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  • 1
    Electronic Resource
    Electronic Resource
    Stress moments of nearly touching spheres in low Reynolds number flow (1988)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 874-884 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract If two spheres are nearly touching, and the flow around them is governed by the Stokes equations, the integral moments of the surface stress are singular functions of the gap width. The method used previously to calculate the singular terms in the zeroth moment (the force) and the antisymmetric first moment (the couple) is extended here to calculate the singular terms in the symmetric first moment (the stresslet) for motions perpendicular to the line of centres. It is shown that the reciprocal theorem requires unexpected relations between the newly found singularities and ones found previously. It is also shown that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets. The series expressions then become valid for all separations of the spheres.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945124
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  • 2
    Electronic Resource
    Electronic Resource
    Orientation of acidic polysaccharides and rhodopsin-oligosaccharides in frog retinal rod outer segments (1978)
    Springer
    Histochemistry and cell biology 56 (1978), S. 65-77 
    Details
    ISSN: 1432-119X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary Using topo-optical staining reactions, the presence and molecular order of three structural components of outer segments of frog retina were studied. These components included (1) an acidic polysaccharide texture, (2) free aldehyde groups which arise during formalin fixation and (3) the oligosaccharide chains of rhodopsin. Quantitative measurements of the dye binding and birefringence effects arising from the individual structural components in rod outer segments were made. Results indicated that all three structural components had a rather well-defined orientation within the ROS. The spherulites phagocytized from the apical ends of ROSs by the pigment epithelium also demonstrate preferred orientation of the three structural components investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00492254
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  • 3
    Electronic Resource
    Electronic Resource
    Symbolic computation in nonlinear dynamics (1995)
    Springer
    Open systems & information dynamics 3 (1995), S. 131-147 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract This paper gives examples of how computer algebra systems can help us to understand nonlinear dynamical systems and their numerical simulations. We caution against naive use of exact arithmetic, but we give examples where elementary use is helpful. We also look at the use of polynomial computations — such as factoring, computation of discriminants, and Gröbner bases — in bifurcation studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02228812
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  • 4
    Electronic Resource
    Electronic Resource
    Practical stabilizability of uncertain dynamical systems: Application to robotic tracking (1985)
    Springer
    Journal of optimization theory and applications 47 (1985), S. 235-252 
    Details
    ISSN: 1573-2878
    Keywords: Uncertain dynamical systems ; robotic tracking ; stability ; deterministic feedback control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The tracking problem for a robotic manipulator withn controlled degrees of freedom and uncertain dynamics is considered. Based on the deterministic theory of Refs. 1–15 and requiring only knowledge of bounds on the system uncertainty, a classC of continuous feedback controls (adapted from Ref. 11) is proposed with respect to which the uncertain tracking system is practically stabilizable in the sense that, given a feasible path to be tracked and an arbitrarily small neighborhood σ of the origin in the appropriate error space, there exists a control inC such that the tracking error for the feedback controlled uncertain system is ultimately bounded with respect to σ. The theory is illustrated in a numerical example of a robot with two degrees of freedom.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940771
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  • 5
    Electronic Resource
    Electronic Resource
    Bounded controllers for robust exponential convergence (1993)
    Springer
    Journal of optimization theory and applications 76 (1993), S. 1-12 
    Details
    ISSN: 1573-2878
    Keywords: Robust control ; bounded control ; uncertain systems ; Lyapunov techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the problem of stabilizing an uncertain system when the norm of the control input is bounded by a prespecified constant. We treat continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded by a known affine function of the norm of the system state and the norm of the control input. Given a prespecified rate of convergence and a ball containing the origin of the state space, we present controllers which guarantee that, for all allowable uncertainties and nonlinearities, there is a region of attraction from which all solutions converge to the given ball with the prespecified convergence rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00952819
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  • 6
    Electronic Resource
    Electronic Resource
    Optimal Control of Rigid Body Angular Velocity with Quadratic Cost (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 507-532 
    Details
    ISSN: 1573-2878
    Keywords: Rigid bodies ; Hamilton–Jacobi equation ; Riccati equation ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by the Euler equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal controllers. These controllers have a very simple structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022656326640
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  • 7
    Electronic Resource
    Electronic Resource
    Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 155-168 
    Details
    ISSN: 1573-2878
    Keywords: Uncertain systems ; deterministic control ; adaptive control ; guaranteed stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider dynamical systems containing uncertain elements due to imperfect knowledge about the model and the input. Since these uncertainties may result in unstable behavior, we seek controllers which guarantee that all possible responses of the system are uniformly bounded and approach a desired response. Toward that end, we present a class of adaptive controllers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934441
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  • 8
    Electronic Resource
    Electronic Resource
    On the LambertW function (1996)
    Springer
    Advances in computational mathematics 5 (1996), S. 329-359 
    Details
    ISSN: 1572-9044
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The LambertW function is defined to be the multivalued inverse of the functionw →we w . It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02124750
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  • 9
    Electronic Resource
    Electronic Resource
    Guaranteed rates of exponential convergence for uncertain systems (1990)
    Springer
    Journal of optimization theory and applications 64 (1990), S. 481-494 
    Details
    ISSN: 1573-2878
    Keywords: Uncertain systems ; exponential convergence ; exponential stability ; robust control ; Lyapunov theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For systems described by ordinary differential equations, we introduce the notion of exponential convergence to a ball containing the origin of the state space. For two specific classes of uncertain systems, controllers are presented which assure this behavior. For one of the system classes, the rate of exponential convergence can be made arbitrarily large.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939420
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  • 10
    Electronic Resource
    Electronic Resource
    Stabilizing uncertain systems with bounded control (1991)
    Springer
    Dynamics and control 1 (1991), S. 227-238 
    Details
    ISSN: 1573-8450
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider the problem of stabilizing an uncertain system when the norm of the control input is bounded by a prespecified constant. We treat continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded by a known constant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02169679
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