Relevant bibliographies by topics / Spectral function

Academic literature on the topic 'Spectral function'

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Published: 4 June 2021
Last updated: 29 January 2023

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Journal articles on the topic "Spectral function"

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Actor, Alfred Arthur. "Zeta Function Resummation of Spectral Functions." Fortschritte der Physik 41, no. 5 (1993): 461–96. http://dx.doi.org/10.1002/prop.19930410505.

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Actor, Alfred Arthur. "Zeta Function Resummation of Spectral Functions." Fortschritte der Physik/Progress of Physics 41, no. 5 (1993): 461–96. http://dx.doi.org/10.1002/prop.2190410505.

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Rubtsova, O. A., and V. N. Pomerantsev. "Spectral shift function for a discretized continuum." Journal of Physics A: Mathematical and Theoretical 55, no. 9 (February 4, 2022): 095301. http://dx.doi.org/10.1088/1751-8121/ac4b8c.

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Abstract A spectral shift function (SSF) is an important object in the scattering theory which is related both to the spectral density and to the scattering matrix. In the paper, it is shown how to employ the SSF formalism to solve scattering problems when the continuum is discretized, e.g. when solving a scattering problem in a finite volume or in the representation of some finite square-integrable basis. A new algorithm is proposed for reconstructing integrated densities of states and the SSF using a union of discretized spectra corresponding to a set of Gaussian bases with the shifted scale parameters. The examples given show that knowledge of the discretized spectra of the total and asymptotic Hamiltonians is sufficient to find the scattering partial phase shifts at any required energy, as well as the resonances parameters.
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Khan, Imran, Abdur Rehman, and Ali Zaman. "Spectral temperature of π− mesons in proton–carbon interactions at 4.2 GeV/c in the framework of UrQMD model." Modern Physics Letters A 35, no. 10 (January 3, 2020): 2050066. http://dx.doi.org/10.1142/s0217732320500662.

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Transverse momentum [Formula: see text] spectra of [Formula: see text] mesons calculated using ultra-relativistic quantum molecular dynamic (UrQMD) model (Latest version 3.3-p2) simulations have been compared with [Formula: see text] spectra of [Formula: see text] mesons, obtained experimentally in interactions of protons beam with carbon nuclei (propane as target) at momentum of 4.2 GeV/c. Spectral temperatures of negative pions obtained in experimental and UrQMD model simulated interactions of protons beam with carbon nuclei have been calculated by fitting both spectra with four different fitting functions, i.e. Hagedorn thermodynamic, Boltzmann distribution, Gaussian and exponential functions. These functions are used commonly for describing hadron spectra and their spectral temperatures. Hagedorn thermodynamic function has been recommended as the most suitable function to extract the temperature of negative pions at above momentum among these four functions.
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Azamov, N. A., A. L. Carey, and F. A. Sukochev. "The Spectral Shift Function and Spectral Flow." Communications in Mathematical Physics 276, no. 1 (August 28, 2007): 51–91. http://dx.doi.org/10.1007/s00220-007-0329-9.

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Voros, A. "Spectral functions, special functions and the Selberg zeta function." Communications in Mathematical Physics 110, no. 3 (September 1987): 439–65. http://dx.doi.org/10.1007/bf01212422.

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Yassine, M., F. Piron, F. Daigne, R. Mochkovitch, F. Longo, N. Omodei, and G. Vianello. "A new fitting function for GRB MeV spectra based on the internal shock synchrotron model." Astronomy & Astrophysics 640 (August 2020): A91. http://dx.doi.org/10.1051/0004-6361/201937057.

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Aims. The physical origin of the gamma-ray burst (GRB) prompt emission is still a subject of debate. Internal shock models have been widely explored, owing to their ability to explain most of the high-energy properties of this emission phase. While the Band function or other phenomenological functions are commonly used to fit GRB prompt emission spectra, we propose a new parametric function that is inspired by an internal shock physical model. We use this function as a proxy of the model to compare it easily to GRB observations. Methods. We built a parametric function that represents the spectral form of the synthetic bursts provided by our internal shock synchrotron model (ISSM). We simulated the response of the Fermi instruments to the synthetic bursts and fit the obtained count spectra to validate the ISSM function. Then, we applied this function to a sample of 74 bright GRBs detected by the Fermi GBM, and we computed the width of their spectral energy distributions around their peak energy. For comparison, we also fit the phenomenological functions that are commonly used in the literature. Finally, we performed a time-resolved analysis of the broadband spectrum of GRB 090926A, which was jointly detected by the Fermi GBM and LAT. This spectrum has a complex shape and exhibits a power-law component with an exponential cutoff at high energy, which is compatible with inverse Compton emission attenuated by gamma-ray internal absorption. Results. This work proposes a new parametric function for spectral fitting that is based on a physical model. The ISSM function reproduces 81% of the spectra in the GBM bright GRB sample, versus 59% for the Band function, for the same number of parameters. It gives also relatively good fits to the GRB 090926A spectra. The width of the MeV spectral component that is obtained from the fits of the ISSM function is slightly larger than the width from the Band fits, but it is smaller when observed over a wider energy range. Moreover, all of the 74 analyzed spectra are found to be significantly wider than the synthetic synchrotron spectra. We discuss possible solutions to reconcile the observations with the internal shock synchrotron model, such as an improved modeling of the shock microphysics or more accurate spectral measurements at MeV energies.
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Azamov, N. A., A. L. Carey, P. G. Dodds, and F. A. Sukochev. "Operator Integrals, Spectral Shift, and Spectral Flow." Canadian Journal of Mathematics 61, no. 2 (April 1, 2009): 241–63. http://dx.doi.org/10.4153/cjm-2009-012-0.

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Abstract. We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fréchet differentiation of operator functions that sharpen existing results, and establish the Birman–Solomyak representation of the spectral shift function of M.G. Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow.
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Korsun, Oleg N., Evgeny I. Mikhaylov, and Magomed Z. Nakhaev. "Speech Spectral Transfer Function." ITM Web of Conferences 10 (2017): 01006. http://dx.doi.org/10.1051/itmconf/20171001006.

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Kampf, A. P., and J. R. Schrieffer. "Spectral function and photoemission spectra in antiferromagnetically correlated metals." Physical Review B 42, no. 13 (November 1, 1990): 7967–74. http://dx.doi.org/10.1103/physrevb.42.7967.

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Dissertations / Theses on the topic "Spectral function"

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Azamov, Nurulla, and azam0001@infoeng flinders edu au. "Spectral shift function in von Neumann algebras." Flinders University. Informatics and Engineering, 2008. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20080129.121422.

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The main subsect of this thesis is the theory of Lifshits-Krein spectral shift function in semifinite von Neumann algebras and its connection with the theory of spectral flow. Main results are an analogue of the Krein trace formula for semifinite von Neumann algebras, the semifinite analogue of the Birman-Solomyak spectral averaging formula, a connection between the spectral shift function and the spectral flow and a Lidskii type formula for Dixmier traces. In particular, it is established that in the case of operators with compact resolvent, the spectral shift function and the spectral flow are identical notions.
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fr, vbruneau@math u.-bordeaux. "Meromorphic Continuation of the Spectral Shift Function." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1073.ps.

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Czapla-Myers, Jeffrey S. "Spectral response function characterization methodologies for imaging spectrometers." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ56168.pdf.

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Megaides, Rodrigo. "Spectral and wave function statistics in quantum digraphs." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/7252.

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Spectral and wave function statistics of the quantum directed graph, QdG, are studied. The crucial feature of this model is that the direction of a bond (arc) corresponds to the direction of the waves propagating along it. We pay special attention to the full Neumann digraph, FNdG, which consists of pairs of antiparallel arcs between every node, and differs from the full Neumann graph, FNG, in that the two arcs have two incommensurate lengths. The spectral statistics of the FNG (with incommensurate bond lengths) is believed to be universal, i.e. to agree with that of the random matrix theory, RMT, in the limit of large graph size. However, the standard perturbative treatment of the field theoretical representation of the 2-point correlation function [1, 2] for a FNG, does not account for this behaviour. The nearest-neighbor spacing distribution of the closely related FNdG is studied numerically. An original, efficient algorithm for the generation of the spectrum of large graphs allows for the observation that the distribution approaches indeed universality at increasing graph size (although the convergence cannot be ascertained), in particular "level repulsion" is confirmed. The numerical technique employs a new secular equation which generalizes the analogous object known for undirected graphs [3, 4], and is based on an adaptation to digraphs of the idea of wave function continuity. In view of the contradiction between the field theory [2] and the strong indications of universality, a non-perturbative approach to analysing the universal limit is presented. The substitution of the FNG by the FNdG results in a field theory with fewer degrees of freedom. Despite this simplification, the attempt is inconclusive. Possible applications of this approach are suggested. Regarding the wave function statistics, a field theoretical representation for the spectral average of the wave intensity on an fixed arc is derived and studied in the universal limit. The procedure originates from the study of wave function statistics on disordered metallic grains [5] and is used in conjunction with the field theory approach pioneered in [2].
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Townsend, Whitney Jeanne. "Discrete function representations utilizing decision diagrams and spectral techniques." Thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-07012002-160303.

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Artiles, Oswaldo. "Multinucleon Short-range Correlation Model for Nuclear Spectral Functions." FIU Digital Commons, 2017. http://digitalcommons.fiu.edu/etd/3384.

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The main goal of the research presented in my dissertation was to develop a theoretical model for relativistic nuclear spectral functions at high missing momenta and removal energies based on the multi-nucleon short-range correlation (SRC) model. The nuclear spectral functions are necessary for the description of high energy nuclear processes currently being studied at different labs such as JLAB, LHC and FNAL. The model followed the effective Feynman diagrammatic approach in order to ac-count for the relativistic effects important in the SRC domain. In addition to the two-nucleon (2N) SRC with center of mass motion contribution, the contribution of the three-nucleon SRCs to the spectral functions was also derived. The latter was modeled based on the assumption that the 3N SRCs are a product of two sequential short range nucleon-nucleon (NN) interactions. The nuclear spectral functions models were derived from two theoretical frameworks for evaluating covariant Feynman diagrams: In the first, referred to as the virtual nucleon approximation, the Feynman diagrams were reduced to the time ordered non-covariant diagrams by evaluating the nucleon spectators in the SRC at their positive energy poles, neglecting explicitly the contribution from vacuum diagrams. In the second approach, referred to as the light-front approximation, the boost invariant nuclear spectral function was formulated in the light-front reference frame in which case the vacuum diagrams are kinematically suppressed and the bound nucleon is described by its light-front variables such as momentum fraction, transverse momentum and invariant mass. On the basis of the derived nuclear spectral functions, the corresponding computational models were developed from which the numerical estimates of the SRC spectral functions, the SRC momentum distributions, and the SRC density matrices were obtained.
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Watson, Simon P. "On the asymptotics of the Dirichlet Laplacian : cones, corners and conduction." Thesis, University of Bristol, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246266.

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Alsaedy, Ammar, and Nikolai Tarkhanov. "Spectral projection for the dbar-Neumann problem." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5861/.

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Hendricks, Jeffrey James. "Spectral Stability of Weak Detonations in the Majda Model." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3626.

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Using analytical and numerical Evans-function techniques, we examine the spectral stability of weak-detonation-wave solutions of Majda's scalar model for a reacting gas mixture. We provide a proof of monotonicity of solutions. Using monotonicity we obtain a bound on possible unstable eigenvalues for weak-detonation-wave solutions that improves on the more general bound given by Humpherys, Lyng, and Zumbrun. We use a numerical approximation of the Evans function to search for possible unstable eigenvalues in the bounded region obtained by the energy estimate. For the parameter values tested, our results combined with the result of Lyng, Raoofi, Texier, and Zumbrun demonstrate that these waves are nonlinearly phase-asymptotically orbitally stable throughout the parameter space for which solutions were obtainable.
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Yoo, Hyungsuk. "Quality of the Volterra transfer function estimation /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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Books on the topic "Spectral function"

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Brown, B. Malcolm, Jan Lang, and Ian G. Wood, eds. Spectral Theory, Function Spaces and Inequalities. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0263-5.

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Nikolskii, N. K., ed. Toeplitz Operators and Spectral Function Theory. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-5587-7.

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Motohashi, Y. Spectral theory of the Riemann zeta-function. Cambridge: Cambridge University Press, 1997.

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Haroske, Dorothee. Some logarithmic function spaces, entropy numbers, applications to spectral theory. Warszawa: Polska Akademia Nauk, Instytut Matematyczny, 1998.

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Treatise on the shift operator: Spectral function theory. Berlin: Springer-Verlag,c, 1986.

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Jan, Lang, Wood Ian G, and SpringerLink (Online service), eds. Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends. Basel: Springer Basel AG, 2012.

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Hedberg, Lars Inge. An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation. Providence, RI: American Mathematical Society, 2007.

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Siegel, Robert. Two-flux Green's function analysis for transient spectral radiation in a composite. Reston, VA: American Institute of Aeronautics and Astronautics, 1996.

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Siegel, Robert. Two-flux Green's function analysis for transient spectral radiation in a composite. Reston, VA: American Institute of Aeronautics and Astronautics, 1996.

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Siegel, Robert. Two-flux Green's function analysis for transient spectral radiation in a composite. Reston, VA: American Institute of Aeronautics and Astronautics, 1996.

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Book chapters on the topic "Spectral function"

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Croisille, Jean-Pierre, and Gilles Lebeau. "The spectral function." In Lecture Notes in Mathematics, 27–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0092518.

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Parmeggiani, Alberto. "The Spectral Zeta Function." In Lecture Notes in Mathematics, 93–110. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11922-4_7.

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Müller, Werner. "The spectral shift function." In Lecture Notes in Mathematics, 74–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077669.

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Carey, Alan, and Galina Levitina. "The Spectral Shift Function." In Lecture Notes in Mathematics, 63–92. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-19436-8_4.

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Iwaniec, Henryk. "The automorphic Green function." In Spectral Methods of Automorphic Forms, 71–79. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/gsm/053/07.

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Benhar, Omar, Adelchi Fabrocini, and Stefano Fantoni. "Correlated Wave Functions Theory of the Spectral Function." In Condensed Matter Theories, 17–25. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4613-0605-4_3.

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Weit, Yitzhak. "Spectral analysis in spaces of continuous functions." In Function Spaces and Applications, 420–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078892.

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Wang, Mingxun, and Nuno Bandeira. "Spectral Library Generating Function for Assessing Spectrum-Spectrum Match Significance." In Lecture Notes in Computer Science, 287–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37195-0_27.

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Freeman, Walter J., and Rodrigo Quian Quiroga. "Image Sampling Based on Spectral Analysis." In Imaging Brain Function With EEG, 125–46. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4984-3_7.

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Badrieh, Fuad. "The Delta Function." In Spectral, Convolution and Numerical Techniques in Circuit Theory, 437–48. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-71437-0_21.

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Conference papers on the topic "Spectral function"

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Ben Lakhdar, Z., and N. Ben Nessib. "Collision width function in a correlated plasma." In Spectral line shapes. AIP, 1990. http://dx.doi.org/10.1063/1.39909.

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English, Samuel. "Tackling DIS Region Using Spectral Function Formalism." In Tackling DIS Region Using Spectral Function Formalism. US DOE, 2021. http://dx.doi.org/10.2172/1826157.

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Kenawy, M. A., M. M. H. El-Naby, M. M. El-Nicklawy, E. F. Hassan, and E. A. Nasr. "Mutual coherence function and degree of coherence of multiple beams." In Spectral line shapes. AIP, 1990. http://dx.doi.org/10.1063/1.39971.

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Calisti, A. "Models For Electronic Electric Field Distribution Function At a Positive Ion." In SPECTRAL LINE SHAPES. AIP, 2002. http://dx.doi.org/10.1063/1.1525463.

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Truong, Syrian. "Implement Spectral Function Model Into GENIE via Wrapper." In Implement Spectral Function Model Into GENIE via Wrapper. US DOE, 2021. http://dx.doi.org/10.2172/1826140.

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Xu, Jie. "Angular spectral dyadic Green's function." In 2014 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2014. http://dx.doi.org/10.1109/aps.2014.6904389.

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Duck, Benjamin C., and Christopher J. Fell. "Improving the spectral correction function." In 2016 IEEE 43rd Photovoltaic Specialists Conference (PVSC). IEEE, 2016. http://dx.doi.org/10.1109/pvsc.2016.7750129.

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Hosseini, S. M. A. T., and H. Amindavar. "Estimation of spectral correlation function based on evolutionary spectral." In 2011 8th International Conference on Information, Communications & Signal Processing (ICICS 2011). IEEE, 2011. http://dx.doi.org/10.1109/icics.2011.6173128.

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Nie, Jinsuo R., Jim Xu, and Joseph I. Braverman. "Development of Target Power Spectral Density Functions Compatible With Design Response Spectra." In ASME 2015 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/pvp2015-45243.

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For seismic analysis of nuclear structures, synthetic acceleration time histories are often required and are generated to envelop design response spectra following the U.S. Nuclear Regulatory Commission, Standard Review Plan (SRP) Section 3.7.1. It has been recognized that without an additional check of the power spectral density (PSD) functions, spectral matching alone may not ensure that synthetic acceleration time histories have adequate power over the frequency range of interest. The SRP Section 3.7.1 Appendix A provides a target PSD function for the Regulatory Guide 1.60 horizontal spectral shape. For other spectral shapes, additional guidance on developing the target PSD functions compatible with the design spectra is desired. This paper presents a general procedure for the development of target PSD functions for any practical design response spectral shapes, which has been incorporated into the recent SRP 3.7.1, Revision 4.
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Mihandoost, Sara, and Mehdi Chehel Amirani. "Electrocardiogram recognition using spectral correlation function." In 2016 24th Iranian Conference on Electrical Engineering (ICEE). IEEE, 2016. http://dx.doi.org/10.1109/iraniancee.2016.7585532.

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Reports on the topic "Spectral function"

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Trishchenko, A., J. Cihlar, and Z. Li. Effects of spectral response function on surface reflectance and NDVI measured with moderate resolution satellite sensors. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 2002. http://dx.doi.org/10.4095/219793.

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Alchanatis, Victor, Stephen W. Searcy, Moshe Meron, W. Lee, G. Y. Li, and A. Ben Porath. Prediction of Nitrogen Stress Using Reflectance Techniques. United States Department of Agriculture, November 2001. http://dx.doi.org/10.32747/2001.7580664.bard.

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Commercial agriculture has come under increasing pressure to reduce nitrogen fertilizer inputs in order to minimize potential nonpoint source pollution of ground and surface waters. This has resulted in increased interest in site specific fertilizer management. One way to solve pollution problems would be to determine crop nutrient needs in real time, using remote detection, and regulating fertilizer dispensed by an applicator. By detecting actual plant needs, only the additional nitrogen necessary to optimize production would be supplied. This research aimed to develop techniques for real time assessment of nitrogen status of corn using a mobile sensor with the potential to regulate nitrogen application based on data from that sensor. Specifically, the research first attempted to determine the system parameters necessary to optimize reflectance spectra of corn plants as a function of growth stage, chlorophyll and nitrogen status. In addition to that, an adaptable, multispectral sensor and the signal processing algorithm to provide real time, in-field assessment of corn nitrogen status was developed. Spectral characteristics of corn leaves reflectance were investigated in order to estimate the nitrogen status of the plants, using a commercial laboratory spectrometer. Statistical models relating leaf N and reflectance spectra were developed for both greenhouse and field plots. A basis was established for assessing nitrogen status using spectral reflectance from plant canopies. The combined effect of variety and N treatment was studied by measuring the reflectance of three varieties of different leaf characteristic color and five different N treatments. The variety effect on the reflectance at 552 nm was not significant (a = 0.01), while canonical discriminant analysis showed promising results for distinguishing different variety and N treatment, using spectral reflectance. Ambient illumination was found inappropriate for reliable, one-beam spectral reflectance measurement of the plants canopy due to the strong spectral lines of sunlight. Therefore, artificial light was consequently used. For in-field N status measurement, a dark chamber was constructed, to include the sensor, along with artificial illumination. Two different approaches were tested (i) use of spatially scattered artificial light, and (ii) use of collimated artificial light beam. It was found that the collimated beam along with a proper design of the sensor-beam geometry yielded the best results in terms of reducing the noise due to variable background, and maintaining the same distance from the sensor to the sample point of the canopy. A multispectral sensor assembly, based on a linear variable filter was designed, constructed and tested. The sensor assembly combined two sensors to cover the range of 400 to 1100 nm, a mounting frame, and a field data acquisition system. Using the mobile dark chamber and the developed sensor, as well as an off-the-shelf sensor, in- field nitrogen status of the plants canopy was measured. Statistical analysis of the acquired in-field data showed that the nitrogen status of the com leaves can be predicted with a SEP (Standard Error of Prediction) of 0.27%. The stage of maturity of the crop affected the relationship between the reflectance spectrum and the nitrogen status of the leaves. Specifically, the best prediction results were obtained when a separate model was used for each maturity stage. In-field assessment of the nitrogen status of corn leaves was successfully carried out by non contact measurement of the reflectance spectrum. This technology is now mature to be incorporated in field implements for on-line control of fertilizer application.
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Falkowski, Bogdan. Spectral Methods for Boolean and Multiple-Valued Input Logic Functions. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.1151.

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Schafer, Ingo. An effective cube comparison method for discrete spectral transformations of logic functions. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.6031.

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Zilberman, Mark. Shouldn’t Doppler 'De-boosting' be accounted for in calculations of intrinsic luminosity of Standard Candles? Intellectual Archive, September 2021. http://dx.doi.org/10.32370/iaj.2569.

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"Doppler boosting / de-boosting" is a well-known relativistic effect that alters the apparent luminosity of approaching/receding radiation sources. "Doppler boosting" alters the apparent luminosity of approaching light sources to appear brighter, while "Doppler de-boosting" alters the apparent luminosity of receding light sources to appear fainter. While "Doppler boosting / de-boosting" has been successfully accounted for and observed in relativistic jets of AGN, double white dwarfs, in search of exoplanets and stars in binary systems it was ignored in the establishment of Standard Candles for cosmological distances. A Standard Candle adjustment appears necessary for "Doppler de-boosting" for high Z, otherwise we would incorrectly assume that Standard Candles appear dimmer, not because of "Doppler de-boosting" but because of the excessive distance, which would affect the entire Standard Candles ladder at cosmological distances. The ratio between apparent (L) and intrinsic (Lo) luminosities as a function of redshift Z and spectral index α is given by the formula ℳ(Z) = L/Lo=(Z+1)^(α-3) and for Type Ia supernova as ℳ(Z) = L/Lo=(Z+1)^(-2). These formulas are obtained within the framework of Special Relativity and may require adjustments within the General Relativity framework.
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Chapman, Martin C., G. A. Bollinger, and Matthew S. Sibol. Modeling Delay-Fired Explosion Spectra and Source Function Deconvolution at Regional Distances. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada260232.

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Chi, Taishih, Yujie Gao, Matthew C. Guyton, Powen Ru, and Shihab Shamma. Spectro-Temporal Modulation Transfer Functions and Speech Intelligibility. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada439776.

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Emre, Erol. Adaptive Estimation and Approximation of Continuously Varying Spectral Density Functions to Airborne Radar. Fort Belvoir, VA: Defense Technical Information Center, November 1993. http://dx.doi.org/10.21236/ada277532.

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Goedecke, George H., Michael DeAntonio, and Harry J. Auvermann. Structure Function Spectra and Acoustic Scattering Due to Homogeneous Isotropic Atmospheric Turbule Ensembles. Fort Belvoir, VA: Defense Technical Information Center, August 1998. http://dx.doi.org/10.21236/ada351833.

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Asenath-Smith, Emily, Emma Ambrogi, Lee Moores, Stephen Newman, and Jonathon Brame. Leveraging chemical actinometry and optical radiometry to reduce uncertainty in photochemical research. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/42080.

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Abstract:
Subtle aspects of illumination sources and their characterization methods can introduce significant uncertainty into the data gathered from light-activated experiments, limiting their reproducibility and technology transition. Degradation kinetics of methyl orange (MO) and carbamazepine (CM) under illumination with TiO₂ were used as a case study for investigating the role of incident photon flux on photocatalytic degradation rates. Valerophenone and ferrioxalate actinometry were paired with optical radiometry in three different illumination systems: xenon arc (XE), tungsten halogen (W-H), and UV fluorescent (UV-F). Degradation rate constants for MO and CM varied similarly among the three light systems as k W-H < kiv-F < kXE, implying the same relative photon flux emission by each light. However, the apparent relative photon flux emitted by the different lights varied depending on the light characterization method. This discrepancy is shown to be caused by the spectral distribution present in light emission profiles, as well as absorption behavior of chemical actinometers and optical sensors. Data and calculations for the determination of photon flux from chemical and calibrated optical light characterization is presented, allowing us to interpret photo-degradation rate constants as a function of incident photon flux. This approach enabled the derivation of a calibrated ‘rate-flux’ metric for evaluating and translating data from photocatalysis studies.
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