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  • Articles  (216)
  • Mathematics  (216)
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  • Articles  (216)
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  • 1
    Electronic Resource
    Electronic Resource
    A calculus for SU(3) leading to an algebraic formula for the Clebsch–Gordan coefficients (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 6530-6569 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We develop a simple computational tool for SU(3) analogous to Bargmann's calculus for SU(2). Crucial new inputs are (i) explicit representation of the Gelfand–Zetlin basis in terms of polynomials in four variables and positive or negative integral powers of a fifth variable, (ii) an auxiliary Gaussian measure with respect to which the Gelfand–Zetlin states are orthogonal but not normalized, (iii) simple generating functions for generating all basis states and also all invariants. As an illustration of our techniques, an algebraic formula for the Clebsch–Gordan coefficients is obtained for the first time. This involves only Gaussian integrations. Thus SU(3) is made as accessible for computations as SU(2) is. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531750
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  • 2
    Electronic Resource
    Electronic Resource
    A new boson calculus for SU(3) (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4854-4862 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the Gelfand-Weyl pattern for SU(3) can be uniquely expressed in terms of four non-negative and one positive or negative free integers. This provides an optimal, albeit non-linear, boson calculus for SU(3) in terms of four harmonic oscillators and one planar rotor. (By optimal it is meant that every irreducible representation is obtained once and once only.) Our techniques can be generalized to other groups. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532129
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  • 3
    Electronic Resource
    Electronic Resource
    On the means of an entire function and its derivatives (1966)
    Springer
    Monatshefte für Mathematik 70 (1966), S. 33-38 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01306997
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  • 4
    Electronic Resource
    Electronic Resource
    The convex hull of two core capacitated network design problems (1993)
    Springer
    Mathematical programming 60 (1993), S. 233-250 
    Details
    ISSN: 1436-4646
    Keywords: Convex hull ; facets ; network design ; capacitated facilities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost. This paper studies two core subproblems of the NLP. The first problem, motivated by a Lagrangian relaxation approach for solving the problem, considers a multiple commodity, single arc capacitated network design problem. The second problem is a three node network; this specialized network arises in larger networks if we aggregate nodes. In both cases, we develop families of facets and completely characterize the convex hull of feasible solutions to the integer programming formulation of the problems. These results in turn strengthen the formulation of the NLP.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580612
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  • 5
    Electronic Resource
    Electronic Resource
    Impulsive rotatory motion of a circular disk in a viscous fluid (1959)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 10 (1959), S. 552-557 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Zusammenfassung Es wird eine analytische Methode für die Bestimmung der Geschwindigkeit der Strömung und der Winkelgeschwindigkeit einer kreisförmigen Scheibe gegeben, die in einer zähen, inkompressiblen Flüssigkeit einen Drehstoss erhält.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01601610
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  • 6
    Electronic Resource
    Electronic Resource
    Lower bounds for maximal and convex layers problems (1989)
    Springer
    Algorithmica 4 (1989), S. 447-459 
    Details
    ISSN: 1432-0541
    Keywords: Time complexity ; Upper bound ; Lower bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we derive tight lower bounds for the maximal and convex layers problems in the plane. Our lower bound proofs for the maxima problem and convex hull problem are simpler than those previously known. We also obtain an Ω(nlog n) lower bound for the maximal depth problem, and the convex depth problem, when the points are given in sorted order of their x-coordinates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01553901
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  • 7
    Electronic Resource
    Electronic Resource
    Average-case analysis of the Modified Harmonic algorithm (1989)
    Springer
    Algorithmica 4 (1989), S. 519-533 
    Details
    ISSN: 1432-0541
    Keywords: Bin packing ; Approximation algorithm ; On-line algorithm ; Worst-case performance ; Average-case performance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we analyze the average-case performance of the Modified Harmonic algorithm for on-line bin packing. We first analyze the average-case performance for arbitrary distribution of item sizes over (0,1]. This analysis is based on the following result. Letf 1 andf 2 be two linear combinations of random variables {N i } i=1 k where theN i 's have a joint multinomial distribution for eachn=σ i=1 k ,N i . LetE(f 1) ≠ O andE(f 2)≠ 0. Then limn →∞E(max(f 1,f 2 ))/n = lim n →∞ max(E(f 1),E(f 2))/n. We then consider the special case when the item sizes are uniformly distributed over (0,1]. For specific values of the parameters, the Modified Harmonic algorithm turns out to be better than the other two linear-time on-line algorithms—Next Fit and Harmonic—in both the worst case as well as the average case. We also obtain optimal values for the parameters of the algorithm from the average-case standpoint. For these values of the parameters, the average-case performance ratio is less than 1.19. This compares well with the performance ratios 1.333. and 1.2865. of the Next Fit algorithm and the Harmonic algorithm, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01553906
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  • 8
    Electronic Resource
    Electronic Resource
    Topological semivector spaces: Convexity and fixed point theory (1974)
    Springer
    Semigroup forum 9 (1974), S. 117-138 
    Details
    ISSN: 1432-2137
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Without speaking too roughly, (topological) semivector spaces are to (topological) semigroups as (topological) vector spaces are to (topological) groups. In Section 1 we introduce the notion of a (topological) semivector space. In Section 2 we study convexity in semivector spaces, in particular “Pointwise convexity,” i.e., convexity of singletons. The main results of the section are astructure theorem (2.7), acancellation theorem (2.11), and anembedding theorem (2.14). In Section 3 we identify and briefly study a hierarchy of local convexity properties in topological semivector spaces. Lastly, in Section 4 we presentfixed point theorems for compact convex subsets enjoying one or another local convexity property in a pointwise convex topological semivector space, indicating associatedminmax theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02194841
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  • 9
    Electronic Resource
    Electronic Resource
    Properties of nonparametric estimators of autocovariance for stationary random fields (1994)
    Springer
    Probability theory and related fields 99 (1994), S. 399-424 
    Details
    ISSN: 1432-2064
    Keywords: 62G05 ; 62G20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We introduce nonparametric estimators of the autocovariance of a stationary random field. One of our estimators has the property that it is itself an autocovatiance. This feature enables the estimator to be used as the basis of simulation studies such as those which are necessary when constructing bootstrap confidence intervals for unknown parameters. Unlike estimators proposed recently by other authors, our own do not require assumptions such as isotropy or monotonicity. Indeed, like nonparametric function estimators considered more widely in the context of curve estimation, our approach demands only smoothness and tail conditions on the underlying curve or surface (here, the autocovariance), and moment and mixing conditions on the random field. We show that by imposing the condition that the estimator be a covariance function we actually reduce the numerical value of integrated squared error.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01199899
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  • 10
    Electronic Resource
    Electronic Resource
    The finite element analysis of elasto-plastic materials by use of dislocation dipole systems (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 277-288 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the stress field due to any prescribed continuous distribution of dislocation dipoles can be determined. This technique then forms the basis of a general method of solution of elasto-plastic material problems. The presentation is limited to situations which conform to either plane stress or strain conditions. Some results are obtained for relatively simple geometrical and loading configurations and compared with classical plasticity solutions. Finally, the method is applied to the problem of a circular hole in a finite strip under tension.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080207
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