Approximations and generalized Newton methods

Mathematical Programming - We present approaches to (generalized) Newton methods in the framework of generalized equations $$0\in f(x)+M(x)$$ , where f is a function and M is a multifunction. The...     

Familien von C∞-Funktionen auf Mannigfaltigkeiten

Ohne Zusammenfassung     

Some criteria for the minimality of pairs of compact convex sets

Some criteria for minimality for a pair of compact convex subsets of a real locally convex vector space are proved. Moreover several examples are given.     

Kinetik der Bromierung von Phenolen und phenolischen Mekrkernverbindungen

The bromination of 15 dinuclear phenolic compounds (dihydroxydiphenylmethanes, methylene bisphenols) by molecular bromine in acetic acid was studied kinetically at 22°C. In all compounds the electrophilic substitution occurred inortho-position to the phenolic hydroxy group of the methyl phenol unit while the non reacting neighboring unit was differently substituted by H, CH₃,t-Bu and NO₂. A decrease in the reaction rate was observed in 2,2′-dihydroxydiphenylmethanes, where the +M-effect of the hydroxy group is diminished by an intramolecular hydrogen bond. The strength of this hydrogen bond may be influenced mainly by steric factors. Strong electron withdrawing substituents like NO₂ show a rate decreasing influence on the reactivity of the neighboring unit also in 2,4′- and 4,4′-dihydroxydiphenylmethanes.     

Gas-phase reactions of atomic lanthanide cations with D2O: room-temperature kinetics and periodicity in reactivity.

Reactions of atomic lanthanide cations (excluding Pm+) with D2O have been surveyed in the gas phase using an inductively coupled plasma/selected-ion flow tube (ICP/SIFT) tandem mass spectrometer to measure rate coefficients and product distributions in He at 0.35+/-0.01 Torr and 295+/-2 K. Primary reaction channels were observed corresponding to O-atom transfer, OD transfer and D2O addition. O-atom transfer is the predominant reaction channel and occurs exclusively with Ce+, Nd+, Sm+, Gd+, Tb+ and Lu+. OD transfer is observed exclusively with Yb+, and competes with O-atom transfer in the reactions with La+ and Pr+. Slow D2O addition is observed with early lanthanide cation Eu+ and the late lanthanide cations Dy+, Ho+, Er+ and Tm+. Higher-order sequential D2O addition of up to five D2O molecules is observed with LnO+ and LnOD+. A delay of more than 50 kcal mol(-1) is observed in the onset of efficient exothermic O-atom transfer, which suggests the presence of kinetic barriers of perhaps this magnitude in the exothermic O-atom transfer reactions of Dy+, Ho+, Er) and Tm+ with D2O. The reaction efficiency for O-atom transfer is seen to decrease as the energy required to promote an electron to make two non-f electrons available for bonding increases. The periodic trend in reaction efficiency along the lanthanide series matches the periodic trend in the electron-promotion energy required to achieve a d1s1 or d2 excited electronic configuration in the lanthanide cation, and also the periodic trends across the lanthanide row reported previously for several alcohols and phenol. An Arrhenius-like correlation is also observed for the dependence of D2O reactivity on promotion energy for early lanthanide cations, and exhibits a characteristic temperature of 2600 K.     

Structures,fragmentation, and protonation of trideoxynucleotide CCC mono- and dianions

Both quantum chemical calculations and ESI mass spectrometry are used here to explore the gas-phase structures, energies, and stabilities against collision-induced dissociation of a relatively small model DNA molecule--a trideoxynucleotide with the sequence CCC, in its singly and doubly deprotonated forms, (CCC-H)(-) and (CCC-2H)(2-), respectively. Also, the gas-phase reactivity of these two anions was measured with HBr, a potential proton donor, using an ESI/SIFT/QqQ instrument. The computational results provide insight into the gas-phase structures of the electrosprayed (CCC-2H)(2-) and (CCC-H)(-) anions and the neutral CCC, as well as the proton affinities of the di- and monoanions. The dianion (CCC-2H)(2-) was found to dissociate upon CID by charge separation via two competing channels: separation into deprotonated cytosine (C-H)(-) and (CCC-(C-H)-2H)(-), and by w(1)(-)/a(2)(-) cleavage of the backbone. The monoanion (CCC-H)(-) loses a neutral cytosine upon CID, and an H/D-exchangeable proton, presumably residing on one of the phosphate groups, is transferred to the partially liberated (C-H)(-) before dissociation. This was confirmed by MS/MS experiments with the deuterated analog. The reaction of (CCC-2H)(2-) with HBr was observed to be rapid, k=(1.4+/-0.4) x 10(-9) cm(3) molecule(-1) s(-1), and to proceed both by addition (78%) and by proton transfer (22%) while (CCC-H)(-) reacts only by HBr addition, k=(7.1+/-2.1) x 10(-10) cm(3) molecule(-1) s(-1). This is in accord with the computed proton affinities of (CCC-2H)(2-) and (CCC-H)(-) anions that bracket the known proton affinity of Br(-).     

Periodicity in collision-induced and remote-bond activation of alkali metal ions attached to polyether ionophores

The collision-induced dissociation of lasalocid and monensin A bound to alkali metal cations has been investigated using electrospray MS/MS. The binding affinity for the metal cations, as measured with collision-induced dissociation, was found to depend on their ionic radius, decreasing with increasing radius. Monensin A was observed to have a greater binding affinity for alkali metal cations than lasalocid acid.