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1.
Clemens G. Raab Georg Regensburger Jamal Hossein Poor 《Journal of Pure and Applied Algebra》2021,225(5):106564
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials. 相似文献
2.
Clemens Winkler 《Fresenius' Journal of Analytical Chemistry》1886,25(1):226-228
Ohne Zusammenfassung 相似文献
3.
F. Prez-Willard C. Sürgers H. Von Lhneysen P. Pfundstein 《Physica E: Low-dimensional Systems and Nanostructures》2004,22(4):872-880
The electronic transport through nanostructured bismuth nanobridges has been investigated at low temperatures (T<2 K) and in magnetic fields B up to 8.5 T. The samples show reproducible resistance fluctuations as a function of B, superimposed on a large magnetoresistance of up to 50%. In addition, time-dependent resistance fluctuations in zero magnetic field demonstrate the presence of bistable scatterers in the constriction region of our samples, which are described by two-level systems. Their dynamics are shown to be sensitive to subtle modifications of the static scatterer configuration in their vicinity, which cannot be detected in the sample magnetofingerprint. 相似文献
4.
Clemens Heuberger 《Periodica Mathematica Hungarica》2004,49(2):65-89
We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bases q, similar results are given which complement those given in [6]. 相似文献
5.
Kristin Fischer Silvio Prause Stefan Spange Frank Cichos Christian Von Borczyskowski 《Journal of Polymer Science.Polymer Physics》2003,41(11):1210-1218
Solvent‐dependent ultraviolet–visible (UV–vis) absorption and Stokes shifts including strong hydrogen‐bond‐donating (HBD) solvents such as 2,2,2‐trifluoroethanol and 1,1,1,3,3,3‐hexafluoro‐2‐propanol of two coumarine dyes (Co 151 and Co 153) were analyzed with multiple‐square analyses of linear solvation energy relationships and the Kamlet–Taft solvent parameter set to α (HBD capacity), β (hydrogen‐bond‐accepting capacity), and π* (dipolarity/polarizability). The UV–vis absorption and emission spectra of Co 151 and Co 153 were measured when adsorbed on various polysaccharides such as different cellulose batches, carboxymethylcelluloses with different degrees of substitution, and chitine. As a result of this evaluation, Co 153 is recommended as an alternative UV–vis probe for evaluating the dipolarity/polarizability of cellulose and cellulose derivates. Multiple adsorption of Co 153 on Linters cellulose took place indicating a wide‐surface polarity distribution, which makes the determination of a rigid polarity parameter questionable. Thus, fluorescence measurements of adsorbed Co 153 are suitable to detect inhomogenities on a surface but not for the determination of empirical polarity parameters. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1210–1218, 2003 相似文献
6.
Clemens Amstler 《Monatshefte für Mathematik》1995,119(3):177-186
In this paper we establish an inequality of Koksma-Hlawka-type for compact groups. We first define a discrepancy for compact groups based on discrepancy operators introduced by W. Fleischer and show the relation to the classicalL
2-discrepancy. Then we prove the inequality for functions in a weightedL
2-space. 相似文献
7.
D. Hugh Powell Andr E. Merbach Gabriel Gonzlez Ern Brücher Kroly Micskei M. Francesca Ottaviani Klaus Khler Alex Von Zelewsky Oleg Ya. Grinberg Yakob S. Lebedev 《Helvetica chimica acta》1993,76(5):2129-2146
EPR Spectra have been measured for aqueous solutions of a series of Gd3+ complexes at variable temperature and a range of magnetic fields; S-band (0.14 T), X-band (0.34 T), Q-band (1.2 T), and 2-mm-band (5.0 T). The major contribution to the observed line widths is magnetic-field-dependent and is interpreted as being due to the modulation of the zero-field splitting produced by distortion of the complexes from perfect symmetry. The transverse and longitudinal relaxation matrices for an 8S ion with such an interaction have been calculated using Redfield theory with vector-coupling methods, and diagonalised numerically to obtain relaxation rates and intensities for the degenerate transitions which contribute to the multiplet. The observed line width, which is inversely proportional to the magnetic field at low temperatures, is best described by the intensity-weighted mean transverse relaxation time for the four transitions with non-zero intensity. A least-squares fit of the data yields the square of the zero-field splitting tensor, Δ2, and a correlation time, τv, with activation energy, Ev. The physical significance of these parameters and the extent of validity of the theoretical approach are considered. The parameters are used to predict the magnetic-field dependence of the longitudinal and transverse electronic relaxation times, which are discussed in the context of their relevance to 1H-NMR relaxivity. 相似文献
8.
9.
Clemens Markett 《Constructive Approximation》1989,5(1):383-404
One of the most far-reaching qualities of an orthogonal system is the presence of an explicit product formula. It can be utilized to establish a convolution structure and hence is essential for the harmonic analysis of the corresponding orthogonal expansion. As yet a convolution structure for Fourier-Bessel series is unknown, maybe in view of the unpractical nature of the corresponding expanding functions called Fourier-Bessel functions. It is shown in this paper that for the half-integral values of the parameter
,n=0, 1, 2,, the Fourier-Bessel functions possess a product formula, the kernel of which splits up into two different parts. While the first part is still the well-known kernel of Sonine's product formula of Bessel functions, the second part is new and reflects the boundary constraints of the Fourier-Bessel differential equation. It is given, essentially, as a finite sum over triple products of Bessel polynomials. The representation is explicit up to coefficients which are calculated here for the first two nontrivial cases
and
. As a consequence, a positive convolution structure is established for
. The method of proof is based on solving a hyperbolic initial boundary value problem.Communicated by Tom H. Koornwinder. 相似文献
10.
Bernhard Von Stengel 《Annals of Operations Research》1988,16(1):161-183
This paper integrates and extends the theory of the decomposition of multiattribute expected-utility functions based on utility independence. In a preliminary section, the standard decision model of expected utility is briefly discussed, including the fact that the decision maker's preference forlotteries with two outcomes determines the utility function uniquely. The decomposition possibilities of a utility function are captured by the concept ofautonomous sets of attributes, an affine separability of some kind known as generalized utility independence.Overlapping autonomous sets lead to biaffine-associative, i.e.multiplicative oradditive decompositions. The multiplicative representation shows that autonomy has strongerclosure properties than utility independence, for instance with respect to set-theoretic difference. Autonomy is also a concept with a wider scope since it applies to the decomposition of Boolean functions, games and a number of other topics in combinatorial optimization. This relationship to the well-known theory ofsubstitution decomposition in discrete mathematics also reveals a kind of discrete core behind the decomposition of utility functions. The entirety of autonomous sets can be represented by a compact data structure, the so-calledcomposition tree, which frequently corresponds to a natural hierarchy of attributes. Multiplicative/additive ormulti-affine functions correspond to the hierarchy steps. The known representation of multi-affine functions is shown to be given by aMoebius inversion formula. The entire approach has the advantage that it allows the application of more sophisticated representation methods on a detailed level, whereas it employs onlyfinite set theory andarithmetic on the main levels in the hierarchy. 相似文献