Instanton counting on blowup. I. 4-dimensional pure gauge theory

We give a mathematically rigorous proof of Nekrasov’s conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on ℝ⁴ gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of ℝ⁴, we derive a differential equation for the Nekrasov’s partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky et al. Mathematics Subject Classification (2000) 14D21, 57R57, 81T13, 81T60     

Blei

Ohne Zusammenfassung     

Geometric shapes withg- bosons in the interacting boson model

Geometric aspects of the extended interacting boson model (gIBM) withs, d andg bosons are studied using coherent states. Algebraic expressions for the coherent state expectation values of various terms in the general gIBM Hamiltonian are derived in terms of the quadrupole and hexadecupole deformation variablesβ ₂ andβ ₄ and the asymmetry angleγ. These in turn are used to determine the equilibrium shape parameters (β ₂ ⁰ ,β ₄ ⁰ ,γ ⁰) in the seven dynamical symmetry limits of gIBM.     

Gold‐Catalyzed Enantioselective Synthesis,Crystal Structure,and Photophysical/Chiroptical Properties of Aza[10]helicenes

The enantioselective synthesis of an aza[10]helicene, possessing two pyridone units, has been achieved by the gold‐catalyzed intramolecular quadruple hydroarylation of a tetrayne. This aza[10]helicene was successfully converted into a fully aromatic aza[10]helicene, possessing two pyridine units. Structure–photophysical and chiroptical properties relationship in a series of azahelicene isomers has also been disclosed.     

Calculation of X‐ray scattering intensities by means of the coupled cluster singles and doubles model

Total X‐ray scattering intensity σ_ee(q) is very sensitive to electron correlation effects. In this study σ_ee(q) of N₂, CO, and N₂O have been computed by the coupled cluster singles and doubles (CCSD) method and compared with configuration interaction singles and doubles (CISD) calculations as well as experimental observations. σ_ee(q) curves by CCSD calculations are rather close to those by CISD, but although small, there still exist some discrepancies between calculated and observed values. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1315–1320, 2001     

Right preconditioned MINRES for singular systems†

We consider solving large sparse symmetric singular linear systems. We first introduce an algorithm for right preconditioned minimum residual (MINRES) and prove that its iterates converge to the preconditioner weighted least squares solution without breakdown for an arbitrary right‐hand‐side vector and an arbitrary initial vector even if the linear system is singular and inconsistent. For the special case when the system is consistent, we prove that the iterates converge to a min‐norm solution with respect to the preconditioner if the initial vector is in the range space of the right preconditioned coefficient matrix. Furthermore, we propose a right preconditioned MINRES using symmetric successive over‐relaxation (SSOR) with Eisenstat's trick. Some numerical experiments on semidefinite systems in electromagnetic analysis and so forth indicate that the method is efficient and robust. Finally, we show that the residual norm can be further reduced by restarting the iterations.     

Effect of formulation of alginate beads on their mechanical behavior and stiffness

The aim of this work was to determine the effect of formulation of alginate beads on their mechani-cal behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusion-dripping method. Single wet beads were compressed at a speed of 40 mm/min,and their elastic limits were investigated,and the corresponding force versus displacement data were obtained. The Young's moduli of the...     

Mono and dinuclear half-sandwich platinum group metal complexes bearing pyrazolyl-pyrimidine ligands: Syntheses and structural studies

Reactions of 0.5 eq. of the dinuclear complexes [(η⁶-arene)Ru(μ-Cl)Cl]₂ (arene = η⁶-C₆H₆, η⁶-p-ⁱPrC₆H₄Me) and [(Cp∗)M(μ-Cl)Cl]₂ (M = Rh, Ir; Cp∗ = η⁵-C₅Me₅) with 4,6-disubstituted pyrazolyl-pyrimidine ligands (L) viz. 4,6-bis(pyrazolyl)pyrimidine (L1), 4,6-bis(3-methyl-pyrazolyl)pyrimidine (L2), 4,6-bis(3,5-dimethyl-pyrazolyl)pyrimidine (L3) lead to the formation of the cationic mononuclear complexes [(η⁶-C₆H₆)Ru(L)Cl]⁺ (L = L1, 1; L2, 2; L3, 3), [(η⁶-p-ⁱPrC₆H₄Me)Ru(L)Cl]⁺ (L = L1, 4; L2, 5; L3, 6), [(Cp∗)Rh(L)Cl]⁺ (L = L1, 7; L2, 8; L3, 9) and [(Cp∗)Ir(L)Cl]⁺ (L = L1, 10; L2, 11; L3, 12), while reactions with 1.0 eq. of the dinuclear complexes [(η⁶-arene)Ru(μ-Cl)Cl]₂ and [(Cp∗)M(μ-Cl)Cl]₂ give rise to the dicationic dinuclear complexes [{(η⁶-C₆H₆)RuCl}₂(L)]²⁺ (L = L1, 13; L2, 14; L3, 15), [{(η⁶-p-ⁱPrC₆H₄Me)RuCl}₂(L)]²⁺ (L = L1, 16; L2, 17; L3, 18), [{(Cp∗)RhCl}₂(L)]²⁺ (L = L1, 19; L2, 20; L3, 21) and [{(Cp∗)IrCl}₂(L)]²⁺ (L = L1 22; L2, 23; L3 24). The molecular structures of [3]PF₆, [6]PF₆, [7]PF₆ and [18](PF₆)₂ have been established by single crystal X-ray structure analysis.     

Study of half-sandwich platinum group metal complexes bearing dpt-NH2 ligand

A quite general approach for the preparation of η⁵-and η⁶-cyclichydrocarbon platinum group metal complexes is reported. The dinuclear arene ruthenium complexes [(η⁶-arene)Ru(μ-Cl)Cl]₂ (arene = C₆H₆, C₁₀H₁₄ and C₆Me₆) and η⁵-pentamethylcyclopentadienyl rhodium and iridium complexes [(η⁶-C₅Me₅)M(μ-Cl)Cl]₂ (M = Rh, Ir) react with 2 equiv. of 4-amino-3,5-di-pyridyltriazole (dpt-NH₂) in presence of NH₄PF₆ to afford the corresponding mononuclear complexes of the type [(η⁶-arene)Ru(dpt-NH₂)Cl]PF₆ {arene = C₁₀H₁₄ (1), C₆H₆ (2) and C₆Me₆ (3)} and [(η⁶-C₅Me₅)M(dpt-NH₂)Cl]PF₆ {M = Rh (4), Ir (5)}. However, the mononuclear η⁵-cyclopentadienyl analogues such as [(η⁵-C₅H₅)Ru(PPh₃)₂Cl], [(η⁵-C₅H₅)Os(PPh₃)₂Br], [(η⁵-C₅Me₅)Ru(PPh₃)₂Cl] and [(η⁵-C₉H₇)Ru(PPh₃)₂Cl] complexes react in presence of 1 equiv. of dpt-NH₂ and 1 equiv. of NH₄PF₆ in methanol yielded mononuclear complexes [(η⁵-C₅H₅)Ru(PPh₃)(dpt-NH₂)]PF₆ (6), [(η⁵-C₅H₅)Os(PPh₃)(dpt-NH₂)]PF₆ (7), [(η⁵-C₅Me₅)Ru(PPh₃)(dpt-NH₂)]PF₆ (8) and [(η⁵-C₉H₇)Ru(PPh₃)(dpt-NH₂)]PF₆ (9), respectively. These compounds have been totally characterized by IR, NMR and mass spectrometry. The molecular structures of 4 and 6 have been established by single crystal X-ray diffraction and some of the representative complexes have also been studied by UV–Vis spectroscopy.