Instanton counting on blowup. II. K-theoretic partition function

We study Nekrasov's deformed partition function $Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ of 5-dimensional supersymmetric Yang-Mills theory compactified on a circle. Mathematically it is the generating function of the characters of the coordinate rings of the moduli spaces of instantons on $\mathbb R^4$. We show that it satisfies a system of functional equations, called blowup equations, whose solution is unique. As applications, we prove (a) $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta) = \varepsilon_1\varepsilon_2 \log Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ is regular at $\varepsilon_1 = \varepsilon_2 = 0$ (a part of Nekrasov's conjecture), and (b) the genus $1$ parts, which are first several Taylor coefficients of $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$, are written explicitly in terms of $\tau = d^2 F(0,0,\vec{a};\mathfrak q,\boldsymbol\beta)/da^2$ in rank $2$ case.     

Thermalization in one- plus two-body ensembles for dense interacting boson systems

Employing one- plus two-body random matrix ensembles for bosons, temperature and entropy are calculated, using different definitions, as a function of the two-body interaction strength λ   for a system with 10 bosons (m=10$m=10$) in five single-particle levels (N=5$N=5$). It is found that in a region λ∼_λt$\lambda \sim {\lambda }_t$, different definitions give essentially the same values for temperature and entropy, thus defining a thermalization region. Also, (m,N)$(m,N)$ dependence of _λt${\lambda }_t$ has been derived. It is seen that _λt${\lambda }_t$ is much larger than the λ values where level fluctuations change from Poisson to GOE and strength functions change from Breit–Wigner to Gaussian.     

Deformed shell model for T = 0, 1 and 2 bands in <Superscript>52</Superscript>Fe and <Superscript>72</Superscript>Kr

Deformed configuration mixing shell model based on Hartree-Fock states with extension to include isospin projection (DSMT) for two- and four-particle configurations (generated by particle-hole excitations) is applied to study the structure of the low-lying T = 0, 1 and 2 bands (or levels) in the even-even N = Z nuclei ⁵²Fe and ⁷²Kr. The pf-shell KB3 interaction for ⁵²Fe and a modified Kuos interaction for ⁷²Kr are employed in the calculations. In this first application of DSMT with four-particle T projection, low-spin (J 10) members of the T = 0, 1 and 2 bands in ⁵²Fe are compared with experiment including the known E2 transition strengths. The agreement between DSMT and experiment is reasonably good. Similarly, the low-spin members of the observed (prolate) yrast band in ⁷²Kr are also well described by DSMT.     

Convergence acceleration of preconditioned conjugate gradient solver based on error vector sampling for a sequence of linear systems

In this article, we focus on solving a sequence of linear systems that have identical (or similar) coefficient matrices. For this type of problem, we investigate subspace correction (SC) and deflation methods, which use an auxiliary matrix (subspace) to accelerate the convergence of the iterative method. In practical simulations, these acceleration methods typically work well when the range of the auxiliary matrix contains eigenspaces corresponding to small eigenvalues of the coefficient matrix. We develop a new algebraic auxiliary matrix construction method based on error vector sampling in which eigenvectors with small eigenvalues are efficiently identified in the solution process. We use the generated auxiliary matrix for convergence acceleration in the following solution step. Numerical tests confirm that both SC and deflation methods with the auxiliary matrix can accelerate the solution process of the iterative solver. Furthermore, we examine the applicability of our technique to the estimation of the condition number of the coefficient matrix. We also present the algorithm of the preconditioned conjugate gradient method with condition number estimation.     

Spectroscopy of η′ Mesic Nuclei with (p, d) Reaction

We are going to perform an inclusive spectroscopy experiment of η′ mesic nuclei with the ¹²C(p,d) reaction to study in-medium properties of the η′ meson. In nuclear medium, the η′ meson mass may be reduced due to partial restoration of chiral symmetry. In case of sufficiently large mass reduction and small absorption width of η′ at normal nuclear density, peak structures of η′ mesic states in ¹¹C will be observed near the η′ emission threshold even in an inclusive spectrum. The experiment will be carried out at GSI with proton beam supplied by SIS using FRS as a spectrometer. The detail of the experiment is described.     

Polymerization of coordinated monomers. XXII. Ab initio molecular orbital study on the binary radical complexes of 2-methoxycarbonyl propyl radical with boron trichloride and with boron trifluoride as a model of growing radical end

The geometrical and electronic structures of the binary radical complexes of 2-methoxycarbonyl propyl radical with boron trichloride and with boron trifluoride were determined by using an ab initio molecular orbital method. The 2-methoxycarbonyl propyl radical complex was a model of the growing radical end in the copolymerization of methyl methacrylate in the presence of boron halides. The most stable structure of the binary radical complex composed of 2-methoxycarbonyl propyl radical with boron trichloride was a twisted form in which the dihedral angle between the vinyl group and the ester group was 32°, while that of the binary radical complex composed of methyl methacrylate radical with boron trifluoride was a planar form as the free radical. The frontier orbital energy of 2-methoxycarbonyl propyl radical was lowered by 0.06 au by the coordination of boron trichloride, while that was lowered only by 0.02 au by the coordination of boron trifluoride. The polymerization mechanism was elucidated on the basis of these predictions. © 1993 John Wiley & Sons, Inc.     

Electrochemical fluorination of chlorine-containing amines

The electrochemical fluorination of chlorine-containing alkylamines has been studied. It was found that, in general, the carbon-chlorine bond in the alkylamines is retained during electrochemical fluorination is anhydrous hydrogen fluoride, yielding chlorine-containing polyfluoroalkylamines. Perfluoroalkylamines and fluorocarbons were also produced.By the use of this method, several new chloropolyfluoroamines such as (CF₃)₂NCF₂CClF₂, (C₂F₅)₂NCF₂CClF₂, (CF₃)(C₂F₅)NCF₂CClF₂, (CClF₂CF₂)₂NCF₃, (CClF₂CF₂)₂NC₂F₅, (C₂F₅)(CClF₂CF₂)NF, (CClF₂CF₂)₂NF, (CF₃)₂NCF₂CF₂CClF₂, $\text{CF}{}_2\text{(CF}{}_2\text{)}{}_3\text{N}$CF₂CClF₂, and $\text{CF}{}_2\text{CF}{}_2\text{OC}{}_2\text{F}{}_4\text{N}$CF₂CClF₂ have been isolated and characterized.     

Solid Phase Extractive Preconcentration of Cobalt and Nickel in Hair Samples Using Ethyl Xanthate Modified Benzophenone

The ethyl xanthate complexes of cobalt and nickel are quantitatively retained on benzophenone in the pH range of 8.0–10.0. The solid mixture consisting of metal complex together with benzophenone is dissolved in 5mL of dimethyl formamide, and the cobalt and nickel contents were determined by flame atomic absorption spectrometry. The calibration graphs are rectilinear over the concentration range of 0–75 (Co) and 0–100 (Ni) µgL^–1. The detection limits of flame AAS for cobalt and nickel are lowered by a factor of 200 due to the solid phase extraction preconcentration procedure. NIES CRM Human Hair No. 5 and IAEA Reference Hair HH-1 certified reference materials were used in order to verify the accuracy of the developed preconcentration method in analysing human hair samples. The results obtained were found to be in excellent agreement with certified values. Furthermore, hair samples collected from various inhabitants of different age groups and sex living in the Indian states of Andhra Pradesh and Tamil Nadu were successfully analysed by flame AAS in conjunction with the solid phase extraction preconcentration procedure developed for cobalt and nickel.     

The arithmetic-geometric mean inequality of indefinite type

Archiv der Mathematik - In this paper, the arithmetic-geometric mean inequalities of indefinite type are discussed. We show that for a J-selfadjoint matrix A satisfying $$I ge ^J A$$ and...     

Three-component,four-centered,one-pot synthesis of 1-(arylethynyl)-2,3,4,9-tetrahydro-1H-pyrido[3,4-b]indole derivatives

An efficient three component, four-centered A3 coupling strategy has been developed for the synthesis of a novel series of 1-arylethynyl-tetrahydro-β-carboline derivatives in good yields with high selectivity. This method is also useful for the preparation of 1-arylethynyl tetrahydroisoquinolines, which can be used for the synthesis of biologically active molecules such as homolaudanosine, dysoxyline, methopoline and almorexant. The use of a readily available ZnCl₂/Et₃N reagent system makes this method simple, convenient and practical.