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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Polymer bulletin 27 (1992), S. 607-613 
    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Polysilanes containing cyclodisilazane units in the backbone were synthesized by the modified Wurtz-type coupling of available dichlorosilanes with N,N′-bis (chlorodimethylsilyl)tetramethylcyclodisilazane in the mixture of solvents. The effect of solvent additives on the polymerization process was examined. These polymers are soluble in common solvents and very easily handled by molding or casting.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Optical and quantum electronics 24 (1992), S. S1095 
    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract In this paper a statistical ensemble of laser light is defined. The lasing field is treated as a classical variable, the spontaneous emission is considered phenomenally by using a random function. Special attention is paid to the transverse mode behaviour. To calculate the ensemble elements, an approach based on Fresnel integration has been developed. Theoretical investigations into some stripe stable resonators have been carried out. Some results for the intensity, the mode spectrum, the correlation between transverse modes, the beam quality, and the spectra of the intensity and the output power fluctuation are presented and discussed.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Optical and quantum electronics 24 (1992), S. S1081 
    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Taking the modal behaviours of the laser field into account, the coherence properties of laser light can be characterized by mode coherence functions (MCFs) and mode coherence coefficients (MCCs). Changes in laser light properties due to optical operations can be described by transformation laws for the MCFs and the MCCs. The transformation laws as well as transformation matrices for propagation in free space, phase transformations, spatial amplitude modulations and aperturizing are given. Furthermore, intensity distributions and intensity moments in the spatial and in the spatial frequency domains are expressed in terms of the MCCs. General expressions for the beam quality factors,M 2s, obtained using the intensity moments and some useful expressions for intensity moments of higher order are discussed.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Optical and quantum electronics 24 (1992), S. S1119 
    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Based on average intensity distributions at two axial positions, an experimental approach to determine the mode coherence coefficients was developed. Using this approach, investigations were carried out for a CO2 laser with a stripe resonator. The power partitions of, and cross-correlations between, modes at different aperture widths and the dependence of the beam quality on the aperture width were studied. The measuring principle, an iterative fit method, and some experimental results are presented and discussed.
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  • 5
    ISSN: 1572-8862
    Keywords: Cubane-like ; double cubane-like ; Molybdenum-copper-sulphur clusters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Two novel heterometallic cubane-like and double cubane-like clusters, {MoCu3S3(S2COEt)}(O)(Ph3P)3 I and {Mo2Cu6S6(SCMe3)2}(O)2(Ph3P)4 II, were synthesized by reaction of {MoCu2S3}(O)(Ph3P)3 with CuS2COEt and CuSCMe3, respectively. ClusterI crystallized in the triclinic space group $$P\overline 1 $$ (2) witha=12.766(6) Å,b=22.904(5) Å,c=10.522(3) Å, α=99.86(2)°, β=109.68(2)°, γ=86.84(3)°,V=2854(2) Å3,Z=2,R=0.049 for 6622 observed reflections (I〉5σ(I)) and 410 variables. ClusterII crystallized in the triclinic space group $$P\overline 1 $$ (2) with dimensionsa=14.212(4) Å,b=14.725(5) Å,c=12.396(8) Å, α=110.32(4)°, β=90.40(5)°, γ=62.88(2)°,V=2129(2) Å3,Z=1,R=0.039 for 6020 observed reflections (I〉3σ(I)) and 461 variables. ClusterI consists of a neutral cubane-like molecule with the core {MoCu3S3(S2COEt)}2+, in which one corner of the cubane-like core is a novel triply bridging bidentate 1,1-dithiolato (xanthate, S2COEt−) ligand. ClusterII is a double cubane-like one, in which two cubane-like cores {MoCu3S3(SCMe3)}2+ are connected by two Cu-S bonds of the triply bridging monothiolato (SCMe 3 − ) ligand. Two different pathways of unit construction from a small heterometallic cluster {MoCu2S3}(O)(Ph3P)3 have been outlined. Comparisons of the selected bond lengths and bond angles for the cubane-like core {MoCu3S3 X} (X=Cl−, Br−, S2COEt−, SCMe 3 − ) are given. Spectroscopic properties of the title clusters are also reported.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 57 (1992), S. 193-202 
    ISSN: 1436-4646
    Keywords: Steiner trees ; approximation performance ratio
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Finding a shortest network interconnecting a given set of points in a metric space is called the Steiner minimum tree problem. The Steiner ratio is the largest lower bound for the ratio between lengths of a Steiner minimum tree and a minimum spanning tree for the same set of points. In this paper, we show that in a metric space, if the Steiner ratio is less than one and finding a Steiner minimum tree for a set of size bounded by a fixed number can be performed in polynomial time, then there exists a polynomialtime heuristic for the Steiner minimum tree problem with performance ratio bigger than the Steiner ratio. It follows that in the Euclidean plane, there exists a polynomial-time heuristic for Steiner minimum trees with performance ratio bigger than $${\textstyle{1 \over 2}}\sqrt 3 $$ . This solves a long-standing open problem.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Multidimensional systems and signal processing 3 (1992), S. 363-380 
    ISSN: 1573-0824
    Keywords: Stability ; multidimensional system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, certain problems concerning nonessential singularities of the second kind (NSSKs), especially continuous NSSKs for 3-D digital filters, are discussed. It is shown that continuous NSSKs, both inT 2 U and onT 3, may exist in stable systems. Based on the Weierstrass theorem of multidimensional complex analysis, the existence criteria of continuous NSSKs inT 2 U and onT 3 are obtained. Certain basic properties of this type of singularities are given. A stability condition for a transfer functionH(Z) with continuous NSSKs and the inverse ofH(Z) is derived. Furthermore, for isolated NSSKs, a new necessary and sufficient condition for stability is developed for a class of systems.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Acta mechanica solida Sinica 5 (1992), S. 35-45 
    ISSN: 0894-9166
    Keywords: boundary element ; multi-domain ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Based on the direct differentiation of boundary element equations to design variables, an algorithm of the boundary element method which is suitable for the shape sensitivity analysis of serial multi-domain elastic structures is built. By the algorithm, it is not necessary to form and solve the equations for the structure as a whole. Each domain can be solved separately. Two computational examples are presented to demonstrate the accuracy and versatility of the algorithm.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 7 (1992), S. 121-135 
    ISSN: 1432-0541
    Keywords: Steiner trees ; Spanning trees ; Steiner ratio ; Convexity ; Hexagonal trees
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetP be a set ofn points on the euclidean plane. LetL s(P) andL m (P) denote the lengths of the Steiner minimum tree and the minimum spanning tree onP, respectively. In 1968, Gilbert and Pollak conjectured that for anyP,L s (P)≥(√3/2)L m (P). We provide a proof for their conjecture in this paper.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 7 (1992), S. 179-191 
    ISSN: 1432-0541
    Keywords: Steiner trees ; Spanning trees ; Steiner ratio ; L p distance ; Bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetL p be the plane with the distanced p (A 1 ,A 2 ) = (¦x 1 −x 2¦ p + ¦y1 −y 2¦p)/1p wherex i andy i are the cartesian coordinates of the pointA i . LetP be a finite set of points inL p . We consider Steiner minimal trees onP. It is proved that, for 1 〈p 〈 ∞, each Steiner point is of degree exactly three. Define the Steiner ratio ϱ p to be inf{L s (P)/L m (P)¦P⊂L p } whereL s (P) andL m (P) are lengths of the Steiner minimal tree and the minimal spanning tree onP, respectively. Hwang showed ϱ1 = 2/3. Chung and Graham proved ϱ2 〉 0.842. We prove in this paper that ϱ{∞} = 2/3 and √(√2/2)ϱ1ϱ2 ≤ ϱp ≤ √3/2 for anyp.
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