909 research outputs found

    Special Functions Related to Dedekind Type DC-Sums and their Applications

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    In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions

    Cardiac fibrosis in aging mice

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    Dystrophic cardiac calcinosis (DCC), also called epicardial and myocardial fibrosis and mineralization, has been detected in mice of a number of laboratory inbred strains, most commonly C3H/HeJ and DBA/2J. In previous mouse breeding studies between these DCC susceptible and the DCC-resistant strain C57BL/6J, 4 genetic loci harboring genes involved in DCC inheritance were identified and subsequently termed Dyscalc loci 1 through 4. Here, we report susceptibility to cardiac fibrosis, a sub-phenotype of DCC, at 12 and 20 months of age and close to natural death in a survey of 28 inbred mouse strains. Eight strains showed cardiac fibrosis with highest frequency and severity in the moribund mice. Using genotype and phenotype information of the 28 investigated strains, we performed genome-wide association studies (GWAS) and identified the most significant associations on chromosome (Chr) 15 at 72 million base pairs (Mb) (P < 10(-13)) and Chr 4 at 122 Mb (P < 10(-11)) and 134 Mb (P < 10(-7)). At the Chr 15 locus, Col22a1 and Kcnk9 were identified. Both have been reported to be morphologically and functionally important in the heart muscle. The strongest Chr 4 associations were located approximately 6 Mb away from the Dyscalc 2 quantitative trait locus peak within the boundaries of the Extl1 gene and in close proximity to the Trim63 and Cap1 genes. In addition, a single-nucleotide polymorphism association was found on chromosome 11. This study provides evidence for more than the previously reported 4 genetic loci determining cardiac fibrosis and DCC. The study also highlights the power of GWAS in the mouse for dissecting complex genetic traits.The authors thank Jesse Hammer and Josiah Raddar for technical assistance. Research reported in this publication was supported by the Ellison Medical Foundation, Parker B. Francis Foundation, and the National Institutes of Health (R01AR055225 and K01AR064766). Mouse colonies were supported by the National Institutes of Health under Award Number AG025707 for the Jackson Aging Center. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The Jackson Laboratory Shared Scientific Services were supported in part by a Basic Cancer Center Core Grant from the National Cancer Institute (CA34196).This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s00335-016-9634-

    Classical Fields Near Thermal Equilibrium

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    We discuss the classical limit for the long-distance (``soft'') modes of a quantum field when the hard modes of the field are in thermal equilibrium. We address the question of the correct semiclassical dynamics when a momentum cut-off is introduced. Higher order contributions leads to a stochastic interpretation for the effective action in analogy to Quantum Brownian Motion, resulting in dissipation and decoherence for the evolution of the soft modes. Particular emphasis is put on the understanding of dissipation. Our discussion focuses mostly on scalar fields, but we make some remarks on the extension to gauge theories.Comment: REVTeX, 6 figure

    A convenient coordinatization of Siegel-Jacobi domains

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    We determine the homogeneous K\"ahler diffeomorphism FCFC which expresses the K\"ahler two-form on the Siegel-Jacobi ball \mc{D}^J_n=\C^n\times \mc{D}_n as the sum of the K\"ahler two-form on \C^n and the one on the Siegel ball \mc{D}_n. The classical motion and quantum evolution on \mc{D}^J_n determined by a hermitian linear Hamiltonian in the generators of the Jacobi group G^J_n=H_n\rtimes\text{Sp}(n,\R)_{\C} are described by a matrix Riccati equation on \mc{D}_n and a linear first order differential equation in z\in\C^n, with coefficients depending also on W\in\mc{D}_n. HnH_n denotes the (2n+1)(2n+1)-dimensional Heisenberg group. The system of linear differential equations attached to the matrix Riccati equation is a linear Hamiltonian system on \mc{D}_n. When the transform FC:(η,W)(z,W)FC:(\eta,W)\rightarrow (z,W) is applied, the first order differential equation in the variable \eta=(\un-W\bar{W})^{-1}(z+W\bar{z})\in\C^n becomes decoupled from the motion on the Siegel ball. Similar considerations are presented for the Siegel-Jacobi upper half plane \mc{X}^J_n=\C^n\times\mc{X}_n, where \mc{X}_n denotes the Siegel upper half plane.Comment: 32 pages, corrected typos, Latex, amsart, AMS font

    Atmospheric nucleation: highlights of the EUCAARI project and future directions

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    Within the project EUCAARI (European Integrated project on Aerosol Cloud Climate and Air Quality interactions), atmospheric nucleation was studied by (i) developing and testing new air ion and cluster spectrometers, (ii) conducting homogeneous nucleation experiments for sulphate and organic systems in the laboratory, (iii) investigating atmospheric nucleation mechanism under field conditions, and (iv) applying new theoretical and modelling tools for data interpretation and development of parameterisations. The current paper provides a synthesis of the obtained results and identifies the remaining major knowledge gaps related to atmospheric nucleation. The most important technical achievement of the project was the development of new instruments for measuring sub-3 nm particle populations, along with the extensive application of these instruments in both the laboratory and the field. All the results obtained during EUCAARI indicate that sulphuric acid plays a central role in atmospheric nucleation. However, also vapours other than sulphuric acid are needed to explain the nucleation and the subsequent growth processes, at least in continental boundary layers. Candidate vapours in this respect are some organic compounds, ammonia, and especially amines. Both our field and laboratory data demonstrate that the nucleation rate scales to the first or second power of the nucleating vapour concentration(s). This agrees with the few earlier field observations, but is in stark contrast with classical thermodynamic nucleation theories. The average formation rates of 2-nm particles were found to vary by almost two orders of magnitude between the different EUCAARI sites, whereas the formation rates of charged 2-nm particles varied very little between the sites. Overall, our observations are indicative of frequent, yet moderate, ion-induced nucleation usually outweighed by much stronger neutral nucleation events in the continental lower troposphere. The most concrete outcome of the EUCAARI nucleation studies are the new semi-empirical nucleation rate parameterizations based on field observations, along with updated aerosol formation parameterizations

    Physics and applications of dusty plasmas: The Perspectives 2023

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    Dusty plasmas are electrically quasi-neutral media that, along with electrons, ions, neutral gas, radiation, and electric and/or magnetic fields, also contain solid or liquid particles with sizes ranging from a few nanometers to a few micrometers. These media can be found in many natural environments as well as in various laboratory setups and industrial applications. As a separate branch of plasma physics, the field of dusty plasma physics was born in the beginning of 1990s at the intersection of the interests of the communities investigating astrophysical and technological plasmas. An additional boost to the development of the field was given by the discovery of plasma crystals leading to a series of microgravity experiments of which the purpose was to investigate generic phenomena in condensed matter physics using strongly coupled complex (dusty) plasmas as model systems. Finally, the field has gained an increasing amount of attention due to its inevitable connection to the development of novel applications ranging from the synthesis of functional nanoparticles to nuclear fusion and from particle sensing and diagnostics to nano-contamination control. The purpose of the present perspectives paper is to identify promising new developments and research directions for the field. As such, dusty plasmas are considered in their entire variety: from classical low-pressure noble-gas dusty discharges to atmospheric pressure plasmas with aerosols and from rarefied astrophysical plasmas to dense plasmas in nuclear fusion devices. Both fundamental and application aspects are covered
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