While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques. 相似文献
The structure of spherical micelles of the diblock copolymer poly(styrene-block-acrylic acid) in water was investigated with small angle neutron scattering and contrast matching. We have monitored intermicelle correlation and the extension of the polyelectrolyte chains in the coronal layer through the overlap concentration. Irrespective of ionic strength, the corona shrinks with increasing packing fraction. Furthermore, at high charge and minimal screening conditions, the corona layers interpenetrate once the volume fraction exceeds the critical value 0.53+/-0.02. 相似文献
Using the theory of Witt vectors, we define ring structures on several well-known groups of arithmetic functions, which in another guise are formal Dirichlet series. The set of multiplicative arithmetic functions over a commutative ring R is shown to have a unique functorial ring structure for which the operation of addition is Dirichlet convolution and the operation of multiplication restricted to the completely multiplicative functions coincides with point-wise multiplication. The group of additive arithmetic functions over R also has a functorial ring structure. In analogy with the ghost homomorphism of Witt vectors, there is a functorial ring homomorphism from the ring of multiplicative functions to the ring of additive functions that is an isomorphism if R is a Q-algebra. The group of rational arithmetic functions, that is, the group generated by the completely multiplicative functions, forms a subring of the ring of multiplicative functions. The latter ring has the structure of a Bin(R)-algebra, where Bin(R) is the universal binomial ring equipped with a ring homomorphism to R. We use this algebra structure to study the order of a rational arithmetic function, as well the powersfα for α∈Bin(R) of a multiplicative arithmetic function f. For example, we prove new results about the powers of a given multiplicative arithmetic function that are rational. Finally, we apply our theory to the study of the zeta function of a scheme of finite type over Z. 相似文献
Ultraviolet organic light emitting diodes with 3,4,9,10-perylenetetracarboxylicdiimide (PTCDI) interlayer have been achieved. The emission spectrum and intensity were strongly dependent on the thickness of PTCDI interlayer, in spite of the fact that PTCDI has neither much lower HOMO nor much higher LUMO level, which is considered necessary for efficient charge blocking layers. The influence of PTCDI layer was investigated in three different device configurations and obtained results are discussed. For optimal device configuration, OLED with emission centered at 370 nm and turn-on voltage of 4.5 V is obtained. 相似文献
The performance of the pulsed-laser atom probe can be limited by both instrument and specimen factors. The experiments described in this article were designed to identify these factors so as to provide direction for further instrument and specimen development. Good agreement between voltage-pulsed and laser-pulsed data is found when the effective pulse fraction is less than 0.2 for pulsed-laser mode. Under the conditions reported in this article, the thermal tails of the peaks in the mass spectra did not show any significant change when produced with either a 10-ps or a 120-fs pulsed-laser source. Mass resolving power generally improves as the laser spot size and laser wavelength are decreased and as the specimen tip radius, specimen taper angle, and thermal diffusivity of the specimen material are increased. However, it is shown that two of the materials used in this study, aluminum and stainless steel, depend on these factors differently. A one-dimensional heat flow model is explored to explain these differences. The model correctly predicts the behavior of the aluminum samples, but breaks down for the stainless steel samples when the tip radius is large. A more accurate three-dimensional model is needed to overcome these discrepancies. 相似文献
Unlike the enchanting yellow‐green flashes of light produced on warm summer evenings by Photinus pyralis, the most common firefly species in North America, the orange lights of Photinus scintillans are infrequently observed. These Photinus species, and likely all bioluminescent beetles, use the same substrates beetle luciferin, ATP and oxygen to produce light. It is the structure of the particular luciferase enzyme that is the key to determining the color of the emitted light. We report here the molecular cloning of the P. scintillans luc gene and the expression and characterization of the corresponding novel recombinant luciferase enzyme. A comparison of the amino acid sequence with that of the highly similar P. pyralis enzyme and subsequent mutagenesis studies revealed that the single conservative amino acid change tyrosine to phenylalanine at position 255 accounted for the entire emission color difference. Additional mutagenesis and crystallographic studies were performed on a H‐bond network, which includes the position 255 residue and five other stringently conserved beetle luciferase residues, that is proximal to the substrate/emitter binding site. The results are interpreted in the context of a speculative proposal that this network is key to the understanding of bioluminescence color determination. 相似文献
The separation of americium(III) from europium(III) was achieved utilizing a bis-2,6-(5,6,7,8-tetrahydro-5,9,9-trimethyl-5,8-methano-1,2,4-benzotriazin-3-yl) pyridine (CA-BTP) chromatographic resin. The extraction chromatographic materials were prepared using various concentrations of CA-BTP. This new, hydrolytically stable extractant was impregnated on an inert polymeric support at 40% loading. The uptake of Am(III) and Eu(III) by this material from 0.1 to 4.0 M aqueous HNO3 solutions was measured. The resulting dry weight distribution ratios, Dw, indicated a strong preference for Am(III) with little affinity for Eu(III). These results are similar to recently reported solvent extraction studies indicating a maximum uptake of Am(III) in the 0.5–1.0 M HNO3 range. The resin preparation, performance, and characterization of the Am/Eu separation are reported herein.
The surface structure of a single-crystal ZnO wafer was studied by angle-resolved x-ray photoelectron spectroscopy (ARXPS) using synchrotron radiation. As a result, well-defined x-ray photoelectron diffraction (XPD) patterns were obtained for the (0001) and (000) polar surfaces using the photoemission from the Zn 2p3/2 and O 1s core levels. The XPD patterns were indexed assuming forward scattering of photoelectrons by neighboring ions. Further, the XPD patterns for the (0001) and (000) surfaces were different from each other, indicating the possibility for using the XPD technique for polarity determination. 相似文献