Approximate convexity and submonotonicity

It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locally Lipschitz approximately convex functions coincides with the class of lower-C¹ functions. Directional approximate convexity is introduced and shown to be a natural extension of the class of lower-C¹ functions in infinite dimensions. The following characterization is established: a multivalued operator is maximal cyclically submonotone if, and only if, it coincides with the Clarke subdifferential of a locally Lipschitz directionally approximately convex function, which is unique up to a constant. Furthermore, it is shown that in Asplund spaces, every regular function is generically approximately convex.     

A novel synthesis of 3′-deoxy-3′-nitrothymidine via nucleophilic substitution with nitrite anion

Nucleophilic substitution at C3′ of 1-(2-deoxy-5-O-trityl-β-D-erythr-pentofuranosyl)-2-methoxy-5-methyl-4(1H)-pyrimidinone (5) with methyl iodide/triphenylphosphine/diethyl azodicarboxylate gave the expected inverted iodide 6 and minor epimer 7 . Treatment of 6 with lithium nitrite/phloroglucinol yielded the desired nitro derivative 8 and subsequent acidic deprotection afforded the title compound 1 . This represents a novel method for the introduction of a nitro group into the furanosyl moiety of a nucleoside. The nmr spectroscopic techniques (COSY, NOESY, nOe, HMQC and HMBC) were used to determine the stereochemistry at C3′ of the nucleosides. Spectral analysis of H-D exchange at the 3′-position of 1 did not indicate the formation of its epimer 10 .     

Synthesis and characterization of novel 99gTc(V) and Re(V) complexes with water-soluble tetraaza diamido dipyridino ligands: single-crystal X-ray structural investigations of mono- and dinuclear complexes

Rhenium and technetium are known for their useful applications in nuclear medicine with similar properties. In this study, new diamido dipyridino (N(4)) water-soluble ligands (2-C(5)H(4)NCH(2)NHCO)(2)CH(2), 1 (L(1)H2), (2-C(5)H(4)NNHNHCO)(2)CH(2), 2, and [2-C(5)H(4)N(+)(O)(-)CH(2)NHCO](2)CH(2), 3, were synthesized. Reaction of L(1)H2 with ReOCl(3)(PPh(3))(2) resulted in the novel six-coordinated rhenium(V) complex, trans-ReO(L(1))(OEt), 4. The complex was characterized by spectroscopic methods, and its X-ray crystallographic analysis revealed that rhenium is coordinated to four nitrogen atoms of the ligand and to two oxygen atoms from the deprotonated ethanol and the oxo group respectively in a distorted octahedral geometry. In solution, complex 4 was transformed to a new complex 5, which was proved to be the dinuclear complex mu-oxo [ReO(L(1))](2)O. Reaction of 1 with [n-Bu(4)N][ReOCl(4)] resulted in the neutral complex 6, trans-[ReO(L(1))]Cl. Similarly, when ligand 1 was reacted with [n-Bu(4)N][(99g)TcOCl(4)], the neutral trans-[(99)TcO(L(1))]Cl complex 7 was formed, which upon dissolution transformed into a cationic complex 8, trans-[(99)TcO(L(1))(OH(2))](+)Cl(-). The single-crystal X-ray structure of 8 reveals that the coordination sphere about technetium is a distorted octahedron with four nitrogen atoms in the equitorial plane, while doubly bonded oxygen and coordinated water occupy the apical positions. Further dissolution of 8 resulted in the formation of dinuclear mu-oxo [TcO(L(1))](2)O, 9. This study shows that Tc and Re have similar metal core structures in solution for diamido dipyridino systems, besides similarity in geometrical structure, proved by the X-ray structures on the same ligands.     

Reactions of 2,2′-bipyridine (bpy) and 1,10-phenanthroline (phen) with yttrium(III) nitrate: preparation,X-ray crystal structures and spectroscopic characterization of the bis-bpy and bis-phen complexes

Y(NO₃)₃ · 5H₂O reacts with 2,2-bipyridine (bpy) and 1,10-phenanthroline (phen) to yield similar complexes of 1:2 yttrium:ligand stoichiometry. The crystal structures of the two complexes, namely, [Y(NO₃)₃(bpy)₂] (1) and [Y(NO₃)₃(phen)₂] (2), are reported. The three nitrate groups are O,O-bidentate and the organic ligands are also bidentate. In both structures the metal ion lies on a crystallographic two-fold axis. The stereochemistry about Y^III can be viewed as a sphenocorona. The new complexes were characterized by elemental analyses and spectroscopic (i.r., ¹H-n.m.r. and ¹³C-n.m.r.) techniques. The data are discussed in terms of the nature of bonding and known solid state structures.     

Protonic Quantum Correlations in the H-Bond Dynamics of Nucleic Acids. Part 1. Conformational comparison of G-C with Benner's κ-π

A new base pair (called κ-π) of Watson-Crick type, with an H-bond pattern different from that in A-T and G-C base pairs, has been recently synthesized by Benner and coworkers and shown to be stable and incorporable into duplex DNA and RNA by polymerases. This new base pair, which contains three H-bonds, is compared with G-C, in the framework of modern dynamical theory of quantum nonlocality and quantum correlations (also called Einstein-Podolsky-Rosen correlations). Connection with the traditional treatment of proton transfer in DNA base pairs, which uses the adiabatic approximation (thus considering the protons as classical particles), is explicitly made. As a result, the dynamics of the H-bond pattern of G-C is shown to exhibit a specific quantum-mechanical phase stability (or: rigidity, stiffness), which is clearly missing in the case of κ-π. This finding is discussed and illustrated, also in connection with recent quantum chemical calculations of proton transfers in DNA base pairs. Additionally, certain speculations concerning a probable ‘evolutionary advantage’ of G-C with respect to κ-π are shortly considered.     

On global attractor for nonlinear parabolic equations of m-Laplacian type

Existence and some regularity results of global attractor in Lq, q?1, for m-Laplacian type quasilinear parabolic equation with a perturbation like a(x)(α|u|u−β|u|u)+f(x) with α>β?0, a(x)?0 are proved. For the proofs Moser's technique is used extensively.