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991.
992.
Maria Hermínia de Paula Leite Mello 《manuscripta mathematica》1987,57(3):263-280
Let be a nonorientable m-plane bundle over a CW complex X of dimension m or less. Given a 2-plane bundle over X, we wish to know whether can be embedded as a sub-bundle of . The bundle need not be orientable. When is even-dimensional there is the added complication of twisted coefficients. In that case, we use Postnikov decomposition of certain nonsimple fibrations in order to describe the obstructions for the embedding problem. Emery Thomas [11] and [12] treated this problem for and both orientable. The results found here are applied to the tangent bundle of a closed, connected, nonorientable smooth manifold, as a special case.The writing of this paper was partially supported by CNPq grant 相似文献
993.
For ν≥0 let cνk be the k-th positive zero of the cylinder functionC v(t)=J v(t)cosα-Y v(t)sinα, 0≤α>π whereJ ν(t) andY ν(t) denote the Bessel functions of the first and the second kind, respectively. We prove thatC v,k 1+H(x) is convex as a function of ν, ifc νk≥x>0 and ν≥0, whereH(x) is specified in Theorem 1.1. 相似文献
994.
Given a graphG onn vertices and a total ordering ≺ ofV(G), the transitive orientation ofG associated with ≺, denotedP(G; ≺), is the partial order onV(G) defined by settingx<y inP(G; ≺) if there is a pathx=x
1
x
2…x
r=y inG such thatx
1 ≺x
j for 1≦i<j≦r. We investigate graphsG such that every transitive orientation ofG contains
2
n
−o(n
2) relations. We prove that almost everyG
n,p satisfies this requirement if
, but almost noG
n,p satisfies the condition if (pn log log logn)/(logn log logn) is bounded. We also show that every graphG withn vertices and at mostcn logn edges has some transitive orientation with fewer than
2
n
−δ(c)n
2 relations.
Partially supported by MCS Grant 8104854. 相似文献
995.
996.
Let {ø n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø n (dμ) when logμ′∈L 1. In what follows we will discuss the asymptotic behavior of the ratioø n (dμ 2)/ø n (dμ 1) on the unit circle whendμ 1 anddμ 2 are close in a sense (e.g.,dμ 2=gdμ 1, where g≥0 is such thatQ(e it )g(t) andQ(e it )/g(t) are bounded for a suitable polynomialQ) and μ 1 ′ >0 almost everywhere or (a somewhat weaker requirement) lim n→∞Φ n (dμ 1,0)=0 for the monic polynomial Φ n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper. 相似文献
997.
András Sütő 《Communications in Mathematical Physics》1987,111(3):409-415
The spectrum (H) of the tight binding Fibonacci Hamiltonian (H
mn=
m,n+1+
m+1,n
+
m,n
v(n),v(n)=
((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary 相似文献
998.
I. Pelant M. N. Popova J. Hála M. AmbroŽ V. Lhotská K. Vacek 《Czechoslovak Journal of Physics》1987,37(10):1183-1197
Dependence of two-photon absorption (TPA) rate on the state of polarization of a laser beam is investigated in the low-temperature orthorhombic modification of Hg2Cl2 crystals. Theoretical calculations of the dependence of TPA rate on the direction of polarization vector of the beam are performed for centrosymmetric points, Y, Z, T, R andS of the Brillouin zone. The domain structure of real crystals is taken into consideration and it is shown that periodicity of the polarization dependence may indicate whether TPA is due to transitions either at, Y, Z, T orR, S points. The polarization dependence of TPA cannot, however, distinguish between points inside these two groups. Comparison of theory with a low-temperature (T 8·5 K) experimental curve of polarization dependence is discussed. It is shown that the experiment can be explained in main features by a model of noninteracting oriented linear dipoles. Further, on the basis of TPA measurements, a simple energy band structure of Hg2Cl2 is proposed regarding Hg2Cl2 crystal as a linear chain of molecules.The authors express thanks to Dr. . Barta for supplying the Hg2Cl2 crystals, Dr. Z. Bryknar for critical comments and Dr. B. Velický for stimulating discussion. We thank also Dr. V. Kohlová for assistance during measurement. 相似文献
999.
A simple analytical model is developed and solved to describe time evolution of the loop voltage and toroidal current when RF and inductive current drive take place simultaneously. A relation for the real value of the RF driven current has been obtained under these conditions. Comparison with experimental data from T-7 tokamak allows to estimate the role of the skin effect during RF current drive.The authors would like to thank A. Ya. Kislov for the basic data on the T-7 tokamak transformer. They are also indebted to V. V. Parail and G.V. Pereverzev for many clarifying discussions. 相似文献
1000.
B. Barabás 《Periodica Mathematica Hungarica》1987,18(2):115-122
The properties of the empirical density function,f
n(x) = k/n(
j
+
–
j-1
+
) if
j-1
+
< x + where
j-1
+
and
j
+
are sample elements and there are exactlyk – 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a good estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions. 相似文献