We study the algebra \({{\mathrm{{\mathcal {MD}}}}}\) of generating functions for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in \({\mathbb {Q}}\) arising from the calculation of the Fourier expansion of multiple Eisenstein series. We show that the algebra \({{\mathrm{{\mathcal {MD}}}}}\) is a filtered algebra equipped with a derivation and use this derivation to prove linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). The (quasi-)modular forms for the full modular group \({{\mathrm{SL}}}_2({\mathbb {Z}})\) constitute a subalgebra of \({{\mathrm{{\mathcal {MD}}}}}\), and this also yields linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). Generating functions of multiple divisor sums can be seen as a q-analogue of multiple zeta values. Studying a certain map from this algebra into the real numbers we will derive a new explanation for relations between multiple zeta values, including those of length 2, coming from modular forms. 相似文献
Minimal free resolutions for prime ideals with generic zero (tn3,tn3?n10tn11,tn3?n20tn2, tn31), n1<n2<n3 positive integers, (n1,n2,n3)=1, are determined. 相似文献
We give uniform estimates of entire functions of exponential type less than having sufficiently small logarithmic sums over real sequences {n} satisfying |n–n|L and n+1–n for fixed positive constants L and . We thereby generalize results about logarithmic sums over the set of integers and so-called relatively h-dense sequences. 相似文献
A clustering method has been developed to group signals that display similar dynamic behavior. The procedure involves using the method of time delay embedding to construct a trajectory in state space from a time series. Certain features that characterize the geometry of the trajectory have been defined. These features were subjected to a series of statistical tests to determine their usefulness in a hierarchical clustering analysis. The latter is aimed at finding groups of similar trajectories. The trajectory-based clustering algorithm has been applied to simulated data, which included both stochastic data generated by a linear AR model, and nonlinear data generated by a Duffing oscillator. The results show that the algorithm works reliably in both cases. 相似文献
The measurement uncertainty of illuminance and, consequently, luminous flux and luminous efficacy of LED lamps can be reduced with a recently introduced method based on the predictable quantum efficient detector (PQED). One of the most critical factors affecting the measurement uncertainty with the PQED method is the determination of the aperture area. This paper describes an upgrade to an optical method for direct determination of aperture area where superposition of equally spaced Gaussian laser beams is used to form a uniform irradiance distribution. In practice, this is accomplished by scanning the aperture in front of an intensity-stabilized laser beam. In the upgraded method, the aperture is attached to the PQED and the whole package is transversely scanned relative to the laser beam. This has the benefit of having identical geometry in the laser scanning of the aperture area and in the actual photometric measurement. Further, the aperture and detector assembly does not have to be dismantled for the aperture calibration. However, due to small acceptance angle of the PQED, differences between the diffraction effects of an overfilling plane wave and of a combination of Gaussian laser beams at the circular aperture need to be taken into account. A numerical calculation method for studying these effects is discussed in this paper. The calculation utilizes the Rayleigh–Sommerfeld diffraction integral, which is applied to the geometry of the PQED and the aperture. Calculation results for various aperture diameters and two different aperture-to-detector distances are presented. 相似文献
In order to deliver reliable results for a multitude of different scenarios, e.g. emergency preparedness, environmental monitoring, nuclear decommissioning and waste management, there is a constant process of method development in the field of radioanalytical chemistry. This work presents the results of a method comparison exercise aimed at quantifying 90Sr and 239,240Pu in environmental soil samples, with the intention of evaluating the performance and applicability of different methods. From the methods examined in this work, recommendations are given in order to find a radioanalytical measurement procedure, for 90Sr and 239,240Pu analysis, which is fit-for-purpose for a particular scenario.
Journal of Radioanalytical and Nuclear Chemistry - Proton-induced reaction (p,α) is one type of nuclear reaction analysis (NRA) suitable especially for light element quantification.... 相似文献
Childhood malnutrition is highly prevalent and associated with high mortality risk. In observational and interventional studies among malnourished children, body composition is increasingly recognised as a key outcome. The deuterium dilution technique has generated high-quality data on body composition in studies of infants and young children in several settings, but its feasibility and accuracy in children suffering from moderate acute malnutrition requires further study. Prior to a large nutritional intervention trial among children with moderate acute malnutrition, we conducted pilot work to develop and adapt the deuterium dilution technique. We refined procedures for administration of isotope doses and collection of saliva. Furthermore, we established that equilibration time in local context is 3?h. These findings and the resulting standard operating procedures are important to improve data quality when using the deuterium dilution technique in malnutrition studies in field conditions, and may encourage a wider use of isotope techniques. 相似文献