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101.
A trajectory-following method for unconstrained optimization 总被引:2,自引:0,他引:2
A trajectory-following method with interesting properties is considered for solving unconstrained nonlinear programming problems. The trajectory is defined by a special system of ordinary differential equations. This system uses only the gradient of the objective function. Numerical examples are given.The work of the second author was supported by the DFG Schwerpunkt Anwendungs-bezogene Optimierung and Steuerung. 相似文献
102.
K. Böröczky Jr. 《Geometriae Dedicata》1990,34(1):13-18
An E R
2 is r-convex if for every x, y E there exists a closed rectangle R such that x, y R and R E. Several results about r-convexity appeared in [1]. Its authors formulated a conjecture about conditions for a compact, convex set in R
2 to be r-convex. We prove this conjecture in the case of convex domains of constant width. 相似文献
103.
It is proved that if a graphG has maximum degreed, then its vertices can be represented by distinct unit vectors inR
2d so that two vectors are orthogonal if and only if the corresponding vertices are adjacent. As a corollary it follows that if a graph has maximum degreed, then it is isomorphic to a unit distance graph inR
2d. 相似文献
104.
Peter Köhler 《Aequationes Mathematicae》1990,39(1):6-18
LetC
m
be a compound quadrature formula, i.e.C
m
is obtained by dividing the interval of integration [a, b] intom subintervals of equal length, and applying the same quadrature formulaQ
n
to every subinterval. LetR
m
be the corresponding error functional. Iff
(r)
> 0 impliesR
m
[f] > 0 (orR
m
[f] < 0),=" then=" we=" say=">C
m
is positive definite (or negative definite, respectively) of orderr. This is the case for most of the well-known quadrature formulas. The assumption thatf
(r)
> 0 may be weakened to the requirement that all divided differences of orderr off are non-negative. Thenf is calledr-convex. Now letC
m
be positive definite or negative definite of orderr, and letf be continuous andr-convex. We prove the following direct and inverse theorems for the errorR
m
[f], where , denotes the modulus of continuity of orderr:
相似文献
105.
Summary We prove that the error inn-point Gaussian quadrature, with respect to the standard weight functionw1, is of best possible orderO(n
–2) for every bounded convex function. This result solves an open problem proposed by H. Braß and published in the problem section of the proceedings of the 2. Conference on Numerical Integration held in 1981 at the Mathematisches Forschungsinstitut Oberwolfach (Hämmerlin 1982; Problem 2). Furthermore, we investigate this problem for positive quadrature rules and for general product quadrature. In particular, for the special class of Jacobian weight functionsw
, (x)=(1–x)(1+x), we show that the above result for Gaussian quadrature is not valid precisely ifw
, is unbounded.Dedicated to Prof. H. Braß on the occasion of his 55th birthday 相似文献
106.
107.
108.
A. Dönni P. Fischer A. Furrer P. Bonville F. Hulliger H. R. Ott 《Zeitschrift für Physik B Condensed Matter》1990,81(1):83-88
A polycrystalline smaple of nonstoichiometric ytterbium phosphide, YbP0.84, was investigated by neutron scattering, Mössbauer spectroscopy and bulk magnetic measurements. Neutron diffraction experiments prove the existence of antiferromagnetic type II ordering belowT
N
=0.64 K, in contrast to the observed antiferromagnetic type III ordering in the stoichiometric Kondo-like compounds YbN and YbAs. The temperature dependence of the average ordered magnetic moment per Yb3+ ion with saturation value Yb = 1.03(7)
B
is similar to that of YbN. Mössbauer experiments prove the magnetic phase transition to be first order with different regions in the sample having slightly different transition temperatures. By means of inelastic neutron scattering the crystal-field level scheme was established to be
6 –
8(19meV) –
7(43meV). 相似文献
109.
The spin content of the proton is investigated by studying the flavor singlet axial structure of the nucleon in a non-topological chiral soliton model. In order to construct a nucleon state we used the generator coordinate projection method as well as a coherent state for the meson wave function. Using a standard set of parameters we found the value g A 0 ? 0.44 for the flavor singlet axial vector coupling constant. This result is not far from that of a typical valence quark model. 相似文献
110.
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