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In this study, we assumed that organizational heterogeneity is a key factor influencing the effects of university–industry cooperation policy in higher education institutes. Gender difference, faculty position, faculty member nationality, and diversity in academic expertise were considered as the indicators of heterogeneity. One-hundred graduate institutes with doctoral programs were selected from 881 departments offering doctoral programs in Taiwan as our target group. Correlation analysis, regression analysis, and curve estimation according to the concept of Blau’s index were conducted to determine the effects of graduate institute heterogeneity. Gender difference in graduate institutes played a crucial role on the effect of university–industry collaboration. The results reveal that excessive or insufficient differentiation among faculty positions has an adverse effect on university–industry collaboration, presenting both advantages and disadvantages in this case. A Blau’s index value of 0.56 for faculty position differentiation indicated optimal performance in university–industry collaboration. To enhance university–industry collaboration, this study suggests that the optimal fit proportion of faculty numbers in graduate institutes is seven professors to two associate professors to one assistant professor. Diversity in expertise in graduate institutes also indicated improved performance in university–industry collaboration. Determining how to diversify the expertise in graduate institutes is critical for improving performance and must be considered at specific institute level. The findings provide specific strategies for graduate institutes to reallocate their human resources to optimize their performance in this field.

For a given molecular wavefunction Ψ, the probability density function Ψ∗Ψ is not the only information that can be extracted from Ψ. We point out in this paper that nonlinear quantum dynamics of a diatomic molecule, completely consistent with the probability prediction of quantum mechanics, does exist and can be derived from the quantum Hamilton equations of motion determined by Ψ. It can be said that the probability density function Ψ∗Ψ is an external representation of the quantum state Ψ, while the related Hamilton dynamics is an internal representation of Ψ, which reveals the internal mechanism underlying the externally observed random events. The proposed internal representation of Ψ establishes a bridge between nonlinear dynamics and quantum mechanics, which allows the methods and tools already developed by the former to be applied to the latter. Based on the quantum Hamilton equations of motion derived from Ψ, vibration, rotation and spin motions of a diatomic molecule and the interactions between them can be analyzed simultaneously. The resulting dynamic analysis of molecular motion is compared with the conventional probability analysis and the consistency between them is demonstrated.

Because of the lack of nonlinear dynamics, up to now no bifurcation phenomenon in its original sense has been discovered directly in quantum mechanical systems. Based on the formalism of complex-valued quantum mechanics, this article derives the nonlinear Hamilton equations from the Schrodinger equation to provide the necessary mathematic framework for the analysis of quantum bifurcation. This new approach makes it possible to identify quantum bifurcation by the direct evidence of the sudden change of fixed points and their surrounding trajectories. As a practical application of the proposed approach, we consider the quantum motion in a Coulombic-like potential modeled by V(r) = A/r2 − B/r, where the first term describes the centrifugal trend and the second deals with the Coulombic attraction. As the bifurcation parameter evolves, we demonstrate how local and global bifurcations in quantum dynamics can be identified by inspecting the changes of fixed points and their surrounding trajectories. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

The second part of this paper deals with quantum trajectories in diatomic molecules, which has not been considered before in the literature. Morse potential serves as a more accurate function than a simple harmonic oscillator for illustrating a realistic picture about the vibration of diatomic molecules. However, if we determine molecular dynamics by integrating the classical force equations derived from a Morse potential, we will find that the resulting trajectories do not consist with the probabilistic prediction of quantum mechanics. On the other hand, the quantum trajectory determined by Bohmian mechanics [Bohm D. A suggested interpretation of the quantum theory in terms of hidden variable. Phys. Rev. 1952;85:166–179] leads to the conclusion that a diatomic molecule is motionless in all its vibrational eigen-states, which also contradicts probabilistic prediction of quantum mechanics. In this paper, we point out that the quantum trajectory of a diatomic molecule completely consistent with quantum mechanics does exist and can be solved from the quantum Hamilton equations of motion derived in Part I, which is based on a complex-space formulation of fractal spacetime [El Naschie MS. A review of E-Infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals 2004;19:209–36; El Naschie MS. E-Infinity theory – some recent results and new interpretations. Chaos, Solitons & Fractals 2006;29:845–853; El Naschie MS. The concepts of E-infinity. An elementary introduction to the cantorian-fractal theory of quantum physics. Chaos, Solitons & Fractals 2004;22:495–511; El Naschie MS. SU(5) grand unification in a transfinite form. Chaos, Solitons & Fractals 2007;32:370–374; Nottale L. Fractal space-time and microphysics: towards a theory of scale relativity. Singapore: World Scientific; 1993; Ord G. Fractal space time and the statistical mechanics of random works. Chaos, Soiltons & Fractals 1996;7:821–843] approach to quantum mechanics. The fine-structure internuclear potentials obtained in Part I will be exploited here to derive the eigen-trajectories corresponding to each vibrational substate and to find the scattering trajectories under molecular dissociation. Quantum trajectories computed from the real spectroscopic data for several diatomic molecules will be demonstrated and compared.

*† ‡ § This paper proposes a new approach to consider nonlinear H∞ control of hovering vehicles described by six-degree-of-freedom nonlinear dynamics with plant uncertainties due to the variation of moments of inertia caused by fuel consumption and/or payload operation. Taking into account nonlinear effect, plant uncertainty, and exogenous disturbances caused by wind gust, we show in this paper that the six-degree-of-freedom nonlinear H∞ controller can be exactly decoupled into two three-degree-of-freedom controllers, one for translational motion and the other for rotational motion, even though longitudinal and lateral dynamics of flight vehicle in hover are highly nonlinear and severely coupled. Nomenclature dx, dy, dz, and dl , dm , dn = applied exogenous forces and moments Fx, Fy , Fz , and L, M ,N = applied forces and moments g = acceleration due to gravity xx I , xz I , …, = the moments of inertia of the flight vehicle s m = vehicle's mass U, V, W, and P, Q, R = linear and angular velocities ,, φ θψ = Euler angles 0 θ = main rotor collective pitch angle 0T θ = tail rotor collective pitch angle 1c θ = lateral cyclic pitch 1s θ = longitudinal cyclic pitch