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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.
Single Crystal to Single Crystal (SC‐to‐SC) Transformation from a Nonporous to Porous Metal–Organic Framework and Its Application Potential in Gas Adsorption and Suzuki Coupling Reaction through Postmodification 下载免费PDF全文
Dr. Rupam Sen Debraj Saha Dr. Subratanath Koner Dr. Paula Brandão Dr. Zhi Lin 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(15):5962-5971
A new amino‐functionalized strontium–carboxylate‐based metal–organic framework (MOF) has been synthesized that undergoes single crystal to single crystal (SC‐to‐SC) transformation upon desolvation. Both structures have been characterized by single‐crystal X‐ray analysis. The desolvated structure shows an interesting 3D porous structure with pendent ?NH2 groups inside the pore wall, whereas the solvated compound possesses a nonporous structure with DMF molecules on the metal centers. The amino group was postmodified through Schiff base condensation by pyridine‐2‐carboxaldehyde and palladium was anchored on that site. The modified framework has been utilized for the Suzuki cross‐coupling reaction. The compound shows high activity towards the C?C cross‐coupling reaction with good yields and turnover frequencies. Gas adsorption studies showed that the desolvated compound had permanent porosity and was microporous in nature with a BET surface area of 2052 m2 g?1. The material also possesses good CO2 (8 wt %) and H2 (1.87 wt %) adsorption capabilities. 相似文献
3.
Brandão Pedro Francisco Ramos Rui Miguel Rodrigues José António 《Analytical and bioanalytical chemistry》2018,410(26):6873-6880
Analytical and Bioanalytical Chemistry - Formaldehyde is often applied in the industrial production of different products, such as textiles, insulation materials, or cosmetics, due to its... 相似文献
4.
Clemens Winkler 《Fresenius' Journal of Analytical Chemistry》1886,25(1):226-228
Ohne Zusammenfassung 相似文献
5.
Thorsten Brand Kyle Ratinac Jeffrey V. Castro Robert G. Gilbert 《Journal of polymer science. Part A, Polymer chemistry》2004,42(22):5706-5713
A method was developed for free‐radical polymerization in the confines of a hollow latex particle. Hollow particles were prepared via the dynamic swelling method from polystyrene seed and divinylbenzene and had hollows of 500–1000 nm. So that these hollow poly(divinylbenzene) particles could function as submicrometer reactors, the particles were filled with a monomer (N‐isopropylacrylamide) via the dispersion of the dried particles in the molten monomer. The monomer that was not contained in the hollows was removed by washing and gentle abrasion. Free‐radical polymerization was then initiated by γ radiolysis in the solid state. Transmission electron microscopy showed that poly(N‐isopropylacrylamide) formed in the hollow interior of the particles, which functioned as submicrometer reactors. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5706–5713, 2004 相似文献
6.
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
7.
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
8.
M. Ferro-Luzzi Z.-L. Zhou J.F.J. van den Brand H.J. Bulten J. Lang H.R. Poolman 《Hyperfine Interactions》1997,110(3-4):239-257
We present data showing hyperfine transitions in an atomic deuterium beam induced by the (476 MHz) radio-frequency field of
a 704 MeV electron beam in a storage ring. A polarized deuterium beam, produced in an atomic beam source, was crossed with
a stored electron beam and analyzed with a Breit--Rabi polarimeter. Electron-beam induced transitions were singled out by
injecting different combinations of hyperfine states. Transition probabilities as high as 70% were measured at large currents
(~ 100 mA). All possible deuterium transitions for a radio-frequency of 476 MHz were observed. In addition, a 1--6 transition
resulting from the first harmonic (952 MHz) was observed.
The effects of these transitions are of general importance for the polarized internal target technique applied in nuclear
and particle physics experiments. The data are reasonably described by numerical estimates. The observed mechanism can be
exploited to create nuclear polarized atoms when injecting electron polarized atoms with no net nuclear polarization into
a storage cell. However, when nuclear polarized atoms are injected, care should be taken to avoid this mechanism, since it
would result in depolarization of the atoms. The studies enabled us to choose the magnetic guide field during our spin-dependent
electron--deuteron scattering experiments, such that electron-beam induced depolarizing effects were avoided.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Lui Lam Flonnie Dowell Helmut Brand Guenter Ahlers 《Journal of statistical physics》1991,64(5-6):899-901
10.