35,304 research outputs found

    Faulhaber's Theorem on Power Sums

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    We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+b,a+2b,...,a+nba+b, a+2b, ..., a+nb is a polynomial in na+n(n+1)b/2na+n(n+1)b/2. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, by utilizing the central factorial numbers as in the approach of Knuth, we derive formulas for rr-fold sums of powers without resorting to the notion of rr-reflexive functions. We also provide formulas for the rr-fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic

    Comparison between the Torquato-Rintoul theory of the interface effect in composite media and elementary results

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    We show that the interface effect on the properties of composite media recently proposed by Torquato and Rintoul (TR) [Phys. Rev. Lett. 75, 4067 (1995)] is in fact elementary, and follows directly from taking the limit in the dipolar polarizability of a coated sphere: the TR ``critical values'' are simply those that make the dipolar polarizability vanish. Furthermore, the new bounds developed by TR either coincide with the Clausius-Mossotti (CM) relation or provide poor estimates. Finally, we show that the new bounds of TR do not agree particularly well with the original experimental data that they quote.Comment: 13 pages, Revtex, 8 Postscript figure

    IL-33 ameliorates Alzheimer’s disease-like pathology and cognitive decline

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    Alzheimer’s disease (AD) is a devastating condition with no known effective treatment. AD is characterized by memory loss as well as impaired locomotor ability, reasoning, and judgment. Emerging evidence suggests that the innate immune response plays a major role in the pathogenesis of AD. In AD, the accumulation of β-amyloid (Aβ) in the brain perturbs physiological functions of the brain, including synaptic and neuronal dysfunction, microglial activation, and neuronal loss. Serum levels of soluble ST2 (sST2), a decoy receptor for interleukin (IL)-33, increase in patients with mild cognitive impairment, suggesting that impaired IL-33/ST2 signaling may contribute to the pathogenesis of AD. Therefore, we investigated the potential therapeutic role of IL-33 in AD, using transgenic mouse models. Here we report that IL-33 administration reverses synaptic plasticity impairment and memory deficits in APP/PS1 mice. IL-33 administration reduces soluble Aβ levels and amyloid plaque deposition by promoting the recruitment and Aβ phagocytic activity of microglia; this is mediated by ST2/p38 signaling activation. Furthermore, IL-33 injection modulates the innate immune response by polarizing microglia/macrophages toward an antiinflammatory phenotype and reducing the expression of proinflammatory genes, including IL-1β, IL-6, and NLRP3, in the cortices of APP/PS1 mice. Collectively, our results demonstrate a potential therapeutic role for IL-33 in AD

    A novel downscaling technique for the linkage of global and regional air quality modeling

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    Recently, downscaling global atmospheric model outputs (GCTM) for the USEPA Community Multiscale Air Quality (CMAQ) Initial (IC) and Boundary Conditions (BC) have become practical because of the rapid growth of computational technologies that allow global simulations to be completed within a reasonable time. The traditional method of generating IC/BC by profile data has lost its advocates due to the weakness of the limited horizontal and vertical variations found on the gridded boundary layers. Theoretically, high quality GCTM IC/BC should yield a better result in CMAQ. Unfortunately, several researchers have found that the outputs from GCTM IC/BC are not necessarily better than profile IC/BC due to the excessive transport of O3 aloft in GCTM IC/BC. In this paper, we intend to investigate the effects of using profile IC/BC and global atmospheric model data. In addition, we are suggesting a novel approach to resolve the existing issue in downscaling. In the study, we utilized the GEOS-Chem model outputs to generate time-varied and layer-varied IC/BC for year 2002 with the implementation of tropopause determining algorithm in the downscaling process (i.e., based on chemical (O3) tropopause definition). The comparison between the implemented tropopause approach and the profile IC/BC approach is performed to demonstrate improvement of considering tropopause. It is observed that without using tropopause information in the downscaling process, unrealistic O3 concentrations are created at the upper layers of IC/BC. This phenomenon has caused over-prediction of surface O3 in CMAQ. In addition, the amount of over-prediction is greatly affected by temperature and latitudinal location of the study domain. With the implementation of the algorithm, we have successfully resolved the incompatibility issues in the vertical layer structure between global and regional chemistry models to yield better surface O3 predictions than profile IC/BC for both summer and winter conditions. At the same time, it improved the vertical O3 distribution of CMAQ outputs. It is strongly recommended that the tropopause information should be incorporated into any two-way coupled global and regional models, where the tropospheric regional model is used, to solve the vertical incompatibility that exists between global and regional models. doi:10.5194/acp-10-4013-2010 Publisher\u27s note: We have discovered that the previously published paper was not the latest version of the manuscript we intended to use. Some corrections made during the second ACPD reviewing process were not incorporated in the text. As a result, the figure numbers (i.e., figure number below the graph) were not referenced correctly in the manuscript. Therefore, we have decided to re-publish this paper as a corrigendum

    A novel downscaling technique for the linkage of global and regional air quality modeling

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    Recently, downscaling global atmospheric model outputs (GCTM) for the USEPA Community Multiscale Air Quality (CMAQ) Initial (IC) and Boundary Conditions (BC) have become practical because of the rapid growth of computational technologies that allow global simulations to be completed within a reasonable time. The traditional method of generating IC/BC by profile data has lost its advocates due to the weakness of the limited horizontal and vertical variations found on the gridded boundary layers. Theoretically, high quality GCTM IC/BC should yield a better result in CMAQ. Unfortunately, several researchers have found that the outputs from GCTM IC/BC are not necessarily better than profile IC/BC due to the excessive transport of O3 aloft in GCTM IC/BC. In this paper, we intend to investigate the effects of using profile IC/BC and global atmospheric model data. In addition, we are suggesting a novel approach to resolve the existing issue in downscaling. In the study, we utilized the GEOS-Chem model outputs to generate time-varied and layer-varied IC/BC for year 2002 with the implementation of tropopause determining algorithm in the downscaling process (i.e., based on chemical (O3) tropopause definition). The comparison between the implemented tropopause approach and the profile IC/BC approach is performed to demonstrate improvement of considering tropopause. It is observed that without using tropopause information in the downscaling process, unrealistic O3 concentrations are created at the upper layers of IC/BC. This phenomenon has caused over-prediction of surface O3 in CMAQ. In addition, the amount of over-prediction is greatly affected by temperature and latitudinal location of the study domain. With the implementation of the algorithm, we have successfully resolved the incompatibility issues in the vertical layer structure between global and regional chemistry models to yield better surface O3 predictions than profile IC/BC for both summer and winter conditions. At the same time, it improved the vertical O3 distribution of CMAQ outputs. It is strongly recommended that the tropopause information should be incorporated into any two-way coupled global and regional models, where the tropospheric regional model is used, to solve the vertical incompatibility that exists between global and regional models
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