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  • 1
    Electronic Resource
    Electronic Resource
    Carotenoid composition of the fruits of Capsicum annuum Cv. Bovet 4 during ripening (1997)
    Springer
    Zeitschrift für Lebensmittel-Untersuchung und -Forschung 205 (1997), S. 388-391 
    Details
    ISSN: 1431-4630
    Keywords: Key words Capsicum annuum ; Carotenoids ; Analyses ; Maturation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract  The changes in the carotenoid pigments of the Capsicum annuum cv. Bovet 4 during ripening have been investigated quantitatively by means of an HPLC technique. In the chromatograms, 56 peaks were detected and 34 carotenoids were identified. In the ripe fruits, capsanthin, capsorubin, zeaxanthin, cucurbitaxanthin A, and β-carotene were found to be the main carotenoids, the remainder being capsanthin 5,6-epoxide, capsanthin 3,6-epoxide, karpoxanthin, cucurbitaxanthin B, violaxanthin, cycloviolaxanthin, antheraxanthin, capsanthone, nigroxanthin, β-cryptoxanthin and several cis isomers and furanoid oxides.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002170050186
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  • 2
    Electronic Resource
    Electronic Resource
    Ramsey-Type Results for Geometric Graphs, I (1997)
    Springer
    Discrete & computational geometry 18 (1997), S. 247-255 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. For any 2-coloring of the ${n \choose 2}$ segments determined by n points in general position in the plane, at least one of the color classes contains a non-self-intersecting spanning tree. Under the same assumptions, we also prove that there exist $\lfloor (n+1)/3 \rfloor$ pairwise disjoint segments of the same color, and this bound is tight. The above theorems were conjectured by Bialostocki and Dierker. Furthermore, improving an earlier result of Larman et al., we construct a family of m segments in the plane, which has no more than $m^{\log 4/\log 27}$ members that are either pairwise disjoint or pairwise crossing. Finally, we discuss some related problems and generalizations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009317
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  • 3
    Electronic Resource
    Electronic Resource
    A Generalization of the Erdos - Szekeres Theorem to Disjoint Convex Sets (1998)
    Springer
    Discrete & computational geometry 19 (1998), S. 437-445 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex position if none of its members is contained in the convex hull of the union of the others. For any fixed k≥ 3 , we estimate P k (n) , the maximum size of a family F with the property that any k members of F are in convex position, but no n are. In particular, for k=3 , we improve the triply exponential upper bound of T. Bisztriczky and G. Fejes Tóth by showing that P 3 (n) 〈 16 n . 〈lsiheader〉 〈onlinepub〉26 June, 1998 〈editor〉Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; 〈pdfname〉19n3p437.pdf 〈pdfexist〉yes 〈htmlexist〉no 〈htmlfexist〉no 〈texexist〉yes 〈sectionname〉 〈/lsiheader〉
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009361
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  • 4
    Electronic Resource
    Electronic Resource
    Note on the Erdos - Szekeres Theorem (1998)
    Springer
    Discrete & computational geometry 19 (1998), S. 457-459 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Let g(n) denote the least integer such that among any g(n) points in general position in the plane there are always n in convex position. In 1935, P. Erdős and G. Szekeres showed that g(n) exists and $2^{n-2}+1\le g(n)\le {2n-4\choose n-2}+1$ . Recently, the upper bound has been slightly improved by Chung and Graham and by Kleitman and Pachter. In this paper we further improve the upper bound to $$g(n)\le {2n-5\choose n-2}+2.$$ 〈lsiheader〉 〈onlinepub〉26 June, 1998 〈editor〉Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; 〈pdfname〉19n3p457.pdf 〈pdfexist〉yes 〈htmlexist〉no 〈htmlfexist〉no 〈texexist〉yes 〈sectionname〉 〈/lsiheader〉
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009363
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  • 5
    Electronic Resource
    Electronic Resource
    Geometric Graphs with Few Disjoint Edges (1999)
    Springer
    Discrete & computational geometry 22 (1999), S. 633-642 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. A geometric graph is a graph drawn in the plane so that the vertices are represented by points in general position, the edges are represented by straight line segments connecting the corresponding points. Improving a result of Pach and Törőcsik, we show that a geometric graph on n vertices with no k+1 pairwise disjoint edges has at most k 3 (n+1) edges. On the other hand, we construct geometric graphs with n vertices and approximately (3/2)(k-1)n edges, containing no k+1 pairwise disjoint edges. We also improve both the lower and upper bounds of Goddard, Katchalski, and Kleitman on the maximum number of edges in a geometric graph with no four pairwise disjoint edges.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009482
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  • 6
    Electronic Resource
    Electronic Resource
    New Bounds on Crossing Numbers (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 623-644 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. The crossing number , cr(G) , of a graph G is the least number of crossing points in any drawing of G in the plane. Denote by κ(n,e) the minimum of cr(G) taken over all graphs with n vertices and at least e edges. We prove a conjecture of Erdos os and Guy by showing that κ(n,e)n 2 /e 3 tends to a positive constant as n→∈fty and n l e l n 2 . Similar results hold for graph drawings on any other surface of fixed genus. We prove better bounds for graphs satisfying some monotone properties. In particular, we show that if G is a graph with n vertices and e≥ 4n edges, which does not contain a cycle of length four (resp. six ), then its crossing number is at least ce 4 /n 3 (resp. ce 5 /n 4 ), where c〉0 is a suitable constant. These results cannot be improved, apart from the value of the constant. This settles a question of Simonovits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010011
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  • 7
    Electronic Resource
    Electronic Resource
    Finite sphere packing and sphere covering (1989)
    Springer
    Discrete & computational geometry 4 (1989), S. 19-40 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A basic problem of finite packing and covering is to determine, for a given number ofk unit balls in Euclideand-spaceE d , (1) the minimal volume of all convex bodies into which thek balls can be packed and (2) the maximal volume of all convex bodies which can be covered by thek balls. In the sausage conjectures by L. Fejes Tóth and J. M. Wills it is conjectured that, for alld≥5, linear arrangements of thek balls are best possible. In the paper several partial results are given to support both conjectures. Furthermore, some relations between finite and infinite (space) packing and covering are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187713
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  • 8
    Electronic Resource
    Electronic Resource
    Ramsey-Type Results for Geometric Graphs, II (1998)
    Springer
    Discrete & computational geometry 20 (1998), S. 375-388 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. We show that for any two-coloring of the ${n \choose 2}$ segments determined by n points in the plane, one of the color classes contains noncrossing cycles of lengths $3,4,\ldots,\lfloor\sqrt{n/2}\rfloor$ . This result is tight up to a multiplicative constant. Under the same assumptions, we also prove that there is a noncrossing path of length Ω(n 2/3 ) , all of whose edges are of the same color. In the special case when the n points are in convex position, we find longer monochromatic noncrossing paths, of length $\lfloor({n+1})/{2}\rfloor$ . This bound cannot be improved. We also discuss some related problems and generalizations. In particular, we give sharp estimates for the largest number of disjoint monochromatic triangles that can always be selected from our segments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00009391
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  • 9
    Electronic Resource
    Electronic Resource
    Finite coverings by translates of centrally symmetric convex domains (1987)
    Springer
    Discrete & computational geometry 2 (1987), S. 353-363 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Bambah and Rogers proved that the area of a convex domain in the plane which can be covered byn translates of a given centrally symmetric convex domainC is at most (n−1)h(C)+a(C), whereh(C) denotes the area of the largest hexagon contained inC anda(C) stands for the area ofC. An improvement with a term of magnitude √n is given here. Our estimate implies that ifC is not a parallelogram, then any covering of any convex domain by at least 26 translates ofC is less economic than the thinnest covering of the whole plane by translates ofC.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187889
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  • 10
    Electronic Resource
    Electronic Resource
    A distributed parameter model for the torsional vibration analysis of turbine-generator shafts (1987)
    Springer
    Electrical engineering 70 (1987), S. 171-175 
    Details
    ISSN: 1432-0487
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Description / Table of Contents: Übersicht Es wird ein modell mit gleichmäßig verteilten Kenngrößen für die Berechnung der Torsionsschwingungen von großen Turbogeneratorwellen auf Grund der elektrischen Analogie vorgestellt. Das entwickelte Rechenverfahren wendet die Wanderwellen-Methode im Zeitbereich und die Vierpolgleichungen für die Analyse im Frequenzbereich an.
    Notes: Contents A distributed parameter model is presented for the calculation of torsional vibrations of large turbine-generator shafts, on the basis of electrical analogy. The developed computer algorithm uses the travelling wave method for the time domain analysis and the two-port equations for the frequency domain analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01574066
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