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31.
Pinar Heggernes 《Discrete Mathematics》2006,306(24):3267-3280
Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that different vertices can be assigned different domination powers. Broadcast domination assigns an integer power f(v)?0 to each vertex v of a given graph, such that every vertex of the graph is within distance f(v) from some vertex v having f(v)?1. The optimal broadcast domination problem seeks to minimize the sum of the powers assigned to the vertices of the graph. Since the presentation of this problem its computational complexity has been open, and the general belief has been that it might be NP-hard. In this paper, we show that optimal broadcast domination is actually in P, and we give a polynomial time algorithm for solving the problem on arbitrary graphs, using a non-standard approach. 相似文献
32.
Gautam Bharali 《Journal of Functional Analysis》2006,236(1):351-368
We begin with the following question: given a closed disc and a complex-valued function , is the uniform algebra on generated by z and F equal to ? When F∈C1(D), this question is complicated by the presence of points in the surface that have complex tangents. Such points are called CR singularities. Let p∈S be a CR singularity at which the order of contact of the tangent plane with S is greater than 2; i.e. a degenerate CR singularity. We provide sufficient conditions for S to be locally polynomially convex at the degenerate singularity p. This is useful because it is essential to know whether S is locally polynomially convex at a CR singularity in order to answer the initial question. To this end, we also present a general theorem on the uniform algebra generated by z and F, which we use in our investigations. This result may be of independent interest because it is applicable even to non-smooth, complex-valued F. 相似文献
33.
We consider two analogues of associativity for ternary algebras: total and partial associativity. Using the corresponding ternary associators, we define ternary analogues of alternative and assosymmetric algebras. On any ternary algebra the alternating sum [a, b, c] = abc − acb − bac + bca + cab − cba (the ternary analogue of the Lie bracket) defines a structure of an anticommutative ternary algebra. We determine the polynomial identities of degree ?7 satisfied by this operation in totally and partially associative, alternative, and assosymmetric ternary algebras. These identities define varieties of ternary algebras which can be regarded as ternary analogues of Lie and Malcev algebras. Our methods involve computational linear algebra based on the representation theory of the symmetric group. 相似文献
34.
Let E\subset \Bbb R
s
be compact and let d
n
E
denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ
n
={ \bf x
k,n
}
k=1
dnE
, n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do
not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R
2
. It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore,
for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes.
November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001. 相似文献
35.
Dimitar K. Dimitrov 《Journal of Mathematical Analysis and Applications》2004,299(1):127-132
We prove that the zeros of the polynomials Pm(a) of degree m, defined by Boros and Moll via
36.
37.
The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector
(MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first
iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain
curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently
by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant
condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one
can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification
based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least
squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”.
R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya
was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear
programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion
of Science. 相似文献
38.
Daniel Carando Silvia Lassalle 《Journal of Mathematical Analysis and Applications》2008,347(1):243-254
We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product , for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X. 相似文献
39.
40.
General local convergence theorems with order of convergence r≥1 are provided for iterative processes of the type xn+1=Txn, where T:D⊂X→X is an iteration function in a metric space X. The new local convergence theory is applied to Newton iteration for simple zeros of nonlinear operators in Banach spaces as well as to Schröder iteration for multiple zeros of polynomials and analytic functions. The theory is also applied to establish a general theorem for the uniqueness ball of nonlinear equations in Banach spaces. The new results extend and improve some results of [K. Do?ev, Über Newtonsche Iterationen, C. R. Acad. Bulg. Sci. 36 (1962) 695–701; J.F. Traub, H. Wo?niakowski, Convergence and complexity of Newton iteration for operator equations, J. Assoc. Comput. Mach. 26 (1979) 250–258; S. Smale, Newton’s method estimates from data at one point, in: R.E. Ewing, K.E. Gross, C.F. Martin (Eds.), The Merging of Disciplines: New Direction in Pure, Applied, and Computational Mathematics, Springer, New York, 1986, pp. 185–196; P. Tilli, Convergence conditions of some methods for the simultaneous computation of polynomial zeros, Calcolo 35 (1998) 3–15; X.H. Wang, Convergence of Newton’s method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20 (2000) 123–134; I.K. Argyros, J.M. Gutiérrez, A unified approach for enlarging the radius of convergence for Newton’s method and applications, Nonlinear Funct. Anal. Appl. 10 (2005) 555–563; M. Giusti, G. Lecerf, B. Salvy, J.-C. Yakoubsohn, Location and approximation of clusters of zeros of analytic functions, Found. Comput. Math. 5 (3) (2005) 257–311], and others. 相似文献