958 resultados para Zeros of partial sums of the Riemann zeta function


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Bibliography: p. [459]-462

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Mode of access: Internet.

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We report on a new technique to reconstruct the 3D dielectric function change in transparent dielectric materials and the application of the technique for on-line monitoring of refractive index modification in BK7 glass during direct femtosecond laser microfabrication. The complex optical field scattered from the modified region is measured using two-beam, single-shot interferogram and the distribution of the modified refractive index is reconstructed by numerically solving the inverse scattering problem in Born approximation. The optical configuration suggested is further development of digital holographic microscopy (DHM). It takes advantage of high spatial resolution and almost the same optical paths for both interfering beams, and allows ultrafast time resolution.

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Background: The aim was to evaluate the validity and repeatability of the auto-refraction function of the Nidek OPD-Scan III (Nidek Technologies, Gamagori, Japan) compared with non-cycloplegic subjective refraction. The Nidek OPD-Scan III is a new aberrometer/corneal topographer workstation based on the skiascopy principle. It combines a wavefront aberrometer, topographer, autorefractor, auto keratometer and pupillometer/pupillographer. Methods: Objective refraction results obtained using the Nidek OPD-Scan III were compared with non-cycloplegic subjective refraction for 108 eyes of 54 participants (29 female) with a mean age of 23.7±9.5 years. Intra-session and inter-session variability were assessed on 14 subjects (28 eyes). Results: The Nidek OPD-Scan III gave slightly more negative readings than results obtained by subjective refraction (Nidek mean difference -0.19±0.36 DS, p<0.01 for sphere; -0.19±0.35 DS, p<0.01 for mean spherical equivalent; -0.002±0.23 DC, p=0.91 for cylinder; -0.06±0.38 DC, p=0.30 for J0 and -0.36±0.31 DC for J45, p=0.29). Auto-refractor results for 74 per cent of spherical readings and 60 per cent of cylindrical powers were within±0.25 of subjective refraction. There was high intra-session and inter-session repeatability for all parameters; 90 per cent of inter-session repeatability results were within 0.25 D. Conclusion: The Nidek OPD-Scan III gives valid and repeatable measures of objective refraction when compared with non-cycloplegic subjective refraction. © 2013 The Authors. Clinical and Experimental Optometry © 2013 Optometrists Association Australia.

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We report on a new technique to reconstruct the 3D dielectric function change in transparent dielectric materials and the application of the technique for on-line monitoring of refractive index modification in BK7 glass during direct femtosecond laser microfabrication. The complex optical field scattered from the modified region is measured using two-beam, single-shot interferogram and the distribution of the modified refractive index is reconstructed by numerically solving the inverse scattering problem in Born approximation. The optical configuration suggested is further development of digital holographic microscopy. It takes advantage of high spatial resolution and almost the same optical paths for both interfering beams, and allows ultrafast time resolution. © Springer Science+Business Media, LLC. 2011.

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2000 Mathematics Subject Classification: 33C10, 33-02, 60K25

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2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12

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We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

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The purpose of this descriptive study was to document the level of awareness that laypersons have regarding the role and function of the nurse practitioner (NP). An instrument developed for a similar study, conducted in 1994, comparing patients' and physicians' level of knowledge of the role and function of the NP, had a low reliability. Revision of the instrument was required before further use could be justified.^ A pilot study of 25 laypersons was conducted to ensure that the revised tool was reliable prior to conducting a study. Reliability for the pilot sample was 0.84.^ The study results indicated that the majority of the sample (83%), (n = 100) knew that a NP was a registered nurse who was qualified to diagnose and treat minor illnesses. The level of layperson awareness was limited regarding prescriptive privileges, well-woman exams, and the NPs' ability to perform physical exams, and interpret lab results and x-rays. ^

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Date of Acceptance: 02/03/2015

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Date of Acceptance: 02/03/2015

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Experiments at Jefferson Lab have been conducted to extract the nucleon spin-dependent structure functions over a wide kinematic range. Higher moments of these quantities provide tests of QCD sum rules and predictions of chiral perturbation theory ($\chi$PT). While precise measurements of $g_{1}^n$, $g_{2}^n$, and $g_1^p$ have been extensively performed, the data of $g_2^p$ remain scarce. Discrepancies were found between existing data related to $g_2$ and theoretical predictions. Results on the proton at large $Q^2$ show a significant deviation from the Burkhardt-Cottingham sum rule, while results for the neutron generally follow this sum rule. The next-to-leading order $\chi$PT calculations exhibit discrepancy with data on the longitudinal-transverse polarizability $\delta_{LT}^n$. Further measurements of the proton spin structure function $g_2^p$ are desired to understand these discrepancies.

Experiment E08-027 (g2p) was conducted at Jefferson Lab in experimental Hall A in 2012. Inclusive measurements were performed with polarized electron beam and a polarized ammonia target to obtain the proton spin-dependent structure function $g_2^p$ at low Q$^2$ region (0.02$<$Q$^2$$<$0.2 GeV$^2$) for the first time. The results can be used to test the Burkhardt-Cottingham sum rule, and also allow us to extract the longitudinal-transverse spin polarizability of the proton, which will provide a benchmark test of $\chi$PT calculations. This thesis will present and discuss the very preliminary results of the transverse asymmetry and the spin-dependent structure functions $g_1^p$ and $g_2^p$ from the data analysis of the g2p experiment .

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We here present a sample MATLAB program for the numerical evaluation of the confluent hypergeometric function Φ2. This program is based on the calculation of the inverse Laplace transform using the algorithm suggested by Simon and Alouini in their reference textbook [1].

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We propose two types of extensions to Hamburger’s theorems on the Dirichlet series with functional equation like the one of the Riemann zeta function, under weaker hypotheses. This builds upon the dictionary betweeen the moderate meromorphic functions with functional equation and the tempered distributions with extended S-support condition.