Strong stability of stationary solutions and Karush-Kuhn-Tucker points in nonlinear optimization

The concepts of strongly stable stationary solutions (in Kojima's sense) and of strongly regular Karush-Kuhn-Tucker points (in Robinson's sense) for optimization problems with twice differentiable data are crucial in theory and applications of nonlinear optimization with data perturbations. In this paper we give interconnections between both concepts and extend some ideas to standard nonlinear programs withC ¹ data (underC ¹ perturbations). The main purpose of this paper is to survey several equivalent characterizations of strong stability in the classical case of programs withC ² data underC ² perturbations. The unified approach proposed here is essentially based on arguments from the analysis of Lipschitzian mappings.Sponsored by the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.     

Optimale Differentiations- und Integrationsformeln in Co [a,b]

Summary LetC _o [a, b] be the Banach space of all real valued continuous functions defined on the interval [a, b], endowed with the supremum norm. In this paper we construct optimal formulas for the numerical differentiation and integration forC _o [a, b].In particular, the questions of Meinguet [2] and Salzer [5] on the existence of such formulas are answered.     

Multiply-charged ions and interstellar chemistry

Gaseous molecules and ions, and even dust grains, can accumulate charge in the interstellar medium (ISM) by harvesting the energy of UV photons, cosmic rays, helium ions and metastable atoms. This Perspective views the various modes of gas-phase formation of multiply-charged cations and the possible impact of their reactions on the chemical and ionization structure of the ISM, in the light of what is still very limited knowledge. Emphasis is given to gas-phase reactions of multiply-charged cations with atoms, molecules and electrons that lead to charge reduction, charge separation and chemical bond formation and these are examined for multiply-charged atoms, small molecules, hydrocarbons, polycyclic aromatic hydrocarbons and fullerenes, primarily as dications but also as a function of charge state. The increased electrostatic interaction due to multiple charge is seen to promote bonding to individual charge sites on large molecules (e.g. fullerenes) and allow ensuing "surface" chemistry under the influence of Coulomb repulsion. The unique ability of multiply charged cations to undergo charge separation reactions, either unimolecular or bimolecular, can feature in the production in the ISM of internally cold, but translationally hot, cations of lower charge state or hot atoms that may provide the driving force for subsequent chemical reactions in what is otherwise an ultracold environment. Available chemical kinetic models that account for the role of multiply-charged ions in the ISM are few and of limited scope and the observation of these ions in the ISM has remained elusive.     

Multi-Component Ion Modifiers and Arcing Suppressants to Enhance Differential Mobility Spectrometry for Separation of Peptides and Drug Molecules

The optimization of ion/molecule chemistry in a differential mobility spectrometer (DMS) is shown to result in improved peak capacity, separation, and sensitivity. We have experimented with a modifier composed of multiple components, where each component accomplishes a specific task on mixtures of peptides and small drug molecules. Use of a higher proton affinity modifier (hexanol) provides increased peak capacity and separation. Analyte ion/modifier proton transfer is suppressed by adding a large excess of low proton affinity modifier (water or methanol), significantly increasing signal intensity and sensitivity for low proton affinity analytes. Finally, addition of an electrical arcing suppressant (chloroform) allows the device to operate reliably at higher separation fields, improving peak capacity and separation. We demonstrate a 20 % increase in the device peak capacity without any loss of sensitivity and estimate that further optimization of the modifier composition can increase this to 50 %. Use of 3-, 4-, or even 5-component modifiers offers the opportunity for the user to fine-tune the modifier performance to maximize the device performance, something not possible with a single component modifier.      

Packing atomic metal cations with C60: Mass spectrometric observation of M(C60)n with M = Sr and Mo and n = 0–4

The atomic cations of Sr and Mo have been observed to add sequentially up to four molecules of C₆₀ in helium at 0.35 Torr and room temperature in the flow tube of a modified inductively coupled plasma/selected-ion flow tube (ICP/SIFT) tandem mass spectrometer. The available center-of-mass energy in collision-induced dissociation experiments of approximately 1.3 eV failed to remove C₆₀ from M⁺(C₆₀)₄. A structure is proposed for M⁺(C₆₀)₄ cations in which the bonding involves η⁶ interaction of the metal with the C₆₀ ligands and η²-to-η² interactions between the C₆₀ ligands.     

Competitive Activation of C?H and C?X Bonds in Reactions of Pt+ with CH3X (X=F,Cl): Experiment and Theory

The reactions of Pt⁺ with CH₃X (X=F, Cl) are studied experimentally by employing an inductively coupled plasma/selected‐ion flow tube tandem mass spectrometer and theoretically by density functional theory. Dehydrogenation and HX elimination are found to be the primary reaction channels in the remarkably different ratios of 95:5 and 60:40 in the fast reactions of Pt⁺ with CH₃F and CH₃Cl, respectively. The observed kinetics are consistent with quantum chemistry calculations, which indicate that both channels in the reaction with CH₃F are exothermic with ground‐state Pt⁺(²D), but that HF elimination is prohibited kinetically because of a transition state that lies above the reactant entrance. The observed HF‐elimination channel is attributed to a slow reaction of CH₃F with excited‐state Pt⁺(⁴F) for which calculations predict a small barrier. The calculations also show that both the HCl‐elimination and dehydrogenation channels observed with CH₃Cl are thermodynamically and kinetically allowed, although the state‐specific product distributions could not be ascertained experimentally. Further CH₃F addition is observed with the primary products to produce PtCH₂⁺(CH₃F)_1,2 and PtCHF⁺(CH₃F)_1,2. With CH₃Cl, sequential HCl elimination is observed with PtCH₂⁺ to form PtC_nH_2n⁺ with n=2, 3, which then add CH₃Cl sequentially to form PtC₂H₄⁺(CH₃Cl)_1–3 and PtC₃H₆⁺(CH₃Cl)_1,2. Also, sequential addition is observed for PtCHCl⁺ to form PtCHCl⁺(CH₃Cl)_1,2.     

Chemical stability and reactivity of deprotonated oligonucleotides (DNA) in the gas phase: protonation and solvation with hydrogen bromide

Selected deprotonated oligodeoxynucleotides generated by electrospray ionization were exposed to a variety of neutral molecules in the gas phase at room temperature in flowing helium gas at 0.35 Torr. Single-stranded [AGTCTG-nH]n- and single- and double-stranded [GCATGC-nH]n- anions were found to be remarkably unreactive with strong oxidants (O3, O2, N2O) and potential intercalators (benzene, pyridine, toluene, and quinoxaline). Hydration also was observed to be inefficient. However, [AGTCTG-nH]n- anions with n=2, 3, 4, and 5 were seen to be sequentially protonated and/or hydrobrominated with HBr (but not damaged) and displayed an interesting "end effect" against protonation. Measurements are provided for the rate coefficients of reaction and the efficiencies of protonation. These experimental results point toward the exciting prospect of measuring the intrinsic chemistry of other bare DNA-like anions, including double-stranded oligonucleotide anions in the gas phase at room temperature.     

Gas-phase observation of the heterolytic dissociation of negative ions into counter ions: Dissociation of [Cu phthalocyanine (SO<Subscript>3</Subscript>)<Subscript>4</Subscript>Na]<Superscript>3−</Superscript>.

Ion pair formation proceeding in solution at room-temperature, where it is driven by energies of solvation, has been observed in the gas-phase in the collision-induced dissociation of [Cu phthalocyanine (SO3)4Na]3- and [Cu phthalocyanine (SO3)4Na2]2- at low energies. The gas-phase observation of these charge separations into positive and negative ions, seemingly counter-intuitive, is favored sufficiently by thermodynamics to proceed at low collision energies. The combination of a high stability of the negative product anion against electron detachment and a low recombination energy of the departing positive counter ion appears to be the key requirement for such dissociations to proceed at low energies in the gas-phase.     

Catalytic oxidation of H2 by N2O in the gas phase: O-atom transport with atomic metal cations

Twenty-five atomic cations, M (+), that lie within the thermodynamic window for O-atom transport catalysis of the oxidation of hydrogen by nitrous oxide, have been checked for catalytic activity at room temperature with kinetic measurements using an inductively-coupled plasma/selected-ion flow tube (ICP/SIFT) tandem mass spectrometer. Only 4 of these 25 atomic cations were seen to be catalytic: Fe (+), Os (+), Ir (+), and Pt (+). Two of these, Ir (+) and Pt (+), are efficient catalysts, while Fe (+) and Os (+) are not. Eighteen atomic cations (Cr (+), Mn (+), Co (+), Ni (+), Cu (+), Ge (+), Se (+), Mo (+), Ru (+), Rh (+), Sn (+), Te (+), Re (+), Pb (+), Bi (+), Eu (+), Tm (+), and Yb (+)) react too slowly at room temperature either in their oxidation with N 2O to form MO (+) or in the reduction of MO (+) by H 2. Many of these reactions are known to be spin forbidden and a few actually may lie outside the thermodynamic window. Three alkaline-earth metal monoxide cations, CaO (+), SrO (+), and BaO (+), were observed to favor MOH (+) formation in their reactions with H 2. A potential-energy landscape is computed for the oxidation of H 2 with N 2O catalyzed by Fe (+)( (6)D) that vividly illustrates the operation of an ionic catalyst and qualitatively accounts for the relative inefficiency of this catalyst.     

Catalytic Hydrogen Atom Transfer (HAT) for Sustainable and Diastereoselective Radical Reduction

Going cyclic! A catalytic cycle and cyclic transition states enable a novel sustainable and catalytic hydrogen atom transfer (HAT) for highly diastereoselective radical reductions. Readily available nontoxic silanes are the terminal reductants for epoxides that are opened by bifunctional titanocene(III) hydride catalysts.