567 research outputs found

    Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

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    Let TT be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over TT, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of TT. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

    Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT

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    Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields (see Commun. Math. Phys. 218 (2001) 417-436; hep-th/0009004). The conformal Hamiltonian HH has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space can be represented as finite linear combinations of basic (doubly periodic) elliptic functions in the conformal time variables (of periods 1 and τ\tau) whose coefficients are, in general, formal power series in q1/2=eiπτq^{1/2}=e^{i\pi\tau} involving spherical functions of the "space-like" fields' arguments. As a corollary, if the resulting expansions converge to meromorphic functions, then the finite temperature correlation functions are elliptic. Thermal 2-point functions of free fields are computed and shown to display these features. We also study modular transformation properties of Gibbs energy mean values with respect to the (complex) inverse temperature τ\tau (Im(τ)=ÎČ/(2π)>0Im(\tau)=\beta/(2\pi)>0). The results are used to obtain the thermodynamic limit of thermal energy densities and correlation functions.Comment: LaTex. 56 pages. The concept of global conformal invariance set in a historical perspective (new Sect. 1.1 in the Introduction), references added; minor corrections in the rest of the pape

    A Novel Target-Height Estimation Approach Using Radar-Wave Multipath Propagation for Automotive Applications

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    This paper introduces a novel target height estimation approach using a Frequency Modulation Continuous Wave (FMCW) automotive radar. The presented algorithm takes advantage of radar wave multipath propagation to measure the height of objects in the vehicle surroundings. A multipath propagation model is presented first, then a target height is formulated using geometry, based on the presented propagation model. It is then shown from Sensor-Target geometry that height estimation of targets is highly dependent on the radar range resolution, target range and target height. The high resolution algorithm RELAX is discussed and applied to collected raw data to enhance the radar range resolution capability. This enables a more accurate height estimation especially for low targets. Finally, the results of a measurement campaign using corner reflectors at different heights are discussed to show that target heights can be very accurately resolved by the proposed algorithm and that for low targets an average mean height estimation error of 0.03 m has been achieved by the proposed height finding algorithm

    Holomorphic Quantization on the Torus and Finite Quantum Mechanics

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    We construct explicitly the quantization of classical linear maps of SL(2,R)SL(2, R) on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics (FQM) on tori of arbitrary integer discretization, is a consistent restriction of the holomorphic quantization of SL(2,Z)SL(2, Z) to the subgroup SL(2,Z)/ΓlSL(2, Z)/\Gamma_l, Γl\Gamma_l being the principal congruent subgroup mod l, on a finite dimensional Hilbert space. The generators of the ``rotation group'' mod l, Ol(2)⊂SL(2,l)O_{l}(2)\subset SL(2,l), for arbitrary values of l are determined as well as their quantum mechanical eigenvalues and eigenstates.Comment: 12 pages LaTeX (needs amssymb.sty). Version as will appear in J. Phys.

    Ex vivo propagation in a novel 3D high-throughput co-culture system for multiple myeloma

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    PURPOSE: Multiple myeloma (MM) remains an incurable hematologic malignancy which ultimately develops drug resistance and evades treatment. Despite substantial therapeutic advances over the past years, the clinical failure rate of preclinically promising anti-MM drugs remains substantial. More realistic in vitro models are thus required to better predict clinical efficacy of a preclinically active compound. METHODS: Here, we report on the establishment of a conical agarose 3D co-culture platform for the preclinical propagation of primary MM cells ex vivo. Cell growth was compared to yet established 2D and liquid overlay systems. MM cell lines (MMCL: RPMI-8226, U266, OPM-2) and primary patient specimens were tested. Drug sensitivity was examined by exploring the cytotoxic effect of bortezomib and the deubiquitinase inhibitor auranofin under various conditions. RESULTS: In contrast to 2D and liquid overlay, cell proliferation in the 3D array followed a sigmoidal curve characterized by an initial growth delay but more durable proliferation of MMCL over 12 days of culture. Primary MM specimens did not expand in ex vivo monoculture, but required co-culture support by a human stromal cell line (HS-5, MSP-1). HS-5 induced a \u3e fivefold increase in cluster volume and maintained long-term viability of primary MM cells for up to 21 days. Bortezomib and auranofin induced less cytotoxicity under 3D vs. 2D condition and in co- vs. monoculture, respectively. CONCLUSIONS: This study introduces a novel model that is capable of long-term propagation and drug testing of primary MM specimens ex vivo overcoming some of the pitfalls of currently available in vitro models

    “What if There's Something Wrong with Her?”‐How Biomedical Technologies Contribute to Epistemic Injustice in Healthcare

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    While there is a steadily growing literature on epistemic injustice in healthcare, there are few discussions of the role that biomedical technologies play in harming patients in their capacity as knowers. Through an analysis of newborn and pediatric genetic and genomic sequencing technologies (GSTs), I argue that biomedical technologies can lead to epistemic injustice through two primary pathways: epistemic capture and value partitioning. I close by discussing the larger ethical and political context of critical analyses of GSTs and their broader implications for just and equitable healthcare delivery

    Variable CW RF power coupler for 345 MHz superconducting cavities

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    This paper reports the development of a CW variable coupler for 345 MHz spoke-loaded superconducting (SC) cavities. The coupler inserts an 80 K copper loop into a 5 cm (2 inch) interior diameter coupling port on several types of spoke-loaded cavity operating at 2 K or 4 K. The coupling loop can be moved during operation to vary the coupling over a range of 50 dB. The coupler is designed to facilitate high-pressure water rinsing and low-particulate clean assembly. Design details and operating characteristics are discussed
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