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Journal articles on the topic 'Scalar-On-Function'

Author: Grafiati

Published: 18 May 2024

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1

Reiss, Philip T., Jeff Goldsmith, Han Lin Shang, and R. Todd Ogden. "Methods for Scalar-on-Function Regression." International Statistical Review 85, no. 2 (February 23, 2016): 228–49. http://dx.doi.org/10.1111/insr.12163.

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2

Fan, Zhaohu, and Matthew Reimherr. "High-dimensional adaptive function-on-scalar regression." Econometrics and Statistics 1 (January 2017): 167–83. http://dx.doi.org/10.1016/j.ecosta.2016.08.001.

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3

Chen, Yakuan, Jeff Goldsmith, and R. Todd Ogden. "Variable selection in function-on-scalar regression." Stat 5, no. 1 (2016): 88–101. http://dx.doi.org/10.1002/sta4.106.

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4

Guo, X., J. Hua, and H. Qin. "Scalar-function-driven editing on point set surfaces." IEEE Computer Graphics and Applications 24, no. 4 (July 2004): 43–52. http://dx.doi.org/10.1109/mcg.2004.16.

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5

Bauer, Alexander, Fabian Scheipl, Helmut Küchenhoff, and Alice-Agnes Gabriel. "An introduction to semiparametric function-on-scalar regression." Statistical Modelling 18, no. 3-4 (January 18, 2018): 346–64. http://dx.doi.org/10.1177/1471082x17748034.

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Abstract: Function-on-scalar regression models feature a function over some domain as the response while the regressors are scalars. Collections of time series as well as 2D or 3D images can be considered as functional responses. We provide a hands-on introduction for a flexible semiparametric approach for function-on-scalar regression, using spatially referenced time series of ground velocity measurements from large-scale simulated earthquake data as a running example. We discuss important practical considerations and challenges in the modelling process and outline best practices. The outline of our approach is complemented by comprehensive R code, freely available in the online appendix. This text is aimed at analysts with a working knowledge of generalized regression models and penalized splines.

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6

Wang, Xu, Jiaqing Kou, and Weiwei Zhang. "Unsteady aerodynamic modeling based on fuzzy scalar radial basis function neural networks." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 14 (March 19, 2019): 5107–21. http://dx.doi.org/10.1177/0954410019836906.

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In this paper, a fuzzy scalar radial basis function neural network is proposed, in order to overcome the limitation of traditional aerodynamic reduced-order models having difficulty in adapting to input variables with different orders of magnitude. This network is a combination of fuzzy rules and standard radial basis function neural network, and all the basis functions are defined as scalar basis functions. The use of scalar basis function will increase the flexibility of the model, thus enhancing the generalization capability on complex dynamic behaviors. Particle swarm optimization algorithm is used to find the optimal width of the scalar basis function. The constructed reduced-order models are used to model the unsteady aerodynamics of an airfoil in transonic flow. Results indicate that the proposed reduced-order models can capture the dynamic characteristics of lift coefficients at different reduced frequencies and amplitudes very accurately. Compared with the conventional reduced-order model based on recursive radial basis function neural network, the fuzzy scalar radial basis function neural network shows better generalization capability for different test cases with multiple normalization methods.

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7

Reiss, Philip T., David L. Miller, Pei-Shien Wu, and Wen-Yu Hua. "Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates." Journal of Computational and Graphical Statistics 26, no. 3 (April 11, 2017): 569–78. http://dx.doi.org/10.1080/10618600.2016.1217227.

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8

Goldsmith, Jeff, and Fabian Scheipl. "Estimator selection and combination in scalar-on-function regression." Computational Statistics & Data Analysis 70 (February 2014): 362–72. http://dx.doi.org/10.1016/j.csda.2013.10.009.

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9

Ciarleglio, Adam, and R. Todd Ogden. "Wavelet-based scalar-on-function finite mixture regression models." Computational Statistics & Data Analysis 93 (January 2016): 86–96. http://dx.doi.org/10.1016/j.csda.2014.11.017.

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10

Yang, Hojin, Veerabhadran Baladandayuthapani, Arvind U. K. Rao, and Jeffrey S. Morris. "Quantile Function on Scalar Regression Analysis for Distributional Data." Journal of the American Statistical Association 115, no. 529 (June 21, 2019): 90–106. http://dx.doi.org/10.1080/01621459.2019.1609969.

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11

Omer, Omer Abdalrhman, and Muhammad Zainul Abidin. "Boundedness of the Vector-Valued Intrinsic Square Functions on Variable Exponents Herz Spaces." Mathematics 10, no. 7 (April 3, 2022): 1168. http://dx.doi.org/10.3390/math10071168.

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In this article, the authors study the boundedness of the vector-valued inequality for the intrinsic square function and the boundedness of the scalar-valued intrinsic square function on variable exponents Herz spaces K˙ρ(·)α,q(·)(Rn). In addition, the boundedness of commutators generated by the scalar-valued intrinsic square function and BMO class is also studied on K˙ρ(·)α,q(·)(Rn).

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12

Mirshani, Ardalan, and Matthew Reimherr. "Adaptive function-on-scalar regression with a smoothing elastic net." Journal of Multivariate Analysis 185 (September 2021): 104765. http://dx.doi.org/10.1016/j.jmva.2021.104765.

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13

Cai, Xiong, Liugen Xue, and Jiguo Cao. "Robust estimation and variable selection for function‐on‐scalar regression." Canadian Journal of Statistics 50, no. 1 (September 29, 2021): 162–79. http://dx.doi.org/10.1002/cjs.11661.

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14

Goldsmith, Jeff, Vadim Zipunnikov, and Jennifer Schrack. "Generalized multilevel function-on-scalar regression and principal component analysis." Biometrics 71, no. 2 (January 25, 2015): 344–53. http://dx.doi.org/10.1111/biom.12278.

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15

Barber, Rina Foygel, Matthew Reimherr, and Thomas Schill. "The function-on-scalar LASSO with applications to longitudinal GWAS." Electronic Journal of Statistics 11, no. 1 (2017): 1351–89. http://dx.doi.org/10.1214/17-ejs1260.

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16

Cheng, Yafeng, Jian Qing Shi, and Janet Eyre. "Nonlinear mixed-effects scalar-on-function models and variable selection." Statistics and Computing 30, no. 1 (April 9, 2019): 129–40. http://dx.doi.org/10.1007/s11222-019-09871-3.

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17

Tekbudak, Merve Yasemin, Marcela Alfaro-Córdoba, Arnab Maity, and Ana-Maria Staicu. "A comparison of testing methods in scalar-on-function regression." AStA Advances in Statistical Analysis 103, no. 3 (October 17, 2018): 411–36. http://dx.doi.org/10.1007/s10182-018-00337-x.

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18

Chikr Elmezouar, Zouaoui, Fatimah Alshahrani, Ibrahim M. Almanjahie, Zoulikha Kaid, Ali Laksaci, and Mustapha Rachdi. "Scalar-on-Function Relative Error Regression for Weak Dependent Case." Axioms 12, no. 7 (June 21, 2023): 613. http://dx.doi.org/10.3390/axioms12070613.

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Analyzing the co-variability between the Hilbert regressor and the scalar output variable is crucial in functional statistics. In this contribution, the kernel smoothing of the Relative Error Regression (RE-regression) is used to resolve this problem. Precisely, we use the relative square error to establish an estimator of the Hilbertian regression. As asymptotic results, the Hilbertian observations are assumed to be quasi-associated, and we demonstrate the almost complete consistency of the constructed estimator. The feasibility of this Hilbertian model as a predictor in functional time series data is discussed. Moreover, we give some practical ideas for selecting the smoothing parameter based on the bootstrap procedure. Finally, an empirical investigation is performed to examine the behavior of the RE-regression estimation and its superiority in practice.

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19

Erdas, Andrea, and Kevin P. Seltzer. "Finite temperature Casimir effect for massive scalars in a magnetic field." International Journal of Modern Physics A 29, no. 17 (June 26, 2014): 1450091. http://dx.doi.org/10.1142/s0217751x14500912.

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The finite temperature Casimir effect for a charged, massive scalar field confined between very large, perfectly conducting parallel plates is studied using the zeta function regularization technique. The scalar field satisfies Dirichlet boundary conditions at the plates and a magnetic field perpendicular to the plates is present. Four equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature, scalar field mass and plate distance. The zeta function is used to calculate the Helmholtz free energy of the scalar field and the Casimir pressure on the plates, in the case of high temperature, small plate distance, strong magnetic field and large scalar mass. In all cases, simple analytic expressions of the zeta function, free energy and pressure are obtained, which are very accurate and valid for practically all values of temperature, plate distance, magnetic field and mass.

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20

Sabbar, Ali Nadhim, and G. N. Shikin. "The Effect of Cosmic Vacuum on the Properties of Scalar Field." International Letters of Chemistry, Physics and Astronomy 61 (November 2015): 58–62. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.61.58.

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The thesis explains the effect of cosmic vacuum of gravitational field on properties of scalar field equation. In the space-time plane, the scalar field equation has periodic solution φx,y,z,t=Acos (kx±ωt). Consideration the cosmic vacuum of gravitational field (using De Sitter metric in its synchronization time) the equation of scalar field will have accurate solution in form of Beseel function. By using the asymptotic representation, the periodic solution (t→±∞) will vanish. The scalar field equation when t→+∞ will decrease regularly, and when t→-∞ it will increasing fluctuate.

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21

Sabbar, Ali Nadhim, and G. N. Shikin. "The Effect of Cosmic Vacuum on the Properties of Scalar Field." International Letters of Chemistry, Physics and Astronomy 61 (November 3, 2015): 58–62. http://dx.doi.org/10.56431/p-l2l41c.

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The thesis explains the effect of cosmic vacuum of gravitational field on properties of scalar field equation. In the space-time plane, the scalar field equation has periodic solution φx,y,z,t=Acos (kx±ωt). Consideration the cosmic vacuum of gravitational field (using De Sitter metric in its synchronization time) the equation of scalar field will have accurate solution in form of Beseel function. By using the asymptotic representation, the periodic solution (t→±∞) will vanish. The scalar field equation when t→+∞ will decrease regularly, and when t→-∞ it will increasing fluctuate.

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22

FERCHICHI, M., and S. TAVOULARIS. "Scalar probability density function and fine structure in uniformly sheared turbulence." Journal of Fluid Mechanics 461 (June 25, 2002): 155–82. http://dx.doi.org/10.1017/s0022112002008285.

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This study is an experimental investigation of the probability density function (p.d.f.) and the fine structure of temperature fluctuations in uniformly sheared turbulence with a passively introduced uniform mean temperature gradient. The shear parameter was relatively large, resulting in vigorous turbulence production and a total mean strain up to 23. The turbulence Reynolds number was up to 253. The scalar fluctuations grew in a self-similar fashion and at the same exponential rate as the turbulence stresses, in conformity with predictions based on an analytical solution of the scalar variance equation. Analytical considerations as well as measurements demonstrate that the scalar p.d.f. is essentially Gaussian and that the scalar–velocity joint p.d.f. is essentially jointly Gaussian, with the conditional expectations of the velocity fluctuations linearly dependent on the scalar value. Joint statistics of the scalar and its dissipation rate indicate a statistical independence of the two parameters. The fine structure of the scalar was invoked from statistics of derivatives and differences of the scalar, in both the streamwise and transverse directions. Probability density functions of scalar derivatives and differences in the dissipative and the inertial ranges were strongly non-Gaussian and skewed, displaying flared, asymmetric tails. All measurements point to a highly intermittent scalar fine structure, even more intermittent than the fine structure of the turbulent velocity.

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23

Mehrotra, Suchit, and Arnab Maity. "Simultaneous variable selection, clustering, and smoothing in function‐on‐scalar regression." Canadian Journal of Statistics 50, no. 1 (November 22, 2021): 180–99. http://dx.doi.org/10.1002/cjs.11668.

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24

Diehl, Stefan. "On Scalar Conservation Laws with Point Source and Discontinuous Flux Function." SIAM Journal on Mathematical Analysis 26, no. 6 (November 1995): 1425–51. http://dx.doi.org/10.1137/s0036141093242533.

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25

Reiss, Philip T., Maarten Mennes, Eva Petkova, Lei Huang, Matthew J. Hoptman, Bharat B. Biswal, Stanley J. Colcombe, Xi-Nian Zuo, and Michael P. Milham. "Extracting information from functional connectivity maps via function-on-scalar regression." NeuroImage 56, no. 1 (May 2011): 140–48. http://dx.doi.org/10.1016/j.neuroimage.2011.01.071.

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26

McLean, Mathew W., Giles Hooker, and David Ruppert. "Restricted likelihood ratio tests for linearity in scalar-on-function regression." Statistics and Computing 25, no. 5 (April 22, 2014): 997–1008. http://dx.doi.org/10.1007/s11222-014-9473-1.

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27

Zhou, Jing-Zhi, Xukun Zhang, Qing-Hua Zhu, and Zhe Chang. "The third order scalar induced gravitational waves." Journal of Cosmology and Astroparticle Physics 2022, no. 05 (May 1, 2022): 013. http://dx.doi.org/10.1088/1475-7516/2022/05/013.

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Abstract Since the gravitational waves were detected by LIGO and Virgo, it has been promising that lots of information about the primordial Universe could be learned by further observations on stochastic gravitational waves background. The studies on gravitational waves induced by primordial curvature perturbations are of great interest. The aim of this paper is to investigate the third order induced gravitational waves. Based on the theory of cosmological perturbations, the first order scalar induces the second order scalar, vector and tensor perturbations. At the next iteration, the first order scalar, the second order scalar, vector and tensor perturbations all induce the third order tensor perturbations. We present the two point function 〈h λ,(3) h λ',(3)〉 and corresponding energy density spectrum of the third order gravitational waves for a monochromatic primordial power spectrum. The shape of the energy density spectrum of the third order gravitational waves is different from that of the second order scalar induced gravitational waves. And it is found that the third order gravitational waves sourced by the second order scalar perturbations dominate the two point function 〈h λ,(3) h λ',(3)〉 and corresponding energy density spectrum of third order scalar induced gravitational waves.

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28

KRUGLOV, S. I. "ON EXPONENTIAL MODIFIED GRAVITY." International Journal of Modern Physics A 28, no. 24 (September 25, 2013): 1350119. http://dx.doi.org/10.1142/s0217751x13501194.

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A modified theory of gravity with the function F(R) = R exp (αR) instead of Ricci scalar R in the Einstein–Hilbert action is considered and analyzed. The action of the model is converted into Einstein–Hilbert action at small value of the parameter α. From local tests we obtain a bound on the parameter α ≤ 10-6 cm 2. The Jordan and Einstein frames are investigated and the potential of the scalar field in Einstein's frame is found. The mass of a scalar degree of freedom as a function of curvature is obtained. The static solutions of the model are found corresponding to the Schwarzschild–de Sitter space. We show that the de Sitter space is unstable but a solution with zero curvature is stable. The cosmological parameters of the model are calculated. It was demonstrated that the model passes the matter stability test.

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29

Moazzen Sorkhi, Masoumeh, and Esmaeil Mazani. "Fermion localization on branes with non-standard kinetic terms." Modern Physics Letters A 33, no. 40 (December 28, 2018): 1850235. http://dx.doi.org/10.1142/s0217732318502358.

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In this paper, by using the Yukawa coupling mechanism, we consider the fermion localization in two types of braneworld models driven by real scalar fields with non-standard dynamics. Because of the existing freedom in the form of the Yukawa coupling, we consider two coupling forms between the background scalar field and spinors where one is arising from the geometry shape of the warp factor and the other is a function of the background scalar field containing a derivative scalar-fermion coupling. With two coupling functions, it is shown that the massless zero mode of fermion fields is localized on both branes with generalized dynamic depending on the values of the coupling constants. However, there is no localized mode when the Yukawa coupling only contains a derivative term of the background scalar field. Furthermore, effects of the parameters of the models on the zero mode and fermion effective potential are addressed.

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30

Fomin, Igor, and Sergey Chervon. "Exact and Slow-Roll Solutions for Exponential Power-Law Inflation Connected with Modified Gravity and Observational Constraints." Universe 6, no. 11 (October 29, 2020): 199. http://dx.doi.org/10.3390/universe6110199.

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We investigate the ability of the exponential power-law inflation to be a phenomenologically correct model of the early universe. We study General Relativity (GR) scalar cosmology equations in Ivanov–Salopek–Bond (or Hamilton–Jacobi like) representation where the Hubble parameter H is the function of a scalar field ϕ. Such approach admits calculation of the potential for given H(ϕ) and consequently reconstruction of f(R) gravity in parametric form. By this manner the Starobinsky potential and non-minimal Higgs potential (and consequently the corresponding f(R) gravity) were reconstructed using constraints on the model’s parameters. We also consider methods for generalising the obtained solutions to the case of chiral cosmological models and scalar-tensor gravity. Models based on the quadratic relationship between the Hubble parameter and the function of the non-minimal interaction of the scalar field and curvature are also considered. Comparison to observation (PLANCK 2018) data shows that all models under consideration give correct values for the scalar spectral index and tensor-to-scalar ratio under a wide range of exponential-power-law model’s parameters.

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31

Blair, D. E., and A. J. Ledger. "Critical associated metrics on contact manifolds. II." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 3 (December 1986): 404–10. http://dx.doi.org/10.1017/s1446788700033863.

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AbstractThe study of the integral of the scalar curvature, ∫MRdVg, as a function on the set of all Riemannian metrics of the same total volume on a compact manifold is now classical, and the critical points are the Einstein metrics. On a compact contact manifold we consider this and ∫M (R − R* − 4n2) dv, with R* the *-scalar curvature, as functions on the set of metrics associated to the contact structure. For these integrals the critical point conditions then become certain commutativity conditions on the Ricci operator and the fundamental collineation of the contact metric structure. In particular, Sasakian metrics, when they exist, are maxima for the second function.

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32

Dalianis, Ioannis, Alex Kehagias, Ioannis Taskas, and George Tringas. "On the Vacuum Structure of the N=4 Conformal Supergravity." Universe 7, no. 11 (October 28, 2021): 409. http://dx.doi.org/10.3390/universe7110409.

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We consider N=4 conformal supergravity with an arbitrary holomorphic function of the complex scalar S which parametrizes the SU(1,1)/U(1) coset. Assuming non-vanishings vevs for S and the scalars in a symmetric matrix Eij of the 10¯ of SU(4) R-symmetry group, we determine the vacuum structure of the theory. We find that the possible vacua are classified by the number of zero eigenvalues of the scalar matrix and the spacetime is either Minkowski, de Sitter, or anti-de Sitter. We determine the spectrum of the scalar fluctuations and we find that it contains tachyonic states which, however, can be removed by appropriate choice of the unspecified at the supergravity level holomorphic function. Finally, we also establish that S-supersymmetry is always broken whereas Q-supersymmetry exists only on flat Minkowski spacetime.

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33

LEUNG, MAN CHUN. "CONSTRUCTION OF BLOW-UP SEQUENCES FOR THE PRESCRIBED SCALAR CURVATURE EQUATION ON Sn I: UNIFORM CANCELLATION." Communications in Contemporary Mathematics 14, no. 02 (April 2012): 1250008. http://dx.doi.org/10.1142/s0219199712500083.

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For n ≥ 6, using the Lyapunov–Schmidt reduction method, we describe how to construct (scalar curvature) functions on Sn, so that each of them enables the conformal scalar curvature equation to have an infinite number of positive solutions, which form a blow-up sequence. The prescribed scalar curvature function is shown to have Cn - 1,β smoothness. We present the argument in two parts. In this first part, we discuss the uniform cancellation property in the Lyapunov–Schmidt reduction method for the scalar curvature equation. We also explore relation between the Kazdan–Warner condition and the first-order derivatives of the reduced functional, and symmetry in the second-order derivatives of the reduced functional.

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34

Lepore, J., and L. Mydlarski. "Finite-Péclet-number effects on the scaling exponents of high-order passive scalar structure functions." Journal of Fluid Mechanics 713 (October 26, 2012): 453–81. http://dx.doi.org/10.1017/jfm.2012.469.

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AbstractThe effect of scalar-field (temperature) boundary conditions on the inertial-convective-range scaling exponents of the high-order passive scalar structure functions is studied in the turbulent, heated wake downstream of a circular cylinder. The temperature field is generated two ways: using (i) a heating element embedded within the cylinder that generates the hydrodynamic wake (thus creating a heated cylinder) and (ii) a mandoline (an array of fine, heated wires) installed downstream of the cylinder. The hydrodynamic field is independent of the scalar-field boundary conditions/injection methods, and the same in both flows. Using the two heat injection mechanisms outlined above, the inertial-convective-range scaling exponents of the high-order passive scalar structure functions were measured. It is observed that the different scalar-field boundary conditions yield significantly different scaling exponents (with the magnitude of the difference increasing with structure function order). Moreover, the exponents obtained from the mandoline experiment are smaller than the analogous exponents from the heated cylinder experiment (both of which exhibit a significant departure from the Kolmogorov prediction). Since the observed deviation from the Kolmogorov $n/ 3$ prediction arises due to the effects of internal intermittency, the typical interpretation of this result would be that the scalar field downstream of the mandoline is more internally intermittent than that generated by the heated cylinder. However, additional measures of internal intermittency (namely the inertial-convective-range scaling exponents of the mixed, sixth-order, velocity–temperature structure functions and the non-centred autocorrelations of the dissipation rate of scalar variance) suggest that both scalar fields possess similar levels of internal intermittency – a distinctly different conclusion. Examination of the normalized high-order moments reveals that the smaller scaling exponents (of the high-order passive scalar structure functions) obtained for the mandoline experiment arise due to the smaller thermal integral length scale of the flow (i.e. the narrower inertial-convective subrange) and are not solely the result of a more intermittent scalar field. The difference in the passive scalar structure function scaling exponents can therefore be interpreted as an artifact of the different, finite Péclet numbers of the flows under consideration – an effect that is notably less prominent in the other measures of internal intermittency.

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35

Puggaard-Rode, Rasmus. "Analyzing time-varying spectral characteristics of speech with function-on-scalar regression." Journal of Phonetics 95 (November 2022): 101191. http://dx.doi.org/10.1016/j.wocn.2022.101191.

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36

Antonia, R. A., and P. Orlandi. "Dependence of the second-order scalar structure function on the Schmidt number." Physics of Fluids 14, no. 4 (April 2002): 1552–54. http://dx.doi.org/10.1063/1.1458010.

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37

Parodi, Alice, and Matthew Reimherr. "Simultaneous variable selection and smoothing for high-dimensional function-on-scalar regression." Electronic Journal of Statistics 12, no. 2 (2018): 4602–39. http://dx.doi.org/10.1214/18-ejs1509.

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38

Liu, Yusha, Meng Li, and Jeffrey S. Morris. "Function-on-scalar quantile regression with application to mass spectrometry proteomics data." Annals of Applied Statistics 14, no. 2 (June 2020): 521–41. http://dx.doi.org/10.1214/19-aoas1319.

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39

Kwon, Young-Sam. "Asymptotic Limit to Shocks for Scalar Balance Laws Using Relative Entropy." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/690801.

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40

Horndeski, Gregory W. "The hidden scalar Lagrangians within Horndeski theory." International Journal of Modern Physics D 29, no. 14 (September 9, 2020): 2043004. http://dx.doi.org/10.1142/s021827182043004x.

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In this paper, I show that there exists a new way to obtain scalar–tensor field theories by combining a special scalar field on the cotangent bundle with a scalar field on spacetime. These two scalar fields act as a generating function for the metric tensor. When using these two scalar fields in the Horndeski Lagrangians, we discover, while seeking Friedmann–Lemaître–Robertson–Walker-type cosmological solutions, that hidden in the Horndeski Lagrangians are nondegenerate second-order scalar Lagrangians. In accordance with Ostrogradsky’s work, these hidden scalar Lagrangians lead to multiple vacuum solutions, and thereby predict the existence of the multiverse. The multiverse is comprised of numerous different types of individual universes. For example, some begin explosively, and then coast along exponentially forever at an accelerated rate, while others begin in that manner, and then stop expanding and contract.

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41

BUCATARU, IOAN, and ZOLTÁN MUZSNAY. "FINSLER METRIZABLE ISOTROPIC SPRAYS AND HILBERT’S FOURTH PROBLEM." Journal of the Australian Mathematical Society 97, no. 1 (May 20, 2014): 27–47. http://dx.doi.org/10.1017/s1446788714000111.

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AbstractIt is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In our main result we show that the isotropy condition, together with three other conditions on the Jacobi endomorphism, characterize sprays that are metrizable by Finsler functions of scalar flag curvature. We call these conditions the scalar flag curvature (SFC) test. The proof of the main result provides an algorithm to construct the Finsler function of scalar flag curvature, in the case when a given spray is metrizable. Hilbert’s fourth problem asks to determine the Finsler functions with rectilinear geodesics. A Finsler function that is a solution to Hilbert’s fourth problem is necessarily of constant or scalar flag curvature. Therefore, we can use the constant flag curvature (CFC) test, which we developed in our previous paper, Bucataru and Muzsnay [‘Sprays metrizable by Finsler functions of constant flag curvature’, Differential Geom. Appl.31 (3)(2013), 405–415] as well as the SFC test to decide whether or not the projective deformations of a flat spray, which are isotropic, are metrizable by Finsler functions of constant or scalar flag curvature. We show how to use the algorithms provided by the CFC and SFC tests to construct solutions to Hilbert’s fourth problem.

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42

Montefalcone, Gabriele, Vikas Aragam, Luca Visinelli, and Katherine Freese. "WarmSPy: a numerical study of cosmological perturbations in warm inflation." Journal of Cosmology and Astroparticle Physics 2024, no. 01 (January 1, 2024): 032. http://dx.doi.org/10.1088/1475-7516/2024/01/032.

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Abstract We present WarmSPy, a numerical code in Python designed to solve for the perturbations' equations in warm inflation models and compute the corresponding scalar power spectrum at CMB horizon crossing. In models of warm inflation, a radiation bath of temperature T during inflation induces a dissipation (friction) rate of strength Q ∝ Tc /ϕm in the equation of motion for the inflaton field ϕ. While for a temperature-independent dissipation rate (c = 0) an analytic expression for the scalar power spectrum exists, in the case of a non-zero value for c the set of equations can only be solved numerically. For c > 0 (c < 0), the coupling between the perturbations in the inflaton field and radiation induces a growing (decaying) mode in the scalar perturbations, generally parameterized by a multiplicative function G(Q) which we refer to as the scalar dissipation function. Using WarmSPy, we provide an analytic fit for G(Q) for the cases of c = {3,1,-1}, corresponding to three cases that have been realized in physical models. Compared to previous literature results, our fits are more robust and valid over a broader range of dissipation strengths Q ∈ [10-7,104]. Additionally, for the first time, we numerically assess the stability of the scalar dissipation function against various model parameters, inflationary histories as well as the effects of metric perturbations. As a whole, the results do not depend appreciably on most of the parameters in the analysis, except for the dissipation index c, providing evidence for the universal behaviour of the scalar dissipation function G(Q).

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Ceno, Stela. "Some properties of the superior and inferior semi inner product function associated to the 2-norm." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 5 (June 30, 2016): 6254–60. http://dx.doi.org/10.24297/jam.v12i5.322.

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Special properties that the scalar product enjoys and its close link with the norm function have raised the interest of researchers from a very long period of time. S.S. Dragomir presents concrete generalizations of the scalar product functions in a normed space and deals with the interesting properties of them. Based on S.S. Dragomirs idea in this paper we treat generalizations of superior and inferior scalar product functions in the case of semi-normed spaces and 2-normed spaces.

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ZHAI, XIANG-HUA, YAN-YAN ZHANG, and XIN-ZHOU LI. "CASIMIR PISTONS FOR MASSIVE SCALAR FIELDS." Modern Physics Letters A 24, no. 05 (February 20, 2009): 393–400. http://dx.doi.org/10.1142/s0217732309027170.

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The Casimir force on two-dimensional pistons for massive scalar fields with both Dirichlet and hybrid boundary conditions is computed. The physical result is obtained by making use of generalized ζ-function regularization technique. The influence of the mass and the position of the piston in the force is studied graphically. The Casimir force for massive scalar field is compared to that for massless scalar field.

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HO, PAK TUNG. "RESULTS RELATED TO PRESCRIBING PSEUDO-HERMITIAN SCALAR CURVATURE." International Journal of Mathematics 24, no. 03 (March 2013): 1350020. http://dx.doi.org/10.1142/s0129167x13500201.

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In this paper, we consider the problem of prescribing pseudo-Hermitian scalar curvature on a compact strictly pseudoconvex CR manifold M. Using geometric flow, we prove that for any negative smooth function f we can prescribe the pseudo-Hermitian scalar curvature to be f, provided that dim M = 3 and the CR Yamabe invariant of M is negative. On the other hand, we establish some uniqueness and non-uniqueness results on prescribing pseudo-Hermitian scalar curvature.

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Hu, Yuping, Siyu Wu, Sanying Feng, and Junliang Jin. "Estimation in Partial Functional Linear Spatial Autoregressive Model." Mathematics 8, no. 10 (October 1, 2020): 1680. http://dx.doi.org/10.3390/math8101680.

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Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when response variables are dependence spatial variables. In this paper, we introduce a new partial functional linear spatial autoregressive model which explores the relationship between a scalar dependence spatial response variable and explanatory variables containing both multiple real-valued scalar variables and a function-valued random variable. By means of functional principal components analysis and the instrumental variable estimation method, we obtain the estimators of the parametric component and slope function of the model. Under some regularity conditions, we establish the asymptotic normality for the parametric component and the convergence rate for slope function. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies.

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Prößdorf, S., and F. O. Speck. "A factorisation procedure for two by two matrix functions on the circle with two rationally independent entries." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 115, no. 1-2 (1990): 119–38. http://dx.doi.org/10.1017/s0308210500024616.

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SynopsisThe aim of this paper is the explicit canonical or standard factorisation of matrix functions with Wiener algebra elements. The present approach covers all regular 2 × 2 matrices where two entries are arbitrary and the remaining two are linear combinations of the former with rational coefficient functions. It is based on the knowledge of how to factorise scalar functions and rational matrix functions. In general, one also needs the approximation of any scalar Wiener algebra function with a rational function. However, this can be easily circumvented in many applications by intuitive manipulations with rational matrix functions.

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Li, Weijie, Changxia Liang, Fan Yang, Bo Ai, Qingtong Shi, and Guannan Lv. "A Spherical Volume-Rendering Method of Ocean Scalar Data Based on Adaptive Ray Casting." ISPRS International Journal of Geo-Information 12, no. 4 (April 5, 2023): 153. http://dx.doi.org/10.3390/ijgi12040153.

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There are some limitations in traditional ocean scalar field visualization methods, such as inaccurate expression and low efficiency in the three-dimensional digital Earth environment. This paper presents a spherical volume-rendering method based on adaptive ray casting to express ocean scalar field. Specifically, the minimum bounding volume based on spherical mosaic is constructed as the proxy geometry, and the depth texture of the seabed terrain is applied to determine the position of sampling points in the spatial interpolation process, which realizes the fusion of ocean scalar field and seabed terrain. Then, we propose an adaptive sampling step algorithm according to the heterogeneous depth distribution and data change rate of the ocean scalar field dataset to improve the efficiency of the ray-casting algorithm. In addition, this paper proposes a nonlinear color-mapping enhancement scheme based on the skewness characteristics of the datasets to optimize the expression effect of volume rendering, and the transparency transfer function is designed to realize volume rendering and local feature structure extraction of ocean scalar field data in the study area.

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YAZADJIEV, STOYTCHO S. "SELF-SIMILAR COLLAPSE OF A SCALAR FIELD IN DILATON GRAVITY AND CRITICAL BEHAVIOR." International Journal of Modern Physics A 19, no. 15 (June 20, 2004): 2495–504. http://dx.doi.org/10.1142/s0217751x04017793.

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We present new analytical self-similar solutions describing a collapse of a massless scalar field in scalar–tensor theories. The solutions exhibit a type of critical behavior. The black hole mass for the near critical evolution is analytically obtained for several scalar–tensor theories and the critical exponent is calculated. Within the framework of the analytical models we consider it is found that the black hole mass law for some scalar–tensor theories is of the form M BH =f(p-p cr )(p-p cr )γ which is slightly different from the general relativistic law M BH = const (p-p cr )γ. The explicit form of the function f depends on the particular scalar–tensor theory.

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YEUNG, P. K. "Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations." Journal of Fluid Mechanics 427 (January 25, 2001): 241–74. http://dx.doi.org/10.1017/s0022112000002391.

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A study of the Lagrangian statistical properties of velocity and passive scalar fields using direct numerical simulations is presented, for the case of stationary isotropic turbulence with uniform mean scalar gradients. Data at higher grid resolutions (up to 5123 and Taylor-scale Reynolds number 234) allow an update of previous velocity results at lower Reynolds number, including intermittency and dimensionality effects on vorticity time scales. The emphasis is on Lagrangian scalar time series which are new to the literature and important for stochastic mixing models. The variance of the ‘total’ Lagrangian scalar value (ϕ˜+, combining contributions from both mean and fluctuations) grows with time, with the velocity–scalar cross-correlation function and fluid particle displacements playing major roles. The Lagrangian increment of ϕ˜+ conditioned upon velocity and scalar fluctuations is well represented by a linear regression model whose parameters depend on both Reynolds number and Schmidt number. The Lagrangian scalar fluctuation is non-Markovian and has a longer time scale than the velocity, which is due to the strong role of advective transport, and is in contrast to results in an Eulerian frame where the scalars have shorter time scales. The scalar dissipation is highly intermittent and becomes de-correlated in time more rapidly than the energy dissipation. Differential diffusion for scalars with Schmidt numbers between 1/8 and 1 is characterized by asymmetry in the two-scalar cross-correlation function, a shorter time scale for the difference between two scalars, as well as a systematic decrease in the Lagrangian coherency spectrum up to at least the Kolmogorov frequency. These observations are consistent with recent work suggesting that differential diffusion remains important in the small scales at high Reynolds number.

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