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  • 1
    ISSN: 1573-8698
    Keywords: 49K ; 49L ; 93
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We present a unified approach to a complex of related issues in control theory, one based to a great extent on the methods of nonsmooth analysis. The issues include invariance, stability, equilibria, monotonicity, the Hamilton-Jacobi equation, feedback synthesis, and necessary conditions.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Keywords: optimal control ; differential games ; Euler polygonal arcs ; nonsmooth analysis ; proximal aiming ; infinitesimal decrease ; discontinuous universal near-optimal feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a general fixed-duration optimal control problem, the proximal aiming technique of nonsmooth analysis is employed in order to construct a discontinuous feedback law, whose Euler solutions are all optimal to within a prescribed tolerance, universally for all initial data in a prescribed bounded set. The technique is adapted in order to construct universal near-saddle points for two-player fixed-duration differential games of the Krasovskii–Subbotin type.
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  • 3
    ISSN: 1573-2878
    Keywords: State-dependent control restraints ; state restraints ; maximality ; time-optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the control system $$\dot x = Ax + Bu,$$ subject to the state-dependent control restraint $$u(t) \in \Omega \cap (\mathcal{H}{\text{ + }}Cx(t)\} ,$$ where Ω is a compact convex set, ℋ is a subspace, andC is a matrix. The existence of time-optimal maximal controls is proven. A natural application of this result is in solving time-optimal problems under the control restraintu(t)∈Ω and the requirement that the outputy=Sx be maintained at zero during the transfer, whereS is a given matrix. An example is provided.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1437-3262
    Keywords: Precambrian ; Geochronology ; Geochemistry ; Crustal evolution ; Africa
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract This paper provides new geochemical and isotopic data on the evolution of the western foreland to the Nubian shield of north-east Africa. There is abundant evidence for early to middle Proterozoic crust west of the River Nile, but this was severely affected by the Pan-African (≈ 500–900 Ma) orogenic cycle. The results are reported of Rb-Sr whole rock and zircon evaporation geochronological studies and whole rock Sm-Nd and feldspar Pb isotopic analyses for four rock units around Wadi Halfa in northernmost Sudan. These results indicate the presence of heterogeneous pre-Pan-African crustal components, preserved in mylonitic gneisses and in conglomerates that unconformably overlie the gneisses. Several episodes of crust formation, inferred from zircon ages, are preserved in the gneisses : 2.6, 2.4, 2.0, 1.7, 1.2 and 0.72 Ga. Nd model ages for the same units are invariably older than the zircon ages, yet still record a predominantly late Archaean and Palaeoproterozoic history, with depleted mantle model ages between 1.3 and 2.8 Ga. The earliest recorded Pan-African magmatic event is about 720 Ma and dates the beginning of collisional deformation. A younger Pan-African volcanic sequence (≈ 650 Ma) has isotopic compositions of Sr and Nd compatible with derivation from late Prote rozoic asthenospheric mantle. A ≈ 530 Ma anorogenic ‘A-type’ granite also has isotopic compositions suggesting derivation from a primitive source. The inferred tectonic evolution began with rifting to form an oceanic re-entrant. This was followed by subduction leading to collision at about 700 Ma, accompanied by post-orogenic rifting at about 650 Ma.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    International journal of earth sciences 83 (1994), S. 473-473 
    ISSN: 1437-3262
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    International journal of earth sciences 83 (1994), S. 473-473 
    ISSN: 1437-3262
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1437-3262
    Keywords: Precambrian ; Geochronology ; Geochemistry ; Crustal evolution ; Africa
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract This paper provides new geochemical and isotopic data on the evolution of the western foreland to the Nubian shield of north-east Africa. There is abundant evidence for early to middle Proterozoic crust west of the River Nile, but this was severely affected by the Pan-African (≈ 500–900 Ma) orogenic cycle. The results are reported of Rb-Sr whole rock and zircon evaporation geochronological studies and whole rock Sm-Nd and feldspar Pb isotopic analyses for four rock units around Wadi Halfa in northernmost Sudan. These results indicate the presence of heterogeneous pre-Pan-African crustal components, preserved in mylonitic gneisses and in conglomerates that unconformably overlie the gneisses. Several episodes of crust formation, inferred from zircon ages, are preserved in the gneisses : 2.6, 2.4, 2.0, 1.7, 1.2 and 0.72 Ga. Nd model ages for the same units are invariably older than the zircon ages, yet still record a predominantly late Archaean and Palaeoproterozoic history, with depleted mantle model ages between 1.3 and 2.8 Ga. The earliest recorded Pan-African magmatic event is about 720 Ma and dates the beginning of collisional deformation. A younger Pan-African volcanic sequence (≈ 650 Ma) has isotopic compositions of Sr and Nd compatible with derivation from late Prote rozoic asthenospheric mantle. A ≈ 530 Ma anorogenic ‘A-type’ granite also has isotopic compositions suggesting derivation from a primitive source. The inferred tectonic evolution began with rifting to form an oceanic re-entrant. This was followed by subduction leading to collision at about 700 Ma, accompanied by post-orogenic rifting at about 650 Ma.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Keywords: Linear autonomous control systems ; polyhedral restraints ; extremal controls ; subspace exit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a linear control system setting, we derive conditions under which extremal controls give rise to trajectories which exit a given subspace. An application is in determining effectiveness of linear state restraints in time-optimal problems.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    International journal of earth sciences 83 (1994), S. 669-669 
    ISSN: 1437-3262
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
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  • 10
    ISSN: 1432-0967
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences
    Notes: Abstract Nd- and Sr-isotopic data are reported for lavas from 23 submarine and 3 subaerial volcanoes in the northern Mariana and southern Volcano arcs. Values of εNd range from +2.4 to +9.5 whereas 87Sr/86Sr ranges from 0.70319 to 0.70392; these vary systematically between and sometimes within arc segments. The Nd-and Sr-isotopic compositions fall in the field of ocean island basalt (OIB) and extend along the mantle array. Lavas from the Volcano arc, Mariana Central Island Province and the southern part of the Northern Seamount Province have εNd to +10 and 87Sr/86Sr=0.7032 to 0.7039. These are often slightly displaced toward higher 87Sr/86Sr at similar εNd. In contrast, those lavas from the northern part of the Mariana Northern Seamount Province as far north as Iwo Jima show OIB isotopic characteristics, with εNd and 87Sr/86Sr=0.7035 to 0.7039. Plots of 87Sr/86Sr and εNd versus Ba/La and (La/Yb)n support a model in which melts from the Mariana and Volcano arcs are derived by mixing of OIB-type mantle (or melts therefrom) and a metasomatized MORB-type mantle (or melts therefrom). An alternate interpretation is that anomalous trends on the plots of Nd- and Sr-isotopic composition versus incompatible-element ratios, found in some S-NSP lavas, suggest that the addition of a sedimentary component may be locally superimposed on the two-component mixing of mantle end-members.
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