Journal articles: 'Spectral function'

1

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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Wallace, S., S. G. Lambrakos, and L. Massa. "Density function theory (DFT) calculated infrared absorption spectra for nitrosamines." Water Science and Technology 80, no. 10 (November 15, 2019): 1967–74. http://dx.doi.org/10.2166/wst.2020.018.

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Abstract Absorption spectra within the infrared (IR) range of frequencies for nitrosamines in water are calculated using density function theory (DFT). Calculated in this study, are the IR spectra of C2H6N2O, C4H10N2O, C6H14N2O, C4H8N2O, C3H8N2O, and C8H18N2O. DFT calculated absorption spectra corresponding to vibration excited states of these molecules in continuous water background can be correlated with additional information obtained from laboratory measurements. The DFT software Gaussian was used for the calculations of excited states presented here. This case study provides proof of concept, viz., that such DFT calculated spectra can be used for their practical detection in environmental samples. Thus, DFT calculated spectra may be used to construct templates, for spectral-feature comparison, and thus detection of spectral-signature features associated with target materials.

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Dehghani Tazehkand, I., and A. Jodayree Akbarfam. "On Inverse Sturm-Liouville Problems with Spectral Parameter Linearly Contained in the Boundary Conditions." ISRN Mathematical Analysis 2011 (December 25, 2011): 1–23. http://dx.doi.org/10.5402/2011/754718.

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In this paper, we study Sturm-Liouville problems with spectral parameter linearly contained in one of the boundary conditions. We prove uniqueness theorems for the solution of the inverse problems according to the Weyl function, spectral data, and two spectra. Then, we recover the potential function and coefficients of boundary conditions from the spectral data by the method of spectral mappings.

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Eilers, Anna–Christina, David W. Hogg, Bernhard Schölkopf, Daniel Foreman-Mackey, Frederick B. Davies, and Jan–Torge Schindler. "A Generative Model for Quasar Spectra." Astrophysical Journal 938, no. 1 (October 1, 2022): 17. http://dx.doi.org/10.3847/1538-4357/ac8ead.

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Abstract We build a multi-output generative model for quasar spectra and the properties of their black hole engines, based on a Gaussian process latent-variable model. This model treats every quasar as a vector of latent properties such that the spectrum and all physical properties of the quasar are associated with non-linear functions of those latent parameters; the Gaussian process kernel functions define priors on the function space. Our generative model is trained with a justifiable likelihood function that allows us to treat heteroscedastic noise and missing data correctly, which is crucial for all astrophysical applications. It can simultaneously predict unobserved spectral regions and the physical properties of quasars in held-out test data. We apply the model to rest-frame ultraviolet and optical quasar spectra for which precise black hole masses (based on reverberation-mapping measurements) are available. Unlike reverberation-mapping studies that require multi-epoch data, our model predicts black hole masses from single-epoch spectra—even with limited spectral coverage. We demonstrate the capabilities of the model by predicting black hole masses and unobserved spectral regions. We find that we predict black hole masses at close to the best possible accuracy.

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Xiangli Bin, Yuan Yan, and Lyu Qun-Bo. "Spectral transfer function of the Fourier transform spectral imager." Acta Physica Sinica 58, no. 8 (2009): 5399. http://dx.doi.org/10.7498/aps.58.5399.

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Christian, John T. "Generating Seismic Design Power Spectral Density Functions." Earthquake Spectra 5, no. 2 (May 1989): 351–68. http://dx.doi.org/10.1193/1.1585526.

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The most widely used way to describe earthquake motions for purposes of design is the response spectrum, but it is often difficult to apply a response spectrum when dealing with multiple degrees of freedom or with complex representations of structural behavior. The power spectral density function, which is a more fundamental description of the frequency content of ground motion, has found increasing use and is essential in the most popular methods of developing artificial earthquake time histories. Although in theory the response spectrum and the power spectral density are closely related, in practice it has proven difficult to compute one from the other. Two integration schemes described in the literature have been implemented in an interactive micro-computer program SPEED and are found to give substantially identical results. When they are used to find a power spectral density function that corresponds to a standard design response spectrum, the results do not converge at frequencies above 10 Hz. Possible explanations for this lie in the shape of the prescribed standard response spectra, the methodology used to generate them, and the lack of statistical variation at high frequencies. When power spectral density functions are calculated for response spectra determined from a statistical evaluation of strong motion across the full range of frequencies, the calculations converge rapidly.

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Zhou, Ping, Zhe Zhao, Hong-Yuan Huo, and Zhansheng Liu. "Retrieval of Photometric Parameters of Minerals Using a Self-Made Multi-Angle Spectrometer Based on the Hapke Radiative Transfer Model." Remote Sensing 13, no. 15 (August 1, 2021): 3022. http://dx.doi.org/10.3390/rs13153022.

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In this paper, a self-made, mineral, multi-angle, spectrum measurement device is employed to measure the multi-angle spectra of olivine and plagioclase; the multi-angle spectra of ilmenite in the Reflectance Experiment Laboratory (RELAB) Spectral Library are collected; and the optimized retrieval of the photometric parameters of the Hapke model is realized. Importantly, the derived result of the single-scattering albedo (SSA) is stable and has both mathematical meaning and physical meaning. The derived Legendre polynomial coefficients of the phase function can better simulate the variation in the mineral spectra with angle. This paper compares the effects of multi-angle and single-angle spectral data on the photometric parameter derived results. The setting of the Legendre polynomial coefficient of the scattering phase function mainly affects the simulation accuracy of the mineral spectra as a function of angle. Using this coefficient to optimize the retrieval, the simulation accuracy is moderately improved compared with the single-angle simulation. The estimation of photometric parameters based on multi-angle spectral data can provide a basis for setting the empirical values of the phase function parameters from single-angle spectral calculations, which can more truly reflect the law of reflectance spectra changing with angle than Lucey’s traditional empirical value of the phase function (b = −0.4 and c = 0.25). The results of multi-angle spectra retrieval in this paper show that the Legendre polynomial coefficients of the phase function vary with wavelength rather than being constant and that different minerals differ greatly.

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Müther, H., and W. H. Dickhoff. "Single-particle spectral function ofO16." Physical Review C 49, no. 1 (January 1, 1994): R17—R20. http://dx.doi.org/10.1103/physrevc.49.r17.

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Aarts, Gert. "Spectral function at high temperature." Nuclear Physics B - Proceedings Supplements 106-107 (March 2002): 534–36. http://dx.doi.org/10.1016/s0920-5632(01)01771-6.

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Ustinov, V. N. "Spectral evaluation of gastric function." Bulletin of Experimental Biology and Medicine 108, no. 1 (July 1989): 912–14. http://dx.doi.org/10.1007/bf00839763.

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Francos, Nicolas, Daniela Heller-Pearlshtien, José A. M. Demattê, Bas Van Wesemael, Robert Milewski, Sabine Chabrillat, Nikolaos Tziolas, et al. "A Spectral Transfer Function to Harmonize Existing Soil Spectral Libraries Generated by Different Protocols." Applied and Environmental Soil Science 2023 (January 20, 2023): 1–17. http://dx.doi.org/10.1155/2023/4155390.

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Soil spectral libraries (SSLs) are important big-data archives (spectra associated with soil properties) that are analyzed via machine-learning algorithms to estimate soil attributes. Since different spectral measurement protocols are applied when constructing SSLs, it is necessary to examine harmonization techniques to merge the data. In recent years, several techniques for harmonization have been proposed, among which the internal soil standard (ISS) protocol is the most largely applied and has demonstrated its capacity to rectify systematic effects during spectral measurements. Here, we postulate that a spectral transfer function (TF) can be extracted between existing (old) SSLs if a subset of samples from two (or more) different SSLs are remeasured using the ISS protocol. A machine-learning TF strategy was developed, assembling random forest (RF) spectral-based models to predict the ISS spectral condition using soil samples from two existing SSLs. These SSLs had already been measured using different protocols without any ISS treatment the Brazilian (BSSL, generated in 2019) and the European (LUCAS, generated in 2009–2012) SSLs. To verify the TF’s ability to improve the spectral assessment of soil attributes after harmonizing the different SSLs’ protocols, RF spectral-based models for estimating organic carbon (OC) in soil were developed. The results showed high spectral similarities between the ISS and the ISS–TF spectral observations, indicating that post-ISS rectification is possible. Furthermore, after merging the SSLs with the TFs, the spectral-based assessment of OC was considerably improved, from R2 = 0.61, RMSE (g/kg) = 12.46 to R2 = 0.69, RMSE (g/kg) = 11.13. Given our results, this paper enhances the importance of soil spectroscopy by contributing to analyses in remote sensing, soil surveys, and digital soil mapping.

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Abdraimov, R. T., B. E. Vintaykin, P. A. Saidakhmetov, N. K. Madiyarov, and M. A. Abdualiyeva. "SOLVING MINERALOGY PROBLEMS WITH THE HELP OF THE “ORIGIN" PACKAGE." BULLETIN 386, no. 4 (August 15, 2020): 6–12. http://dx.doi.org/10.32014/2020.2518-1467.97.

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Algorithms for solving typical mineralogical problems associated with quantitative x-ray spectral analysis and quantitative x-ray phase analysis using the program “Origin” are developed. The calculation of the areas and midpoint of spectral lines using the tabular processor of the program “Origin” is considered. Various approaches to determining the parameters of spectral lines using the least squares method using the standard functions of the program “Origin” were tested. The creation of a user function for approximation of diffraction maxima by the Cauchy function taking into account the doublet character of Ka series of x-rays is also considered. Various built-in algorithms for smoothing functions (based on averaging, polynomial approximation and Fourier analysis – synthesis) were tested to find weak diffraction maxima against strong noise; optimal schemes for the application of these algorithms were found. The considered algorithms can be applied in universities when processing the results of laboratory works on the topics "Analysis of spectra of emission of atoms", "Quantitative x-ray spectral analysis" and "Quantitative x-ray phase analysis".

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Kowalski, N., D. A. Depireux, and S. A. Shamma. "Analysis of dynamic spectra in ferret primary auditory cortex. II. Prediction of unit responses to arbitrary dynamic spectra." Journal of Neurophysiology 76, no. 5 (November 1, 1996): 3524–34. http://dx.doi.org/10.1152/jn.1996.76.5.3524.

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1. Responses of single units and multiunit clusters were recorded in the ferret primary auditory cortex (AI) with the use of broadband complex dynamic spectra. Previous work has demonstrated that simpler spectra consisting of single moving ripples (i.e., sinusoidally modulated spectral profiles that travel at a constant velocity along the logarithmic frequency axis) could be used effectively to characterize the response fields and transfer functions of AI cells. 2. A complex dynamic spectral profile can be thought of as being the sum of moving ripple spectra. Such a decomposition can be computed from a two-dimensional spectrotemporal Fourier transform of the dynamic spectral profile with moving ripples as the basis function. 3. Therefore, if AI units were essentially linear, satisfying the superposition principle, then their responses to arbitrary dynamic spectra could be predicted from the responses to single moving ripples, i.e., from the units' response fields and transfer functions (spectral and temporal impulse response functions, respectively). 4. This conjecture was tested and confirmed with data from 293 combinations of moving ripples, involving complex spectra composed of up to 15 moving ripples of different ripple frequencies and velocities. For each case, response predictions based on the unit transfer functions were compared with measured responses. The correlation between predicted and measured responses was found to be consistently high (84% with rho > 0.6). 5. The distribution of response parameters suggests that AI cells may encode the profile of a dynamic spectrum by performing a multiscale spectrotemporal decomposition of the dynamic spectral profile in a largely linear manner.

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Centeno, Rebecca, Natasha Flyer, Lipi Mukherjee, Ricky Egeland, Roberto Casini, Tanausú del Pino Alemán, and Matthias Rempel. "Convolutional Neural Networks and Stokes Response Functions." Astrophysical Journal 925, no. 2 (February 1, 2022): 176. http://dx.doi.org/10.3847/1538-4357/ac402f.

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Abstract In this work, we study the information content learned by a convolutional neural network (CNN) when trained to carry out the inverse mapping between a database of synthetic Ca ii intensity spectra and the vertical stratification of the temperature of the atmospheres used to generate such spectra. In particular, we evaluate the ability of the neural network to extract information about the sensitivity of the spectral line to temperature as a function of height. By training the CNN on sufficiently narrow wavelength intervals across the Ca ii spectral profiles, we find that the error in the temperature prediction shows an inverse relationship to the response function of the spectral line to temperature, that is, different regions of the spectrum yield a better temperature prediction at their expected regions of formation. This work shows that the function that the CNN learns during the training process contains a physically meaningful mapping between wavelength and atmospheric height.

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Langer, H., A. Markus, and V. Matsaev. "Self-adjoint analytic operator functions and their local spectral function." Journal of Functional Analysis 235, no. 1 (June 2006): 193–225. http://dx.doi.org/10.1016/j.jfa.2005.10.003.

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Zorn, Reiner. "Applicability of distribution functions for the Havriliak-Negami spectral function." Journal of Polymer Science Part B: Polymer Physics 37, no. 10 (May 15, 1999): 1043–44. http://dx.doi.org/10.1002/(sici)1099-0488(19990515)37:10<1043::aid-polb9>3.0.co;2-h.

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Matuszewski, Maciej, Małgorzata Słomion, Janusz Musiał, and Andres Bustilo. "Application of surface frequency functions to assess the state of the kinematic pair elements." MATEC Web of Conferences 182 (2018): 02019. http://dx.doi.org/10.1051/matecconf/201818202019.

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In this paper the possibility of using frequency functions of the kinematic pair surface layer elements was analyzed for evaluation of the surface layer condition. The function of spectral power density and autocorrelation which were accepted for analysis was characterized. Evaluation of the elements condition was made on the quantify way as changes in degree of isotropy and in the qualitative way based on the graphs of the analyzed frequency functions. After tribological tests the surface structures were adopted to assess the changes. Spectral graphs for structures without cooperation (directly after-machining) and for the different friction distance, were analyzed. Conditions during tribological tests were taken as permanent. The determined degree of isotropy basis on the frequency functions and received graphs of spectra power density function and autocorrelation become useful in evaluation of the surface layer changes during its transformation.

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GEISLER, R., V. KOSTRYKIN, and R. SCHRADER. "CONCAVITY PROPERTIES OF KREIN’S SPECTRAL SHIFT FUNCTION." Reviews in Mathematical Physics 07, no. 02 (February 1995): 161–81. http://dx.doi.org/10.1142/s0129055x95000098.

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We prove that the integrated Krein’s spectral shift function for one particle Schrödinger operators in R3 is concave with respect to the perturbation potential. The proof is given by showing that the spectral shift function is the limit in the distributional sense of the difference of the counting functions for the given Hamiltonian and the free Hamiltonian in a finite domain Λ with Dirichlet boundary conditions when Λ→∞.

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Citro, Roberta, Stefania De Palo, Nicolas Victorin, Anna Minguzzi, and Edmond Orignac. "Spectral Function of a Boson Ladder in an Artificial Gauge Field." Condensed Matter 5, no. 1 (March 10, 2020): 15. http://dx.doi.org/10.3390/condmat5010015.

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We calculate the spectral function of a boson ladder in an artificial magnetic field by means of analytic approaches based on bosonization and Bogoliubov theory. We discuss the evolution of the spectral function at increasing effective magnetic flux, from the Meissner to the Vortex phase, focussing on the effects of incommensurations in momentum space. At low flux, in the Meissner phase, the spectral function displays both a gapless branch and a gapped one, while at higher flux, in the Vortex phase, the spectral function displays two gapless branches and the spectral weight is shifted at a wavevector associated to the underlying vortex spatial structure, which can indicate a supersolid-like behavior. While the Bogoliubov theory, valid at weak interactions, predicts sharp delta-like features in the spectral function, at stronger interactions we find power-law broadening of the spectral functions due to quantum fluctuations as well as additional spectral weight at higher momenta due to backscattering and incommensuration effects. These features could be accessed in ultracold atom experiments using radio-frequency spectroscopy techniques.

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Mogilevskii, Vadim. "Spectral Functions for the Vector-Valued Fourier Transform." Journal of Function Spaces 2018 (October 1, 2018): 1–17. http://dx.doi.org/10.1155/2018/9584150.

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A scalar distribution function σ(s) is called a spectral function for the Fourier transform φ^(s)=∫Reitsφ(t)dt (with respect to an interval I⊂R) if for each function φ∈L2(R) with support in I the Parseval identity ∫Rφ^s2dσ(s)=∫Rφt2dt holds. We show that in the case I=R there exists a unique spectral function σ(s)=(1/2π)s, in which case the above Parseval identity turns into the classical one. On the contrary, in the case of a finite interval I=(0,b), there exist infinitely many spectral functions (with respect to I). We introduce also the concept of the matrix-valued spectral function σ(s) (with respect to a system of intervals {I1,I2,…,In}) for the vector-valued Fourier transform of a vector-function φ(t)={φ1(t),φ2(t),…,φn(t)}∈L2(I,Cn), such that support of φj lies in Ij. The main result is a parametrization of all matrix (in particular scalar) spectral functions σ(s) for various systems of intervals {I1,I2,…,In}.

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Xu, Yunnan, Pang Du, Ryan Senger, John Robertson, and James L. Pirkle. "ISREA: An Efficient Peak-Preserving Baseline Correction Algorithm for Raman Spectra." Applied Spectroscopy 75, no. 1 (October 8, 2020): 34–45. http://dx.doi.org/10.1177/0003702820955245.

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A critical step in Raman spectroscopy is baseline correction. This procedure eliminates the background signals generated by residual Rayleigh scattering or fluorescence. Baseline correction procedures relying on asymmetric loss functions have been employed recently. They operate with a reduced penalty on positive spectral deviations that essentially push down the baseline estimates from invading Raman peak areas. However, their coupling with polynomial fitting may not be suitable over the whole spectral domain and can yield inconsistent baselines. Their requirement of the specification of a threshold and the non-convexity of the corresponding objective function further complicates the computation. Learning from their pros and cons, we have developed a novel baseline correction procedure called the iterative smoothing-splines with root error adjustment (ISREA) that has three distinct advantages. First, ISREA uses smoothing splines to estimate the baseline that are more flexible than polynomials and capable of capturing complicated trends over the whole spectral domain. Second, ISREA mimics the asymmetric square root loss and removes the need of a threshold. Finally, ISREA avoids the direct optimization of a non-convex loss function by iteratively updating prediction errors and refitting baselines. Through our extensive numerical experiments on a wide variety of spectra including simulated spectra, mineral spectra, and dialysate spectra, we show that ISREA is simple, fast, and can yield consistent and accurate baselines that preserve all the meaningful Raman peaks.

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Sinha, Kalyan B., and A. N. Mohapatra. "Spectral shift function and trace formula." Proceedings / Indian Academy of Sciences 104, no. 4 (November 1994): 819–53. http://dx.doi.org/10.1007/bf02830804.

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Boumenir, Amin. "Direct computation of the spectral function." Proceedings of the American Mathematical Society 123, no. 11 (November 1, 1995): 3431. http://dx.doi.org/10.1090/s0002-9939-1995-1283541-5.

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Morita, H., and T. Suzuki. "A Realistic Spectral Function of 4He." Progress of Theoretical Physics 86, no. 3 (September 1, 1991): 671–84. http://dx.doi.org/10.1143/ptp/86.3.671.

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Mendizabal, Sebastián, and Juan Cristobal Rojas. "Backreaction effects on nonequilibrium spectral function." International Journal of Modern Physics A 32, no. 21 (July 30, 2017): 1750126. http://dx.doi.org/10.1142/s0217751x17501263.

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We show how to compute the spectral function for a scalar theory in two different scenarios: one which disregards backreaction, i.e. the response of the environment to the external particle, and the other one where backreaction is considered. The calculation was performed using the Kadanoff–Baym equation through the Keldysh formalism. When backreaction is neglected, the spectral function is equal to the equilibrium one, which can be represented as a Breit–Wigner distribution. When backreaction is introduced we observed a damping in the spectral function of the thermal bath. Such behavior modifies the damping rate for particles created within the bath.

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Islam, A. K. M. A., F. N. Islam, and M. N. Islam. "Model spectral function for MgB2 superconductor." Physics Letters A 286, no. 5 (August 2001): 357–61. http://dx.doi.org/10.1016/s0375-9601(01)00434-0.

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Potapov, Denis, Anna Skripka, and Fedor Sukochev. "Spectral shift function of higher order." Inventiones mathematicae 193, no. 3 (November 17, 2012): 501–38. http://dx.doi.org/10.1007/s00222-012-0431-2.

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Velytsky, Alexander. "Quarkonium Spectral Function from Anisotropic Lattice." Nuclear Physics A 783, no. 1-4 (February 2007): 477–80. http://dx.doi.org/10.1016/j.nuclphysa.2006.11.031.

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von Kienlin, Markus, and Raymond Mejia. "Spectral localization with optimal pointspread function." Journal of Magnetic Resonance (1969) 94, no. 2 (September 1991): 268–87. http://dx.doi.org/10.1016/0022-2364(91)90106-4.

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Warner, R. E., A. Okihana, M. Fujiwara, N. Matsuoka, K. Tamura, M. Tosaki, T. Ohsawa, K. Fukunaga, P. A. Kimoto, and N. Koori. "Spectral function of thep3/2nucleons inLi6." Physical Review C 38, no. 6 (December 1, 1988): 2945–48. http://dx.doi.org/10.1103/physrevc.38.2945.

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Birman, M. Sh, and A. B. Pushnitski. "Spectral shift function, amazing and multifaceted." Integral Equations and Operator Theory 30, no. 2 (June 1998): 191–99. http://dx.doi.org/10.1007/bf01238218.

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Petrillo, C., and F. Sacchetti. "Calculated spectral weight function in aluminum." Il Nuovo Cimento D 5, no. 1 (January 1985): 14–22. http://dx.doi.org/10.1007/bf02453199.

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van den Berg, M. "Spectral Bounds for the Torsion Function." Integral Equations and Operator Theory 88, no. 3 (April 26, 2017): 387–400. http://dx.doi.org/10.1007/s00020-017-2371-0.

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Schweiger, Anna K., Jeannine Cavender-Bares, Shan Kothari, Philip A. Townsend, Michael D. Madritch, Jake J. Grossman, Hamed Gholizadeh, Ran Wang, and John A. Gamon. "Coupling spectral and resource-use complementarity in experimental grassland and forest communities." Proceedings of the Royal Society B: Biological Sciences 288, no. 1958 (September 2021): 20211290. http://dx.doi.org/10.1098/rspb.2021.1290.

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Reflectance spectra provide integrative measures of plant phenotypes by capturing chemical, morphological, anatomical and architectural trait information. Here, we investigate the linkages between plant spectral variation, and spectral and resource-use complementarity that contribute to ecosystem productivity. In both a forest and prairie grassland diversity experiment, we delineated n -dimensional hypervolumes using wavelength bands of reflectance spectra to test the association between the spectral space occupied by individual plants and their growth, as well as between the spectral space occupied by plant communities and ecosystem productivity. We show that the spectral space occupied by individuals increased with their growth, and the spectral space occupied by plant communities increased with ecosystem productivity. Furthermore, ecosystem productivity was better explained by inter-individual spectral complementarity than by the large spectral space occupied by productive individuals. Our results indicate that spectral hypervolumes of plants can reflect ecological strategies that shape community composition and ecosystem function, and that spectral complementarity can reveal resource-use complementarity.

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Zayed, E. M. E. "Eigenvalues of the negative Laplacian for arbitrary multiply connected domains." International Journal of Mathematics and Mathematical Sciences 19, no. 3 (1996): 581–86. http://dx.doi.org/10.1155/s0161171296000804.

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The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function∑k=1∞{μk(σ1,…,σn)+P}−2asP→∞. Further results may be obtained.

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Barton, Sinead, Salaheddin Alakkari, Kevin O’Dwyer, Tomas Ward, and Bryan Hennelly. "Convolution Network with Custom Loss Function for the Denoising of Low SNR Raman Spectra." Sensors 21, no. 14 (July 6, 2021): 4623. http://dx.doi.org/10.3390/s21144623.

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Raman spectroscopy is a powerful diagnostic tool in biomedical science, whereby different disease groups can be classified based on subtle differences in the cell or tissue spectra. A key component in the classification of Raman spectra is the application of multi-variate statistical models. However, Raman scattering is a weak process, resulting in a trade-off between acquisition times and signal-to-noise ratios, which has limited its more widespread adoption as a clinical tool. Typically denoising is applied to the Raman spectrum from a biological sample to improve the signal-to-noise ratio before application of statistical modeling. A popular method for performing this is Savitsky–Golay filtering. Such an algorithm is difficult to tailor so that it can strike a balance between denoising and excessive smoothing of spectral peaks, the characteristics of which are critically important for classification purposes. In this paper, we demonstrate how Convolutional Neural Networks may be enhanced with a non-standard loss function in order to improve the overall signal-to-noise ratio of spectra while limiting corruption of the spectral peaks. Simulated Raman spectra and experimental data are used to train and evaluate the performance of the algorithm in terms of the signal to noise ratio and peak fidelity. The proposed method is demonstrated to effectively smooth noise while preserving spectral features in low intensity spectra which is advantageous when compared with Savitzky–Golay filtering. For low intensity spectra the proposed algorithm was shown to improve the signal to noise ratios by up to 100% in terms of both local and overall signal to noise ratios, indicating that this method would be most suitable for low light or high throughput applications.

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SAIKAWA, TAIICHIRO, and ALVARO FERRAZ. "ANISOTROPIC PSEUDOGAP IN THE HALF-FILLING TWO-DIMENSIONAL HUBBARD MODEL AT FINITE TEMPERATURE." International Journal of Modern Physics B 14, no. 21 (August 20, 2000): 2271–86. http://dx.doi.org/10.1142/s0217979200002156.

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We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperatures. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.

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Parkinson, M. L., K. M. Hannah, and P. L. Dyson. "Complexity in the high latitude HF radar spectral width boundary region." Annales Geophysicae 26, no. 4 (May 13, 2008): 877–92. http://dx.doi.org/10.5194/angeo-26-877-2008.

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Abstract. SuperDARN radars are sensitive to the collective Doppler characteristics of decametre-scale irregularities in the high latitude ionosphere. The radars routinely observe a distinct transition from large spectral width (>100 m s−1) located at higher latitudes to low spectral width (<50 m s−1) located at lower latitudes. Because of its equatorward location, the TIGER Tasmanian radar is very sensitive to the detection of the spectral width boundary (SWB) in the nightside auroral ionosphere. An analysis of the line-of-sight velocities and 2-D beam-swinging vectors suggests the meso-scale (~100 km) convection is more erratic in the high spectral width region, but slower and more homogeneous in the low spectral width region. The radar autocorrelation functions are better modelled using Lorentzian Doppler spectra in the high spectral width region, and Gaussian Doppler spectra in the low spectral width region. However, paradoxically, Gaussian Doppler spectra are associated with the largest spectral widths. Application of the Burg maximum entropy method suggests the occurrence of double-peaked Doppler spectra is greater in the high spectral width region, implying the small-scale (~10 km) velocity fluctuations are more intense above the SWB. These observations combined with collective wave scattering theory imply there is a transition from a fast flowing, turbulent plasma with a correlation length of velocity fluctuations less than the scattering wavelength, to a slower moving plasma with a correlation length greater than the scattering wavelength. Peak scaling and structure function analysis of fluctuations in the SWB itself reveals approximately scale-free behaviour across temporal scales of ~10 s to ~34 min. Preliminary scaling exponents for these fluctuations, αGSF=0.18±0.02 and αGSF=0.09±0.01, are even smaller than that expected for MHD turbulence.

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Chekhov, Leonid, and Paul Norbury. "Topological recursion with hard edges." International Journal of Mathematics 30, no. 03 (March 2019): 1950014. http://dx.doi.org/10.1142/s0129167x19500149.

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We prove a Givental type decomposition for partition functions that arise out of topological recursion applied to spectral curves. Copies of the Konstevich–Witten KdV tau function arise out of regular spectral curves and copies of the Brezin–Gross–Witten KdV tau function arise out of irregular spectral curves. We present the example of this decomposition for the matrix model with two hard edges and spectral curve [Formula: see text].

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Ewans, K. C., E. M. Bitner-Gregersen, and C. Guedes Soares. "Estimation of Wind-Sea and Swell Components in a Bimodal Sea State." Journal of Offshore Mechanics and Arctic Engineering 128, no. 4 (December 18, 2004): 265–70. http://dx.doi.org/10.1115/1.2166655.

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Methods for separating the spectral components and describing bimodal wave spectra are evaluated with reference to wave spectra from directional wave measurements made at the Maui location off the west coast of New Zealand. Two methods involve partitioning bimodal wave spectra into wind-sea and swell components and then fitting a spectral function to each component, while the third assigns an average spectral shape based on the integrated spectral parameters. The partitioning methods involve separating the wave spectrum into two frequency bands: a low-frequency peak, the swell component, and a high-frequency peak, the wind-sea. One partitioning method uses only the frequency spectrum while the other analyzes the complete frequency-direction spectrum. Comparison of the spectral descriptions and derived parameters against the measured counterparts provides insight into the accuracy of the different approaches to describing actual bimodal sea states.

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Caudal, G. V. "Imbalance of energy and momentum source terms of the sea wave transfer equation for fully developed seas." Ocean Science Discussions 9, no. 4 (July 31, 2012): 2581–619. http://dx.doi.org/10.5194/osd-9-2581-2012.

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Abstract. Using a two-dimensional empirical sea wave spectral model at full development, this paper performs an assessment of the compatibility of the energy and momentum budgets of sea waves over the whole spectral range. Among the various combinations of model functions for wave breaking and wind source terms tested, no one fulfilled simultaneously the energy and momentum balance of the transfer equation. Based on experimental and theoretical grounds, wave breaking is known to contribute to frequency downshift of a narrow-banded wave spectrum, when the modulational instability is combined with wave breaking. On those grounds, it is assumed that, in addition to dissipation, wave breaking produces a spectral energy flux directed toward low wavenumbers. I show that it is then possible to remove the energy and momentum budget inconsistency, and correlatively the required strength of this spectral flux is estimated. Assuming such a downward spectral flux permits to fulfill both energy and momentum balance conditions, while slightly reducing the consistency between source terms and empirical spectra, as estimated by a cost function K. Other tests were performed in which it was further assumed that wave breaking would also be associated with azimuthal diffusion of the spectral energy. This could allow a slight improvement of the cost function K, and might correlatively reduce the required downward spectral flux by a factor of 4, although it would not be able to remove it entirely.

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Journal articles on the topic 'Spectral function'

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