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1.
2.
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
3.
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
4.
5.
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
6.
Ab initio Hartree–Fock band structure and molecular calculations have been performed to study the electronic structure of LiN3 in a monoclinic C 2/m crystal structure. The total energy, band structure, density of states, and charge densities are computed. The calculated lattice energy (energy to separate the ions infinitely apart) of 8.6 eV agrees very well with 8.45 eV deduced from Madelung and London polarizability energies. The calculated split of the N 1s core bands of 5.0 eV compares favorably with the experimental X-ray photoelectron value of 4.4 eV. This good agreement is not contributed to crystalline environment effects as proposed in earlier MO studies of N where the best values obtained were 5.1, 5.8, and 6.3 eV, but to the quality of the nitrogen core basis set. The calculated valence density of states supports one of two competing interpretations that peak III observed in the X-ray photoelectron spectrum arises from contaminations or other extrinsic states. 相似文献
7.
Clemens C. Freyhardt Michael Wiebcke Jürgen Felsche Günter Engelhardt 《Journal of inclusion phenomena and macrocyclic chemistry》1994,18(2):161-175
Single-crystal X-ray structure analyses of N(nPr)4[B5O6(OH)4][B(OH)3]2,1, and N(nBu)4 [B5O6(OH)4][B(OH)3]2,2, reveal that these materials are novel clathrates, the isotypic host structures of which are three-dimensional assemblies of hydrogen-bonded [B5O6(OH)4]– ionsand B(OH)3 molecules. The assembly of only the pentaborate anions is a distorted (i.e., along [102] elongated) fourconnected diamond-related network. The N(nPr)
4
+
and N(nBu)
4
+
ions are trapped within the complex three-dimensional channel systems of the host frameworks. Both1 and2 crystallize monoclinically with space groupP21/c andZ=4. The cell constants are:1:a=13.592(5),b=12.082(2),c=17.355(6) Å, =106.60(2)° (298K);2:a=13.874(3),b=12.585(1),c=17.588(4) Å, =107.04(1)° (238 K). The results obtained by both11B and13C MAS NMR spectroscopy are discussed. Thermogravimetric studies under a flowing inert-gas atmosphere suggest that water, stemming from polycondensation of the hydrous borate species, is released from the clathrates at ca. 443 K (1) and 398 K (2) before the decomposition of the organic cations starts at ca. 603 K (1) and 603 K (2).Author for correspondence.
Supplementary Data relating to this article are deposited with the British Library as supplementary publication No. SUP 82172 (82 pages). 相似文献
8.
W. Kunz J. Barthel L. Klein T. Cartailler P. Turq B. Reindl 《Journal of solution chemistry》1991,20(9):875-891
A variety of methods has been used for the study of lithium bromide solutions in acetonitrile yielding by their combination reliable information on different levels of approximation. Osmotic coefficients based on precise vapor pressure measurements are reproduced by CM (chemical model) and HNC (hypernetted chain) calculations and by BD (brownian dynamics) simulations. The results of neutron scattering experiments are treated with the help of HNC and BD methods. Hartree-Fock calculations on isolated LiBr pairs and solvated lithium ions yield reliable particle distances and reveal the geometry of the lithium solvation sphere. 相似文献
9.
The mixed‐valent oxotantalate Eu1.83Ta15O32 was prepared from a compressed mixture of Ta2O5 and the metals in a sealed Ta ampoule at 1400 °C. The crystal structure was determined by means of single crystal X‐ray diffraction: space group R3¯, a = 777.2(6) pm and c = 3523.5(3) pm, Z = 3, 984 symmetrically independent reflections, 83 variables, RF = 0.027 for I > 2σ (I). The structure is isotypic to Ba2Nb15O32. The salient feature is a [Ta(+8/3)6O12iO6a] cluster consisting of an octahedral Ta6 core bonded to 12 edge‐bridging inner and six outer oxygen atoms. The clusters are arranged to slabs which are sandwiched by layers of [Ta(+5)3O13] triple octahedra. Additional Ta(+5) and Eu(+2) atoms provide the cohesion of these structural units. Twelve‐fold coordinated Eu(+2) atoms are situated on a triply degenerate position 33 pm displaced from the threefold axis of symmetry. A depletion of the Eu(+2) site from 6 to 5.5 atoms per unit cell reduces the number of electrons available for Ta‐Ta bonding from 15 to 14.67 electrons per cluster. Between 125 and 320 K Eu1.83Ta15O32 is semi‐conducting with a band gap of 0.23 eV. The course of the magnetization is consistently described with the Brillouin function in terms of a Mmol/(NAμB) versus B/T plot in the temperature range 5 K — 320 K and at magnetic flux densities 0.1 T — 5 T. At moderate flux densities (< 1 T) the magnetic moment agrees fairly well with the expected value of 7.94 μB for free Eu (2+) ions with 4f7 configuration in 8S7/2 ground state. Below 5 K, anisotropic magnetization measurements at flux densities B < 1 T point to an onset of an antiferromagnetic ordering of Eu spins within the layers and an incipient ferromagnetic ordering perpendicular to the layers. 相似文献
10.
Clemens von Sonntag Heinz-Peter Schuchmann 《Angewandte Chemie (International ed. in English)》1991,30(10):1229-1253
Whenever free radicals are formed, independent of whether this occurs thermally, is induced by UV or ionizing irradiation, or takes place in redox reactions, they are converted rapidly into the corresponding peroxyl radicals in the presence of oxygen. Peroxyl radical reactions in aqueous environments are observed not only in aquatic systems (e.g., rivers, lakes and oceans) but also in the living cell and to a considerable degree even in the atmosphere (in water droplets). The peroxyl radical chemistry occurring in this medium is often very different from that observed in the gas phase or in organic solvents. In spite of the great importance of these reactions in medicine (for example in anti-cancer irradiation therapy and ischaemia) there have been comparatively few studies of peroxyl reactions in aqueous media. Radiation-chemical techniques such as pulse radiolysis offer the best means for carrying out such studies, so that it is not surprising that the majority of the information available in this area has been obtained with the help of radiation-chemical methods. The radiation chemistry of water can be con trolled in such a manner that the main products are ˙OH radicals (90 % yield), which react with substrate molecules to give substrate radicals and in the presence of oxygen to give substrate peroxyl radicals. The experimental conditions can also be varied in such a way that HO/O radicals can be formed in 100 % yield and caused to react with substrates. We therefore have a simple access to these intermediates, which are extremely important in biological systems. A detailed product analysis, supported by kinetic studies carried out with the help of pulse radiolysis, has been used to clarify the chemistry of a series of peroxyl radicals, so that sufficient material is now available to justify a review of the variety of the peroxyl radical reactions studied by means of radiation-chemical methods. A more general survey of the physical properties of the peroxyl radicals and their unimolecular and bimolecular reactions will be followed by a discussion of selected examples of various classes of substance. Because of the great biological importance of radical-induced DNA damage this area will also be treated briefly. 相似文献