6,470 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

    Factorization and reduction methods for optimal control of distributed parameter systems

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    A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given

    IVA the robot: Design guidelines and lessons learned from the first space station laboratory manipulation system

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    The first interactive Space Station Freedom (SSF) lab robot exhibit was installed at the Space and Rocket Center in Huntsville, AL, and has been running daily since. IntraVehicular Activity (IVA) the robot is mounted in a full scale U.S. Lab (USL) mockup to educate the public on possible automation and robotic applications aboard the SSF. Responding to audio and video instructions at the Command Console, exhibit patrons may prompt IVA to perform a housekeeping task or give a speaking tour of the module. Other exemplary space station tasks are simulated and the public can even challenge IVA to a game of tic tac toe. In anticipation of such a system being built for the Space Station, a discussion is provided of the approach taken, along with suggestions for applicability to the Space Station Environment

    The 2p yields 1s pionic transition

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    Pion-atomic transitions, perturbation theory, S waves, and P wave

    Inverse problems in the modeling of vibrations of flexible beams

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    The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented

    Notes and Comments

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    THERMAL DIFFUSION AS A PURIFICATION TOOL

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72201/1/j.1749-6632.1966.tb49745.x.pd

    Chandrasekhar equations and computational algorithms for distributed parameter systems

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    The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas

    Mathematical Musings of a Urologist

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    The derivatives with respect to the variable rr of πr2\pi r^2 and 43πr3\frac{4}{3}\pi r^3 are 2πr2\pi r and 4πr24\pi r^2, respectively. This relates, through the derivative, the area enclosed in a circle to the length of that circle and, likewise, the volume of a sphere to the surface area of that sphere. The reasons why this works are basic to a first course in calculus. In this brief article, we expand on these ideas to shapes other than circles and spheres. Our approach is with the first year calculus student in mind

    Determination of Strong-Interaction Widths and Shifts of Pionic X-Rays with a Crystal Spectrometer

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    Pionic 3d-2p atomic transitions in F, Na, and Mg have been studied using a bent crystal spectrometer. The pionic atoms were formed in the production target placed in the external proton beam of the Space Radiation Effects Laboratory synchrocyclotron. The observed energies and widths of the transitions are E=41679(3) eV and Γ=21(8) eV, E=62434(18) eV and Γ=22(80) eV, E=74389(9) eV and Γ=67(35) eV, in F, Na, and Mg, respectively. The results are compared with calculations based on a pion-nucleus optical potential
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