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41.
42.
R.?Mitchell C.?M.?CarrEmail author M.?Parfitt J.?C.?Vickerman C.?Jones 《Cellulose (London, England)》2005,12(6):629-639
The surface chemical composition of raw unscoured cotton was successfully investigated by the surface analytical techniques
X-ray Photoelectron Spectroscopy (XPS) and Time of Flight Secondary Ion Mass Spectrometry (ToF-SIMS). The presence of non-cellulosic
material at the fibre surface was established and determined to be a complex mixture of fatty acids, alcohols, alkanes, esters
and glycerides. The effect of scouring and bleaching was to reduce the surface concentration of these materials but even after
aqueous processing some non-cellulosic material residue was still detected at the fibre surface. 相似文献
43.
Some new pyridyl alcohols with the cis-bicyclo[3.3.0]octane scaffold were synthesized and used as chiral ligands for the enantioselective addition of diethylzinc to aldehydes. Ligands 4 were found to be far superior to the C2-symmetric ligands 2 in terms of enantioselectivities. Quantitative yields and enantiomeric excesses of up to 92% were obtained when the ligand 4 was used. The carbonyl function in 4 proved to be beneficial for the high enantioselectivities in the addition of diethylzinc to aldehydes. Conversion of the carbonyl group into oxime or oxime ether group led to a sort of more active ligands, which catalyzed the same reaction with rate acceleration. 相似文献
44.
R. C. Milward 《Fresenius' Journal of Analytical Chemistry》1973,264(3):195-199
Summary This article describes a new commercial Far-Infrared Fourier Spectrometer system which has been developed for routine spectroscopy in the 10–1000 cm–1 spectral region. The instrument incorporates real-time data processing and has been automated wherever possible for foolproof operation. A versatile sample chamber allows a wide range of spectroscopic studies to be performed, on solids, liquids and gases over a wide range of temperatures. A number of spectra are presented to illustrate the performance and typical applications of this Fourier spectrometer.
Ein neues fourier-spektrometer für das ferne infrarot
Zusammenfassung Nach einer kurzen Einführung in die Methode der Fourier-Spektroskopie wird ein neues kommerzielles Fern-Infrarot-Fourier-Spektrometer mit real-time Datenverarbeitungsanlage beschrieben. Das Gerät ist für die Spektroskopie im Bereich 10–1000 cm–1 konstruiert und weitgehend automatisiert. Eine vielseitig verwendbare Probenkammer ermöglicht umfangreiche spektroskopische Untersuchungen von Festkörpern, Flüssigkeiten und Gasen in einem sehr großen Temperaturbereich. Anhand einer Reihe von Spektren werden Leistung und typische Anwendungen dieses Fourier-Spektrometers erläutert.
Lecture presented at Euroanalysis I Conference, 28. 8.–1. 9. 1972 in Heidelberg, Germany. 相似文献
45.
A. Gameiro Pais 《Aequationes Mathematicae》1984,27(1):49-56
This paper is concerned with the problem of solving linear difference equations of ordern with constant coefficients and with given initial conditions in which the variable runs not only through the integers but over . The main idea is the introduction of a suitable commutative ring of functions with discrete convolution as multiplication rule which works, although it is not a field. The existence of inverses is studied and, after the introduction of suitable functions, the problem is reduced by means of a Laplace-like relation to an algebraic equation. Examples of application are given. Finally some remarks make the connection with the Operational Calculus of Mikusinski and with the Operational Calculus of Fenyö. The advantages of this method lie in the fact that it is applicable to functions others than the step functions, in its simplicity from the theoretical point of view, in its usefulness even when computation is required and in its formal similarity to the classical treatment of linear differential equations with constant coefficients. 相似文献
46.
W. T. Tutte 《Aequationes Mathematicae》1978,17(1):121-140
The equations of the title appear in the author's paper Chromatic Sums for Rooted Planar Triangulations, V: Special Equations. (Canadian Journal of Mathematics, 26 (1974), 893–907). They appear in that paper as Equations (24) and (25). They are simultaneous equations for two unknown functionsl andy
2 of two variablesy
1 andz. A parameter is involved. The main result is that for = 2 cos (2/n), wheren is a positive integer >1, the two equations can be reduced to a single equation (numbered (49)). Solutions of this are known forn <7. From such solutions we can expect to get information about the averaged chromatic polynomials of planar triangulations with a given number of triangles.The present work is basically an expository paper on the theory given in Chromatic Sums, V, but it includes some new results and many simplifications. 相似文献
47.
Let f C[a, b]. LetP be a subset ofC[a, b], L b – a be a given real number. We say thatp P is a best approximation tof fromP, with arc length constraintL, ifA[p]
b
a
[1 + (p(x))
2]dx L andp – f q – f for allq P withA[q] L. represents an arbitrary norm onC[a, b]. The constraintA[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755. 相似文献
48.
LetA be anM-matrix in standard lower block triangular form, with diagonal blocksA
ii irreducible. LetS be the set of indices such that the diagonal blockA
is singular. We define the singular graph ofA to be the setS with partial order defined by > if there exists a chain of non-zero blocksA
i, Aij, , Al.Let 1 be the set of maximal elements ofS, and define thep-th level
p
,p = 2, 3, , inductively as the set of maximal elements ofS
\(
1
p-1). Denote by
p
the number of elements in
p
. The Weyr characteristic (associated with 0) ofA is defined to be (A) = (
1, 2,,
h
), where
1 + +
p
= dim KerA
p
,p = 1, 2, , and
h > 0, h+1 = 0.Using a special type of basis, called anS-basis, for the generalized eigenspaceE(A) of 0 ofA, we associate a matrixD withA. We show that(A) = (
1, , h) if and only if certain submatricesD
p,p+1
,p = 1, , h – 1, ofD have full column rank. This condition is also necessary and sufficient forE(A) to have a basis consisting of non-negative vectors, which is a Jordan basis for –A.
We also consider a given finite partially ordered setS, and we find a necessary and sufficient condition that allM-matricesA with singular graphS have(A) = (
1, , h). This condition is satisfied ifS is a rooted forest.The work of the second-named author was partly supported by the National Science Foundation, under grant MPS-08618 A02. 相似文献
49.
Helmut Karzel 《Aequationes Mathematicae》1978,17(1):83-90
A permutation set (M, I) consisting of a setM and a set of permutations ofM, is calledsymmetric, if for any two permutations, the existence of anx M with (x) (x) and
–1
(x) =
–1
(x) implies
–1
=
–1
, andsharply 3-transitive, if for any two triples (x
1,x
2,x
3), (y
1,y
2,y
3) M
3 with|{x
1,x
2,x
3
}| = |{y
1,y
2,y
3
}| = 3 there is exactly one permutation with(x
1) =y
1,(x
2) =y
2,(x
3) =y
3. The following theorem will be proved.THEOREM.Let (M, ) be a sharply 3-transitive symmetric permutation set with |M|3, such that contains the identity. Then is a group and there is a commutative field K such that and the projective linear group PGL(2, K) are isomorphic. 相似文献
50.
M. A. Wolfe 《Numerische Mathematik》1978,31(2):153-174
Summary Given an iterative methodM
0, characterized byx
(k+1=G
0(x(
k
)) (k0) (x(0) prescribed) for the solution of the operator equationF(x)=0, whereF:XX is a given operator andX is a Banach space, it is shown how to obtain a family of methodsM
p characterized byx
(k+1=G
p
(x(
k
)) (k0) (x(0) prescribed) with order of convergence higher than that ofM
o. The infinite dimensional multipoint methods of Bosarge and Falb [2] are a special case, in whichM
0 is Newton's method.Analogues of Theorems 2.3 and 2.36 of [2] are proved for the methodsM
p, which are referred to as extensions ofM
0. A number of methods with order of convergence greater than two are discussed and existence-convergence theorems for some of them are proved.Finally some computational results are presented which illustrate the behaviour of the methods and their extensions when used to solve systems of nonlinear algebraic equations, and some applications currently being investigated are mentioned. 相似文献