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  • 1
    ISSN: 1420-8954
    Keywords: Computational Complexity ; Randomization ; Decision Trees ; Boolean Functions ; Lower Bounds ; Octants ; MAX Problem ; 68Q15 ; 68Q25 ; 68Q40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We introduce a new powerful method for provinglower bounds onrandomized anddeterministic analytic decision trees, and give direct applications of our results towards some concrete geometric problems. We design alsorandomized algebraic decision trees for recognizing thepositive octant in ℝ n or computing MAX in ℝ n in depth log O(1) n. Both problems are known to have linear lower bounds for the depth of any deterministic analytic decision tree recognizing them. The mainnew (andunifying) proof idea of the paper is in the reduction technique of the signs oftesting functions in a decision tree to the signs of theirleading terms at the specially chosen points. This allows us to reduce the complexity of adecision tree to the complexity of a certainBoolean circuit.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1420-8954
    Keywords: Computational Complexity ; Randomized Algebraic Decision Trees ; Knapsack ; Element Distinctness ; Integer Programming ; 68Q15 ; 68Q25 ; 68Q40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We prove the firstnontrivial (andsuperlinear) lower bounds on the depth ofrandomized algebraic decision trees (with two-sided error) for problems being finite unions of hyperplanes and intersections of halfspaces, solving a long standing open problem. As an application, among other things, we derive, for the first time, an Ω(n 2)randomized lower bound for theKnapsack Problem, and an Ω(n logn)randomized lower bound for theElement Distinctness Problem which were previously known only for deterministic algebraic decision trees. It is worth noting that for the languages being finite unions of hyperplanes our proof method yields also a new elementary lower bound technique for deterministic algebraic decision trees without making use of Milnor's bound on Betti number of algebraic varieties.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1022-1352
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Block copolymers of unsubstituted poly(p-xylylene)(PPX) and Ge- or Sn-organic bridged PPX (GePPX and SnPPX) were prepared by pyrolysis of specially synthesized organometallic p-cyclophane precursors followed by deposition and polymerization of the thus produced p-xylylene monomers. The copolymer structure and thermal behavior were investigated depending on deposition temperature (10 and -196°C). The copolymer PPX-GePPX obtained from solid monomers deposited at -196°C (2a) consists of long quasi-independent PPX and GePPX blocks and has paracrystalline structure. Thermal treatment of 2a near 160°C yields crystalline regions of PPX along with paracrystalline aggregates of GePPX. Pyrolysis of this system near 300°C in an inert atmosphere results in the formation of Ge crystals in PPX matrix. In contrast, the copolymer PPX-GePPX produced by simultaneous deposition and polymerization at 10°C (2a′) contains shorter blocks of PPX and GePPX than the copolymer deposited at -196°C. Copolymer 2a′ turns to the amorphous state during thermal treatment, and its pyrolysis does not lead to Ge-crystal formation; hence the supramolecular structure of the polymer plays an important role in inorganic phase formation. The copolymer PPX-SnPPX (2b) is formed only at a deposition temperature of -196°C; deposition at 10°C yields oligomeric resins. The structure of 2b is nearly the same as that of 2a; pyrolysis of 2b in air results in SnO2-crystal formation in a PPX matrix.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 0268-2605
    Keywords: organotin(IV) complexes ; diphosphoryl ligands ; NMR ; Mössbauer spectroscopy ; X-ray analysis ; antitumour activity ; Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The series of organotin halide complexes with tetraethyl ethylene- and propylene-diphosphonates RnSnX4-n,·L [n=0, X=Cl; n=1, R=Me, X=Cl, Br; n=1, R=Ph, X=Cl; n=2, R=Me, Et, Bu, X=Cl, Br; n=2, R=Ph, X=Cl; L=(EtO)2P(O)CH2CHR'P(O)(OEt)2, R'=H, Me] were synthesized and characterized by means of NMR and Mössbauer spectroscopy. The crystal structure of the complex of diphenyltin dichloride with propylenediphosphonate was determined. The complex consists of polymer chains with bridging bidentate ligands and an octahedral tin environment containing two types of phosphoryl fragments. All of the R2SnX2 adducts have trans-R2SnX4 geometries of tin coordination octahedra according to the quadrupole splitting values in the Mössbauer spectra. The 31P and 119Sn NMR studies at low temperatures revealed that RSnHal3 complexes in solution form isomers with different mutual orientations of phosphoryl ligands and organic groups in the coordination sphere. The diethyltin dichloride adduct with ethylene-diphosphonate appeared to be active against lung cancer NCI-H522 cells.
    Additional Material: 2 Ill.
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  • 5
    ISSN: 0044-2313
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: mehrkernige Technetium-Cluster. I. Synthese, Kristall- und Molekularstruktur der Bromide achtkerniger prismatischer und sechskerniger oktaedrischer Cluster des TechnetiumsE werden die Synthese, Kristall- und Molekularstruktur erster Vertreter mehrkerniger Technetium-Cluster er Zusammensetzung: [Tc8Br4μ—Br8]Br. 2 H2O; [H(H2O)2][Tc8Br4μ—Br8]Br; [H(H2O)2]2[Tc8Br4μ—Br8]Br2; [H3O(H2O)3]2[Tc6Br6μ3—Br5]; [(C4H9)4N]2[Tc6Br6μ3—Br5]; [H3O(H2O)3]2[Tc6Br6μ3—Br5]. 4 H2O beschrieben. Diese Verbindungen unterscheiden sich in ihrem Bau wesentlich von bekannten Clustern anderer d-Elemente. Die Kristall- und Molekularstruktur von Hexabromotechnetiumsäure, (H3O)2TcBr6, ist untersucht worden.
    Notes: The synthesis, crystal and molecular structure of the first representatives of polynuclear technetium clusters are described. The composition of these clusters is: [Tc8Br4μ—Br8]Br. 2H2O; [H(H2O)2][Tc8Br4μ—Br8]Br; [H(H2O)2]2[Tc8Br4μ—Br8]Br2; [H3O(H2O)3]2[Tc6Br6μ3—Br5]; [(C4H9)4N]2[Tc6Br6μ3—Br5]; [H3O3]2[Tc6Br6μ3—Br5]. 4 H2O. It is shown that these clusters strongly differ in their structure from the known clusters of other d-elements. The crystal and molecular structure of hexabromotechetium acid (H3O)2TcBr6 is studied too.
    Additional Material: 4 Ill.
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  • 6
    ISSN: 0009-286X
    Keywords: Chemistry ; Industrial Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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