for the semigroup associated to the Hamiltonian. We prove this Feynman-Kac formula in the local field setting as a consequence of the Hille-Yosida theory of semi-groups. The text was submitted by the authors in English.     

Concise syntheses of three ω-3 polyunsaturated fatty acids

The synthesis of the three ω-3 polyunsaturated fatty acids, eicosatetraenoic acid (3), docosapentaenoic acid (4), and stearidonic acid (5) has been achieved using eicosapentaenoic acid or docosahexaenoic acid as the starting materials.     

Four-component relativistic Kohn-Sham theory

A four-component relativistic implementation of Kohn-Sham theory for molecular systems is presented. The implementation is based on a nonredundant exponential parametrization of the Kohn-Sham energy, well suited to studies of molecular static and dynamic properties as well as of total electronic energies. Calculations are presented of the bond lengths and the harmonic and anharmonic vibrational frequencies of Au(2), Hg(2+)(2), HgAu(+), HgPt, and AuH. All calculations are based on the full four-component Dirac-Coulomb Hamiltonian, employing nonrelativistic local, gradient-corrected, and hybrid density functionals. The relevance of the Coulomb and Breit operators for the construction of relativistic functionals is discussed; it is argued that, at the relativistic level of density-functional theory and in the absence of a vector potential, the neglect of current functionals follows from the neglect of the Breit operator.     

Tetrasubstituted phenanthrolines as highly potent, water-soluble, and selective g-quadruplex ligands

Small molecules capable of stabilizing the G-quadruplex (G4) structure are of interest for the development of improved anticancer drugs. Novel 4,7-diamino-substituted 1,10-phenanthroline-2,9-dicarboxamides that represent hybrid structures of known phenanthroline-based ligands have been designed. An efficient synthetic route to the compounds has been developed and their interactions with various G4 sequences have been evaluated by F?rster resonance energy transfer (FRET) melting assays, fluorescent intercalator displacement (FID), electrospray ionization mass spectrometry (ESI-MS), and circular dichroism (CD) spectroscopy. The preferred compounds have high aqueous solubility and are strong and potent G4 binders with a high selectivity over duplex DNA; thus, they represent a significant improvement over the lead compounds. Two of the compounds are inhibitors of HeLa and HT1080 cell proliferation.     

Stereoselective total synthesis of ieodomycin C

A concise stereoselective synthesis of the marine natural product ieodomycin C (3) has been achieved from commercially available pyridinium-1-sulfonate (8) in eight linear steps and 14% overall yield. The key synthetic steps included a B-alkyl Suzuki–Miyaura cross-coupling reaction and an Evans–Nagao acetate aldol reaction. The same synthetic sequence was used for preparing the enantiomer of ieodomycin C (3). Our efforts confirmed the structure of the antibacterial natural product 3.     

Quadratic response functions in the relativistic four-component Kohn-Sham approximation

A formulation and implementation of the quadratic response function in the adiabatic four-component Kohn-Sham approximation is presented. The noninteracting reference state is time-reversal symmetric and formed from Kramers pair spinors, and the energy density is gradient corrected. Example calculations are presented for the optical properties of disubstituted halobenzenes in their meta and ortho conformations. It is demonstrated that correlation and relativistic effects are not additive, and it is shown that relativity alone reduces the mubeta-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. Of the employed functionals, CAM-B3LYP shows the best performance and gives hyperpolarizabilities beta distinctly different from B3LYP.     

Tetrasubstituted Phenanthrolines as Highly Potent,Water‐Soluble,and Selective G‐Quadruplex Ligands

Small molecules capable of stabilizing the G‐quadruplex (G4) structure are of interest for the development of improved anticancer drugs. Novel 4,7‐diamino‐substituted 1,10‐phenanthroline‐2,9‐dicarboxamides that represent hybrid structures of known phenanthroline‐based ligands have been designed. An efficient synthetic route to the compounds has been developed and their interactions with various G4 sequences have been evaluated by Förster resonance energy transfer (FRET) melting assays, fluorescent intercalator displacement (FID), electrospray ionization mass spectrometry (ESI‐MS), and circular dichroism (CD) spectroscopy. The preferred compounds have high aqueous solubility and are strong and potent G4 binders with a high selectivity over duplex DNA; thus, they represent a significant improvement over the lead compounds. Two of the compounds are inhibitors of HeLa and HT1080 cell proliferation.