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Journal articles on the topic 'Lie Groups, Harmonic and Fourier Analysis'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Celeghini, Enrico, Manuel Gadella, and Mariano del Olmo. "Hermite Functions, Lie Groups and Fourier Analysis." Entropy 20, no. 11 (October 23, 2018): 816. http://dx.doi.org/10.3390/e20110816.

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In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R + , which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis. This can be done in terms of a unified framework based on the use of rigged Hilbert spaces. We find a relation between the universal enveloping algebra of the symmetry groups with the fractional Fourier transform. The results obtained are relevant in quantum mechanics as well as in signal processing as Fourier analysis has a close relation with signal filters. In addition, we introduce some new results concerning a discretized Fourier transform on the circle. We introduce new functions on the circle constructed with the use of Hermite functions with interesting properties under Fourier transformations.

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2

Barbaresco, Frédéric, and Jean-Pierre Gazeau. "Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century." Entropy 21, no. 3 (March 6, 2019): 250. http://dx.doi.org/10.3390/e21030250.

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For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

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3

Sarkar, Rudra P., and Alladi Sitaram. "The Helgason Fourier transform for semisimple Lie groups I: The Case of SL2(ℝ)." Bulletin of the Australian Mathematical Society 73, no. 3 (June 2006): 413–32. http://dx.doi.org/10.1017/s0004972700035437.

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4

Liao, Ming. "Lévy processes and Fourier analysis on compact Lie groups." Annals of Probability 32, no. 2 (April 2004): 1553–73. http://dx.doi.org/10.1214/009117904000000306.

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5

Donley, Robert W. "Orthogonality Relations and Harmonic Forms for Semisimple Lie Groups." Journal of Functional Analysis 170, no. 1 (January 2000): 141–60. http://dx.doi.org/10.1006/jfan.1999.3511.

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6

Lin, Ying-Fen, Jean Ludwig, and Carine Molitor-Braun. "Nilpotent Lie Groups: Fourier Inversion and Prime Ideals." Journal of Fourier Analysis and Applications 25, no. 2 (December 1, 2017): 345–76. http://dx.doi.org/10.1007/s00041-017-9586-y.

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7

Giulini, Saverio, and Giancarlo Travaglini. "Central Fourier analysis for Lorentz spaces on compact Lie groups." Monatshefte f�r Mathematik 107, no. 3 (September 1989): 207–15. http://dx.doi.org/10.1007/bf01300344.

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8

Tricot, C. "AN INTRODUCTION TO HARMONIC ANALYSIS ON SEMI-SIMPLE LIE GROUPS." Bulletin of the London Mathematical Society 23, no. 2 (March 1991): 204–8. http://dx.doi.org/10.1112/blms/23.2.204.

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9

Yang, Jae-Hyun. "Harmonic analysis on the quotient spaces of Heisenberg groups." Nagoya Mathematical Journal 123 (September 1991): 103–17. http://dx.doi.org/10.1017/s0027763000003676.

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A certain nilpotent Lie group plays an important role in the study of the foundations of quantum mechanics ([Wey]) and of the theory of theta series (see [C], [I] and [Wei]). This work shows how theta series are applied to decompose the natural unitary representation of a Heisenberg group.

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10

Yang, Dilian. "Functional Equations and Fourier Analysis." Canadian Mathematical Bulletin 56, no. 1 (March 1, 2013): 218–24. http://dx.doi.org/10.4153/cmb-2011-136-7.

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AbstractBy exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation-on compact groups.

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11

Baklouti, A., K. Smaoui, and J. Ludwig. "Estimate of the Lp-Fourier transform norm on nilpotent Lie groups." Journal of Functional Analysis 199, no. 2 (April 2003): 508–20. http://dx.doi.org/10.1016/s0022-1236(02)00106-4.

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12

Choi, Yemon, and Mahya Ghandehari. "Weak and cyclic amenability for Fourier algebras of connected Lie groups." Journal of Functional Analysis 266, no. 11 (June 2014): 6501–30. http://dx.doi.org/10.1016/j.jfa.2014.03.012.

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13

Wolf, Joseph A. "Book Review: An introduction to harmonic analysis on semisimple Lie groups." Bulletin of the American Mathematical Society 28, no. 2 (April 1, 1993): 367–71. http://dx.doi.org/10.1090/s0273-0979-1993-00365-3.

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14

Dooley, A. H., and N. J. Wildberger. "Harmonic analysis and the global exponential map for compact Lie groups." Functional Analysis and Its Applications 27, no. 1 (January 1993): 21–27. http://dx.doi.org/10.1007/bf01768664.

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15

Gudmundsson, Sigmundur, and Anna Sakovich. "Harmonic morphisms from the classical compact semisimple Lie groups." Annals of Global Analysis and Geometry 33, no. 4 (October 18, 2007): 343–56. http://dx.doi.org/10.1007/s10455-007-9090-8.

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16

Eichhorn, Jurgen, and Rudolf Schmid. "Lie groups of Fourier integral operators on open manifolds." Communications in Analysis and Geometry 9, no. 5 (2001): 983–1040. http://dx.doi.org/10.4310/cag.2001.v9.n5.a3.

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17

Fan, Dashan, and Zengfu Xu. "Characterization of lipschitz spaces on compact Lie groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 58, no. 2 (April 1995): 200–209. http://dx.doi.org/10.1017/s1446788700038234.

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AbstractLipschitz spaces are important function spaces with relations to Hp spaces and Campanato spaces, the other two important function spaces in harmonic analysis. In this paper we give some characterizations for Lipschitz spaces on compact Lie groups, which are analogues of results in Euclidean spaces.

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18

Gudmundsson, Sigmundur, and Anna Sakovich. "Harmonic morphisms from the classical non-compact semisimple Lie groups." Differential Geometry and its Applications 27, no. 1 (February 2009): 47–63. http://dx.doi.org/10.1016/j.difgeo.2008.10.003.

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19

Nordström, Jonas. "Riemannian Lie groups with no left-invariant complex-valued harmonic morphisms." Annals of Global Analysis and Geometry 45, no. 1 (May 29, 2013): 1–10. http://dx.doi.org/10.1007/s10455-013-9383-z.

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20

Penney, Richard. "Realization of representations of completely solvable Lie groups in spaces of L2 harmonic forms." Journal of Functional Analysis 97, no. 1 (April 1991): 71–111. http://dx.doi.org/10.1016/0022-1236(91)90017-y.

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21

Naicker, V., and F. Petruccione. "A Lie Symmetry Analysis of the Caldeira-Leggett Model." Open Systems & Information Dynamics 17, no. 04 (December 2010): 409–17. http://dx.doi.org/10.1142/s1230161210000254.

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An important model in the theory of open quantum systems is the Caldeira-Leggett quantum Brownian motion model for the behaviour of a massive quantum particle weakly interacting with a bath of harmonic oscillators. The model is formulated in terms of a (1 + 2) dimensional partial differential equation (PDE) for the reduced density matrix of the particle. In this paper we analyze this PDE from the perspective of Lie symmetry groups. A Lie point symmetry analysis is performed and a number of canonical reductions are obtained. Of note are new analytic solutions to the model obtained by mapping the model to the linear diffusion equation.

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22

Gudmundsson, Sigmundur, and Martin Svensson. "Harmonic morphisms from the compact semisimple Lie groups and their non-compact duals." Differential Geometry and its Applications 24, no. 4 (July 2006): 351–66. http://dx.doi.org/10.1016/j.difgeo.2005.12.003.

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23

Alexopoulos, G. "An application of homogenization theory to harmonic analysis on solvable Lie groups of polynomial growth." Pacific Journal of Mathematics 159, no. 1 (May 1, 1993): 19–45. http://dx.doi.org/10.2140/pjm.1993.159.19.

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24

Gudmundsson, Sigmundur, and Marko Sobak. "r-Harmonic and Complex Isoparametric Functions on the Lie Groups $${{\mathbb {R}}}^m \ltimes {{\mathbb {R}}}^n$$ and $${{\mathbb {R}}}^m \ltimes \mathrm {H}^{2n+1}$$." Annals of Global Analysis and Geometry 58, no. 4 (September 21, 2020): 477–96. http://dx.doi.org/10.1007/s10455-020-09736-3.

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Abstract In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products $${{\mathbb {R}}}^m \ltimes {{\mathbb {R}}}^n$$ R m ⋉ R n and $${{\mathbb {R}}}^m \ltimes \mathrm {H}^{2n+1}$$ R m ⋉ H 2 n + 1 , where $$\mathrm {H}^{2n+1}$$ H 2 n + 1 denotes the classical $$(2n+1)$$ ( 2 n + 1 ) -dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.

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25

Gudmundsson, Sigmundur, and Marko Sobak. "Proper r-harmonic functions from Riemannian manifolds." Annals of Global Analysis and Geometry 57, no. 1 (December 10, 2019): 217–23. http://dx.doi.org/10.1007/s10455-019-09696-3.

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AbstractWe introduce a new method for constructing complex-valued r-harmonic functions on Riemannian manifolds. We then apply this for the important semisimple Lie groups $$\mathbf{SO }(n)$$SO(n), $$\mathbf{SU }(n)$$SU(n), $$\mathbf{Sp }(n)$$Sp(n), $$\mathbf{SL }_{n}({\mathbb {R}})$$SLn(R), $$\mathbf{Sp }(n,{\mathbb {R}})$$Sp(n,R), $$\mathbf{SU }(p,q)$$SU(p,q), $$\mathbf{SO }(p,q)$$SO(p,q), $$\mathbf{Sp }(p,q)$$Sp(p,q), $$\mathbf{SO }^*(2n)$$SO∗(2n) and $$\mathbf{SU }^*(2n)$$SU∗(2n).

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26

Gokhale, M. H. "Study of long period global oscillations of Sun through spherical harmonic Fourier analysis of sunspot activity." Symposium - International Astronomical Union 123 (1988): 219–22. http://dx.doi.org/10.1017/s0074180900158115.

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A spherical-harmonic-fourier analysis of the maximum areas of sunspot groups listed in Ledgers I and II of Greenwich photoheliographic results for 1933–1954 yield significant peaks at the 11y periodicity for some spherical harmonic modes: especially the mode (ℓ = 6, m = 0). A similar analysis of the daily areas of the spotgroups during 1944–1954 yields 11y periodicity peaks only for some non-axisymmetric modes. These results suggest that the sunspot activity may be physically related to long period global oscillations of the sun.

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27

Yuan, Xiao Dong, Qun Li, Jin Hui, and Bin Chen. "Research on the Existence of Genuine Inter-Harmonic Components Based on the Component Appearance Rate." Advanced Materials Research 875-877 (February 2014): 1847–51. http://dx.doi.org/10.4028/www.scientific.net/amr.875-877.1847.

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The inter-harmonic spectrum of an electrical voltage or current from discrete Fourier transform can not only be caused by genuine inter-harmonic components, but can also be caused by other system disturbances. Therefore, the existence determination of genuine inter-harmonic s from the spectrum becomes the premise for further calculation of inter-harmonic parameters. From the theoretical perspective, this paper firstly analyzes and points out that the waveform difference among each cycle in the analysis window is the cause of the existence of inter-harmonic spectrum, and then presents a method to determine the existence of genuine inter-harmonic components, which is based on inter-harmonic time-frequency contour chart and the component appearance rate. The presented method firstly performs continuous discrete Fourier transform on the captured signal with certain duration and obtains the corresponding absolute time-frequency matrix, and then the genuine inter-harmonics can be distinguished based on the component appearance rate of the matrix and the criterion threshold. The method is easy to implement with clear principle, it can distinguish the genuine inter-harmonic s from the measured signal. The analysis on several data groups from real measurements verifies the effectiveness and the practicability of the method.

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28

Amini, Massoud, and Alireza Medghalchi. "Restricted Algebras on Inverse Semigroups—Part II: Positive Definite Functions." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/324821.

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The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier-Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.

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29

Alexopoulos, G. "An Application of Homogenization Theory to Harmonic Analysis: Harnack Inequalities And Riesz Transforms on Lie Groups of Polynomial Growth." Canadian Journal of Mathematics 44, no. 4 (August 1, 1992): 691–727. http://dx.doi.org/10.4153/cjm-1992-042-x.

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AbstractWe prove a homogenization formula for a sub-Laplacian are left invariant Hörmander vector fields) on a connected Lie group Gof polynomial growth. Then using a rescaling argument inspired from M. Avellanedaand F. H. Lin [2], we prove Harnack inequalities for the positive solutions of the equation (∂/∂t+ L)u= 0. Using these inequalities and further exploiting the algebraic structure of Gwe prove that the Riesz transforms , are bounded on Lq,1 < q <+∞ and from L1to weak-L1.

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30

Skrzypczak, Leszek. "Heat and Harmonic Extensions for Function Spaces of Hardy–Sobolev–Besov Type on Symmetric Spaces and Lie Groups." Journal of Approximation Theory 96, no. 1 (January 1999): 149–70. http://dx.doi.org/10.1006/jath.1998.3223.

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31

SELVARAJU, K., K. KIRUBAVATHI, N. VIJAYAN, and S. KUMARARAMAN. "SYNTHESIS, GROWTH, STRUCTURAL, SPECTROSCOPIC, OPTICAL, THERMAL AND MECHANICAL STUDIES OF A SEMI-ORGANIC NONLINEAR OPTICAL CRYSTAL: L-GLUTAMIC ACID HYDROCHLORIDE." Modern Physics Letters B 23, no. 06 (March 10, 2009): 861–69. http://dx.doi.org/10.1142/s0217984909018990.

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The semi-organic nonlinear optical single crystal of L-glutamic acid hydrochloride was grown by slow evaporation solution growth technique at room temperature. The cell parameters of the grown crystal were estimated by single crystal X-ray diffraction analysis. The presence of various functional groups was identified from Fourier transform infrared analysis. The transmission spectrum of this crystal show that the lower cut-off wavelength lies at 248 nm. Thermal analysis was performed to study the thermal stability of the grown crystal. The Kurtz powder second harmonic generation test shows that the crystal is a potential candidate for optical second harmonic generation. Mechanical properties of the grown crystal were determined and Vickers' hardness number was calculated.

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32

SORIA, S., D. SCHUHMACHER, G. MAROWSKY, R. BARBERI, F. CIUCHI, S. PAUS, and T. RASING. "PROBING ALIGNMENT OF LIQUID CRYSTALS ON SILANE DERIVATIVES BY SECOND HARMONIC GENERATION." Journal of Nonlinear Optical Physics & Materials 10, no. 02 (June 2001): 133–42. http://dx.doi.org/10.1142/s0218863501000486.

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We studied surface second-harmonic generation from thin films of 4'-n-pentyl-4-cyano-biphenyl (5CB) nematic liquid crystal (NLC) deposited onto layers of several silanes dipped on conductive glasses. We also studied a new liquid crystalline polymer deposited onto silanized substrates. The cinnamoyl side groups of this polymer can be aligned by linearly polarized UV light. The average orientation and surface order of the nematic were determined by Fourier analysis of the reflected and transmitted angular dependent second harmonic signal. The aim was to check the possible use of these materials as a control layer for the anchoring properties of nematics.

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33

Parrish, John J., Javeria Arshad, M. A. Awan, and S. Akhter. "PSXII-17 Fertility prediction model for Nilli-Ravi buffalo bulls through Fourier harmonic analysis of sperm." Journal of Animal Science 99, Supplement_3 (October 8, 2021): 424. http://dx.doi.org/10.1093/jas/skab235.761.

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Abstract A model to predict Nili-ravi buffalo bull fertility was developed based on Fourier harmonic analysis of sperm. Seventeen bulls with 3032 AI records were categorizes based on fertility rate (FR) as low (36.5±0.2, n = 6: SD< ˗1 from mean FR), medium (39.9±0.2, n = 3; SD +1 to -1 from mean FR) and high fertility (41.4±0.1, n = 8; SD > +1 from mean FR). Cryopreserved semen samples from these bulls were investigated for Fourier harmonic analysis of sperm nuclear shape. Hoechst-33342 and YOYO-1 fluorescent stains were used to identify live and dead sperm. Digital images were analyzed to get sperm nuclear perimeter points at different phase angles to generate Fourier functions. Mean harmonic amplitude (HA) 0 was different (P < 0.05) for 1700 live vs. 1294 dead sperm from the 17 bulls, thus live sperm were used for remaining analyses. The mean, variance, skewness and kurtosis values of 100 live sperm nuclei/bull were compared for HA0-5 between high (n = 6) and low (n = 6) fertility groups, considering equal number of bulls in each category. The mean HA2 (0.739±0.01 vs 0.686±0.00) and 4 (0.105±0.001 vs 0.007±0.001) were higher in high vs low fertility group respectively (P < 0.05). Sperm nuclear perimeter among high fertility group sperm was more elongated. There was also an increased skewness of HA0 as fertility increased (P < 0.05). Discriminant analysis defined a fertility model by using mean HA4, skewness HA0 and variance HA2, that resulted in 91.7% bulls into their correct fertility group upon cross-validation (canonical correlation=0.928; P < 0.05). Higher values of mean HA4, skewness HA0 and variance HA2 increase the chance of bulls being placed in the high fertility group. In conclusion, sperm nuclear shape in Nili-ravi buffalo bull is related to in vivo fertility. A fertility model using reported discriminant measures could be used to objectively identify Nili-ravi buffalo bulls of varying fertility.

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34

Yeh, Chia-Chen, R. Timothy Patterson, and Robert H. Osborne. "Fourier analysis of the planktonic foraminifer <i>Neogloboquadrina pachyderma</i> (Ehrenberg) from the Pleistocene Santa Barbara Formation, California." Journal of Micropalaeontology 8, no. 1 (June 1, 1989): 77–85. http://dx.doi.org/10.1144/jm.8.1.77.

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Abstract. A Fourier analysis was performed on three hundred and fifty two specimens of Neogloboquadrina pachyderma. obtained from eleven sedimentary rock samples of the Pleistocene Santa Barbara Formation. Statistical analytical methods, including Chi square values, Q-mode cluster analysis, O-mode factor analysis and discriminant function classification, were also carried out on these specimens.Two natural groups are recognized which can be correlated with the assemblages previously defined as warm and cool Neogloboquadrina pachyderma phenotypes, as recognized by microscope. The amplitude values of the second, third, fourth, and seventh harmonics of the warm phenotype specimens are greater than those of the cool phenotype specimens. On the other hand, the amplitude values of the fifth harmonic of the warm phenotype specimens are less than those of the cool phenotype specimens. Only the second harmonic is statistically significant in describing the shape differences between the warm and cool phenotypes. Increased compaction of the cool phenotype tends to decrease elongation, resulting in low amplitude values for the second harmonic. An intergradational form between the warm and cool water phenotypes comprises 9.4 percent of the specimens.This intergradation, albeit narrow, identified by Fourier analysis and the discriminant function indicates that the controlling factors in the shape variation of the test are local, and are caused by variation in seasonal surface circulation patterns. The warm and cool water phenotypes of Neogloboquadrina pachyderma are therefore ecophenotypic varients within a single species.

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35

Gát, György. "Convergence and divergence of Fejér means of Fourier series on one and two-dimensional Walsh and Vilenkin groups." Facta universitatis - series: Electronics and Energetics 21, no. 3 (2008): 291–307. http://dx.doi.org/10.2298/fuee0803291g.

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It is a highly celebrated issue in dyadic harmonic analysis the pointwise convergence of the Fej?r (or (C, 1)) means of functions on the Walsh and Vilenkin groups both in the point of view of one and two dimensional cases. We give a resume of the very recent developments concerning this matter, propose unsolved problems and throw a glance at the investigation of Vilenkin-like systems too. .

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36

Schindler, J. R., R. L. Monson, K. L. Willenburg, and J. J. Parrish. "267 DIFFERENCES IN BULL SPERM NUCLEAR SHAPE BETWEEN FLOW-SORTED AND NON-SORTED SPERM USING FOURIER HARMONIC ANALYSIS." Reproduction, Fertility and Development 21, no. 1 (2009): 231. http://dx.doi.org/10.1071/rdv21n1ab267.

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The objective of the study was to evaluate sperm nuclear shape in sex-sorted and non-sorted semen using Fourier Harmonic Amplitudes (FHA). Frozen semen was obtained from a single commercially available source. Mature bulls (n = 15) from the same breed with an average age of 4.42 ± 2.08 years were collected and the semen was either frozen or X-chromosome sorted using a flow cytometer and then frozen. Frozen straws were transported to the lab and analyzed for FHA. Briefly, straws were thawed and cells were incubated with 1.6 μm Hoechst 33342. Cells were then washed, fixed, dried to a slide and analyzed for nuclear head shape. Harmonic amplitudes 0 to 5 (HA0–HA5), derived from FHA, were previously shown to be an accurate, objective, and repeatable measure of sperm nuclear shape. HA0 describes the overall nuclear size of the sperm, whereas HA1 describes the anterior head, HA2 the length of the sperm along the longitudinal axis, and HA3 to 5 the distal, post-nuclear curvature of the sperm head. Each unit of semen was evaluated for motility and FHA. There was a significant decrease in motility in the sorted group (77 ± 1% v. 54 ± 3%; P < 0.0001). Multivariate ANOVA showed that there were differences between the sorted and non-sorted groups in HA1 to 4 (P < 0.02). Harmonic amplitude means ± SD (microns) for sorted and non-sorted treatments are as follows: HA1 (0.117 ± 0.003 v. 0.109 ± 0.003), HA2 (1.087 ± 0.005 v. 1.063 ± 0.005), HA3 (0.139 ± 0.003 v. 0.130 ± 0.003), and HA4 (0.201 ± 0.004 v. 0.191 ± 0.004), respectively. The nuclear shape of X-sorted sperm is longer and more pinched in both the anterior and posterior head. Interestingly there was no difference in HA0 (P = 0.119) indicating that the overall size of the sperm head is not affected by the sorting process. The differences in harmonic amplitudes may be due to the size and a restricted location of the X v. Y chromosome in the sperm nucleus.

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37

Malliga, P., R. Umamaheshwari, and A. Joseph Arul Pragasam. "Studies on the Growth Aspects of Thiourea Doped L-Alanine Hydrogenchloride: A Promising NLO Crystal." Advanced Materials Research 584 (October 2012): 70–73. http://dx.doi.org/10.4028/www.scientific.net/amr.584.70.

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A single crystal of L-alanine hydrogenchloride doped with thiourea has been synthesized and grown successfully by slow evaporation technique at room temperature. The cell parameters were determined by the X-ray diffraction analysis. The UV - visible spectral analysis has been recorded to study the optical transmittance in the range from 200nm to1200nm.The Fourier transform infrared analysis identified various functional groups present in the material.The dielectric measurement was made as function of frequency.HR-SEM studies confirms the inclusion of the dopant thiourea. The second harmonic generation efficiency has been determined by Kurtz powder test.

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38

Akincioglu, Dorukcan, Onder Ayyildiz, Gokcen Gokce, Umut Karaca, and Fatih Mehmet Mutlu. "Fourier analysis of corneal Scheimpflug imaging: clinical use in keratoconus." International Journal of Ophthalmology 14, no. 12 (December 18, 2021): 1963–69. http://dx.doi.org/10.18240/ijo.2021.12.23.

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AIM: To evaluate the clinical use of Fourier analysis of videokeratography data in the diagnosis and follow-up of keratoconus (KC). METHODS: We conducted a chart review of consecutive patients presented to our cornea clinic. A team of two experienced cornea specialists divided the patients into three groups: normal cornea, forme fruste KC (FFKC), and clinical KC. The exclusion criteria were a history of previous ocular surgery, any accompanying corneal pathology other than KC, high myopia (>6.00 diopters), amblyopia, pregnancy, breastfeeding, or any current autoimmune disease. The data of Fourier series harmonic analysis were evaluated for their diagnostic capacity using the receiver operating characteristic (ROC) curve. A binary logistic regression analysis was also conducted to construct a diagnostic model. A total of 259 eyes showed progression in the clinical KC group and underwent a combination of accelerated corneal collagen cross-linking and topography-guided customized treatment with an excimer laser. RESULTS: The study included 1262 eyes (618 normal, 530 KC, and 114 FFKC) of 1262 patients. We observed that maximum decentration (MaxDec) was almost as good as maximum keratometry (Kmax) in detecting progressive KC. The area under the curve (AUC) was 0.95 for KC [95% confidence interval (CI): 0.93-0.96] and 0.84 for FFKC (95%CI: 0.79-0.88). Higher predictive accuracy was obtained using a model combining the spherical component, MaxDec, irregularity, and regular astigmatism in the center of the cornea (AUC: 0.97; sensitivity: 89%, and specificity: 96%). CONCLUSION: Decentration, Kmax, and posterior radii of curvatures from a 3.0-mm optical zone centered on the thinnest point of the cornea provide the highest accuracy with low reproducibility of Kmax.

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39

T R, Beena. "GROWTH AND CHARACTERIZATION OF A SEMIORGANIC NLO MATERIAL: L-HISTIDINE BARIUM CHLORIDE DIHYDRATE." Green Chemistry & Technology Letters 2, no. 1 (March 10, 2016): 26–30. http://dx.doi.org/10.18510/gctl.2015.215.

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L-Histidine Barium Chloride dihydrate (LHBC), a semi organic nonlinear optical material was grown from aqueous solution by slow solvent evaporation method at room temperature. The LHBC crystals were characterized by X-ray powder diffraction analysis. The presence of functional groups was identified through Fourier Transform Infrared Spectroscopy. Thermogravimetric and Differential Thermal Analysis confirm that the crystal is stable up to 269oC. The mechanical properties of the grown crystals have been studied using Vickers microhardness test. The second harmonic generation behavior of LHBC crystal was tested by Kurtz-Perry powder technique.

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Peng, Bo, Ching-Hsing Luo, Nilotpal Sinha, Cheng-Chi Tai, Xiaohua Xie, and Haiqing Xie. "Fourier Series Analysis for Novel Spatiotemporal Pulse Waves: Normal, Taut, and Slippery Pulse Images." Evidence-Based Complementary and Alternative Medicine 2019 (November 27, 2019): 1–9. http://dx.doi.org/10.1155/2019/5734018.

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In this article, a three-dimensional pulse image (3DPI) instead of a one-dimensional temporal pulse wave is studied to elucidate its spatiotemporal characteristics. To check the spatial and temporal properties of 3DPI, adopted is Fourier series, in which a ratio (r) is defined as one amplitude divided by the sum of the first three amplitudes of harmonics. A ratio sequence is constituted from 70 to 90 ratios in a heartbeat with 70–90 3DPIs by sampling. Twenty-four subjects (14 males and 10 females with age of 22.2 ± 3.7 years, 20.4 ± 1.4 BMI, and 112.1 ± 4.7 mmHg systolic blood pressure) are involved in this research. There are significant statistical differences in the groups of the normal, taut, and slippery 3DPIs by the first harmonic ratio average (r1¯) and ratio difference (Δr1) produced from the ratio sequence. The proposed method of this study gives us a novel viewpoint to clarify the spatiotemporal characteristics of pulse images, which can translate and quantize the pulse feeling in Chinese medicine texts.

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KATOK, ANATOLE, VIOREL NIŢICĂ, and ANDREI TÖRÖK. "Non-abelian cohomology of abelian Anosov actions." Ergodic Theory and Dynamical Systems 20, no. 1 (February 2000): 259–88. http://dx.doi.org/10.1017/s0143385700000122.

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We develop a new technique for calculating the first cohomology of certain classes of actions of higher-rank abelian groups (${\mathbb Z}^k$ and ${\mathbb R}^k$, $k\ge 2$) with values in a linear Lie group. In this paper we consider the discrete-time case. Our results apply to cocycles of different regularity, from Hölder to smooth and real-analytic. The main conclusion is that the corresponding cohomology trivializes, i.e. that any cocycle from a given class is cohomologous to a constant cocycle. The principal novel feature of our method is its geometric character; no global information about the action based on harmonic analysis is used. The method can be developed to apply to cocycles with values in certain infinite dimensional groups and to rigidity problems.

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Dunne, J. F. "Subharmonic-Response Computation and Stability Analysis for a Nonlinear Oscillator Using a Split-Frequency Harmonic Balance Method." Journal of Computational and Nonlinear Dynamics 1, no. 3 (February 20, 2006): 221–29. http://dx.doi.org/10.1115/1.2198875.

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A split-frequency harmonic balance method (SF-HBM) is developed to obtain subharmonic responses of a nonlinear single-degree-of-freedom oscillator driven by periodic excitation. This method is capable of generating highly accurate periodic solutions involving a large number of solution harmonics. Responses at the excitation period, or corresponding multiples (such as period 2 and period 3), can be readily obtained with this method, either in isolation or as combinations. To achieve this, the oscillator equation error is first expressed in terms of two Mickens functions, where the assumed Fourier series solution is split into two groups, nominally associated with low-frequency or high-frequency harmonics. The number of low-frequency harmonics remains small compared to the number of high-frequency harmonics. By exploiting a convergence property of the equation-error functions, accurate low-frequency harmonics can be obtained in a new iterative scheme using a conventional harmonic balance method, in a separate step from obtaining the high-frequency harmonics. The algebraic equations (needed in the HBM part of the method) are generated wholly numerically via a fast Fourier transform, using a discrete-time formulation to include inexpansible nonlinearities. A nonlinear forced-response stability analysis is adapted for use with solutions obtained with this SF-HBM. Period-3 subharmonic responses are obtained for an oscillator with power-law nonlinear stiffness. The paper shows that for this type of oscillator, two qualitatively different period-3 subharmonic response branches can be obtained across a broad frequency range. Stability analysis reveals, however, that for an increasingly stiff model, neither of these subharmonic branches are stable.

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Chen, Fun-Jou, Hong-Song Wang, Chih-Yang Huang, and Yueh-Sheng Chen. "Pulse Analysis in Bipolar Disordered and Nonpsychotic Human Subjects." American Journal of Chinese Medicine 40, no. 03 (January 2012): 455–65. http://dx.doi.org/10.1142/s0192415x12500358.

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The research literature indicates that patients with bipolar disorder (BPD) differ from healthy individuals in various ways that are also recognized in traditional Chinese medicine. The purpose of the current study was to analyze the pulse spectra in BPD patients to determine any differences from nonpsychotic healthy individuals. Sphygmography was used to measure the radial arterial pulse waves in all subjects. We analyzed the original waveforms and then transformed them into frequency spectra via Fourier transformation. The relative strength of each harmonic, believed to be connected to meridians in Chinese medicine, was identified from the frequency, and we compared the differences among the harmonics. A total of sixty individuals, thirty with BPD and thirty nonpsychotic healthy controls, participated in the study. The harmonic values of C4 (Lung Meridian) on the right hand, 401.33 ± 50.10 vs. 762.44 ± 125.17, were significantly different (p < 0.05) between the BPD group and the nonpsychotic healthy group. The harmonic percentage of C3 (Spleen Meridian) on the right hand, 7.85 ± 0.59% vs. 10.79 ± 1.01%, and C4 (Lung Meridian), 1.80 ± 0.15 vs. 3.24 ± 0.43, was significantly different (p < 0.05) between the two groups. The results were similar for the right and left hands. In this study, we objectively detected constitutional differences between BPD patients and healthy controls through arterial pulse analysis. The pulse spectrum analyzer is a non-invasive diagnostic tool that can be used to integrate scientific technology with traditional Chinese medicine. We plan further study in this field to improve the accuracy of diagnosis in Chinese medicine.

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Maslikov, Alexander, and Guennady Volkov. "Ternary SU(3)-group symmetry and its possible applications in hadron-quark substructure. Towards a new spinor-fermion structure." EPJ Web of Conferences 204 (2019): 02007. http://dx.doi.org/10.1051/epjconf/201920402007.

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The questions on the existence of the three color quark symmetry and three quark-lepton generations could have the origin associated with the new exotic symmetries outside the Cartan-Killing-Lie algebras/groups. Our long-term search for these symmetries has been began with our Calabi-Yau space classification on the basis of the n-ary algebra for the reflexive projective numbers and led us to the expansion of the binary n = 2 complex and hyper complex numbers in the framework of the n-ary complex and hyper-complex numbers with n = 3, 4, … where we constructed new Abelian and non-Abelian symmetries. We have studied then norm-division properties of the Abelian nary complex numbers and have built the infinite chain of the Abelian groups U(n–1) = [U(1) × … × U(1)](n–1). We have developed the n-ary holomorphic (polymorphic) analysis on the n-ary complex space NC{n}, which led us to the generalization of the quadratic Laplace equations for the harmonic functions. The generalized Laplace equations for the n-ary harmonic functions give us the n-th order homogeneous differential equations which are invariant with respect to the Abelian n-ary groups U(n–1) and with some new spatial properties. Further consideration of the non-Abelian n-ary hyper-complex numbers opens the infinite series of the non-Abelian TnSU(n)-Lie groups(n=3,4,…) and its corresponding tnsu(n) algebras. One of the exceptional features of these symmetry groups is the appearance of some new n-dimensional spinors that could lead to an extension of the concept of the SU(2)-spin, to the appearance of n-dimensional quantum structures -exotic “n-spinor” matter(n = 3, 4, … - maarcrions). It is natural to assume that these new exotic “quantum spinor states” could be candidates for the pra-matter of the quark-charge leptons or/and for the dark matter. We will be also interested in the detection of the exotic quantum ’n-spinor” matter in the neutrino and hadron experiments.

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Ma, Longxiang, and Weining Liu. "A numerical train–floating slab track coupling model based on the periodic-Fourier-modal method." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232, no. 1 (September 23, 2016): 315–34. http://dx.doi.org/10.1177/0954409716668552.

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A numerical model based on the periodic-Fourier-modal method is proposed for the dynamic analysis of a train-floating slab track coupling system with random track irregularity. In the model, each vehicle of the train is modeled as a multiple-degree-of-freedom vibration system consisting of one car body, two bogies, four wheelsets, and two groups of spring-damper suspension devices. The floating slab track is modeled as a periodic-infinite structure with discrete supports and discontinuous slabs. Linear springs are used to couple the train and the track. In order to establish this numerical model, an efficient periodic approach named periodic-Fourier-modal method for solving the dynamic response of the floating slab track under a harmonic moving load is first developed. Based on this, a strategy is then proposed which can couple the moving train to the track with random irregularity and express the wheel–rail force as a superposition of a series of harmonic loads. With the solved wheel–rail force, the vehicle response can be directly calculated through vehicle dynamics, while track response can be calculated through the principle of superposition and the reuse of the initially proposed periodic-Fourier-modal method. Using this train–floating slab track coupling model, the solution of the dynamic response of the infinite track can be transformed to perform only within a single periodic range, which can save the calculation time significantly. The numerical results of the Beijing subway, based on the proposed model, are discussed in detail, and some important conclusions are drawn.

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Sudhahar, S., M. Krishna Kumar, A. Silambarasan, R. Muralidharan, and R. Mohan Kumar. "Studies on Structural, Spectral, and Optical Properties of Organic Nonlinear Optical Single Crystal: 2-Amino-4,6-dimethylpyrimidinium p-Hydroxybenzoate." Journal of Materials 2013 (March 28, 2013): 1–7. http://dx.doi.org/10.1155/2013/539312.

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2-Amino-4,6-dimethylpyrimidinium p-hydroxybenzoate (ADPHB), a novel organic material, was synthesized, and crystals were grown by slow evaporation solution growth method. The cell parameters and crystalline perfection of the grown crystal were studied by single crystal and powder X-ray diffraction analyses. The presence of various functional groups of the grown crystal was confirmed using Fourier Transform infrared spectral analysis. UV-Visible spectrum shows that ADPHB crystals have high transmittance in the range 305–900 nm. The refractive index and transient photoluminescence properties of the grown crystal were analyzed. The laser induced surface damage threshold, optical birefringence, and second harmonic generation efficiency of the grown crystal were studied.

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Hosn, W. Aboul, P. Dutilleul, and D. Boisclair. "Use of spectral analysis to estimate short-term periodicities in growth rates of brook trout Salvelinus frontinalis." Canadian Journal of Fisheries and Aquatic Sciences 54, no. 7 (July 1, 1997): 1532–41. http://dx.doi.org/10.1139/f97-060.

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We used spectral analysis to investigate the periodic components of relative growth rates (on a mass and length basis) in two groups of six\b young-of-the-year brook trout (Salvelinus fontinalis). Fish were measured every 2 days for 25 days according to a repeated measures design in time. The predominant frequency components were estimated at the end of a stepwise procedure involving the analysis of the multifrequential periodogram. We found mainly two superimposed periodic components that resulted in short rhythms; these had a period of about 5 and 10 days for the growth rate in mass and of about 4 and 6 days for the growth rate in length (R2 = 91% for mass and 90% for length, both including an autocorrelation term). Repeatability of rhythms was assessed by ANOVA of the finite Fourier transform, which showed that the two groups of fish reared under the same experimental conditions exhibited growth rhythms that were not significantly different from each other. On that basis, we present a harmonic model which predicts short-term variation in growth rate of brook trout in mass (R2pred = 0.73, with an autocorrelation term) and in length (R2pred = 0.72).

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PASUPATHI, G., and P. PHILOMINATHAN. "CRYSTAL GROWTH, THERMAL, OPTICAL AND MICROHARDNESS STUDIES OF TRIS (THIOUREA) MAGNESIUM SULPHATE: A SEMIORGANIC NLO MATERIAL." Modern Physics Letters B 23, no. 25 (October 10, 2009): 3035–43. http://dx.doi.org/10.1142/s0217984909021107.

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Single crystals of tris (Thiourea) magnesium sulphate (MTS) were grown from aqueous solution by low temperature solution growth technique. The grown crystals have been characterized by X-ray diffraction to confirm the formation of the crystalline phases. The presence of functional groups was identified by Fourier transform infrared spectroscopy. The optical transmission spectrum showed that a lower cut-off wavelength of MTS crystal is below 300 nm and it has a wide transparency window, which is suitable for second harmonic generation of laser in the blue region. The thermal stabilities were studied by differential thermal analysis (DTA) and thermo gravimetric analysis (TGA). Nonlinear optical characteristics of MTS were studied using Q-switched Nd:YAG laser (λ=1064 nm ). The micro-hardness studies reveal the mechanical properties of the grown crystals.

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Jagadeesh, M. R., H. M. Suresh Kumar, and R. Ananda Kumari. "Crystal growth and characterization of a semi-organic nonlinear optical (NLO) material: L-phenylalanine cadmium chloride." Canadian Journal of Physics 93, no. 11 (November 2015): 1296–301. http://dx.doi.org/10.1139/cjp-2014-0571.

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L-phenylalanine cadmium chloride (LPCC) single crystals were grown from aqueous solution using the slow evaporation solution technique. The grown crystals were analyzed through various characterization techniques. Structural study reveals that LPCC belongs to a monoclinic crystal system with the space group P1. The presences of various functional groups were identified by Fourier transform infrared analysis. Optical absorption study was carried out and complete transparency in the visible region was observed with a lower cutoff wavelength of 261 nm. The surface morphology was analyzed through scanning electron micrograph studies. LPCC is thermally stable up to 265 °C as determined by thermogravimetric – differential thermal analysis studies. Dielectric behavior as a function of frequency was examined. The mechanical behavior was studied by Vicker’s microhardness tester. To explore the nonlinear optical property, the Kurtz powder method was employed and second harmonic generation efficiency was determined.

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Manimekalai, R., and S. Chidambaram. "Growth and Characterization of Adipic Acid Doped Potassium Hydrogen Phthalate: A Nonlinear Optical Single Crystal." Asian Journal of Chemistry 32, no. 1 (November 18, 2019): 79–83. http://dx.doi.org/10.14233/ajchem.2020.22273.

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Adipic acid doped potassium hydrogen phthalate (AAKHP) and pure potassium hydrogen phthalate single crystals were grown by slow evaporation method. Single crystal X-ray diffraction analysis was carried out to determine the lattice parameters in a = 6.47 Å, b = 9.59 Å, c = 13.25 Å and space group of Pca21. This confirms the grown AAKHP belongs to the orthorhombic system. Various diffracting planes of the grown crystal were indexed using powder X-ray diffraction study. Fourier-transform infrared studies confirm the presence of various functional groups in the grown crystal. The transmittance spectrum shows that the lower cutoff wavelength is around 290 nm. The nonlinear optical property of the grown crystal has been studied by Kurtz powder second harmonic generation (SHG) analysis. EDAX analysis confirms the presence of various elements in the AAKHP crystal. Vickers micro-hardness studies are used for the analysis of mechanical behaviour of the grown crystal. The paramagnetic nature of the grown crystal was confirmed by vibration spectrum magnetometer technique.

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