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Journal articles on the topic 'Atomic function'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Abdel-Khalek, S., M. S. Almalki, and E. Edfawy. "Dynamical Properties of Scaled Atomic Wehrl Entropy of Multiphoton JCM in the Presence of Atomic Damping." Advances in Condensed Matter Physics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/879058.

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We study the dynamics of the atomic inversion, scaled atomic Wehrl entropy, and marginal atomicQ-function for a single two-level atom interacting with a one-mode cavity field taking in the presence of atomic damping. We obtain the exact solution of the master equation in the interaction picture using specific initial conditions. We examine the effects of atomic damping parameter and number of multiphoton transition on the scaled atomic Wehrl entropy, atomicQ-function, and their marginal distribution. We observe an interesting monotonic relation between the different physical quantities in the

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2

Alexander, S. A., and R. L. Coldwell. "Atomic wave function forms." International Journal of Quantum Chemistry 63, no. 5 (1997): 1001–22. http://dx.doi.org/10.1002/(sici)1097-461x(1997)63:5<1001::aid-qua9>3.0.co;2-1.

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3

Brysina, Iryna Victorivna, and Victor Olexandrovych Makarichev. "ATOMIC FUNCTIONS AND THEIR GENERALIZATIONS IN DATA PRO-CESSING: FUNCTION THEORY APPROACH." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 3 (October 30, 2018): 4–10. http://dx.doi.org/10.32620/reks.2018.3.01.

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Theory of atomic functions, which are solutions with a compact support of the linear functional differential equations with a constant coefficients and linear transforms of the argument, was created in the 70's of the 20th century because of the necessity to solve different applied problems, in particular, boundary value problems. One of the reasons for the appearance of atomic functions and some other classes of functions was the inability to use such classic approximation tools as algebraic and trigonometric polynomials. V.A. Rvachev up-function is the most famous and widely used atomic func

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4

YONEDA, Yasuhiro. "Atomic Pair Distribution Function (PDF) Analysis of Ferroelectric Materials." Nihon Kessho Gakkaishi 54, no. 3 (2012): 155–58. http://dx.doi.org/10.5940/jcrsj.54.155.

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5

Pegg, DT. "Wave Function Collapse in Atomic Physics." Australian Journal of Physics 46, no. 1 (1993): 77. http://dx.doi.org/10.1071/ph930077.

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Wave function collapse has been a contentious concept in quantum mechanics for a considerable time. Here we show examples of how the concept can be used to advantage in predicting the statistical results of three experiments in atomic physics and quantum optics: photon antibunching, single-photon phase difference states and interrupted single-atom fluorescence. We examine the question of whether or not collapse is 'really' a physical process, and discuss the consequences of simply omitting it but including the observer as a part of the overall system governed by the laws of quantum mechanics.

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Vavruk, T. O., O. S. Tcareva, O. G. Malko, L. M. Hobur, and N. D. Podubinska. "MATHEMATICAL MODEL FOR CALCULATING THE STRUCTURE OF A LIQUID (MELT) USING DISTRIBUTION FUNCTIONS." METHODS AND DEVICES OF QUALITY CONTROL, no. 1(46) (June 28, 2021): 125–31. http://dx.doi.org/10.31471/1993-9981-2021-1(46)-125-131.

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This article considers a spatio-temporal study of the structure of melts using the correlation functions of the distribution of physical and chemical analysis. The authors consider the properties of metallic melts and their dependence on the physical state of the melt. The dynamic structure of the melt is considered, the numerical description is given. The binary distribution function is distinguished as the one that best corresponds to the structure of the fluid. With the help of the atomic distribution function, if the interaction potentials are known, it is possible to find the equation of

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7

SONG, LIANG, CHAOQIANG TAN, and LIXIN YAN. "AN ATOMIC DECOMPOSITION FOR HARDY SPACES ASSOCIATED TO SCHRÖDINGER OPERATORS." Journal of the Australian Mathematical Society 91, no. 1 (2011): 125–44. http://dx.doi.org/10.1017/s1446788711001376.

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AbstractLetL=−Δ+Vbe a Schrödinger operator on ℝnwhereVis a nonnegative function in the spaceL1loc(ℝn) of locally integrable functions on ℝn. In this paper we provide an atomic decomposition for the Hardy spaceH1L(ℝn) associated toLin terms of the maximal function characterization. We then adapt our argument to give an atomic decomposition for the Hardy spaceH1L(ℝn×ℝn) on product domains.

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8

Bentley, Jason. "Construction of Regular Non-Atomic Strictly-Positive Measures in Second-Countable Non-Atomic Locally Compact Hausdorff Spaces." Annales Mathematicae Silesianae 36, no. 1 (2022): 15–25. http://dx.doi.org/10.2478/amsil-2022-0005.

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Abstract This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable non-atomic locally compact Hausdorff space. This construction involves a sequence of finitely-additive set functions defined recursively on an ascending sequence of rings of subsets with a set function limit that is extendable to a measure with the desired properties. Non-atomicity of the space provides a meticulous way to ensure that the set function limit is σ-additive.

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9

Carbó-Dorca, Ramon. "Quantum Molecular Polyhedra and Atomic Populations." Scientific World 14, no. 14 (2021): 6–13. http://dx.doi.org/10.3126/sw.v14i14.34976.

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The present paper uses the LCAO MO theory formalism. The structure of the first order electronic density function is decomposed in two kinds of quantum polyhedra to discuss the behavior of quantum atomic populations. Among the many aspects one can consider about atomic populations here, the quantum mechanical structure of the density function is taken as the most important characteristic to think about. Apart of the usual one-electron basis set, centered in the molecular atoms, there is also discussed the possibility that the three-dimensional space where the molecular structures are described

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10

Halakatti, S. C. P., and Akshata Kengangutti. "A Study on Atomic Hausdorff and Atomic Regular Measure Manifolds." Journal of the Tensor Society 10, no. 01 (2007): 69–77. http://dx.doi.org/10.56424/jts.v10i01.10573.

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In this paper atomic Hausdorff and atomic regular measure manifolds are generated by using the tools of inverse function theorem for measure manifold and pullback function on a measure manifold. Also, we investigate the possibility of generating a broader class of atomic measure manifolds.

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11

Rvachov, Volodimir Olexijovych, Tatiana Volodimirivna Rvachova, and Evgenia Pavlovna Tomilova. "TOMIC FUNCTIONS AND LACUNARY INTERPOLATION SERIES IN BOUNDARY VALUE PROBLEMS FOR PARTIAL DERIVATIVES EQUATIONS AND IMAGE PROCESSING." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 1 (January 28, 2020): 58–69. http://dx.doi.org/10.32620/reks.2020.1.06.

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In the paper we consider and solve the problem of construction of the so called tomic functions – the systems of infinitely differentiable functions which while retaining many important properties of the shifts of atomic function up(x) such as locality and representation of algebraic polynomials and being based on the atomic functions nevertheless have nonuniform character and therefore allow to take into account the inhomogeneous and changing character of the data encountered in real world problems in particular in boundary value problems for partial differential equations with variable coeff

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12

Sadagov, Yuri M., Alexander D. Levin, and Irina V. Biryukova. "Transformation functions in electrothermal atomic absorption spectrometry." Izmeritel`naya Tekhnika, no. 4 (2021): 63–67. http://dx.doi.org/10.32446/0368-1025it.2021-4-63-67.

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The problem of calibration of an analytical instrument and analysis procedure with an unknown composition and origin of the analyzed sample are considered. The transformation functions of the Zeeman atomic absorption spectrometer with electrothermal atomization have been investigated. The method for establishing a two-parameter transformation function of the spectrometer using a single calibration sample is proposed and the possibility of measuring the analyte concentration in a real sample using the refined transformation function of the spectrometer is considered.

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13

Ikuhara, Yuichi, Naoya Shibata, Teruyasu Mizoguchi, and Eiji Abe. "Atomic Scale Characterization of Function Providing Elements." Materia Japan 48, no. 6 (2009): 284–89. http://dx.doi.org/10.2320/materia.48.284.

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14

Shamoto, S., K. Kodama, S. Iikubo, and T. Taguchi. "Atomic pair distribution function analysis on nanomaterials." Acta Crystallographica Section A Foundations of Crystallography 64, a1 (2008): C73—C74. http://dx.doi.org/10.1107/s0108767308097651.

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15

Freyberger, Matthias, Stefan H. Kienle, and Valery P. Yakovlev. "Interferometric measurement of an atomic wave function." Physical Review A 56, no. 1 (1997): 195–201. http://dx.doi.org/10.1103/physreva.56.195.

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16

Bauch, Andreas. "Caesium atomic clocks: function, performance and applications." Measurement Science and Technology 14, no. 8 (2003): 1159–73. http://dx.doi.org/10.1088/0957-0233/14/8/301.

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17

ARULMOZHIRAJA, S., and P. KOLANDAIVEL. "Condensed Fukui function: dependency on atomic charges." Molecular Physics 90, no. 1 (1997): 55–62. http://dx.doi.org/10.1080/002689797172868.

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18

Schnurr, C., T. A. Savard, L. J. Wang, and J. E. Thomas. "Atomic Wave-Function Imaging via Optical Coherence." Physical Review Letters 74, no. 8 (1995): 1331–34. http://dx.doi.org/10.1103/physrevlett.74.1331.

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19

Scherr, Charles W. "A simple non-exponential function for use in atomic and molecular wave functions for use in atomic and molecular wave functions." International Journal of Quantum Chemistry 6, S6 (2009): 51–58. http://dx.doi.org/10.1002/qua.560060608.

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20

Petkov, V. "Atomic-scale structure of nanocrystals by the atomic pair distribution function technique." Molecular Simulation 31, no. 2-3 (2005): 101–5. http://dx.doi.org/10.1080/08927020412331308485.

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21

Brysina, Iryna Victorivna, and Victor Olexandrovych Makarichev. "GENERALIZED ATOMIC WAVELETS." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 1 (February 23, 2018): 23–31. http://dx.doi.org/10.32620/reks.2018.1.03.

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The problem of big data sets processing is considered. Efficiency of algorithms depends mainly on the appropriate mathematical tools. Now there exists a wide variety of different constructive tools for information analysis. Atomic functions are one of them. Theory of atomic functions was developed by V. A. Rvachev and members of his scientific school. A number of results, which prove that application of atomic functions is reasonable, were obtained. In particular, atomic functions are infinitely differentiable. This property is quite useful for smooth data processing (for example, color photos

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22

Stelbovics, AT, and T. Winata. "A Study of L2 Approximations in Atomic Scattering." Australian Journal of Physics 43, no. 5 (1990): 485. http://dx.doi.org/10.1071/ph900485.

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The approximation of Coulomb continuum functions by an L 2 basis is studied using a Laguerre� function basis which can be extended to completeness. Also studied is the convergence rate of L2 approximations to Born matrix elements for electron impact ionisation as a function of basis�set size. This important class of matrix elements occurs in pseudo�state close-coupling calculations, accounting for scattering to the three�body continuum. Convergence rates in both cases are derived analytically and confirmed numerically. We find that the rate of pointwise convergence of L2 expansions to the cont

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23

Nellist, P. D., and S. J. Pennycook. "Quantitative Information from Image Processing in ADF Stem." Microscopy and Microanalysis 3, S2 (1997): 1149–50. http://dx.doi.org/10.1017/s1431927600012630.

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Annular dark-field (ADF) imaging in the scanning transmission electron microscope (STEM) at atomic resolution can be regarded as being almost perfect incoherent imaging, which has two major advantages over conventional high-resolution transmission electron microscopy (HRTEM), which is close to being perfectly coherent: Firstly, the images formed are direct structure images of the projected atomic structure, with regions of intensity located at the positions of the atomic columns. Secondly, the images can be written as the convolution between two real and positive functions: a point-spread func

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24

Makarichev, Victor, and Vyacheslav Kharchenko. "Application of dynamic programming approach to computation of atomic functions." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 4 (November 29, 2021): 36–45. http://dx.doi.org/10.32620/reks.2021.4.03.

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The special class of atomic functions is considered. The atomic function is a solution with compact support of linear differential functional equation with constant coefficients and linear transformations of the argument. The functions considered are used in discrete atomic compression (DAC) of digital images. The algorithm DAC is lossy and provides better compression than JPEG, which is de facto a standard for compression of digital photos, with the same quality of the result. Application of high precision values of atomic functions can improve the efficiency of DAC, as well as provide the de

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25

Kokhan, Yaroslav. "SYMBOLIC LOGIC: RETURN TO THE ORIGINS. PAPER II. BASIC CATEGORIES." Bulletin of Yaroslav Mudryi National Law University. Series: Philosophy, philosophy of law, political science, sociology. 47, no. 4 (2020): 47–57. https://doi.org/10.21564/2075-7190.47.218958.

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Problem setting. The paper is the Part II o f the large research, dedicated to both revision o f the system o f basic logical categories and generalization o f the modern predicate logic to functional logic. Basic categories o f functional logic are the following: an individual, a function, representation, and a sequence. Paper objective. The main task o f the paper is to describe every one o f the categories in question. The more expansive task of all the paper series is to expose the whole system o f functional logic and to prove its advantagies. Recent research and publications analysis. Fu

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26

Hutem, Artit, and Piyarut Moonsri. "Evaluated Excited-State Time-Independent Correlation Function and Eigenfunction of the Harmonics Oscillator Cosine Asymmetric Potential via Numerical Shooting Method." Physics Research International 2015 (February 23, 2015): 1–10. http://dx.doi.org/10.1155/2015/609495.

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We aimed to evaluate the ground-state and excite-state energy eigenvalue (En), wave function, and the time-independent correlation function of the atomic density fluctuation of a particle under the harmonics oscillator Cosine asymmetric potential (Saad et al. 2013). Instead of using the 6-point kernel of 4 Green’s function (Cherroret and Skipetrov, 2008), averaged over disorder, we use the numerical shooting method (NSM) to solve the Schrödinger equation of quantum mechanics system with Cosine asymmetric potential. Since our approach does not use complicated formulas, it requires much less com

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27

Guo, Liqiu, Hao Lu, D. Y. Li, Q. X. Huang, Xu Wang, and J. A. Szpunar. "Crystallographic anisotropy in surface properties of brass and its dependence on the electron work function." Journal of Applied Crystallography 51, no. 6 (2018): 1715–20. http://dx.doi.org/10.1107/s160057671801573x.

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The crystallographic anisotropy of the electric current or conductance, adhesive force, elastic modulus, and deformation magnitude of alpha brass were investigated through property mapping using an atomic force microscope. Surface electron work functions of differently oriented grains in the brass were also analyzed using atomic force microscopy. The mapped surface properties are closely related to the electron work function; the work function reflects the surface activity, which is itself dependent on the surface energy. The anisotropy of the properties is closely correlated to the in situ me

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28

Jin, Yongmei M., and Armen G. Khachaturyan. "Atomic density function theory and modeling of microstructure evolution at the atomic scale." Journal of Applied Physics 100, no. 1 (2006): 013519. http://dx.doi.org/10.1063/1.2213353.

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29

Coelho, A. A., P. A. Chater, and A. Kern. "Fast synthesis and refinement of the atomic pair distribution function." Journal of Applied Crystallography 48, no. 3 (2015): 869–75. http://dx.doi.org/10.1107/s1600576715007487.

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A fast method for calculating the atomic pair distribution function is described in the context of performing refinements of structural models. Central to the speed of synthesis is the approximation of Gaussian functions of varying full widths at half-maximum using a narrower Gaussian with a fixed full width at half-maximum. The initial Gaussians are first laid down as delta functions which are then convoluted with the narrower Gaussian to form the final pattern. The net result is an algorithm, which has been included in the Rietveld refinement computer programTOPAS, that synthesizes and refin

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30

Fourie, J. T. "Atomic Resolution in Crystal Aperture Stem." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 1 (1990): 236–37. http://dx.doi.org/10.1017/s0424820100179932.

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The attempts at improvement of electron optical systems to date, have largely been directed towards the design aspect of magnetic lenses and towards the establishment of ideal lens combinations. In the present work the emphasis has been placed on the utilization of a unique three-dimensional crystal objective aperture within a standard electron optical system with the aim to reduce the spherical aberration without introducing diffraction effects. A brief summary of this work together with a description of results obtained recently, will be given.The concept of utilizing a crystal as aperture i

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31

Plujko, V. A., O. M. Gorbachenko, E. P. Rovenskykh, and V. O. Zheltonoshskii. "E1 gamma-transitions in hot atomic nuclei." Nuclear Physics and Atomic Energy 13, no. 4 (2012): 340–45. https://doi.org/10.15407/jnpae2012.04.340.

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New version of the modified Lorentzian approach for radiative strength function is proposed. Renewed systematics for giant dipole resonance (GDR) parameters is given. The gamma-decay strength functions are calculated using renewed GDR parameters and compared with experimental data. It is demonstrated that closed-form approaches with asymmetric shape of the gamma strength, as a rule, provide the reliable simple method for description of gamma-decay processes.

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32

Journal, Baghdad Science. "A study of some atomic properties for He-like selected ions." Baghdad Science Journal 4, no. 2 (2007): 301–4. http://dx.doi.org/10.21123/bsj.4.2.301-304.

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The atomic properties have been studied for He-like ions (He atom, Li+, Be2+ and B3+ions). These properties included, the atomic form factor f(S), electron density at the nucleus , nuclear magnetic shielding constant and diamagnetic susceptibility ,which are very important in the study of physical properties of the atoms and ions. For these purpose two types of the wave functions applied are used, the Hartree-Fock (HF) waves function (uncorrelated) and the Configuration interaction (CI) wave function (correlated). All the results and the behaviors obtained in this work have been discussed, int

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33

Grosse, H., and A. Pflug. "Atomic level order as function of angular momentum." American Journal of Physics 53, no. 10 (1985): 978–81. http://dx.doi.org/10.1119/1.14015.

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34

Shamoto, Shin-ichi. "Spherical Nanoparticle Effects on Atomic Pair Distribution Function." Journal of the Physical Society of Japan 79, no. 3 (2010): 034601. http://dx.doi.org/10.1143/jpsj.79.034601.

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35

Billinge, S. J. L. "Nanostructure studied using the atomic pair distribution function." Zeitschrift für Kristallographie 2007, suppl_26 (2007): 17–26. http://dx.doi.org/10.1524/zkri.2007.2007.suppl_26.17.

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36

Catterall, William. "Sodium Channel Structure and Function at Atomic Resolution." Biophysical Journal 102, no. 3 (2012): 7a—8a. http://dx.doi.org/10.1016/j.bpj.2011.11.061.

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37

Triebel, Hans, and Heike Winkelvoß. "Intrinsic atomic characterizations of function spaces on domains." Mathematische Zeitschrift 221, no. 1 (1996): 647–73. http://dx.doi.org/10.1007/bf02622138.

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38

Danker, T., and H. Oberleithner. "Nuclear pore function viewed with atomic force microscopy." Pflügers Archiv - European Journal of Physiology 439, no. 6 (2000): 671–81. http://dx.doi.org/10.1007/s004240000249.

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39

Danker, T., and H. Oberleithner. "Nuclear pore function viewed with atomic force microscopy." Pflügers Archiv 439, no. 6 (2000): 671. http://dx.doi.org/10.1007/s004240050992.

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40

Edelman, Marvin, and Vladimir Sobolev. "Using atomic-level structure to probe protein function." ACM SIGBIO Newsletter 19, no. 3 (1999): 13–14. http://dx.doi.org/10.1145/340358.340383.

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41

Billinge, S. J. L. "Nanostructure studied using the atomic pair distribution function." Zeitschrift für Kristallographie Supplements 2007, suppl_26 (2007): 17–26. http://dx.doi.org/10.1524/zksu.2007.2007.suppl_26.17.

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42

López-Flores, Leticia, Laura L. Yeomans-Reyna, Martín Chávez-Páez, and Magdaleno Medina-Noyola. "The overdamped van Hove function of atomic liquids." Journal of Physics: Condensed Matter 24, no. 37 (2012): 375107. http://dx.doi.org/10.1088/0953-8984/24/37/375107.

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43

Triebel, Hans, and Heike Winkelvoß. "Intrinsic atomic characterizations of function spaces on domains." Mathematische Zeitschrift 221, no. 4 (1996): 647–73. http://dx.doi.org/10.1007/pl00004525.

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44

Jabri, H., H. Eleuch, and T. Djerad. "Lifetimes of atomic Rydberg states by autocorrelation function." Laser Physics Letters 2, no. 5 (2005): 253–57. http://dx.doi.org/10.1002/lapl.200410184.

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45

Kabanov, K. I., and V. M. Kolodyazhny. "Characterization of the Distributions with Atomic Function Densities." Cybernetics and Systems Analysis 51, no. 3 (2015): 410–15. http://dx.doi.org/10.1007/s10559-015-9732-y.

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46

Farkas, Walter. "Atomic and Subatomic Decompositions in Anisotropic Function Spaces." Mathematische Nachrichten 209, no. 1 (2000): 83–113. http://dx.doi.org/10.1002/(sici)1522-2616(200001)209:1<83::aid-mana83>3.0.co;2-1.

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47

Angulo, J. C., R. J. Y��ez, J. S. Dehesa, and E. Romera. "Monotonicity properties of the atomic charge density function." International Journal of Quantum Chemistry 58, no. 1 (1996): 11–21. http://dx.doi.org/10.1002/(sici)1097-461x(1996)58:1<11::aid-qua2>3.0.co;2-0.

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48

Li, XiaoHui, HaiTao Wu, YuJing Bian, and DanNi Wang. "Satellite virtual atomic clock with pseudorange difference function." Science in China Series G: Physics, Mechanics and Astronomy 52, no. 3 (2009): 353–59. http://dx.doi.org/10.1007/s11433-009-0059-4.

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49

Yerokhin, Vladimir A., Vojtěch Patkóš, and Krzysztof Pachucki. "Atomic Structure Calculations of Helium with Correlated Exponential Functions." Symmetry 13, no. 7 (2021): 1246. http://dx.doi.org/10.3390/sym13071246.

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The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1, r2 and r = |r→1−r→2|. The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) allows us to construct an accurate and compact representation of the

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50

Baltenkov, Arkadiy S., and Igor Woiciechowski. "Interference Phenomenon in Electron-Molecule Collisions." Atoms 10, no. 4 (2022): 105. http://dx.doi.org/10.3390/atoms10040105.

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This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combina

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