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101.
102.
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
103.
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
104.
Let T be a c.n.u. contraction on a Hilbert spaceH and let u-(u1,...,un) be an n-tuple of H(T). We calculate various joint spectra of u(T) and apply the results to study the spectral and index theories of elementary operators associated with n-tuples of the above type.Both authors have been partially supported by NSF grants. 相似文献
105.
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
106.
107.
A very special case of one of the theorems of the authors states as follows: Let 1a
1a
2... be an infinite sequence of integers for which all the sumsa
i
+a
j
, 1ij, are distinct. Then there are infinitely many integersk for which 2k can be represented in the forma
i
+a
j
but 2k+1 cannot be represented in this form. Several unsolved problems are stated.Dedicated to our friend Professor E. Hlawka on the occasion of his seventieth birthday 相似文献
108.
Alvaro M Corma A Das D Fornés V García H 《Chemical communications (Cambridge, England)》2004,(8):956-957
Preparation of hybrid organic-inorganic MCM-41 and SBA-15 silicas functionalized with perfluoroalkylsulfonic acid groups has been achieved in a single step by reacting the mesoporous silicas with 1,2,2-trifluoro-2-hydroxy-1-trifluoromethylethane sulfonic acid beta-sultone; the catalysts showed higher activity than commercial Nafion-silica composite for the esterification of long chain fatty acids with ethanol. 相似文献
109.
Crystal orbital calculations on cis- and trans-polyacethylene chains indicate two kinds of geometry changes on charge transfer. (1) increase (decrease) of the CC bond lenght and CCC bond angles in the trans conformer taking up (losing) electrons, and a tendency towards bond-length equalization on electron uptake and loss for both conformers. 相似文献
110.