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31.
Let Hn be an n-dimensional Haar subspace of
and let Hn−1 be a Haar subspace of Hn of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from Hn onto Hn−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1]. 相似文献
32.
Andrew V. Goldberg Michael D. Grigoriadis Robert E. Tarjan 《Mathematical Programming》1991,50(1-3):277-290
Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n
2
m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467. 相似文献
33.
Axel Kohnert 《Discrete Applied Mathematics》2007,155(11):1451-1457
We construct new linear two-weight codes over the finite field with q elements. To do so we solve the equivalent problem of finding point sets in the projective geometry with certain intersection properties. These point sets are in bijection to solutions of a Diophantine linear system of equations. To reduce the size of the system of equations we restrict the search for solutions to solutions with special symmetries.Two-weight codes can be used to define strongly regular graphs. We give tables of the two-weight codes and the corresponding strongly regular graphs. In some cases we find new distance-optimal two-weight codes and also new strongly regular graphs. 相似文献
34.
Ronald I. Becker Isabella Lari Andrea Scozzari Giovanni Storchi 《Annals of Operations Research》2007,150(1):65-78
In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively
studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path
which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject
to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity
of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(nℓ) respectively, where n is the number of vertices of the grid and ℓ is the cardinality of the path to be located.
The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous
spaces and network facility location. We will show that the problems presented here have a close connection with continuous
dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional
facilities location in the continuous case. 相似文献
35.
如果一个图G存在一个k-列表安排使得G具有一个唯一列表染色,则称 G是唯一列表可染色图,简称UkLC图.我们称图G具有M(k)性质当且仅当G不 是UkLC图.本文在借鉴θr,s,t-图概念的基础上引入θr,s,t-图的定义,并证明:除了 r=s=t=2以外,θr,s,t-图都是U2LC图.利用如上结果我们给出M.Mahdian and E.S.Mahmoodian对U2LC图所作特征化的一个简单证明. 相似文献
36.
Marston Conder Aleksander Malnič Dragan Marušič Primž Potočnik 《Journal of Algebraic Combinatorics》2006,23(3):255-294
A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This
list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer
algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several
previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its
girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms,
its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite
families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of
the list are identified with these. The special case of those graphs having K1,3 as a normal quotient is investigated in detail.
Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201)
Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506.
Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University
of Auckland for hospitality during his visit there in 2003. 相似文献
37.
The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods.In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.This is a written account of an invited lecture delivered by the second author on occasion of the 12. Symposium on Operations Research, Passau, 9.–11. 9. 1987. 相似文献
38.
A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity. 相似文献
39.
Topological indices are graph invariants used in computational chemistry to encode molecules. A frequent problem when performing structure-activity studies is that topological indices are inter-correlated. We consider a simple topological index and show asymptotic independence for a random tree model. This continues previous work on the correlation among topological indices. These findings suggest that a size-dependence in a certain class of distance-based topological indices can be eliminated.AMS subject classification: 05C80, 60E10, 92E10 相似文献
40.
W. Grüner R. Giegerich D. Strothmann C. Reidys J. Weber I. L. Hofacker P. F. Stadler P. Schuster 《Monatshefte für Chemie / Chemical Monthly》1996,127(4):355-374
Summary Global relations between RNA sequences and secondary structures are understood as mappings from sequence space into shape space. These mappings are investigated by exhaustive folding of allGC andAU sequences with chain lengths up to 30. The computed structural data are evaluated through exhaustive enumeration and used as an exact reference for testing analytical results derived from mathematical models and sampling based on statistical methods. Several new concepts of RNA sequence to secondary structure mappings are investigated, among them that ofneutral networks (being sets of sequences folding into the same structure). Exhaustive enumeration allows to test several previously suggested relations: the number of (minimum free energy) secondary structures as a function of the chain length as well as the frequency distribution of structures at constant chain length (commonly resulting in generalized forms ofZipf's law).
Analyse der Beziehungen zwischen RNA-Sequenzen und Sekundärstrukturen durch vollständige Faltung, 1. Mitt. Faltung, Neutrale Netzwerke
Zusammenfassung Die globalen Benziehungen zwischen RNA-Sequenzen und Sekundärstrukturen werden als Abbildungen aus einem Raum aller Sequenzen in einen Raum aller Strukturen aufgefaßt. Diese Abbildungen werden durch Falten aller binären Sequenzen desGC-undAU-Alphabets mit Kettenlängen bis zun=30 untersucht. Die berechneten Strukturdaten werden durch vollständiges Abzählen ausgewertet und als eine exakte Referenz zum Überprüfen analytischer Resultate aus mathematischen Modellen sowie zum Testen statistisch erhobener Proben verwendet. Einige neuartige Konzepte zur Beschreibung der Beziehungen zwischen Sequenzen und Strukturen werden eingehend untersucht, unter ihnen der Begriff derneutralen Netzwerke. Ein neutrales Netzwerk besteht aus allen Sequenzen, die eine bestimmte Struktur ausbilden. Vollständiges Abzählen ermöglicht beispielsweise die Bestimmung aller Strukturen minimaler freier Energie in Abhängigkeit von der Kettenlänge ebenso wie die Bestimmung der Häufigkeitsverteilungen der Strukturen bei konstanten Kettenlängen. Die letzteren folgen einer verallgemeinerten FormZipfschen Gesetzes.相似文献