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  • 1
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Convergence rates of Newton-Goldstein sequences are estimated for convex constrained minimization problems with singular solutionsξ, i.e., solutions at which the local quadratic approximationQ(ξ, x) to the objective functionF grows more slowly than ∥x − ξ∥2 for admissible vectorsx nearξ. For a large class of iterative minimization methods with quadratic subproblems, it is shown that the valuesr n =F(x n )−infΩ F are of orderO(n −1/3) at least. For the Newton—Goldstein method this estimate is sharpened slightly tor n =O(n −1/2) when the second Fréchet differentialF″ is Lipschitz continuous and the admissible set Ω is bounded. Still sharper estimates are derived when certain growth conditions are satisfied byF or its local linear approximation atξ. The most surprising conclusion is that Newton—Goldstein sequences can convergesuperlinearly to a singular extremalξ when〈F′(ξ), x − ξ〉 ≥ A∥x − ξ∥ v for someA 〉 0, somev ∈ (2,2.5) and allx in Ω nearξ, and that this growth condition onF′(ξ) is entirely natural for a nontrivial class of constrained minimization problems on feasible sets Ω =ℒ 1{[0,1],U} withU a uniformly convex set in ℝ d . Feasible sets of this kind are commonly encountered in the optimal control of continuous-time dynamical systems governed by differential equations, and may be viewed as infinite-dimensional limits of Cartesian product setsU k in ℝ kd . Superlinear convergence of Newton—Goldstein sequences for the problem (Ω,F) suggests that analogous sequences for increasingly refined finite-dimensional approximation (U kd ,F k ) to (Ω,F) will exhibit convergence properties that are in some sense “uniformly good” ink ask → ∞.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 159 (1947), S. 197-197 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] INFORMATION recently to hand in the lay press1 that Theorell, Davide and Sjögren have developed an anti-tuberculosis remedy from the pyocyanic bacillus has prompted, at this early stage of its investigation, the following record of the isolation and characteristics of what may ...
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  • 3
    ISSN: 1573-269X
    Keywords: Beam ; gravity effect ; method of multiple scales ; nonlinear oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A critical problem in designing large structures for space applications, such as space stations and parabolic antennas, is the limitation of testing these structures and their substructures on earth. These structures will exhibit very high flexibilities due to the small loads expected to be encountered in orbit. It has been reported in the literature that the gravitational sag effect under dead weight is of extreme importance during ground tests of space-station structural components [1–4]. An investigation of a horizontal, pinned-pinned beam with complete axial restraint and undergoing large-amplitude oscillations about the statically deflected position is presented here. This paper presents a solution for the frequency-amplitude relationship of the nonlinear free oscillations of a horizontal, immovable-end beam under the influence of gravity. The governing equation of motion used for the analysis is the Bernoulli-Euler type modified to include the effects of mid-plane stretching and gravity. Boundary conditions are simply supported such that at both ends there is no bending moment and no transverse and axial displacements. These boundary conditions give rise to an initial tension in the statically deflected shape. The displacement function consists of an assumed space mode using a simple sine function and unknown amplitude which is a function of time. This assumption provides for satisfaction of the boundary conditions and leads to an ordinary differential equation which is nonlinear, containing both quadratic and cubic functions of the amplitude. The perturbation method of multiple scales is used to provide an approximate solution for the fundamental frequency-amplitude relationship. Since the beam is initially deflected the small-amplitude fundamental natural frequency always increases relative to the free vibration situation provided in zero gravity. The nonlinear equation provides for interactions between frequency and amplitude in that both hardening and softening effects arise. The coefficient of the quadratic term in the nonlinear equation arises from the static (dead load) portion of the deflection. This quadratic term, depending upon its magnitude, introduces a softening effect that overcomes the hardening term (due to initial axial tension developed by deflection) for large slenderness ratios. For very large slender, immovable-end beams, the fundamental natural frequency is greater than that of beams without axial constraints undergoing small amplitude oscillations. This phenomenon is attributed to the stiffening effect of the statically-induced axial tension. However, the stiffening effect of axial tension in beams with slenderness ratios greater than approximately 392 undergoing large-amplitude symmetric-mode oscillations is overpowered by the presence of gravitational loading.
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  • 4
    ISSN: 1432-1793
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Cross-infection experiments were performed to determine the influence of temperature on infection rate in the Chondrus crispus Stackhouse-Petersenia pollagaster (Petersen) Sparrow pathosystem. C. crispus thalli were collected at Pubnico Harbor, Nova Scotia, Canada in the fall of 1981 to 1984. Infective zoospores were used to inoculate healthy thalli at five different temperatures. The highest infection rate was obtained at 20°C, while significantly lower rates were obtained at temperature extremes. The parasite's life cycle, consisting of infection of healthy thalli, endobiotic development, and release of zoospores, was completed in 48 to 72 h at 15° to 20°C.
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  • 5
    Publication Date: 2013-08-31
    Description: Engineering model design of equipment comprising precision pointing control system
    Keywords: NAVIGATION
    Type: TRW-13900-6011-R0-01 , NASA-CR-121912
    Format: application/pdf
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  • 6
    Publication Date: 1947-02-01
    Print ISSN: 0028-0836
    Electronic ISSN: 1476-4687
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Published by Springer Nature
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  • 7
    Publication Date: 1984-10-01
    Print ISSN: 0095-4616
    Electronic ISSN: 1432-0606
    Topics: Mathematics
    Published by Springer
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