28,475 research outputs found

    Chandrasekhar equations for infinite dimensional systems

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    Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included

    A Canonical Ensemble Approach to the Fermion/Boson Random Point Processes and its Applications

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    We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein, Fermi-Dirac statistics, respectively, in a finite volume. Focusing on the distribution of positions of the particles, we have point processes of the fixed number of points in a bounded domain. By taking the thermodynamic limit such that the particle density converges to a finite value, the boson/fermion processes are obtained. This argument is a realization of the equivalence of ensembles, since resulting processes are considered to describe a grand canonical ensemble of points. Random point processes corresponding to para-particles of order two are discussed as an application of the formulation. A statistics of a system of composite particles at zero temperature are also considered as a model of determinantal random point processes.Comment: 26pages, Some typos are corrected, to be published in Commun. Math. Phy

    Legendre-Tau approximations for functional differential equations

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    The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made

    Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

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    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made

    Preparation of linear hydroxy substituted polyphosphazenes

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    The synthesis of partially hydroxy-substituted phosphazene prepolymers amenable to processing into cellular, flexible polyurethane foams was investigated. Factors determined include (1) the environment of the hydroxyl group; (2) the ease of the hexachlorocyclotriphosphazene polymerization; (3) the nature of the nonreactive substituents; and (4) the mode of introduction of the hydroxyl entity. The specific approaches taken, the rationale of the selections made, and the results are discussed

    Oscillator strengths and line widths of dipole-allowed transitions in Ā¹ā“Nā‚‚ between 89.7 and 93.5ā€‚nm

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    Line oscillator strengths in the 20 electric dipole-allowed bands of Ā¹ā“Nā‚‚ in the 89.7ā€“93.5nm (111480ā€“106950cmā»Ā¹) region are reported from photoabsorptionmeasurements at an instrumental resolution of āˆ¼6mƅ (0.7cmā»Ā¹) full width at half maximum. The absorptionspectrum comprises transitions to vibrational levels of the 3pĻƒįµ¤cā€²ā‚„Ā¹Ī£įµ¤āŗ, 3pĻ€įµ¤cĀ³Ī įµ¤, and 3sĻƒgoā‚ƒĀ¹Ī įµ¤Rydberg states and of the bā€²Ā¹Ī£įµ¤āŗ and bĀ¹Ī įµ¤ valence states. The J dependences of band f values derived from the experimental line f values are reported as polynomials in Jā€²(Jā€²+1) and are extrapolated to Jā€²=0 in order to facilitate comparisons with results of coupled Schrƶdinger-equation calculations. Most bands in this study are characterized by a strong J dependence of the band f values and display anomalous P-, Q-, and R-branch intensity patterns. Predissociation line widths, which are reported for 11 bands, also exhibit strong J dependences. The f value and line width patterns can inform current efforts to develop comprehensive spectroscopic models that incorporate rotational effects and predissociation mechanisms, and they are critical for the construction of realistic atmospheric radiative-transfer models.This work was supported in part by NASA Grant No. NNG05GA03G to Wellesley College and Australian Research Council Discovery Program Grant No. DP0558962
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