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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.
3.
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
4.
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
5.
B. Sun Yu. A. Litvinov P. M. Walker K. Beckert P. Beller F. Bosch D. Boutin C. Brandau L. Chen C. Dimopoulou H. Geissel R. Knöbel C. Kozhuharov J. Kurcewicz S. A. Litvinov M. Mazzocco J. Meng C. Nociforo F. Nolden W. R. Plass C. Scheidenberger M. Steck H. Weick M. Winkler 《The European Physical Journal A - Hadrons and Nuclei》2007,31(3):393-394
A new long-lived isomeric state in the near proton dripline nucleus 125Ce has been identified with Schottky mass spectrometry at GSI. The excitation energy E
* = 103(12)keV and the decay time of 193(1)s have been obtained from a single stored fully ionized 125m
Ce58+ ion. The data implies an E3 transition and a 1/2+ assignment for the spin of the isomer. 相似文献
6.
The FRS-ESR facility at GSI provides one of the most efficient methods for direct mass measurements. In the present experiment,
exotic nuclei were produced via fragmentation of 152Sm projectiles in a thick beryllium target at 500-600 MeV/u, separated in-flight with the fragment separator FRS, and injected
into the storage-cooler ring ESR. Time-resolved Schottky Mass Spectrometry was applied for mass measurements of stored and
electron-cooled bare and few-electron ions. 373 different nuclides were identified by means of the spectra of their revolution
frequencies. Masses for 18 nuclides (84Zr, 92Ru, 94Rh, 107,108,110Sb, 111,112,114I, 118Ba, 122,123La, 124Ce, 127Pr, 129Nd, 132Pm, 134Sm, 137Eu) have been determined for the first time. Masses for 111,112I and 113Xe have been obtained via known α-decay energies. The experiment and first results will be presented. 相似文献
7.
8.
C. Scheidenberger K. Beckert P. Beller F. Bosch C. Brandau D. Boutin L. Chen B. Franzke H. Geissel R. Knöbel C. Kozhuharov J. Kurcewicz S. A. Litvinov Yu. A. Litvinov M. Mazzocco G. Münzenberg F. Nolden W. R. Plaß M. Steck B. Sun H. Weick M. Winkler 《Hyperfine Interactions》2006,173(1-3):61-66
One important goal of the ILIMA project at FAIR is the study of masses and decay properties of relativistic isomeric beams
stored and cooled in the planned storage-ring complex. A new scheme is described, where a storage-cooler ring is used for
high-resolution mass separation. Experimental results on the separation of the isobaric pair 140Pr-140Ce are presented.
P. Beller, deceased. 相似文献
9.
We discuss the coarse-grained level density of the Hénon-Heiles system above the barrier energy, where the system is nearly
chaotic. We use periodic orbit theory to approximate its oscillating part semiclassically via Gutzwiller’s semiclassical trace
formula (extended by uniform approximations for the contributions of bifurcating orbits). Including only a few stable and
unstable orbits, we reproduce the quantum-mechanical density of states very accurately. We also present a perturbative calculation
of the stabilities of two infinite series of orbits (Rn and Lm), emanating from the shortest librating straight-line orbit (A) in a bifurcation cascade just below the barrier, which at the barrier have two common asymptotic Lyapunov exponents χR and χL. 相似文献
10.
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