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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Dynamics of nonlinear structures with multiple equilibria: A singular perturbation-invariant manifold approach (1999)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 50 (1999), S. 892-924 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Nonlinear structural dynamics, singular perturbations, slow invariant manifold.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. This work analyzes the motions of a stiff linear oscillator coupled to a soft nonlinear oscillator and subject to a forcing term. This system is a representative of a large class of structural dynamical systems with stiff and soft substructures and with multiple equilibrium states. Using the methodology of singular perturbations and the theory of invariant manifolds, we describe globally (in time) the motions in a finite neighborhood of the origin in phase space. It is shown that, every motion of the system depends on a slowly varying component and a component which rapidly decays with time. The long term behavior of the system is, thus, described by a lower order slow system, which is the restriction of the system to an invariant manifold that contains all the slow motions of the system. For slow periodic forcing, the slow manifold is periodic. The dynamics of the slow system on the invariant manifold, as well as the effects of the singular perturbation parameter on the validity of the slow manifold approximation are also explored.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000330050185
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  • 5
    Electronic Resource
    Electronic Resource
    A class of ompA mutants of Escherichia coliK12 affected in the interaction of OmpA protein and the core region of lipopolysaccharide (1983)
    Springer
    Molecular genetics and genomics 189 (1983), S. 162-165 
    Details
    ISSN: 1617-4623
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary A group of ompA mutants of Escherichia coli K12 are described which were sensitive to bacteriophage K3 in a background wild-type for lipopolysaccharide (LPS). With mutant LPS in vivo (lacking some core sugar residues), however, the ompA mutations gave resistance to K3. Outer membrane levels of OmpA protein were normal or near-normal when the mutations resided in either wild-type or mutant LPS backgrounds. Strains in which the mutations occurred in a wild-type LPS background adsorbed K3 phage at the same initial rate and to the same extent as a wild-type strain, but the efficiency of plaquing of the adsorbed K3 was reduced to 25–50% of wild-type levels. Under conditions where a wild-type strain irreversibly adsorbed over 90% of available phage K3 within 3 min, double mutants (ompA mutant, LPS mutant) left 90% of the phage viable after 1h. The 10% of inactivated phage did not form plaques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00326070
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  • 6
    Electronic Resource
    Electronic Resource
    Asymptotic stability of singularly perturbed systems that have marginally stable boundary-layer systems (1991)
    Springer
    Dynamics and control 1 (1991), S. 95-108 
    Details
    ISSN: 1573-8450
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A class of linear singularly perturbed systems with singular perturbation parameter µ 〉 0 is considered. To assure asymptotic stability of the full-order system for sm 〉 0 sufficiently small, it is customary to require that both the reduced-order system (µ = 0) and the boundary-layer system are asymptotically stable. Here we relax the requirement on the boundary-layer system to stability (i.e., stability, but not necessarily asymptotic stability) and show that, subject to one additional condition, the full-order system is asymptotically stable for sufficiently small µ. The result is illustrated by an application in which we consider the stability robustness of a feedback-controlled mechanical system with respect to an unmodeled flexibility.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02169427
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Suboptimal Control of Rigid Body Motion with a Quadratic Cost (1998)
    Springer
    Dynamics and control 8 (1998), S. 55-81 
    Details
    ISSN: 1573-8450
    Keywords: Rigid body ; quadratic cost ; Lyapunov functions ; Linear matrix inequalities ; stabilization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008278929841
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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
    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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