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Journal articles on the topic 'Tangent'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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1

Дмитриева, И., I. Dmitrieva, Геннадий Иванов, and Gennadiy Ivanov. "Competence Approach in Teaching the Topic "Tangent Plane and Normal"." Geometry & Graphics 6, no. 4 (January 29, 2019): 47–54. http://dx.doi.org/10.12737/article_5c21f80e2925c6.80568562.

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Qualified presentation of the topic "Tangent Plane and Surface Normal" in terms of competence approach is possible with the proper level for students' attention focusing on both intra-subject and inter-subject relations of descriptive geometry. Intra-subject connections follow from the position that the contingence is a particular (limit) case of intersection. Therefore, the line of intersection of the tangent plane and the surface, or two touching surfaces, has a special point at the tangency point. It is known from differential geometry [1] that this point can be nodal, return, or isolated one. In turn, this point’s appearance depends on differential properties of the surface(s) in this point’s vicinity. That's why, for the competent solution of the considered positional problem account must be also taken of the inter-subject connections for descriptive and differential geometry. In the training courses of descriptive geometry tangent planes are built only to the simplest surfaces, containing, as a rule, the frames of straight lines and circles. Therefore, the tangent plane is defined by two tangents drawn at the tangency point to two such lines. In engineering practice, as such lines are used cross-sections a surface by planes parallel to any two coordinate planes. That is, from the standpoints for the course of higher mathematics, the problem is reduced to calculation for partial derivatives. Although this topic is studied after the course of descriptive geometry, it seems possible to give geometric explanation for computation of partial derivatives in a nutshell. It also seems that the study of this topic will be stimulated by a story about engineering problems, which solution is based on construction of the tangent plane and the normal to the technical surface. In this paper has been presented an example for the use of surface curvature lines for programming of milling processing for 3D-harness surfaces.

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2

Koval, Galyna, Margarita Lazarchuk, and Liudmila Ovsienko. "APPLICATION OF CIRCLES FOR CONJUGATION OF FLAT CONTOURS OF THE FIRST ORDER OF SMOOTHNESS." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 100 (May 24, 2021): 162–71. http://dx.doi.org/10.32347/0131-579x.2021.100.162-171.

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In geometric modeling of contours, especially for conjugation of sections of flat contours of the first order of smoothness, arcs of circles can be applied. The article proposes ways to determine the equations of a circle for two ways of its problem: the problem of a circle with a point and two tangents, none of which contains a given point, and the problem of a circle with three tangents. The equations of the circles were determined in both cases using a projective coordinate system. In the first case, when a circle is given by a point and two tangents, neither of which contains this point, the center of the conjugation circle is defined as the point of intersection of two locus of points - the bisector of the angle between the tangents and the parabola, the focus of which is a given point. given tangents. In the general case, there are 2 conjugation circles for which canonical equations are defined. Parametric equations of conjugate circles, the parameters of which are equal to 0 and ∞ on tangents and equal to one at a given point, with the help of affine and projective coordinates of points of contact are determined first in the projective coordinate system, and then translated into affine system. For the second case, when specifying a circle using three tangent lines, the equation of the second-order curve tangent to these lines is first determined in the projective coordinate system. The tangent lines are taken as the coordinate lines of the projective coordinate system. The unit point of the projective coordinate system is selected in the metacenter of the thus obtained base triangle. The equation of the tangent to the base lines of the second order contains two unknown variables, positive or negative values which determine the location of four possible tangents of the second order. After writing the vector-parametric equation of the tangent curve of the second order in the affine coordinate system, the equation is written to determine the parameters of cyclic points. In order for the equation of the tangent curve of the second order obtained in the projective plane to be an equation of a circle, it must satisfy the coordinates of the cyclic points of the plane, which allows to write the second equation to determine the parameters of cyclic points. By solving a system of two equations, we obtain the required equations of circles tangent to three given lines.

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3

Watkins, G. G. "Clarke's tangent vectors as tangents to lipschitz continuous curves." Journal of Optimization Theory and Applications 45, no. 2 (February 1985): 325–34. http://dx.doi.org/10.1007/bf00939984.

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4

Lê, Công-Trình, and Tien-Son Phạm. "On tangent cones at infinity of algebraic varieties." Journal of Algebra and Its Applications 17, no. 08 (July 8, 2018): 1850143. http://dx.doi.org/10.1142/s0219498818501438.

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In this paper, we define the geometric and algebraic tangent cones at infinity of algebraic varieties and establish the following version at infinity of Whitney’s theorem [Local properties of analytic varieties, in Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse) (Princeton University Press, Princeton, N. J., 1965), pp. 205–244; Tangents to an analytic variety, Ann. of Math. 81 (1965) 496–549]: The geometric and algebraic tangent cones at infinity of complex algebraic varieties coincide. The proof of this fact is based on a geometric characterization of the geometric tangent cone at infinity using the global Łojasiewicz inequality with explicit exponents for complex algebraic varieties. Moreover, we show that the tangent cone at infinity of a complex algebraic variety is actually the part at infinity of this variety [G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, 2nd extended edn. (Springer, Berlin, 2008)]. We also show that the tangent cone at infinity of a complex algebraic variety can be computed using Gröbner bases.

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5

Qi, Feng. "Derivatives of tangent function and tangent numbers." Applied Mathematics and Computation 268 (October 2015): 844–58. http://dx.doi.org/10.1016/j.amc.2015.06.123.

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6

Stanley, P. "Tangent Circles." Mathematical Gazette 86, no. 507 (November 2002): 386. http://dx.doi.org/10.2307/3621129.

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7

Simis, Aron, Bernd Ulrich, and Wolmer V. Vasconcelos. "Tangent algebras." Transactions of the American Mathematical Society 364, no. 2 (February 1, 2012): 571–94. http://dx.doi.org/10.1090/s0002-9947-2011-05161-5.

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8

Doris Devenport. "Another Tangent." Appalachian Heritage 36, no. 3 (2008): 55. http://dx.doi.org/10.1353/aph.2008.0032.

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9

Martin, D. H., and G. G. Watkins. "Cores of Tangent Cones and Clarke's Tangent Cone." Mathematics of Operations Research 10, no. 4 (November 1985): 565–75. http://dx.doi.org/10.1287/moor.10.4.565.

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10

Choi, Woocheol, and Raphaël Ponge. "Tangent maps and tangent groupoid for Carnot manifolds." Differential Geometry and its Applications 62 (February 2019): 136–83. http://dx.doi.org/10.1016/j.difgeo.2018.11.002.

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11

Corcino, Cristina B., Roberto B. Corcino, and Jay M. Ontolan. "Approximations of Tangent Polynomials, Tangent –Bernoulli and Tangent – Genocchi Polynomials in terms of Hyperbolic Functions." Journal of Applied Mathematics 2021 (November 29, 2021): 1–10. http://dx.doi.org/10.1155/2021/8244000.

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Asymptotic approximations of Tangent polynomials, Tangent-Bernoulli, and Tangent-Genocchi polynomials are derived using saddle point method and the approximations are expressed in terms of hyperbolic functions. For each polynomial there are two approximations derived with one having enlarged region of validity.

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12

Corcino, Cristina Bordaje, and Roberto Bagsarsa Corcino. "Fourier Series for the Tangent Polynomials, Tangent–Bernoulli and Tangent–Genocchi Polynomials of Higher Order." Axioms 11, no. 3 (February 22, 2022): 86. http://dx.doi.org/10.3390/axioms11030086.

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In this paper, the Fourier series expansion of Tangent polynomials of higher order is derived using the Cauchy residue theorem. Moreover, some variations of higher-order Tangent polynomials are defined by mixing the concept of Tangent polynomials with that of Bernoulli and Genocchi polynomials, Tangent–Bernoulli and Tangent–Genocchi polynomials. Furthermore, Fourier series expansions of these variations are also derived using the Cauchy residue theorem.

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13

Zhe, Jingping, and Stewart A. Greenhalgh. "A new kinematic method for mapping seismic reflectors." GEOPHYSICS 64, no. 5 (September 1999): 1594–602. http://dx.doi.org/10.1190/1.1444663.

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This paper presents a modern version of an old technique of common tangent reflection migration. Rather than using the graphical method of swinging arcs and looking for the envelope of touching tangents on widely separated geophones, we use a numerical scheme of searching along each isochron, constructed by a wave‐equation‐based modeling scheme for arbitrary velocity media, to find the common tangent points. The assumption is made that the receivers are close together so that the interface can be locally approximated by a straight line, although different pairs of receivers permit different tangents to be found, enabling a curved boundary to be migrated. The technique can be extended to several shot gathers to map multiple curved boundaries. Synthetic examples are used to illustrate the capabilities of the method and the effect of using an erroneous velocity distribution.

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14

Karimoi, Reza Yaghoobi, and Azra Yaghoobi Karimoi. "Classification of EEG signals using Hyperbolic Tangent-Tangent Plot." International Journal of Intelligent Systems and Applications 6, no. 8 (July 8, 2014): 39–45. http://dx.doi.org/10.5815/ijisa.2014.08.04.

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15

Ryoo, C. S. "Multiple q-tangent zeta functions and q-tangent polynomials." Applied Mathematical Sciences 8 (2014): 3755–61. http://dx.doi.org/10.12988/ams.2014.45329.

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16

Körpinar, Zeliha, and Talat Körpinar. "Optical tangent hybrid electromotives for tangent hybrid magnetic particle." Optik 247 (December 2021): 167823. http://dx.doi.org/10.1016/j.ijleo.2021.167823.

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17

Kadaoui Abbassi, Mohamed Tahar, and Noura Amri. "Natural Ricci Solitons on Tangent and Unit Tangent Bundles." Zurnal matematiceskoj fiziki, analiza, geometrii 17, no. 1 (January 25, 2021): 3–29. http://dx.doi.org/10.15407/mag17.01.003.

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18

Elgindi, Ali M. "A topological obstruction to the removal of a degenerate complex tangent and some related homotopy and homology groups." International Journal of Mathematics 26, no. 05 (May 2015): 1550025. http://dx.doi.org/10.1142/s0129167x15500251.

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In this paper, we derive a topological obstruction to the removal of an isolated degenerate complex tangent to an embedding of a 3-manifold into ℂ3 (without affecting the structure of the remaining complex tangents). We demonstrate how the vanishing of this obstruction is both a necessary and sufficient condition for the (local) removal of the isolated complex tangent. The obstruction is a certain homotopy class of the space 𝕐 consisting of totally real 3-planes in the Grassmannian of real 3-planes in ℂ3(= ℝ6). We further compute additional homotopy and homology groups for the space 𝕐 and of its complement 𝕎 consisting of "partially complex" 3-planes in ℂ3.

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19

Butler, Steven. "Tangent Line Transformations." College Mathematics Journal 34, no. 2 (March 2003): 105. http://dx.doi.org/10.2307/3595781.

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20

Acala, Nestor Gonzales, and Maribeth B. Montero. "Truncated Tangent Polynomials." European Journal of Pure and Applied Mathematics 13, no. 4 (October 31, 2020): 948–63. http://dx.doi.org/10.29020/nybg.ejpam.v13i4.3839.

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In this paper, we introduce a class of truncated tangent polynomials which generalizes tangent numbers and polynomials, and establish various properties and identities. Moreover, we obtain some interesting correlations of truncated tangent polynomials with the Stirling numbers of the second kind and with the hypergeometric Bernoulli polynomials.

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21

Berrendero, José R., and Javier Cárcamo. "The Tangent Classifier." American Statistician 66, no. 3 (August 2012): 185–94. http://dx.doi.org/10.1080/00031305.2012.710511.

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22

Butler, Steven. "Tangent Line Transformations." College Mathematics Journal 34, no. 2 (March 2003): 105–6. http://dx.doi.org/10.1080/07468342.2003.11921991.

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23

Courant, T. "Tangent Lie algebroids." Journal of Physics A: Mathematical and General 27, no. 13 (July 7, 1994): 4527–36. http://dx.doi.org/10.1088/0305-4470/27/13/026.

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24

Eisum, E. Frank. "TANGENT SCREEN ILLUMINATION." Acta Ophthalmologica 37, no. 4 (May 27, 2009): 386–87. http://dx.doi.org/10.1111/j.1755-3768.1959.tb03450.x.

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25

Courant, T. "Tangent Dirac structures." Journal of Physics A: Mathematical and General 23, no. 22 (November 21, 1990): 5153–68. http://dx.doi.org/10.1088/0305-4470/23/22/010.

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26

Schwartzman, Sol. "Parallel tangent hyperplanes." Proceedings of the American Mathematical Society 130, no. 5 (December 27, 2001): 1457–58. http://dx.doi.org/10.1090/s0002-9939-01-06522-4.

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27

Kutateladze, S. S. "Infinitesimal tangent cones." Siberian Mathematical Journal 26, no. 6 (1986): 833–41. http://dx.doi.org/10.1007/bf00969104.

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28

Malajovich, Gregorio, and Jorge P. Zubelli. "Tangent Graeffe iteration." Numerische Mathematik 89, no. 4 (October 2001): 749–82. http://dx.doi.org/10.1007/s002110100278.

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29

McQuillan, Daniel, and Rob Poodiack. "On the Differentiation Formulae for Sine, Tangent, and Inverse Tangent." College Mathematics Journal 45, no. 2 (March 2014): 140–42. http://dx.doi.org/10.4169/college.math.j.45.2.140.

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30

Ryoo, C. S. "Multiple tangent zeta function and tangent polynomials of higher order." Advanced Studies in Theoretical Physics 8 (2014): 457–62. http://dx.doi.org/10.12988/astp.2014.4442.

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31

de León, M., Isabel Méndez, and M. Salgado. "Integrablep-almost tangent manifolds and tangent bundles ofp 1-velocities." Acta Mathematica Hungarica 58, no. 1-2 (March 1991): 45–54. http://dx.doi.org/10.1007/bf01903546.

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32

Buczolich, Zoltán. "Micro tangent sets of continuous functions." Mathematica Bohemica 128, no. 2 (2003): 147–67. http://dx.doi.org/10.21136/mb.2003.134036.

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33

Cordero, Luis A., Manuel de León, Isabel Méndez, and Modesto Salgado. "Existence of $p$-almost tangent structures." Czechoslovak Mathematical Journal 42, no. 2 (1992): 225–34. http://dx.doi.org/10.21136/cmj.1992.128337.

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34

Boeckx, E., and L. Vanhecke. "Harmonic and minimal vector fields on tangent and unit tangent bundles." Differential Geometry and its Applications 13, no. 1 (July 2000): 77–93. http://dx.doi.org/10.1016/s0926-2245(00)00021-8.

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35

Whitmore, Stephen A. "Real Gas Extensions to Tangent-Wedge and Tangent-Cone Analysis Methods." AIAA Journal 45, no. 8 (August 2007): 2024–32. http://dx.doi.org/10.2514/1.28521.

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36

Ryoo, Cheon. "Symmetric Identities for (P,Q)-Analogue of Tangent Zeta Function." Symmetry 10, no. 9 (September 11, 2018): 395. http://dx.doi.org/10.3390/sym10090395.

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The goal of this paper is to define the ( p , q ) -analogue of tangent numbers and polynomials by generalizing the tangent numbers and polynomials and Carlitz-type q-tangent numbers and polynomials. We get some explicit formulas and properties in conjunction with ( p , q ) -analogue of tangent numbers and polynomials. We give some new symmetric identities for ( p , q ) -analogue of tangent polynomials by using ( p , q ) -tangent zeta function. Finally, we investigate the distribution and symmetry of the zero of ( p , q ) -analogue of tangent polynomials with numerical methods.

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37

Collins, Kent M., and Raymond A. Krammes. "Preliminary Validation of a Speed-Profile Model for Design Consistency Evaluation." Transportation Research Record: Journal of the Transportation Research Board 1523, no. 1 (January 1996): 11–21. http://dx.doi.org/10.1177/0361198196152300102.

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The validity of a speed-profile model for design consistency evaluation was tested, including (a) the speed reduction estimation ability of the model and (b) assumptions about deceleration and acceleration characteristics approaching and departing horizontal curves. Detailed speed data were collected at a sample of 10 horizontal tangent-curve sections on two-lane rural highways in Texas. The results indicate that the model provides a reasonable, albeit simplified, representation of speed profiles on horizontal alignments consisting of long tangents and isolated curves. The model provides reasonable estimates of speed reductions from long approach tangents to curves but does not account for the effect of nearby intersections on speeds. The results also indicate that the assumed 0.85 m/sec2 value is reasonable for deceleration rates approaching curves that require speed reductions but may overestimate acceleration rates departing curves. The model's assumptions that deceleration occurs entirely on the approach tangent and that speeds are constant throughout a curve were not confirmed by observed speed behavior. The observations that deceleration continues after entering a curve and that speed adjustments occur throughout a curve are indicators of the difficulty drivers experience in judging appropriate speeds through curves.

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38

KONG, L. B., L. LIU, J. W. ZHAI, Z. W. LI, and Z. H. YANG. "REVISIT TO DIELECTRIC PROPERTIES OF FERRITE CERAMICS." Journal of Advanced Dielectrics 02, no. 03 (July 2012): 1230010. http://dx.doi.org/10.1142/s2010135x12300101.

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Dielectric properties of ferrite ceramics have been less reported than their magnetic properties. Our recent study indicated that ferrite ceramics with very low dielectric loss tangent can be developed by using appropriate sintering aids, together with the optimization of other sintering parameters such as sintering temperature and time duration. Among various candidates of sintering aids, Bi 2 O 3 is the most promising one. It is important to find that the optimized concentration of sintering aid for full densification is not sufficient to achieve lowest dielectric loss tangent. This short review was aimed to summarize the understanding in microstructural evolution, grain growth, densification and dielectric properties of ferrite ceramics as a function of sintering aid concentration and sintering parameters, which could be used as a guidance to develop ferrite ceramics with low dielectric loss tangents for various applications.

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39

Polyakova, K. "Maps generating normals on a manifold." Differential Geometry of Manifolds of Figures, no. 50 (2019): 110–25. http://dx.doi.org/10.5922/0321-4796-2019-50-13.

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The first- and second-order canonical forms are considered on a smooth m-manifold. The approach connected with coordinate expressions of basic and fiber forms, and first- and second-order tangent vectors on a manifold is implemented. It is shown that the basic first- and secondorder tangent vectors are first- and second-order Pfaffian (generalized) differentiation operators of functions set on a manifold. Normals on a manifold are considered. Differentials of the basic first-order (second-order) tangent vectors are linear maps from the first-order tangent space to the second-order (third-order) tangent space. Differentials of the basic first-order tangent vectors (basic vectors of the first-order normal) set a map which takes a first-order tangent vector into the second-order normal for the first-order tangent space of (into the third-order normal for second-order tangent space). The map given by differentials of the basic first-order tangent vectors takes all tangent vectors to the vectors of the second-order normal. Such splitting the osculating space in the direct sum of the first-order tangent space and second-order normal defines the simplest (canonical) affine connection which horizontal subspace is the indicated normal. This connection is flat and symmetric. The second-order normal is the horizontal subspace for this connection. Derivatives of some basic vectors in the direction of other basic vectors are equal to values of differentials of the first vectors on the second vectors, and the order of differentials is equal to the order of vectors along which differentiation is made. The maps set by differentials of basic vectors of r-order normal for (r – 1)-order tangent space take the basic first-order tangent vectors to the basic vectors of (r + 1)-order normal for r-order tangent space. Horizontal vectors for the simplest second-order connection are constructed. Second-order curvature and torsion tensors vanish in this connection. For horizontal vectors of the simplest second-order connection there is the decomposition by means of the basic vectors of the secondand third-order normals.

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40

Rabin, Jeffrey M. "Tangent Lines without Calculus." Mathematics Teacher 101, no. 7 (March 2008): 499–503. http://dx.doi.org/10.5951/mt.101.7.0499.

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A problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. It encourages problem solving and multiple solutions.

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41

Gordon, Russell A., and Brian C. Dietel. "Off on a Tangent." College Mathematics Journal 34, no. 1 (January 2003): 62. http://dx.doi.org/10.2307/3595849.

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42

Rigby, J. F. "Cycles and Tangent Rays." Mathematics Magazine 64, no. 3 (June 1, 1991): 155. http://dx.doi.org/10.2307/2691294.

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43

Whitehead, Lance. "The tangent strikes again." Early Music XXVIII, no. 1 (February 2000): 144–46. http://dx.doi.org/10.1093/earlyj/xxviii.1.144.

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44

Burla, M. C., C. Giacovazzo, and G. Polidori. "A robust tangent procedure." Journal of Applied Crystallography 46, no. 6 (October 26, 2013): 1592–602. http://dx.doi.org/10.1107/s0021889813024709.

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Third-generation direct methods programs are based on a phasing algorithm (e.g.the tangent or the parameter shift method) and on dual space refinement techniques. The two spaces may be alternated during the phasing procedure or used in a sequential way: for example, first phase and after extend and refine. The tangent approach inSIR2011belongs to the second category: phases are first estimated by the tangent formula, then their extension and refinement is performed in direct spaceviaelectron density modification techniques. In this article a number of new algorithms are described, with the aim of improving theSIR2011tangent step and allowing more efficient phase extension and refinement. New criteria were chosen for defining the number of reflections to phase, for modifying the tangent weighting scheme, and for fixing the active use of the psi-0 triplets and of the quartet invariants. Each tangent trial may now be submitted to the RELAX procedure, a tool for moving to the correct position a well oriented but misplaced structural model. The resulting procedure shows surprising efficiency, testified by a wide set of applications. The experimental results have been compared with the tangent and VLD (vive la différence) approaches implemented inSIR2011.

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45

Ursescu, C. "Adjacent and tangent regularity." Optimization 30, no. 2 (January 1994): 105–18. http://dx.doi.org/10.1080/02331939408843975.

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46

Rigby, J. F. "Cycles and Tangent Rays." Mathematics Magazine 64, no. 3 (June 1991): 155–67. http://dx.doi.org/10.1080/0025570x.1991.11977599.

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47

Baragar, Arthur, and Alex Kontorovich. "Efficiently Constructing Tangent Circles." Mathematics Magazine 93, no. 1 (January 1, 2020): 27–32. http://dx.doi.org/10.1080/0025570x.2020.1682447.

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48

Ohira, Takashi. "Efficiency Tangent [Enigmas, etc.]." IEEE Microwave Magazine 18, no. 5 (July 2017): 134. http://dx.doi.org/10.1109/mmm.2017.2693718.

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49

Salkov, Nikolay. "Ellipse: tangent and normal." Геометрия и графика 1, no. 1 (June 14, 2013): 35–37. http://dx.doi.org/10.12737/470.

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50

Ward, Doug. "The Quantificational Tangent Cones." Canadian Journal of Mathematics 40, no. 3 (June 1, 1988): 666–94. http://dx.doi.org/10.4153/cjm-1988-029-6.

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Nonsmooth analysis has provided important new mathematical tools for the study of problems in optimization and other areas of analysis [1, 2, 6-12, 28]. The basic building blocks of this subject are local approximations to sets called tangent cones.Definition 1.1. Let E be a real, locally convex, Hausdorff topological vector space (abbreviated l.c.s.). A tangent cone (on E) is a mapping A:2E × E → 2E such that A(C, x) is a (possibly empty) cone for all nonempty C in 2E and x in E.In the sequel, we will say that a tangent cone has a certain property (e.g. “A is closed” or “A is convex“) if A(C, x) has that property for all non-empty sets C and all x in C. (If A(C, x) is empty, it will be counted as having the property trivially.)

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