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Journal articles on the topic 'Line-shape function'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

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1

Eliseev, P. G. "Line shape function for semiconductor laser modelling." Electronics Letters 33, no. 24 (1997): 2046. http://dx.doi.org/10.1049/el:19971385.

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2

Garland, J. W., H. Abad, M. Viccaro, and P. M. Raccah. "Line shape of the optical dielectric function." Applied Physics Letters 52, no. 14 (1988): 1176–78. http://dx.doi.org/10.1063/1.99641.

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3

Bolotov, B. M., D. A. Aksenov, A. I. Polyakov, and S. P. Senshin. "NMR Line Shape Function Analysis in Solids." physica status solidi (b) 139, no. 2 (1987): K137—K140. http://dx.doi.org/10.1002/pssb.2221390239.

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4

Lu, Xing-Ji, Zhen-Song Cao, Tu Tan, Yin-Bo Huang, Xiao-Ming Gao, and Rui-Zhong Rao. "Instrument line shape function of laser heterodyne spectrometer." Acta Physica Sinica 68, no. 6 (2019): 064208. http://dx.doi.org/10.7498/aps.68.20181620.

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5

Han, Yunfei, Hailiang Shi, Haiyan Luo, et al. "Research on calculation Method of On-Orbit Instrumental Line Shape Function for the Greenhouse Gases Monitoring Instrument on the GaoFen-5B Satellite." Remote Sensing 16, no. 12 (2024): 2171. http://dx.doi.org/10.3390/rs16122171.

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The Greenhouse Gases Monitoring Instrument is based on the spectroscopic principle of spatial heterodyne spectroscopy technology and has the characteristics of no moving parts, a hyperspectral resolution, and a large luminous flux. The instrumental line shape function is one of the most important parameters characterizing the features of the instrument, and it plays a vital role in the system error analysis of the instrument’s measurements. To accurately obtain the instrumental line shape function of a spatial heterodyne spectrometer during the on-orbit period and improve the accuracy of gas concentration retrieval, this study develops a method to model and characterize the characteristics of the instrumental line shape function, including modulation loss and phase error. This study employs the solar calibration spectrum in the 1.568–1.583 μm bands to conduct iterative calculations of the instrumental line shape function error model. After the instrumental line function is updated, the average relative deviation is reduced from 1.83% to 0.756% between the theoretical and measured solar spectra. Additionally, the average relative deviation is reduced from 7.049% to 2.106% between the GMI nadir and theoretical nadir spectra. The findings demonstrate that updating the instrumental line shape function mitigates the impact of variations in the spectrometer’s instrumental line shape due to alterations in the orbital environment. This study offers a dependable reference for both the enhancement and oversight of a spectrometer’s instrumental line shape function, along with an investigation of shifts in instrument parameters.

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6

Li, Chun Tao, Xiang Qi, Jian Shi, Zhong Kun Shi, and Huan Qi. "Ship Lines Modeling Theory of High-Speed Ship Based on the Partial Differential Equations." Advanced Materials Research 602-604 (December 2012): 1827–30. http://dx.doi.org/10.4028/www.scientific.net/amr.602-604.1827.

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Based on the analysis of molded line geometrical characteristic and boundary conditions of high-speed frigate’s hull by using differential geometry, we report a curve modeling principle to express the hull line geometry through differential geometry application. The starting point of this molded-line automatic generation method is using the planar curve to express 3D surface shape. The first problem to be solved is how to get shape functions which describe every design ship curves via the the hull type curves geometry. The second problem to be solved is how the two-dimensional function, which describe ship lines, transformed to the hull shape function designed of three-dimensional hull surface, namely “mathematic ship”.

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7

Zhao, Haoxin, Lydia N. Raines, and Stanley Ching-Cheng Huang. "Molecular Chaperones: Molecular Assembly Line Brings Metabolism and Immunity in Shape." Metabolites 10, no. 10 (2020): 394. http://dx.doi.org/10.3390/metabo10100394.

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Molecular chaperones are a set of conserved proteins that have evolved to assist the folding of many newly synthesized proteins by preventing their misfolding under conditions such as elevated temperatures, hypoxia, acidosis and nutrient deprivation. Molecular chaperones belong to the heat shock protein (HSP) family. They have been identified as important participants in immune functions including antigen presentation, immunostimulation and immunomodulation, and play crucial roles in metabolic rewiring and epigenetic circuits. Growing evidence has accumulated to indicate that metabolic pathways and their metabolites influence the function of immune cells and can alter transcriptional activity through epigenetic modification of (de)methylation and (de)acetylation. However, whether molecular chaperones can regulate metabolic programs to influence immune activity is still largely unclear. In this review, we discuss the available data on the biological function of molecular chaperones to immune responses during inflammation, with a specific focus on the interplay between molecular chaperones and metabolic pathways that drive immune cell fate and function.

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8

Buishvili, L. L., and G. V. Kobakhidze. "On the shape of EPR line in magnetodilute crystals." Low Temperature Physics 20, no. 11 (1994): 935–36. https://doi.org/10.1063/10.0033739.

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The shape of the absorption line in magnetodilute samples at low temperatures is analyzed by the memory function method. It is shown that, in contrast to the approximation of the cut-off Lorentzian shape of the line, the memory function method gives the Gaussian decrease in absorption for a detuning above the cut-off parameter.

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9

Kummrow, A., S. H. Ashworth, and K. Lenz. "Resonance Raman and Optical Dephasing Study of Hitci." Laser Chemistry 19, no. 1-4 (1999): 41–44. http://dx.doi.org/10.1155/1999/87468.

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Line shape analysis based on resonance Raman spectra of HITCI is used to determine the details of the vibrational part of the line broadening function. Forced Light Scattering with 20 fs pulses from a Ti: sapphire laser measured optical dephasing probing with an Ar+ laser. The observed response is well described by the line broadening function derived from the fluorescence line shape.

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10

Jingde, Li, Tang Xingui, Fan Yangcai, and Zhou Zhenhong. "Time Domain Spectroscopy Function and Line Shape of Slow Responses." Chinese Physics Letters 12, no. 12 (1995): 763–65. http://dx.doi.org/10.1088/0256-307x/12/12/016.

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11

David, W. I. F., and J. C. Matthewman. "Profile refinement of powder diffraction patterns using the Voigt function." Journal of Applied Crystallography 18, no. 6 (1985): 461–66. http://dx.doi.org/10.1107/s0021889885010718.

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The Voigt function has been incorporated as a peak-shape description into a program for the refinement of constant-wavelength X-ray and neutron diffraction patterns. The results obtained for neutron diffraction are encouraging and indicate that the Voigt function describes the symmetrical component of the profile peak shape to high accuracy even in the presence of substantial line broadening from particle-size effects. In contrast with approximations to the Voigt function, such as the pseudo-Voigt and Pearson VII functions, the present treatment allows the angular dependences of line-broadening effects resulting from particle-size and instrumental contributions to be coded independently from each other in the Rietveld technique. The present treatment, which details improvements to the symmetrical component of the peak shape, does not offer a fully rigorous description of the peak shape as asymmetry corrections such as those given by Howard [J. Appl. Cryst. (1982), 15, 615–620] are not included.

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12

STÉPHAN, GUY. "AN AIRY FUNCTION FOR THE LASER." Journal of Nonlinear Optical Physics & Materials 05, no. 03 (1996): 551–57. http://dx.doi.org/10.1142/s0218863596000374.

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We give a general equation which allows the description of the evolution of the laser properties when the gain is varied from below to above threshold. The method is general in the context of the semi-classical theory of lasers. It is numerically illustrated in the simplest case of a single mode laser with a source term characterized by a very narrow spectrum. The transformation of the Airy line shape of the passive Fabry-Perot cavity into the laser line shape is described. A classical linewidth which complements the usual quantum limit can thus be introduced, together with its control parameters.

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13

Popovych, Volodymyr, Mariusz Bester, Ireneusz Stefaniuk, and Marian Kuzma. "Dyson line and modified Dyson line in the EPR measurements." Nukleonika 60, no. 3 (2015): 385–88. http://dx.doi.org/10.1515/nuka-2015-0068.

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Abstract The difficulty in determining the electron paramagnetic resonance (EPR) line parameters of ferromagnetic semiconductors has been addressed. For these materials, the resonance line is very broad and lies at low resonance field, so that only a part of the line can be detected experimentally. Moreover, the line is of asymmetric (Dysonian) shape as described by the line shape parameter α. We have compared values of line parameters derived by computer fitting of the whole experimental EPR line to the Dyson function (or modified Dyson function) with the values obtained by applying this procedure to the left and the right half of the line.

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14

Kang, Nam Lyong, and Sang Don Choi. "A new approach to electron-spin resonance absorption line shape function." Journal of Mathematical Physics 49, no. 7 (2008): 073501. http://dx.doi.org/10.1063/1.2944994.

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15

Matyushov, Dmitry V. "Kubo’s Line Shape Function for a Linear-Quadratic Chromophore–Solvent Coupling." Journal of Physical Chemistry B 119, no. 29 (2014): 9006–8. http://dx.doi.org/10.1021/jp5081059.

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16

Alomar, Abdulazeez S. "Impact of Faddeeva–Voigt broadening on line-shape analysis at critical points of dielectric functions." AIP Advances 12, no. 6 (2022): 065127. http://dx.doi.org/10.1063/5.0092287.

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Faddeeva–Voigt broadening (FVB) couples the physical characteristics of both Lorentzian and Gaussian profiles as a combined analytic function shaping the dielectric response. Accurate extraction of the Gaussian and Lorentzian broadening contents in line-shape analysis is essential for reliable optical characterization of semiconductors and dielectrics. By adding the Gaussian-broadening width to each Lorentzian width, we investigate how FVB affects critical-point (CP) analysis. We revisit a selection of earlier work based on classical Lorentz broadening in modulation spectroscopy and spectral ellipsometry. To generalize CP analysis, we derive the FVB’s analytical representation in terms of fractional derivatives of the Faddeeva function and apply the twenty-pole Martin–Donoso–Zamudio approximation for its precise and efficient computation of the FVB of model dielectric functions and derivatives. We investigate the FVB of the electroreflectance line shape of HgCdTe for three-dimensional M0 transitions and of the photoreflectance line shape of InP excitonic E0 transitions. Furthermore, we explore how FVB affects the dielectric functions of three-dimensional excitonic and two-dimensional M0 transitions vs Tanguy’s analytical two-dimensional exciton E1 and E1+Δ1 fits of GaAs to the second-order derivatives. We use the Akaike information criterion to quantitatively estimate the goodness of fit that statistically penalizes overfitting due to extraneous parameters. By consolidating both Gaussian and Lorentzian broadenings, the FVB significantly affects the CP analysis of modulation-spectroscopy line shapes and second-order derivatives of the dielectric function.

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17

Munir, Nur Azliana Azlin, Normi Abdul Hadi, and Mohd Agos Salim Nasir. "Constrained for G1 cubic trigonometric spline curve interpolation." Malaysian Journal of Fundamental and Applied Sciences 18, no. 3 (2022): 323–31. http://dx.doi.org/10.11113/mjfas.v18n3.2353.

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This paper presented the G1 cubic trigonometric spline function with three shape parameters that generate a constrained curve that interpolates 2D data. The purpose of this research is to ensure the generated curve passes through all data point yet satisfied the three cases of line constraints given. The three cases are: the data must lie above line Li the data must lie below line Li and lastly, the data must lie between two lines Li,1 and Li,2. A simpler theorem is implemented involving the roles of shape parameters. Two of the shape parameters are set free, while another parameter is fixed to fulfil all the three cases stated. The results show that a smooth curve of the G1 cubic trigonometric spline function can be produced within the constrained line by using the theorem developed while the hereditary shape of the data is preserved. Numerical examples are illustrated and discussed.

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18

EFETOV, K. B., and V. N. PRIGODIN. "NMR IN A SYSTEM OF SMALL METALLIC PARTICLES: A NOVEL MESOSCOPIC PHENOMENON." Modern Physics Letters B 07, no. 15 (1993): 981–97. http://dx.doi.org/10.1142/s0217984993000989.

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We consider the NMR line shape for a system of small metal particles. The problem is reduced to calculation of the local density of states distribution function. We present the first exact calculation of this quantity for the mesoscopic system. Using the super-symmetry method, we calculated exactly the whole distribution function which gives the resonance-line shape. It turns out that at low temperatures, the line becomes very broad and asymmetric. The Knight shift defined as the maximum of the line decreases when decreasing the temperature. We found a good agreement of our results with a few experiments done long ago.

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19

Sug, Joung Young, Sang Gyu Jo, and Sang Don Choi. "Cyclotron resonance line shape function from the equilibrium density projection operator technique." Physical Review E 60, no. 6 (1999): 6538–48. http://dx.doi.org/10.1103/physreve.60.6538.

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20

Black, David R., Marcus H. Mendenhall, Albert Henins, James Filliben, and James P. Cline. "Certification of SRM 640f line position and line shape standard for powder diffraction." Powder Diffraction 35, no. 3 (2020): 156–59. http://dx.doi.org/10.1017/s0885715620000366.

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The National Institute of Standards and Technology (NIST) certifies a suite of Standard Reference Materials (SRMs) to be used to evaluate specific aspects of the instrument performance of both X-ray and neutron powder diffractometers. This report describes SRM 640f, the seventh generation of this powder diffraction SRM, which is designed to be used primarily for calibrating powder diffractometers with respect to line position; it also can be used for the determination of the instrument profile function. It is certified with respect to the lattice parameter and consists of approximately 7.5 g of silicon powder prepared to minimize line broadening. A NIST-built diffractometer, incorporating many advanced design features, was used to certify the lattice parameter of the Si powder. Both statistical and systematic uncertainties have been assigned to yield a certified value for the lattice parameter at 22.5 °C of a = 0.5431144 ± 0.000008 nm.

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21

Hiroto, Kikuchi. "A Method to Calculate Functions of the Product of G and F Used in Wilson's GF Matrix Method." International Journal of Trend in Scientific Research and Development 2, no. 4 (2018): 2516–19. https://doi.org/10.31142/ijtsrd15667.

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Wilson's GF matrix method is generally utilized to obtain normal vibrations and normal coordinates of molecules. The function of the product of G and F in Wilson's GF matrix method is also a key to determine the line shape function LSF which expresses molecular absorption or emission spectra. In this paper, the method for calculating the function of the product of G and F is shown. Hiroto Kikuchi "A Method to Calculate Functions of the Product of G and F Used in Wilson's GF Matrix Method" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: https://www.ijtsrd.com/papers/ijtsrd15667.pdf

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22

Kang, Nam Lyong, and Sang Don Choi. "Derivation of Line Shape Function in the Optical Conductivity by a New Diagram Method." Advances in Condensed Matter Physics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/560287.

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A new diagram method for the line shape function in the optical conductivity formula is introduced and the result obtained applying the method to an electron-phonon system is compared with that derived using the projection-reduction method. The result satisfies the population criterion, which states that the distribution functions for electrons and phonons should be combined in multiplicative forms and gives physical intuition to quantum dynamics of electrons in a solid. This method can be called the “KC diagram” method because it originates from the proper application of the Kang-Choi reduction identity and a state-dependent projection operator.

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23

Zhang, Yuan Xun, Qian Tang, and Xian Zhi Ye. "Anonymous Function Method and its Application in Screw Pump’s Design and Processing." Applied Mechanics and Materials 86 (August 2011): 500–503. http://dx.doi.org/10.4028/www.scientific.net/amm.86.500.

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Matlab anonymous function method combining graph with analytical method was proposed in this paper, which was based on the low solving efficiency and low precision of trigonometry transcendental equation for shape line design and sectional profile calculation of screw pump rotor. Parameters of anonymous function can be nested within each other to solve enveloping conditional formula of shape design or intersecting line of sectional profile design for screw pump, the process of which only took several seconds with high precision of 10E-08mm. What’s more, this method could also be adopted in the forming tool design with spiral cross section, which could largely improve design efficiency and calculation precision.

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24

Li, Renjie, Fei Li, Xin Lin, and Xilong Yu. "Error Analysis of Integrated Absorbance for TDLAS in a Nonuniform Flow Field." Applied Sciences 11, no. 22 (2021): 10936. http://dx.doi.org/10.3390/app112210936.

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As an effective optical diagnosis method, tunable diode-laser absorption spectroscopy (TDLAS) has increasingly moved to examine nonuniform flows, such as two-dimensional combustion diagnosis. To investigate the effect of nonuniformity along the line of sight in a measurement using TDLAS, the integrated absorbance (IA, the key intermediate quantity in TDLAS) error was quantified. The error distribution is obtained from the line-shape parameters through the comprehensive analysis of the line-shape function and the fitting method. The effects of the fitting function and the absorption line overlap are also considered. A general method for estimating the error is given. The work illustrates the applicability of TDLAS technology in nonuniform flow fields and provides input parameters for the evaluation of tunable diode laser absorption tomography error.

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25

Beyerlein, K. R., R. L. Snyder, and P. Scardi. "Powder diffraction line profiles from the size and shape of nanocrystallites." Journal of Applied Crystallography 44, no. 5 (2011): 945–53. http://dx.doi.org/10.1107/s0021889811030743.

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A numerical procedure to carry out the integral on the powder diffraction sphere in reciprocal space and obtain accurate powder diffraction peak profiles for small crystallites is presented. In doing so, the literature surrounding the effect of crystallite size and shape on the powder peak profile is briefly reviewed. Powder patterns simulated by this technique are compared with those calculated by the tangent plane approximation and Debye function for spherical, cubic and cylindrical crystallites having sizes of only a few nanometres. The tangent plane approximation is found to produce inaccurate peak profiles and peak positions in simulated patterns of the cubic and cylindrical nanocrystallites. This performance is in contrast to that of the proposed powder integration technique, which results in powder patterns that are in good agreement with those from the Debye function, for all crystallite sizes and shapes considered here.

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26

Zhang, Xiao Ping, Chang Jian Zhi, Rui Ren та Xiao Zhong Du. "Development of a Combined Shape and Gauge Control Scheme Based on Function Φ". Advanced Materials Research 418-420 (грудень 2011): 1118–23. http://dx.doi.org/10.4028/www.scientific.net/amr.418-420.1118.

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Combined shape and gauge control is a hot issue in continuous hot plate and strip rolling field. Due to the coupled function of shape and gauge control in rolling process, mutual effects must be considered when shape control is carried out. Traditional shape and gauge control theories are of independent and the control systems are also separated, so it is difficult to ensure the quality of shape and gauge simultaneously. Based on the shape theory of shape and gauge control and function Φ derived from the load distribution method of Ichiro Imai , a combined shape and gauge control scheme was developed, which can adjust rolling regulations on-line according to the deviation of strip crown measured at the exit of the rolling mill. The method can ensure gauge precision while strip crown is adjusted and the purpose of combined shape and gauge control is reached.

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27

Gates, John. "Shape distributions for planar triangles by dual construction." Advances in Applied Probability 26, no. 2 (1994): 324–33. http://dx.doi.org/10.2307/1427438.

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A random triangle in the plane is constructed using three independent elements from a convex set of lines. Expressions are given to calculate the shape distribution from the internal width function of the line set. Two examples are given together with their maximum angle distributions; a simple inequality implies a zero collinearity constant in general. A relationship between the shape distribution and inter-line angle distribution is given.

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28

Gates, John. "Shape distributions for planar triangles by dual construction." Advances in Applied Probability 26, no. 02 (1994): 324–33. http://dx.doi.org/10.1017/s0001867800026215.

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A random triangle in the plane is constructed using three independent elements from a convex set of lines. Expressions are given to calculate the shape distribution from the internal width function of the line set. Two examples are given together with their maximum angle distributions; a simple inequality implies a zero collinearity constant in general. A relationship between the shape distribution and inter-line angle distribution is given.

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29

Wang, Junyang, Patrick Ehlers, Isak Silander, Jonas Westberg, and Ove Axner. "Speed-dependent Voigt dispersion line-shape function: applicable to techniques measuring dispersion signals." Journal of the Optical Society of America B 29, no. 10 (2012): 2971. http://dx.doi.org/10.1364/josab.29.002971.

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30

Read, J. I., G. A. Mamon, E. Vasiliev, et al. "Breaking beta: a comparison of mass modelling methods for spherical systems." Monthly Notices of the Royal Astronomical Society 501, no. 1 (2020): 978–93. http://dx.doi.org/10.1093/mnras/staa3663.

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ABSTRACT We apply four different mass modelling methods to a suite of publicly available mock data for spherical stellar systems. We focus on the recovery of the density and velocity anisotropy as a function of radius, either using line-of-sight velocity data only or adding proper motion data. All methods perform well on isotropic and tangentially anisotropic mock data, recovering the density and velocity anisotropy within their 95 per cent confidence intervals over the radial range 0.25 &lt; R/R1/2 &lt; 4, where R1/2 is the half-light radius. However, radially anisotropic mocks are more challenging. For line-of-sight data alone, only methods that use information about the shape of the velocity distribution function are able to break the degeneracy between the density profile and the velocity anisotropy, β, to obtain an unbiased estimate of both. This shape information can be obtained through directly fitting a global phase-space distribution function, by using higher order ‘virial shape parameters’ or by assuming a Gaussian velocity distribution function locally, but projecting it self-consistently along the line of sight. Including proper motion data yields further improvements, and in this case, all methods give a good recovery of both the radial density and velocity anisotropy profiles.

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31

Cai, Zhaonan, Kang Sun, Dongxu Yang, et al. "On-Orbit Characterization of TanSat Instrument Line Shape Using Observed Solar Spectra." Remote Sensing 14, no. 14 (2022): 3334. http://dx.doi.org/10.3390/rs14143334.

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The Chinese carbon dioxide measurement satellite (TanSat) has collected a large number of measurements in the solar calibration mode. To improve the accuracy of XCO2 retrieval, the Instrument Line Shape (ILS, also known as the slit function) must be accurately determined. In this study, we characterized the on-orbit ILS of TanSat by fitting measured solar irradiance from 2017 to 2018 with a well-calibrated high-spectral-resolution solar reference spectrum. We used various advanced analytical functions and the stretch/sharpen of the tabulated preflight ILS to represent the ILS for each wavelength window, footprint, and band. Using super Gaussian+P7 and the stretch/sharpen functions substantially reduced the fitting residual in O2 A-band and weak CO2 band compared with using the preflight ILS. We found that the difference between the derived ILS width and on-ground preflight ILS was up to −3.5% in the weak CO2 band, depending on footprint and wavelength. The large amplitude of the ILS wings, depending on the wavelength, footprint, and bands, indicated possible uncorrected stray light. Broadening ILS wings will cause additive offset (filling-in) on the deep absorption lines of the spectra, which we confirmed using offline bias correction of the solar-induced fluorescence retrieval. We estimated errors due to the imperfect ILS using simulated TanSat spectra. The results of the simulations showed that XCO2 retrieval is sensitive to errors in the ILS, and 4% uncertainty in the full width of half maximum (FWHM) or 20% uncertainty in the ILS wings can induce an error of up to 1 ppm in the XCO2 retrieval.

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32

BATRA, T. R. "COMPARISON OF TWO MATHEMATICAL MODELS IN FITTING LACTATION CURVES FOR PURELINE AND CROSSLINE DAIRY COWS." Canadian Journal of Animal Science 66, no. 2 (1986): 405–14. http://dx.doi.org/10.4141/cjas86-042.

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Weekly milk yield of 2066 first, 1407 second, and 755 third lactation pureline and crossline cows was used to study environmental and genetic effects on the coefficients of the lactation curves derived by modified gamma and inverse polynomial functions. The inverse polynomial function provided a better fit than the modified gamma function based on comparison of R2 values. Coefficients of the two models were analyzed to evaluate environmental and genetic effects on the shape of the lactation curve. The model included station, year of calving, month of calving, age at calving, days open, line of sire, line of dam, interaction of line of sire with line of dam, and sires within line of sire. In addition, coefficients of the lactation curve were analyzed by another model which included station, year of calving, month of calving, age at calving, days open, breed additive, maternal, and heterosis effects. Effects of station, year of calving, month of calving, and days open were mostly significant (P < 0.05); however the effect of age at calving was not significant on the coefficients of the lactation curves. Significant (P < 0.05) line of sire and line of dam effects on the level of initial yield suggest that genetic improvement of this trait could be achieved through selection. Breed additive and maternal effects were mostly nonsignificant on the coefficients of the lactation curves indicating shape of the lactation curve could not be changed by selection. There was very little evidence of nonadditive genetic variation associated with the coefficients of lactation curves. Key words: Lactation curves, pureline, crossline, dairy cows

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33

May, A. D., W. K. Liu, F. R. W. McCourt, et al. "The impact theory of spectral line shapes: a paradigm shift." Canadian Journal of Physics 91, no. 11 (2013): 879–95. http://dx.doi.org/10.1139/cjp-2012-0345.

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An overview of the binary collision impact theory of spectral line shapes has been given to provide a unified statistical mechanical approach to line-shape theory, laser theory, nonlinear optics, and transport phenomena in dilute gases. The computation of spectral line profiles corresponding to those obtained from ultra-high-resolution spectral line-shape measurements requires numerical ab initio calculation of scattering amplitudes directly from the underlying dynamics of collisions between radiatively active molecules and their perturbers. The Wigner distribution function–density matrix is utilized to describe the kinetic theory of spectral line shapes and to discuss the various collisional processes that contribute to the kernel of kinetic equations. The influence of features of the potential energy surface on spectral parameters is also discussed, and the importance of comparing experimental line profiles directly with numerically computed line shapes obtained from reliable interaction potentials is emphasized. This contrasts sharply with the universal practice of comparing experimental line widths and shifts using some average or approximate theoretical scattering cross-sections and it contrasts sharply with fitting experimental profiles to some convenient analytical line-shape model; hence the phrase “a paradigm shift” in the title of this work.

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34

Liu, Yuhong, Fuguo Li, Shuxin Wang, and S. Jack Hu. "Preform Design of Powder Metallurgy Turbine Disks Using Equi-Potential Line Method." Journal of Manufacturing Science and Engineering 128, no. 3 (2006): 677–82. http://dx.doi.org/10.1115/1.2194066.

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In a material hot forging process, rational preform design not only ensures that metal flows properly in die cavity and that final products have excellent quality, but also reduces tooling cost. In the present work, it is proved in theory that the differential equation of electric potential (∇2ϕ=0) in the electrostatic field is similar to the differential equations of velocity potential function (∇2φ=0) and velocity stream function (∇2ψ=0) in velocity field during the material forming process, with all three represented in the form of the Laplace equation. Moreover, the material flow in the plastic stage and the energy in electrostatic field all meet the least-energy principle. Therefore, according to the similarity criteria, an equi-potential line (EPL) method is proposed for the design of the preform shape in material hot forging. Different voltages are applied to the billet shape and the final product shape to generate a proper electrostatic field. One optimal equi-potential line is selected among the innumerable equi-potential lines as the basic shape of the preform shape and is processed into the preform shape following a three-step procedure. The preform design by the EPL method is compared with that by the traditional industrial method. The results show that the proposed method for preform design is feasible and reliable for practical applications.

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35

Ma, Q., R. H. Tipping, G. Birnbaum, and C. Boulet. "Sum rules and the symmetry of the memory function in spectral line shape theories." Journal of Quantitative Spectroscopy and Radiative Transfer 59, no. 3-5 (1998): 259–71. http://dx.doi.org/10.1016/s0022-4073(97)00115-5.

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36

Sug, J. Y., S. G. Jo, and S. D. Choi. "The Direct Optical Transition Line Shape Function from the Equilibrium Density Projection Operator Technique." Progress of Theoretical Physics 102, no. 4 (1999): 789–801. http://dx.doi.org/10.1143/ptp.102.789.

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37

Mendonca, Joseph, Kimberly Strong, Debra Wunch, et al. "Using a speed-dependent Voigt line shape to retrieve O<sub>2</sub> from Total Carbon Column Observing Network solar spectra to improve measurements of XCO<sub>2</sub>." Atmospheric Measurement Techniques 12, no. 1 (2019): 35–50. http://dx.doi.org/10.5194/amt-12-35-2019.

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Abstract. High-resolution, laboratory, absorption spectra of the a1Δg←X3Σg- oxygen (O2) band measured using cavity ring-down spectroscopy were fitted using the Voigt and speed-dependent Voigt line shapes. We found that the speed-dependent Voigt line shape was better able to model the measured absorption coefficients than the Voigt line shape. We used these line shape models to calculate absorption coefficients to retrieve atmospheric total columns abundances of O2 from ground-based spectra from four Fourier transform spectrometers that are a part of the Total Carbon Column Observing Network (TCCON). Lower O2 total columns were retrieved with the speed-dependent Voigt line shape, and the difference between the total columns retrieved using the Voigt and speed-dependent Voigt line shapes increased as a function of solar zenith angle. Previous work has shown that carbon dioxide (CO2) total columns are better retrieved using a speed-dependent Voigt line shape with line mixing. The column-averaged dry-air mole fraction of CO2 (XCO2) was calculated using the ratio between the columns of CO2 and O2 retrieved (from the same spectra) with both line shapes from measurements taken over a 1-year period at the four sites. The inclusion of speed dependence in the O2 retrievals significantly reduces the air mass dependence of XCO2, and the bias between the TCCON measurements and calibrated integrated aircraft profile measurements was reduced from 1 % to 0.4 %. These results suggest that speed dependence should be included in the forward model when fitting near-infrared CO2 and O2 spectra to improve the accuracy of XCO2 measurements.

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38

Shah, Jagesh V. "Cells in tight spaces: the role of cell shape in cell function." Journal of Cell Biology 191, no. 2 (2010): 233–36. http://dx.doi.org/10.1083/jcb.201009048.

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In this issue, Pitaval et al. (2010. J. Cell Biol. doi:10.1083/jcb.201004003) demonstrate that cell geometry can regulate the elaboration of a primary cilium. Their findings and approaches are part of a historical line of inquiry investigating the role of cell shape in intracellular organization and cellular function.

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Giustolisi, L., F. Leone, M. Stift, M. Giarrusso, and J. Rosato. "Polarised line shape calculations for conditions encountered in stellar magnetic atmospheres." Journal of Physics: Conference Series 2439, no. 1 (2023): 012006. http://dx.doi.org/10.1088/1742-6596/2439/1/012006.

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Abstract We present new investigations into spectral line shapes under conditions typical for magnetic stellar atmospheres. Our method for simulating line profiles takes into account the coupled Zeeman and Stark effects. The calculations presented here will ultimately help to correctly model the Stokes parameters of peculiar stellar objects such as the Magnetic White Dwarfs (MWDs), retrieving their magnetic field geometries from spectropolarimetric observations. For the magnetic analysis of this class of stars, in general only Stokes I profiles as a function of rotational phase have been used in the past, in a very few cases, also Stokes V. The present improved simulations of the full Stokes parameters are expected to provide a powerful tool for the analysis of strong magnetic fields like those found in the MWDs.

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40

Li, Xuegang, Shuyou Wu, Shengli Su, Lan Ding, and Guoqing Jiang. "Method and Experiment Study of the Array Shape Calibration for Underwater Vertical Line Arrays." Journal of Physics: Conference Series 2458, no. 1 (2023): 012010. http://dx.doi.org/10.1088/1742-6596/2458/1/012010.

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Abstract Vertical line arrays have been widely used in underwater target location and noise measurement, and the attitude and shape of the vertical array have a significant influence on detection accuracy. The paper presents an array shape calibration method for underwater vertical acoustic array-based measurement systems. Firstly, a standard acoustic source was used to transmit underwater acoustic signals at a certain distance from the acoustic array, and the target location based on the received data of the acoustic array was estimated concerning distance and depth to obtain the two-dimensional ambiguity function of the depth and distance of the array. Then, the ambiguity function was used to calculate the center depth and the inclination angle of the vertical acoustic array and to further obtain the shape and location information of the acoustic array. Finally, a lake experiment study was carried out. The results showed that the calibrated array shape was in good agreement with the actual location, and the sound source location estimated by using the calibrated array shape was consistent with the actual sound source location, thereby effectively reducing the impact on the measurement accuracy due to the inclination of the measurement system under the influence of water current.

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Khan, Ayan, Saurabh Basu, and B. Tanatar. "Investigating dirty crossover through fidelity susceptibility and density of states." International Journal of Modern Physics B 28, no. 14 (2014): 1450083. http://dx.doi.org/10.1142/s0217979214500830.

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We investigate the BCS–BEC crossover in an ultracold atomic gas in the presence of disorder. The disorder is incorporated in the mean-field formalism through Gaussian fluctuations. We observe evolution to an asymmetric line-shape of fidelity susceptibility (FS) as a function of interaction coupling with increasing disorder strength which may point to an impending quantum phase transition (QPT). The asymmetric line-shape is further analyzed using the statistical tools of skewness and kurtosis. We extend our analysis to density of states (DOS) for a better understanding of the crossover in the disordered environment.

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Stephens, Peter W. "Phenomenological model of anisotropic peak broadening in powder diffraction." Journal of Applied Crystallography 32, no. 2 (1999): 281–89. http://dx.doi.org/10.1107/s0021889898006001.

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Anisotropic line-shape broadening (peak width which is not a smooth function ofd-spacing) is frequently observed in powder diffraction patterns, and can be a source of considerable difficulty for whole-pattern fitting or Rietveld analysis. A model of the multi-dimensional distribution of lattice metrics within a powder sample is developed, leading naturally to a few parameters which can be varied to achieve optimal line-shape fits. Conditions on these parameters are derived for all crystal systems, and the method is illustrated with two examples: sodiump-hydroxybenzoate and rubidium fulleride.

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Masson, O., E. Dooryhée, and A. N. Fitch. "Instrument line-profile synthesis in high-resolution synchrotron powder diffraction." Journal of Applied Crystallography 36, no. 2 (2003): 286–94. http://dx.doi.org/10.1107/s0021889803001031.

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An accurate method for synthesizing the instrumental line profile of high-resolution synchrotron powder diffraction instruments is presented. It is shown that the instrumental profile can be modelled by the convolution of four physical aberration functions: the equatorial intensity distribution, the monochromator and analyser transfer functions, and the axial divergence aberration function. Moreover, each equatorial aberration is related to an angle-independent function by a scale transform factor. The principles of the instrument line-profile calculation are general. They are applied in the case of the angle-dispersive powder X-ray diffraction beamline BM16 at the ESRF. The effects of each optical element on the overall instrument profile are discussed and the importance of the quality of the different optical elements of the instrument is emphasized. Finally, it is shown that the high resolution combined with the precise modelling of the instrument profile shape give access to a particle size as large as 3 µm.

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SHCHERBAN, Volodymyr, Valentin ISHCHENKO, Oksana KOLISKO, Genadij MELNIK, and Yuryj SHCHERBAN. "STRUCTURE OF A COMPUTER PROGRAM FOR DETERMINING THE OPTIMAL PATH DIRECTED GRAPH USING DIJKSTRA’S ALGORITHM." Herald of Khmelnytskyi National University. Technical sciences 315, no. 6(1) (2022): 270–73. http://dx.doi.org/10.31891/2307-5732-2022-315-6-270-273.

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Ensuring the minimum tension during thread processing on technological equipment allows to reduce equipment downtime due to the elimination or significant reduction of thread breaks. Minimization of tension is ensured by optimization of the shape of the thread filling line, in which the total angle of coverage of the guides will be minimal. This problem is solved by using Dijkstra’s algorithm in finding the optimal path of a directed graph. The computer program for implementing this algorithm allows you to optimize the form of filling the thread on the technological equipment. The development of application packages of computer programs allows to reduce the time for the design of technological processes in the light and textile industry as much as possible. This is due to the modernization of the thread filling line on the technological equipment, which allows to minimize thread tension in the working area. Minimization of tension is ensured by optimization of the shape of the thread filling line, in which the total angle of coverage of the guides will be minimal. This problem is solved by using Dijkstra’s algorithm in finding the optimal path of a directed graph. Construction of the optimal path of the directed graph will allow to obtain the minimum tension in the working area. Constructive structural elements in the form of guides, elements of tensioning devices, break control devices, which have a cylindrical, elliptical shape, and discrete segments of a straight line act as obstacles in the path of the thread. Straight line segments can have an inclination relative to the vertical axis. Taking into account the large number of structural elements of the thread feeding system on light and textile industry machines and their location, there is a need to develop a special computer program for determining the optimal shape of the thread feeding line using the Dijkstra algorithm when searching for the optimal path of a directed graph. The objective function in the problem is the minimum necessary tension, which is the minimum sum of the angles covered by the thread of guide surfaces that have a cylindrical, elliptical shape, discrete segments of a straight line. The use of a computer program allows you to determine tensions and changes in relative tension in the filling zones of light and textile industry machines, which allows you to optimize the shape of the thread supply line even at the stage of designing the technological process. The use of algorithms for computer programs for finding the optimal path of an undirected graph, for cylindrical, elliptical guides, discrete segments of a straight line, allows you to determine the influence of coverage angles on the target tension function. Determining the effect of coverage angles, for cylindrical, elliptical guides, discrete segments of a straight line, on the objective function during the computer determination of the optimal path for an oriented graph is an important component of the optimization of thread tension in the working area of machines of the light and textile industry, the formation of knitted and textile products.

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Hatano, Naoya, Masahiro Ikeda, Isao Ishikawa, and Yoshihiro Sawano. "Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit." Journal of Function Spaces 2024 (January 18, 2024): 1–6. http://dx.doi.org/10.1155/2024/3262798.

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This paper concerns the universality of the two-layer neural network with the k-rectified linear unit activation function with k=1,2,… with a suitable norm without any restriction on the shape of the domain in the real line. This type of result is called global universality, which extends the previous result for k=1 by the present authors. This paper covers k-sigmoidal functions as an application of the fundamental result on k-rectified linear unit functions.

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46

Mendelevich, L. V., and Yu A. Koksharov. "Analytical Formula for the Relation between the Experimental and Theoretical Parameters of the Tsallis Spectral Line." Радиотехника и электроника 68, no. 5 (2023): 424–31. http://dx.doi.org/10.31857/s0033849423050145.

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An exact analytical formula is obtained that relates the experimental and theoretical parameters of the spectral line described by the Tsallis function, which includes the Gaussian, Lorentzian, line shapes intermediate between them, and super-Lorentzian as special cases. The procedure for the numerical calculation of the theoretical parameters of the line shape is studied by the example of electron spin resonance spectra. The effect of complicating experimental factors, including the noise and the analog signal digitization discreteness, on the accuracy of determining the theoretical Tsallian parameters is examined. It is shown that the proposed method for determining the theoretical parameters of the spectral line is not inferior in accuracy to the method for minimizing the root-mean-square error functional. It is predicted that the new approach can be used as an alternative to the available spectral line shape analysis techniques.

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García, Omaira E., Esther Sanromá, Frank Hase, et al. "Impact of instrumental line shape characterization on ozone monitoring by FTIR spectrometry." Atmospheric Measurement Techniques 15, no. 15 (2022): 4547–67. http://dx.doi.org/10.5194/amt-15-4547-2022.

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Abstract. Retrieving high-precision concentrations of atmospheric trace gases from FTIR (Fourier transform infrared) spectrometry requires a precise knowledge of the instrumental performance. In this context, this paper examines the impact on the ozone (O3) retrievals of several approaches used to characterize the instrumental line shape (ILS) function of ground-based FTIR spectrometers within NDACC (Network for the Detection of Atmospheric Composition Change). The analysis has been carried out at the subtropical Izaña Observatory (IZO, Spain) by using the 20-year time series of the high-resolution FTIR solar absorption spectra acquired between 1999 and 2018. The theoretical quality assessment and the comparison to independent O3 observations available at IZO (Brewer O3 total columns and electrochemical concentration cell, ECC, sondes) reveal consistent findings. The inclusion of a simultaneous retrieval of the ILS parameters in the O3 retrieval strategy allows, on the one hand, a rough instrumental characterization to be obtained and, on the other hand, the precision of the FTIR O3 products to be slightly improved. The improvement is of special relevance above the lower stratosphere, where the cross-interference between the O3 vertical distribution and the instrumental performance is more significant. However, it has been found that the simultaneous ILS retrieval leads to a misinterpretation of the O3 variations on daily and seasonal scales. Therefore, in order to ensure the independence of the O3 retrievals and the instrumental response, the optimal approach to deal with the FTIR instrumental characterization is found to be the continuous monitoring of the ILS function by means of independent observations, such as gas cell measurements.

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48

Abdul Karim, Samsul Ariffin, and Azizan Saaban. "Shape Preserving Interpolation Using Rational Cubic Ball Function and Its Application in Image Interpolation." Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/7459218.

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New rational cubic Ball interpolation with one parameter is proposed for shape preserving interpolation such as positivity, monotonicity, and convexity preservations and constrained data lie on the same side of the given straight line. To produce shape preserving interpolant, the data dependent sufficient condition is derived on the parameter. The rational bicubic Ball function is constructed by using tensor product approach and it will be used for application in image upscaling. Numerical and graphical results are presented by using Mathematica and MATLAB including comparison with some existing scheme.

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Leonardi, Alberto, Matteo Leoni, and Paolo Scardi. "Directional pair distribution function for diffraction line profile analysis of atomistic models." Journal of Applied Crystallography 46, no. 1 (2013): 63–75. http://dx.doi.org/10.1107/s0021889812050601.

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The concept of the directional pair distribution function is proposed to describe line broadening effects in powder patterns calculated from atomistic models of nano-polycrystalline microstructures. The approach provides at the same time a description of the size effect for domains of any shape and a detailed explanation of the strain effect caused by the local atomic displacement. The latter is discussed in terms of different strain types, also accounting for strain field anisotropy and grain boundary effects. The results can in addition be directly read in terms of traditional line profile analysis, such as that based on the Warren–Averbach method.

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ALTİNİSİK, Yasin, and Emel ÇANKAYA. "Exponentiated generalized Ramos-Louzada distribution with properties and applications." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 73, no. 1 (2023): 76–103. http://dx.doi.org/10.31801/cfsuasmas.1147449.

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In this paper, we propose a new generalization of Ramos-Louzada (RL) distribution based on two additional shape parameters. Along with the genesis of its distributional form, the derivation of cumulative density function (cdf), survival and hazard rate functions, the quantile function (qf), moments, moment generating function (mgf), Shannon and Renyi entropies, order statistics and a linear representation of the proposed distribution are inspected. Several estimation methods of the model parameters are discussed throughout two comprehensive simulation studies conducted to compare its performance against some lifetime distributions. Application of a real dataset is presented to illustrate the potentiality of this distribution in line with the simulation studies.

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