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1.
Mathematische Semesterberichte - Von Euler stammt eine Parametrisierung einer Klasse von magischen 4 ✕ 4-Quadraten, deren Einträge Quadratzahlen sind und noch...  相似文献   
2.
Abstract

Although it is well known that the growth of Thompson's group F is exponential, the exact growth function is still unknown. Elements of its submonoid of positive words can be described using a binary rooted tree, whose norm can be computed assigning weights to each caret. Combining this fact with a combinatorial argument, the growth function of the submonoid is computed and thus providing a first step in the computation of the growth function of the group, as well as a lower bound for the growth rate for the group.  相似文献   
3.
Atomically precise alloying and de‐alloying processes for the formation of Ag–Au and Cu–Au nanoparticles of 25‐metal‐atom composition (referred to as AgxAu25?x(SR)18 and CuxAu25?x(SR)18, in which R=CH2CH2Ph) are reported. The identities of the particles were determined by matrix‐assisted laser desorption ionization mass spectroscopy (MALDI‐MS). Their structures were probed by fragmentation analysis in MALDI‐MS and comparison with the icosahedral structure of the homogold Au25(SR)18 nanoparticles (an icosahedral Au13 core protected by a shell of Au12(SR)18). The Cu and Ag atoms were found to preferentially occupy the 13‐atom icosahedral sites, instead of the exterior shell. The number of Ag atoms in AgxAu25?x(SR)18 (x=0–8) was dependent on the molar ratio of AgI/AuIII precursors in the synthesis, whereas the number of Cu atoms in CuxAu25?x(SR)18 (x=0–4) was independent of the molar ratio of CuII/AuIII precursors applied. Interestingly, the CuxAu25?x(SR)18 nanoparticles show a spontaneous de‐alloying process over time, and the initially formed CuxAu25?x(SR)18 nanoparticles were converted to pure Au25(SR)18. This de‐alloying process was not observed in the case of alloyed AgxAu25?x(SR)18 nanoparticles. This contrast can be attributed to the stability difference between CuxAu25?x(SR)18 and AgxAu25?x(SR)18 nanoparticles. These alloyed nanoparticles are promising candidates for applications such as catalysis.  相似文献   
4.
In Nature, enzymes provide hydrophobic cavities and channels for sequestering small alkanes or long‐chain alkyl groups from water. Similarly, the porous metal oxide capsule [{MoVI6O21(H2O)6}12{(MoV2O4)30(L)29(H2O)2}]41? (L=propionate ligand) features distinct domains for sequestering differently sized alkanes (as in Nature) as well as internal dimensions suitable for multi‐alkane clustering. The ethyl tails of the 29 endohedrally coordinated ligands, L, form a spherical, hydrophobic “shell”, while their methyl end groups generate a hydrophobic cavity with a diameter of 11 Å at the center of the capsule. As such, C7 to C3 straight‐chain alkanes are tightly intercalated between the ethyl tails, giving assemblies containing 90 to 110 methyl and methylene units, whereas two or three ethane molecules reside in the central cavity of the capsule, where they are free to rotate rapidly, a phenomenon never before observed for the uptake of alkanes from water by molecular cages or containers.  相似文献   
5.
We estimate discrete Fourier transform, ambiguity, and Hamming-auto-correlation of \(m\) -ary sequences in terms of their (periodic) correlation measure of order 4. Roughly speaking, we show that every pseudorandom sequence, that is, any sequence with small correlation measure up to a sufficiently large order, cannot have a large discrete Fourier transform, ambiguity, or Hamming-autocorrelation. Conversely, there are sequences, for example the two-prime generator, with large correlation measure of order 4 but small discrete Fourier transform, ambiguity, autocorrelation, and Hamming-autocorrelation.  相似文献   
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7.
Abstract

Copper transporter 1 (CTR1) is the main copper transporter in the eukaryotic system. CTR1 has several important roles: It binds Cu(II) ions that are present in the blood; it reduces those Cu(II) ions to Cu(I); and it subsequently transfers Cu(I) to the cytoplasmic domain, where the ion is delivered to various cellular pathways. Here, we seek to identify CTR1 binding sites for Cu(II) and Cu(I) and to shed light on the Cu(II)-to-Cu(I) reduction process. We focus on the first 14 amino acids of CTR1. This N-terminal segment is rich with histidine and methionine residues, which are known to bind Cu(II) and Cu(I), respectively; thus, this region has been suggested to have an important function in recruiting Cu(II) and reducing it to Cu(I). We utilize electron paramagnetic resonance (EPR) spectroscopy together with nuclear magnetic resonance (NMR) and UV-VIS spectroscopy and alanine substitution to reveal Cu(II) and Cu(I) binding sites in the focal 14-amino-acid segment. We show that H5 and H6 directly coordinate to Cu(II), whereas M7, M9, and M12 are involved in Cu(I) binding. This research is another step on the way to a complete understanding of the cellular copper regulation mechanism in humans.  相似文献   
8.
The anisotropic hyperfine coupling constants (AHCC) from the electron spin resonance (E.S.R.) spectra of a variety of atoms in organic radicals have been calculated by means of semiempirical molecular orbital wavefunctions in the INDO approximation. Hyperfine tensors involving 1H, 13C and 19F nuclei are obtained for the ?H, ?H3, CH3?H2, (CH3)3? hydrocarbon radicals, malonic acid radical, ?H2F, ?F2H, ?F3 and CF3?H2 radicals. The calculated values are compared with available experimental, non-empirical and semiempirical values for these radicals. All integrals of the operator entering the electronic contributions have been evaluated over Slater type orbitals. The introduction of deorthogonalized wavefunctions gives generally better calculated results. In particular, the tensor components of the 19F AHCC are in good agreement with the experimental results without the necessity of readjusting the effective nuclear charges.  相似文献   
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