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31.
This article completes and simplifies earlier results on the derivation of best linear, or affine, unbiased estimates in the general Gauss-Markov model with a singular dispersion matrix and additional restrictions under very general conditions. We provide the class of all linear representations of the best affine unbiased estimator with precise statements concerning its indeterminacy. 相似文献
32.
33.
34.
Walter Feit 《Israel Journal of Mathematics》1993,82(1-3):141-156
LetK be a field and letG be a finite group.G isK-admissible if there exists a Galois extensionL ofK withG=Gal(L/K) such thatL is a maximal subfield of a centralK-division algebra. This paper contains a characterization of those number fields which areQ
16-admissible. This is the same class of number fields which are 2A
6=SL(2, 9) and 2A
7 admissible.
Dedicated to John Thompson to celebrate his Wolf Prize in Mathematics 1992 相似文献
35.
Diemar A. Plattner Andreas Brunner Max Dobler Hans-Martin Müller Walter Petter Peter Zbinden Dieter Seebach 《Helvetica chimica acta》1993,76(5):2004-2033
Cyclic Oligomers of (R)-3-Hydroxybutanoic Acid: Preparation and Structural Aspects The oligolides containing three to ten (R)-3-hydroxybutanoate (3-HB) units (12-through 40-membered rings 1–8 ) are prepared from the hydroxy acid itself, its methyl ester, its lactone (‘monolide’), or its polymer (poly(3-HB), mol. wt. ca. 106 Dalton) under three sets of conditions: (i) treatment of 3-HB ( 10 ) with 2,6-dichlorobenzoyl chloride/pyridine and macrolactonization under high dilution in toluene with 4-(dimethylamino)pyridine (Fig. 3); (ii) heating a solution (benzene, xylene) of the β-lactone 12 or of the methyl ester 13 from 3-HB with the tetraoxadistanna compound 11 as trans-esterification catalyst (Fig. 4); (iii) heating a mixture of poly(3-HB) and toluene-sulfonic acid in toluene/1,2-dichloroethane for prolonged periods of time at ca. 100° (Fig. 6). In all three cases, mixtures of oligolides are formed with the triolide 1 being the prevailing component (up to 50% yield) at higher temperatures and with longer reaction times (thermodynamic control, Figs. 3–6). Starting from rac-β-lactone rac- 12 , a separable 3:1 to 3:2 mixture of the l,u- and the l,l-triolide diasteroisomers rac- 14 and rac- 1 , respectively, is obtained. An alternative method for the synthesis of the octolide 6 is also described: starting from the appropriate esters 15 and 17 and the benzyl ether 16 of 3-HB, linear dimer, tetramer, and octamer derivatives 18–23 are prepared, and the octamer 23 with free OH and CO2H group is cyclized (→ 6 ) under typical macrolactonization conditions (see Scheme). This ‘exponential fragment coupling protocol’ can be used to make higher linear oligomers as well. The oligolides 1–8 are isolated in pure form by vacuum distillation, chromatography, and crystallization, an important analytical tool for determining the composition of mixtures being 13C-NMR spectroscopy (each oligolide has a unique and characteristic chemical shift of the carbonyl C-atom, with the triolide 1 at lowest, the decolide 8 at highest field). The previously published X-ray crystal structures of triolide 1 , pentolide 3 , and hexolide 4 (two forms), as well as those of the l,u-triolide rac- 14 , of tetrolide ent- 2 , of heptolide 5 , and of two modifications of octolide 6 described herein for the first time are compared with each other (Figs. 7–10 and 12–15, Tables 2 and 5–7) and with recently modelled structures (Tables 3 and 4, Fig. 11). The preferred dihedral angles τ1 to τ4 found along the backbone of the nine oligolide structures (the hexamer and the larger ones all have folded rings!) are mapped and statistically evaluated (Fig. 16, Tables 5–7). Due to the occurrence of two conformational minima of the dihedral angle O? CO? CH2? CH (τ3 = + 151 or ?43°), it is possible to locate two types of building blocks for helices in the structures at hand: a right-handed 31 and a left-handed 21 helix; both have a ca. 6 Å pitch, but very different shapes and dispositions of the carbonyl groups (Fig. 17). The 21 helix thus constructed from the oligolide single-crystal data is essentially superimposable with the helix derived for the crystalline domains of poly(3-HB) from stretched-fiber X-ray diffraction studies. The absence of the unfavorable (E)-type arrangements around the OC? OR bond (‘cis-ester’) from all the structures of (3-HB) oligomers known so far suggests that the model proposed for a poly(3-HB)-containing ion channel (Fig. 2) must be modified. 相似文献
36.
37.
The sensitivity of neutron-proton scattering observables to the recently reported charge-independence breaking of the isospinT=13
P nucleon-nucleon interaction has been calculated. It is shown that only the analyzing powerA
y
() at extreme forward angles and at =90° c.m. and the spin-correlation coefficientA
zx
() at 90° c.m. exhibit a measurable sensitivity. It is concluded that the determination ofA
y
at 90° c.m. is currently the most accurate approach to verify independently charge-independence breaking in the3
P nucleon-nucleon phase shifts, considering the status of present experimental techniques. 相似文献
38.
Cross ratios constitute an important tool in classical projective geometry. Using the theory of Tutte groups as discussed in [6] it will be shown in this note that the concept of cross ratios extends naturally to combinatorial geometries or matroids. From a thorough study of these cross ratios which, among other observations, includes a new matroid theoretic version and proof of the Pappos theorem, it will be deduced that for any projective space M=
n
(K) of dimension n2 of M over some skewfield K the inner Tutte group is isomorphic to the commutator factor group K
*/[K
*, K
*] of K
*K{0}. This shows not only that in case M=
n
(K) our matroidal cross ratios are nothing but the classical ones. It can also be used to correlate orientations of the matroid M=
n
(K) with the orderings of K. And it implies that Dieudonné's (non-commutative) determinants which, by Dieudonné's definition, take their values in K
*/[K
*, K
*] as well, can be viewed as a special case of a determinant construction which works for just every combinatorial geometry.Research supported by the DFG (Deutsche Forschungsgemeinschaft). 相似文献
39.
Walter A. Carnielli 《Studies in Applied Mathematics》1990,82(1):59-69
A hyper-rook domain of an element x in the space (words of length n over alphabets with k elements) is a sphere with center x and fixed radius j in Hamming distance. The number j determines the dimension of the hyper-rook domain. The classical (and far from solved) problem of covering by rook domains (here considered as the 1-dimensional case) is the problem of finding minimal coverings of by such spheres. Very few results are known in the literature for dimensions ≥ 2. We prove in this paper certain classes of inequalities based on coverings using matrices, which give upper and lower bounds for several cases of the problem for higher dimensions. 相似文献
40.
Richard A. Reid Walter A. StarkJr 《The Journal of the Operational Research Society》1988,39(2):135-139
Individual/group replacement models were used to identify the minimum-cost policy for replacing protective gloves that are utilized in product fabrication at a nuclear processing facility. Since historical data on glove longevity were not available to determine the failure-rate distribution, the classical replacement model for items that fail was modified to consider glove life as a normally distributed variable. Moreover, the absence of replacement-cost required that the classical model be transformed to incorporate the ratio of single to unit-group replacement cost. Sensitivity analysis on these two input parameter values provided guidance for the development of an appropriate replacement policy. 相似文献