Kinetic energy operator approach to the quantum three-body problem with Coulomb interactions

We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body Laplacian operator with the respective masses. Through a four-step reduction process, the nine dimensional problem is reduced to a one dimensional coupled system of ordinary differential equations, amenable to accurate numerical solution as an infinite-dimensional algebraic eigenvalue problem. A key observation in this reduction process is that in the functional subspace of the kinetic energy operator where all the rotational degrees of freedom have been projected out, there is an intrinsic symmetry which can be made explicit through the introduction of Jacobi-spherical coordinates. A numerical scheme is presented whereby the Coulomb matrix elements are calculated to a high degree of accuracy with minimal effort, and the truncation of the linear equations is carried out through a systematic procedureComment: 56 pages, 11 figure

Commenting on Interorganizational Relationship in Franchising Systems: Governance for Learning and Collaborative Research

Abstract. Inter-organizational relationship is increasingly important for modern business world because of its benefits for efficient integration for resources from various parties, facilitation for new knowledge creation, and synergetic use of the collective decision, action and idiosyncratic capabilities. I tend to offer a conceptual discussion for the connections among inter-organizational relationship, governance for organizational learning, and collaborative research in a franchising system context. Important research imperatives were proposed finally.Keywords. Interorganizational relationship, Franchising system, Governance for learning, Collaborative research.JEL. M10, M11, M14

Asymptotic Correction Schemes for Semilocal Exchange-Correlation Functionals

Aiming to remedy the incorrect asymptotic behavior of conventional semilocal exchange-correlation (XC) density functionals for finite systems, we propose an asymptotic correction scheme, wherein an exchange density functional whose functional derivative has the correct (-1/r) asymptote can be directly added to any semilocal density functional. In contrast to semilocal approximations, our resulting exchange kernel in reciprocal space exhibits the desirable singularity of the type O(-1/q^2) as q -> 0, which is a necessary feature for describing the excitonic effects in non-metallic solids. By applying this scheme to a popular semilocal density functional, PBE [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)], the predictions of the properties that are sensitive to the asymptote are significantly improved, while the predictions of the properties that are insensitive to the asymptote remain essentially the same as PBE. Relative to the popular model XC potential scheme, our scheme is significantly superior for ground-state energies and related properties. In addition, without loss of accuracy, two closely related schemes are developed for the efficient treatment of large systems.Comment: 7 pages, 2 figures, 2 tables, supplementary material not include

Commenting on Interorganizational Relationship in Franchising Systems: Governance for Learning and Collaborative Research

Abstract. Inter-organizational relationship is increasingly important for modern business world because of its benefits for efficient integration for resources from various parties, facilitation for new knowledge creation, and synergetic use of the collective decision, action and idiosyncratic capabilities. I tend to offer a conceptual discussion for the connections among inter-organizational relationship, governance for organizational learning, and collaborative research in a franchising system context. Important research imperatives were proposed finally.Keywords. Interorganizational relationship, Franchising system, Governance for learning, Collaborative research.JEL. M10, M11, M14

Diversity, emotion, and decision to implement innovation in family business

Abstract. Family firms are generally small and medium-sized, characterized by ‘flat’ organizational structures and internal succession patterns and relying upon self-financing. One way to overcome inherent liability of family business is to innovate in critical management aspects and jump out to a new operational model. The capability of a firm to continuously innovate is critical for competitive advantage. It can also contribute to the development for the so-called dynamic capability. A firm’s dynamic capability describes to continuously innovate.Keywords. Household behavior, Family economics, Family business.JEL. D10, D13, D14

Universal R-matrix Of The Super Yangian Double DY(gl(1|1))

Based on Drinfeld realization of super Yangian Double DY(gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another realization $L^{\pm}(u)$ of DY(gl(1|1)) is obtained. These two realizations of DY(gl(1|1)) are related by the supersymmetric extension of Ding-Frenkel map.Comment: 6 pages, latex, no figure