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Journal articles on the topic 'Geometric terms'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Rahmah, Salma Mu'allimatur. "Profil Berpikir Geometri Siswa SMP dalam Menyelesaikan Soal Geometri Ditinjau dari Level Berpikir Van Hiele." MATHEdunesa 9, no. 3 (2021): 562–69. http://dx.doi.org/10.26740/mathedunesa.v9n3.p562-569.

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Abstrak Berpikir geometris merupakan serangkaian aktivitas yang dilakukan oleh siswa dalam menyelesaikan soal geometri meliputi visualisasi, konstruksi, dan penalaran. Terdapat perbedaan dalam proses berpikir geometris yang dilakukan para siswa dalam menyelesaikan soal. Salah satu yang mempengaruhi proses berpikir geometris siswa adalah level berpikir Van Hiele. Penelitian ini merupakan penelitian deskriptif kualitatif yang bertujuan untuk mendeskripsikan profil berpikir geometris siswa dalam menyelesaikan soal geometri ditinjau dari level berpikir Van Hiele. Subjek penelitian ini terdir

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2

Milan, Barman. "A comparative study on the Sulvic and geometric terms." International Journal of Applied Research 2, no. 8, Part C (2016): 192–93. https://doi.org/10.5281/zenodo.7987115.

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The Seers of Śulvasūtras used various terms to make the altars and subsequently contributed to a great Science developed in modern Geometry. In the Śulvasūtra, the Seers sowed the seed of modern Geometry.

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3

Dargys, A. "Optical Mueller matrices in terms of geometric algebra." Optics Communications 285, no. 24 (2012): 4785–92. http://dx.doi.org/10.1016/j.optcom.2012.07.058.

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4

Ewen, H., P. Schaller, and G. Schwarz. "Schwinger terms from geometric quantization of field theories." Journal of Mathematical Physics 32, no. 5 (1991): 1360–67. http://dx.doi.org/10.1063/1.529288.

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5

Khashaba, Mohamed, and Mahmoud El-Shourbagy. "Road Geometric Design in Terms of Value Engineering." Nile Journal of Architecture and Civil Engineering 2, no. 1 (2023): 30–37. http://dx.doi.org/10.21608/njace.2023.278689.

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6

Huilgol,, Medha. "Geometric Circular Graphs." Mapana - Journal of Sciences 5, no. 2 (2006): 19–25. http://dx.doi.org/10.12723/mjs.9.3.

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In this paper we study a class of graphs,which resemble a Circle in a plane in terms of diameter and radius.We introduce the term "Geometric Circular Graphs" for those graphs whose diameter is equal to twice the radius of the graph.Here we have studied some properties of geometric circular graphs.Also we have found some bounds in terms of the number of edges.

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7

Eteje, S. O., O. F. Oduyebo, and P. D. Oluyori. "Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models." Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models. International Journal of Environment, Agriculture and Biotechnology (IJEAB) 4, no. 4 (2019): 1181–94. https://doi.org/10.5281/zenodo.3376613.

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The application of the geometric method of local geoid model determination which requires the fitting of geometric surfaces to known geoid heights to enable geoid heights of new points to be interpolated involves the use of least squares technique for computation of the models' parameters. The selection of polynomial geometric surfaces depends on the size of the study area, the variation of the geoid heights and the number of measurement points. The accuracy of the geometric geoid model increases as the number of observation points approximates the number of geometric surface terms. But in

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8

Dargys, A. "Constitutive relations in optics in terms of geometric algebra." Optics Communications 354 (November 2015): 259–65. http://dx.doi.org/10.1016/j.optcom.2015.06.004.

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9

Alphayta, Büşra, and Hayal Yavuz Mumcu. "Connecting Geometric Reasoning Skill and Self-Efficacy Perception Variables in terms of Cognitive and Perceptual Dimensions." Participatory Educational Research 12, no. 3 (2025): 22–50. https://doi.org/10.17275/per.25.32.12.3.

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This study aims to develop a scale to determine eighth-grade students' self-efficacy perceptions towards geometric reasoning and to evaluate and relate the variables of geometric reasoning skill and self-efficacy perception in terms of cognitive and perceptual dimensions. The research was conducted in two stages. In the first stage, the validity and reliability studies of the developed scale were conducted, and its usability was demonstrated. In the second stage, geometric reasoning skill and self-efficacy perception variables were examined in terms of cognitive and perceptual dimensions. In t

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10

Wang, Zisheng, and Hui Pan. "Geometric phase carried by the observables and its application to quantum computation." Quantum Information and Computation 15, no. 11&12 (2015): 951–61. http://dx.doi.org/10.26421/qic15.11-12-5.

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We investigate geometric phases in terms of Heisenberg equation. We find that, equivalently to Schr\"odinger picture with a memory of its motion in terms of the geometric phase factor contained in the wave function, the observales carry with the geometric message under their evolutions in the Heisenberg picture. Such an intrinsic geometric feature may be particularly useful to implement the multi-time correlation geometric quantum gate in terms of the observables, which leads to a possible reduction in experimental errors as well as gate timing. An application is discussed for nuclear-magnetic

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11

Labesse, J. P. "STABLE TWISTED TRACE FORMULA: ELLIPTIC TERMS." Journal of the Institute of Mathematics of Jussieu 3, no. 4 (2004): 473–530. http://dx.doi.org/10.1017/s1474748004000143.

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This paper deals with the stabilization of the contribution of elliptic elements to the geometric side of the general twisted trace formula. We extend the results of Langlands, Kottwitz and Shelstad to all elliptic elements for the general twisted trace formula.AMS 2000 Mathematics subject classification: Primary 11F72; 11R39; 11R34

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12

MOROZOV, A. YU, ANTTI J. NIEMI, and K. PALO. "GEOMETRIC APPROACH TO SUPERSYMMETRY." International Journal of Modern Physics B 06, no. 11n12 (1992): 2149–57. http://dx.doi.org/10.1142/s0217979292001079.

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We argue that a generic supersymmetric theory can be characterized entirely in terms of loop space symplectic geometry, either in a loop space parametrized by the bosonic variables or in a superloop space parametrized by half of the bosonic and fermionic variables. A Poincare supersymmetric theory is a realization of our construction in terms of space-time variables that admit a natural Lorentz-invariant interpretation. Our approach opens a new, geometric point of view to a large number of problems, including the mechanism of supersymmetry breaking and the structure of topological quantum fiel

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13

Chen, Yanting, Richard J. Boucherie, and Jasper Goseling. "THE INVARIANT MEASURE OF RANDOM WALKS IN THE QUARTER-PLANE: REPRESENTATION IN GEOMETRIC TERMS." Probability in the Engineering and Informational Sciences 29, no. 2 (2015): 233–51. http://dx.doi.org/10.1017/s026996481400031x.

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We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individually satisfy the balance equations in the interior of the state space and further show that the geometric terms in an invariant measure must have a pairwise-coupled structure. Finally, we show that at leas

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14

SUZUKI, Hiromasa, Fumihiko KIMURA, and Toshio SATA. "Treating dimensions in terms of geometric constraints in product models." Journal of the Japan Society for Precision Engineering 52, no. 6 (1986): 1037–42. http://dx.doi.org/10.2493/jjspe.52.1037.

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15

Yatsko, V. A. "The interpretation of Bradford’s law in terms of geometric progression." Automatic Documentation and Mathematical Linguistics 46, no. 2 (2012): 112–17. http://dx.doi.org/10.3103/s0005105512020094.

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16

Bruner, Christopher W. S. "Geometric properties of arbitrary polyhedra in terms of face geometry." AIAA Journal 33, no. 7 (1995): 1350. http://dx.doi.org/10.2514/3.12556.

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17

Petreska, Irina, Pece Trajanovski, Trifce Sandev, Jonathan Rocha, Antonio de Castro, and Ervin Lenzi. "Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints." Mathematics 13, no. 1 (2025): 137. https://doi.org/10.3390/math13010137.

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Here, we investigate a three-dimensional Schrödinger equation that generalizes the standard framework by incorporating geometric constraints. Specifically, the equation is adapted to account for a backbone structure exhibiting memory effects dependent on both time and spatial position. For this, we incorporate an additional term in the Schrödinger equation with a nonlocal dependence governed by short- or long-tailed distributions characterized by power laws associated with Lévy distributions. This modification also introduces a backbone structure within the system. We derive solutions that rev

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18

de Azcárraga, J. A., J. M. Izquierdo, and A. J. Macfarlane. "Current algebra and Wess-Zumino terms: a unified geometric treatment." Annals of Physics 202, no. 1 (1990): 1–21. http://dx.doi.org/10.1016/0003-4916(90)90338-o.

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19

Sreehari, M., and R. Vasudeva. "Characterizations of multivariate geometric distributions in terms of conditional distributions." Metrika 75, no. 2 (2010): 271–86. http://dx.doi.org/10.1007/s00184-010-0326-4.

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20

Demuth, M., W. Kirsch, and I. McGillivray. "SchröDinger operators - geometric estimates in terms of the occupation time." Communications in Partial Differential Equations 20, no. 1-2 (1995): 37–57. http://dx.doi.org/10.1080/03605309508821086.

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21

Grudzień, Kamil, and Lesław Polny. "Harmonized Rating Land Property in Terms of Its Geometric Configuration." Geomatics and Environmental Engineering 10, no. 4 (2016): 39. http://dx.doi.org/10.7494/geom.2016.10.4.39.

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22

Dalla, Leoni, and Telemachos Hatziafratis. "Strict convexity of sets in analytic terms." Journal of the Australian Mathematical Society 81, no. 1 (2006): 49–62. http://dx.doi.org/10.1017/s1446788700014634.

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AbstractWe compare the geometric concept of strict convexity of open subsets of Rn with the analytic concept of 2-strict convexity, which is based on the defining functions of the set, and we do this by introducing the class of 2N-strictly convex sets. We also describe an exhaustion process of convex sets by a sequence of 2-strictly convex sets.

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23

FUJIKAWA, KAZUO. "TOPOLOGICAL PROPERTIES OF BERRY'S PHASE." Modern Physics Letters A 20, no. 05 (2005): 335–43. http://dx.doi.org/10.1142/s0217732305016579.

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By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian in the present formulation. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial for any finite time interval T. The topological interpretation of Berry's phase such as the topological proof of phase-change rule thus fails in the practical Born–

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24

Mark, Leonard S., and James T. Todd. "Describing perceptual information about human growth in terms of geometric invariants." Perception & Psychophysics 37, no. 3 (1985): 249–56. http://dx.doi.org/10.3758/bf03207572.

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25

Aulbach, Martin, Damian Markham, and Mio Murao. "The maximally entangled symmetric state in terms of the geometric measure." New Journal of Physics 12, no. 7 (2010): 073025. http://dx.doi.org/10.1088/1367-2630/12/7/073025.

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26

Di Barba, Paolo, Luisa Fattorusso, and Mario Versaci. "Electrostatic field in terms of geometric curvature in membrane MEMS devices." Communications in Applied and Industrial Mathematics 8, no. 1 (2017): 165–84. http://dx.doi.org/10.1515/caim-2017-0009.

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Abstract In this paper we present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady- state case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychono's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried

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27

Fisanov, V. V. "Formulation of the Snell–Descartes Laws in Terms of Geometric Algebra." Russian Physics Journal 62, no. 5 (2019): 794–99. http://dx.doi.org/10.1007/s11182-019-01779-9.

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28

TERAMOTO, KEISUKE. "FOCAL SURFACES OF WAVE FRONTS IN THE EUCLIDEAN 3-SPACE." Glasgow Mathematical Journal 61, no. 2 (2018): 425–40. http://dx.doi.org/10.1017/s0017089518000277.

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AbstractWe characterise singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric invariants of the initial wave fronts.

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29

Li, Pengzhong, Ruihan Zhao, and Liang Luo. "A Geometric Accuracy Error Analysis Method for Turn-Milling Combined NC Machine Tool." Symmetry 12, no. 10 (2020): 1622. http://dx.doi.org/10.3390/sym12101622.

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Turn-Milling Combined NC machine tool is different from traditional machine tools in structure and process realization. As an important means in the design stage, the analysis method of geometric accuracy error is also different from the traditional method. The actual errors and the error compensation values are a pair of "symmetry" data sets which are connected by the movement of machine tools. The authors try to make them more consistent through this work. The geometric error terms were firstly determined by topological structure analysis, then based on homogeneous coordinate transformation

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30

Asha, G., and N. Unnikrishnan Nair. "Characterization of a Bivariate Geometric Distribution." Calcutta Statistical Association Bulletin 46, no. 1-2 (1996): 23–28. http://dx.doi.org/10.1177/0008068319960103.

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31

Drechsler, W. "Geometric Formulation of Gauge Theories." Zeitschrift für Naturforschung A 46, no. 8 (1991): 645–54. http://dx.doi.org/10.1515/zna-1991-0801.

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AbstractThe development of gauge theories is reviewed beginning with Weyl's theory of 1918 and with the changes introduced by London in the context of quantum mechanics. After a discussion of the Yang-Mills theory and Utiyama's work in the fifties the translation to the modern geometric formulation of gauge theories in terms of fiber bundles is presented

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32

CARTER, J. SCOTT, SEIICHI KAMADA, and MASAHICO SAITO. "GEOMETRIC INTERPRETATIONS OF QUANDLE HOMOLOGY." Journal of Knot Theory and Its Ramifications 10, no. 03 (2001): 345–86. http://dx.doi.org/10.1142/s0218216501000901.

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Geometric representations of cycles in quandle homology theory are given in terms of colored knot diagrams. Abstract knot diagrams are generalized to diagrams with exceptional points which, when colored, correspond to degenerate cycles. Bounding chains are realized, and used to obtain equivalence moves for homologous cycles. The methods are applied to prove that boundary homomorphisms in a homology exact sequence vanish.

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33

Hitha, N., and N. Unnikrishnan Nair. "Characterization of Some Discrete Models by Properties of Residual Life Function." Calcutta Statistical Association Bulletin 38, no. 3-4 (1989): 219–24. http://dx.doi.org/10.1177/0008068319890310.

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34

Marquez, Barbara, Zachary T. Wooten, Ramon M. Salazar, et al. "Analyzing the Relationship between Dose and Geometric Agreement Metrics for Auto-Contouring in Head and Neck Normal Tissues." Diagnostics 14, no. 15 (2024): 1632. http://dx.doi.org/10.3390/diagnostics14151632.

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This study aimed to determine the relationship between geometric and dosimetric agreement metrics in head and neck (H&N) cancer radiotherapy plans. A total 287 plans were retrospectively analyzed, comparing auto-contoured and clinically used contours using a Dice similarity coefficient (DSC), surface DSC (sDSC), and Hausdorff distance (HD). Organs-at-risk (OARs) with ≥200 cGy dose differences from the clinical contour in terms of Dmax (D0.01cc) and Dmean were further examined against proximity to the planning target volume (PTV). A secondary set of 91 plans from multiple institutions valid

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35

Mulyani, Tri, Moh Hasan, and S. Slamin. "Finite Difference Method and Newton's Theorem to Determine the Sum of Series." Jurnal ILMU DASAR 14, no. 2 (2014): 91. http://dx.doi.org/10.19184/jid.v14i2.515.

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Problems that are often faced to prove the truth of a formula if the presented series is a series that is not the formula of arithmetic and geometric series. One proof among the most commonly proofs used is the proof by mathematical induction. This study was conducted to determine the sum of the first n terms formula of: (1) arithmetic series, storied arithmetic series with the basis of arithmetic series, (2) geometric series, (3) storied arithmetic series with the basis of geometric series, and (4) series which are not arithmetic and geometric series that the formula of the n terms is given,

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36

Eteje, S. O., O. F. Oduyebo, and P. D. Oluyori. "Relationship between Polynomial Geometric Surfaces Terms and Observation Points Numbers and Effect in the Accuracy of Geometric Geoid Models." International Journal of Environment, Agriculture and Biotechnology 4, no. 4 (2019): 1181–94. http://dx.doi.org/10.22161/ijeab.4444.

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37

Kargın, Levent. "p-Bernoulli and geometric polynomials." International Journal of Number Theory 14, no. 02 (2018): 595–613. http://dx.doi.org/10.1142/s1793042118500665.

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We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text]-Bernoulli polynomials. These results yield new identities for Bernoulli numbers. Moreover, we evaluate a Faulhaber-type summation in terms of [Formula: see text]-Bernoulli polynomials. Finally, we introduce poly-[Formula: see text]-Bernoulli polynomials and numbers, then study some arithmetical and number theoretical properties of them.

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38

Jin, Xin Qin, Jian Yi Zhang, and Dan Song. "Cognitive Study of Geometric Figure in Man-Machine Interface." Applied Mechanics and Materials 278-280 (January 2013): 2274–77. http://dx.doi.org/10.4028/www.scientific.net/amm.278-280.2274.

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Graphic elements is the most likely form to accept in people’s visual perception of man-machine interface, different people will have different cognitive graphics understanding. In this paper, the rectangular cylindrical, triangular prism, cylindrical, conical, spherical geometry as a stimulus, and test the reaction time of the subjects, the misuse rate of indicators above the 5 geometries recognized. The outcome: In terms of “press”, rectangular cylindrical, triangular prism, cylindrical is more sensitive than conical; In terms of “pull”, triangular prism, cylindrical is more sensitive than s

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39

Wu, Yi-Ting, and Feng Qi. "Schur m-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means." Mathematica Slovaca 73, no. 1 (2023): 3–14. http://dx.doi.org/10.1515/ms-2023-0002.

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Abstract In the paper, the authors present the Schur m-power convexity and concavity for the general geometric Bonferroni mean of multiple parameters and establish comparison inequalities for bounding the general geometric Bonferroni mean in terms of the arithmetic, geometric, and harmonic means. These Schur convexity and concavity provide a unified generalization of the Schur convexity and concavity for the geometric Bonferroni means of two or three parameters.

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40

Fisanov, V. V. "The formulation of the Snell - Descartes laws in terms of geometric algebra." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 5 (May 2019): 54–58. http://dx.doi.org/10.17223/00213411/62/5/54.

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41

Pairet, Eric, Paola Ardon, Michael Mistry, and Yvan Petillot. "Learning Generalizable Coupling Terms for Obstacle Avoidance via Low-Dimensional Geometric Descriptors." IEEE Robotics and Automation Letters 4, no. 4 (2019): 3979–86. http://dx.doi.org/10.1109/lra.2019.2930431.

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42

McNew, Nathan. "On sets of integers which contain no three terms in geometric progression." Mathematics of Computation 84, no. 296 (2015): 2893–910. http://dx.doi.org/10.1090/mcom/2979.

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43

Liu, Baoyu, Weiming Gong, Yingqing Song, and Yuming Chu. "Sharp bounds for Seiffert mean in terms of arithmetic and geometric means." International Journal of Mathematical Analysis 7 (2013): 1765–73. http://dx.doi.org/10.12988/ijma.2013.3349.

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44

Filipovski, Slobodan. "ON THE NUMBER OF DIVISORS OF THE TERMS OF A GEOMETRIC PROGRESSION." Far East Journal of Mathematical Education 26, no. 1 (2024): 29–33. http://dx.doi.org/10.17654/0973563124004.

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45

SONG, YING, NING ZHANG, and TONG WU. "Image evaluation and analysis of fabric with a geometric motif in dress style design." Industria Textila 75, no. 05 (2024): 591–98. http://dx.doi.org/10.35530/it.075.05.2023130.

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To explore the differences in sensory imagery produced by different geometric patterns and dress silhouettes, this study selected and extracted 4 different types of geometric patterns and 4 typical dress silhouettes as research carriers, determined the research samples through cross-combination, and used 8 pairs of sensory word pairs as research semantic space. Consumer sensory evaluations of the dress samples were collected through a survey questionnaire. The results were analysed using SPSS26.0 software, which showed that three sensory factors affect the appearance of the dress style. Accord

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46

Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 1 (1987): 97–104. http://dx.doi.org/10.2307/3214062.

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Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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47

Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 01 (1987): 97–104. http://dx.doi.org/10.1017/s0021900200030643.

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Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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48

Belovas, Igoris. "The Asymptotics of the Geometric Polynomials." Mathematica Slovaca 73, no. 2 (2023): 335–42. http://dx.doi.org/10.1515/ms-2023-0026.

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Abstract The paper investigates the asymptotic behavior of the geometric polynomials, when the polynomial degree tends to infinity. Using the contour integration technique, we obtain an asymptotic formula, given explicitly in terms of the polynomial degree and variable. This type of asymptotics will be applied to derive limit theorems for combinatorial numbers.

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49

FACCHI, PAOLO, and SAVERIO PASCAZIO. "THE GEOMETRY OF THE QUANTUM ZENO EFFECT." International Journal of Geometric Methods in Modern Physics 09, no. 02 (2012): 1260024. http://dx.doi.org/10.1142/s0219887812600249.

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The quantum Zeno effect is described in geometric terms. The quantum Zeno time (inverse standard deviation of the Hamiltonian) and the generator of the quantum Zeno dynamics are both given a geometric interpretation.

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50

Latimer, Cyril, Catherine Stevens, Mark Irish, and Leanne Webber. "Attentional Biases in Geometric form Perception." Quarterly Journal of Experimental Psychology Section A 53, no. 3 (2000): 765–91. http://dx.doi.org/10.1080/713755915.

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This paper reports the operation of robust attentional bias to the top and right during perception of small, single geometric forms. Same/different judgements of successively presented standard and comparison forms are faster when local differences are located at top and right rather than in other regions of the forms. The bias persists when form size is reduced to approximately one degree of visual angle, and it is unaffected by saccadic eye movements and by instructions to attend to other reliably differentiating regions of the forms. Results lend support in various degrees to two of the pos

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