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Journal articles on the topic 'Symmetric products of curves'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Harris, Joe, and Joe Silverman. "Bielliptic curves and symmetric products." Proceedings of the American Mathematical Society 112, no. 2 (1991): 347. http://dx.doi.org/10.1090/s0002-9939-1991-1055774-0.

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2

Bastianelli, F. "On symmetric products of curves." Transactions of the American Mathematical Society 364, no. 5 (2012): 2493–519. http://dx.doi.org/10.1090/s0002-9947-2012-05378-5.

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3

Biswas, Indranil, and Shane D’Mello. "M-curves and symmetric products." Proceedings - Mathematical Sciences 127, no. 4 (2017): 615–24. http://dx.doi.org/10.1007/s12044-017-0347-2.

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4

Kouvidakis, Alexis. "Divisors on symmetric products of curves." Transactions of the American Mathematical Society 337, no. 1 (1993): 117–28. http://dx.doi.org/10.1090/s0002-9947-1993-1149124-5.

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5

Ross, J. "Seshadri constants on symmetric products of curves." Mathematical Research Letters 14, no. 1 (2007): 63–75. http://dx.doi.org/10.4310/mrl.2007.v14.n1.a5.

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6

Vanhaecke, Pol. "Integrable systems and symmetric products of curves." Mathematische Zeitschrift 227, no. 1 (1998): 93–127. http://dx.doi.org/10.1007/pl00004370.

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7

MEJÍA, ISRAEL MORENO. "CHARACTERISTIC CLASSES ON SYMMETRIC PRODUCTS OF CURVES." Glasgow Mathematical Journal 46, no. 3 (2004): 477–88. http://dx.doi.org/10.1017/s0017089504001946.

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8

Wang, Zhi Lan. "Tautological integrals on symmetric products of curves." Acta Mathematica Sinica, English Series 32, no. 8 (2016): 901–10. http://dx.doi.org/10.1007/s10114-016-5565-5.

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9

Franz, Matthias. "Symmetric Products of Equivariantly Formal Spaces." Canadian Mathematical Bulletin 61, no. 2 (2018): 272–81. http://dx.doi.org/10.4153/cmb-2017-032-0.

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AbstractLet X be a CW complex with a continuous action of a topological group G. We show that if X is equivariantly formal for singular cohomology with coefficients in some field , then so are all symmetric products of X and in fact all its Γ-products. In particular, symmetric products of quasi-projective M-varieties are again M-varieties. This generalizes a result by Biswas and D’Mello about symmetric products of M-curves. We also discuss several related questions.

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10

Krug, Andreas. "Stability of tautological bundles on symmetric products of curves." Mathematical Research Letters 27, no. 6 (2020): 1785–800. http://dx.doi.org/10.4310/mrl.2020.v27.n6.a9.

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11

Elencwajg, Georges. "Brauer group of fibrations and symmetric products of curves." Proceedings of the American Mathematical Society 94, no. 4 (1985): 597. http://dx.doi.org/10.1090/s0002-9939-1985-0792268-9.

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12

Aprodu, Marian, and Edoardo Sernesi. "Excess dimension for secant loci in symmetric products of curves." Collectanea Mathematica 68, no. 1 (2016): 1–7. http://dx.doi.org/10.1007/s13348-016-0166-2.

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13

Bastianelli, F. "Remarks on the nef cone on symmetric products of curves." manuscripta mathematica 130, no. 1 (2009): 113–20. http://dx.doi.org/10.1007/s00229-009-0274-3.

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14

HASSETT, BRENDAN, and YURI TSCHINKEL. "ABELIAN FIBRATIONS AND RATIONAL POINTS ON SYMMETRIC PRODUCTS." International Journal of Mathematics 11, no. 09 (2000): 1163–76. http://dx.doi.org/10.1142/s0129167x00000544.

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Given a variety over a number field, are its rational points potentially dense, i.e. does there exist a finite extension over which rational points are Zariski dense? We study the question of potential density for symmetric products of surfaces. Contrary to the situation for curves, rational points are not necessarily potentially dense on a sufficiently high symmetric product. Our main result is that rational points are potentially dense for the Nth symmetric product of a K3 surface, where N is explicitly determined by the geometry of the surface. The basic construction is that for some N, the

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15

CILIBERTO, CIRO, та MIKHAIL ZAIDENBERG. "3-FOLD SYMMETRIC PRODUCTS OF CURVES AS HYPERBOLIC HYPERSURFACES IN ℙ4". International Journal of Mathematics 14, № 04 (2003): 413–36. http://dx.doi.org/10.1142/s0129167x0300182x.

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We construct new examples of Kobayashi hyperbolic hypersurfaces in ℙ4. They are generic projections of the triple symmetric product V = C (3) of a generic genus g ≥ 6 curve C, smoothly embedded in ℙ7.

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16

Biswas, Indranil, Tomás Gómez, and Kyoung-Seog Lee. "Semi-orthogonal decomposition of symmetric products of curves and canonical system." Revista Matemática Iberoamericana 37, no. 5 (2021): 1885–96. http://dx.doi.org/10.4171/rmi/1251.

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17

du Sautoy, Marcus. "Natural boundaries for Euler products of Igusa zeta functions of elliptic curves." International Journal of Number Theory 14, no. 08 (2018): 2317–31. http://dx.doi.org/10.1142/s1793042118501415.

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We study the analytic behavior of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato–Tate conjectures, we prove that these global Igusa zeta functions have some meromorphic continuation until a natural boundary beyond which no continuation is possible.

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18

Ciliberto, Ciro, and Edoardo Sernesi. "On the symmetric products of a curve." Archiv der Mathematik 61, no. 3 (1993): 285–90. http://dx.doi.org/10.1007/bf01198726.

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19

Silverman, Joseph H. "Rational Points on Symmetric Products of a Curve." American Journal of Mathematics 113, no. 3 (1991): 471. http://dx.doi.org/10.2307/2374836.

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20

Xie, Quan, Yaolu Liu, and Jun Fang. "Lamb wave measurement method for in-plane elastic constants of balanced symmetric laminates based on machine learning." Journal of Physics: Conference Series 2808, no. 1 (2024): 012069. http://dx.doi.org/10.1088/1742-6596/2808/1/012069.

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Abstract To achieve in-situ measurement of mechanical properties in large-scale composite structures, this paper introduces a Lamb wave measurement based on machine learning to predict the in-plane engineering elastic constants of balanced symmetric laminates. Firstly, we consider that balanced symmetric laminates are equivalent to orthotropic single-layer plates with nine engineering elastic constants. Secondly, by varying these elastic constants and comparing the dispersion curves at different propagation angles, we conclude that, under low frequency-thickness products, the phase velocity of

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21

DE OLIVERA, FEDERICO, JOSÉ FAJARDO, and ERNESTO MORDECKI. "SKEWED LÉVY MODELS AND IMPLIED VOLATILITY SKEW." International Journal of Theoretical and Applied Finance 21, no. 02 (2018): 1850003. http://dx.doi.org/10.1142/s0219024918500036.

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We introduce skewed Lévy models, characterized by a symmetric jump measure multiplied by a damping exponential factor. These models exhibit a clear implied volatility pattern, where the damping parameter controls the implied volatility curve’s skew, resulting in a measure of the model’s skewness. We show that the variation of this parameter produces the typical smirk observed in implied volatility curves. Some theoretical facts supporting these findings are proved.

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22

Pacienza, Gianluca. "On the nef cone of symmetric products of a generic curve." American Journal of Mathematics 125, no. 5 (2003): 1117–35. http://dx.doi.org/10.1353/ajm.2003.0034.

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23

KAMENSHCHIK, ALEXANDER YU, and ISAAK M. KHALATNIKOV. "SOME PROPERTIES OF THE "STRING GAS" WITH THE EQUATION OF STATE $p = -\frac{1}{3} \rho$." International Journal of Modern Physics D 21, no. 01 (2012): 1250004. http://dx.doi.org/10.1142/s0218271812500046.

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We show that the string gas — a perfect fluid with the equation of state [Formula: see text] possesses rather interesting properties. In Friedmann universes its presence can change the observable topology of the space; in the spherically symmetric spacetimes it produces rather bizzare geometries and in a way its influence on the rotation curves mimics the dark matter effects.

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24

Askar, S. S. "On Complex Dynamics of Differentiated Products: Cournot Duopoly Model under Average Profit Maximization." Discrete Dynamics in Nature and Society 2022 (March 9, 2022): 1–14. http://dx.doi.org/10.1155/2022/8677470.

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In this paper, some important dynamic characteristics such as multistability and synchronization phenomena are investigated for a game of an economic Cournot duopoly whose time evolution is received by the iteration of a noninvertible map in the plane. In the asymmetric case, the equilibrium points of game’s map are calculated, and their stability conditions are obtained. The obtained results show that the Nash equilibrium point loses its stability through flip bifurcation. Under some restrictions, the map’s coordinate axes form an invariant manifold, and hence their dynamics are studied based

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25

Baird, Thomas John. "Symmetric products of a real curve and the moduli space of Higgs bundles." Journal of Geometry and Physics 126 (March 2018): 7–21. http://dx.doi.org/10.1016/j.geomphys.2018.01.003.

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26

Lee, Kyoung-Seog, and Han-Bom Moon. "Derived categories of symmetric products and moduli spaces of vector bundles on a curve." Journal de Mathématiques Pures et Appliquées 197 (May 2025): 103694. https://doi.org/10.1016/j.matpur.2025.103694.

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27

Li, Wenxuan. "Analytical study of spirograph using parametric equations and pattern design by parametric-graphic interactions." Theoretical and Natural Science 10, no. 1 (2023): 64–78. http://dx.doi.org/10.54254/2753-8818/10/20230311.

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Perfectly symmetric curves always have a high degree of aesthetic value. While it is difficult to draw them by hand, Spirograph is an old and popular drawing toy that produces fascinating symmetric patterns. In playing with drawing software, the author explores types of Spirograph patterns, the type identification method, and the parametric equations to express Spirograph mathematically. This paper also discusses the key parameters of a Spirograph pattern and how they affect the pattern shape. Finally, Spirograph pattern design is carried out by analyzing the features of a random pattern and e

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28

SCHERFF, PHILLIP-CHRISTOPH, GEORGE BACIU, and JINLIAN HU. "INTUITIVE PARAMETERIZED INPUT INTERFACE FOR PROPORTIONAL RESHAPING OF HUMAN BODIES." International Journal of Image and Graphics 08, no. 02 (2008): 299–325. http://dx.doi.org/10.1142/s0219467808003106.

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In the computer world garment products need to be simulated on different virtual human bodies. In this paper we are going to change virtual human actors in a proportional way. As part of the work we design a user-friendly interface for a more intuitive input of body parameters. Curves, implemented as NURBS, create an effective/easy input method for the proportional reshaping task. Implementation of an automatic approach for computing an underlying skeleton was done, which enables us to reshape a virtual human. As body proportions are difficult to define, this paper researches on artistic metho

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29

Tang, Anisia P. S., and K. S. Cheng. "Thermal X-Ray Pulses Resulting From Pulsar Glitches." International Astronomical Union Colloquium 177 (2000): 441–42. http://dx.doi.org/10.1017/s0252921100060255.

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AbstractThe non-spherical symmetric and exact thermal evolution model is used to calculate the transient thermal response to pulsar glitches. The three ways of energy release originated from glitches, namely the ‘shell’, ‘ring’ and ‘spot’ cases are compared. The ‘ring’ case is always the middle one in terms of the response time, the response duration and the intensity of the response. Taking the relativistic light bending effect and the rotational effect into consideration, the X-ray light curves resulting from the thermal response to the glitches are calculated. Only the ‘spot’ case produces

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30

Pang, Jihong, Jinkun Dai, Chaohui Zhang, Hongyong Zhou, and Yong Li. "A New Dynamic Fault Tree Analysis Method of Electromagnetic Brakes Based on Bayesian Network Accompanying Wiener Process." Symmetry 14, no. 5 (2022): 968. http://dx.doi.org/10.3390/sym14050968.

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Product fault diagnosis has always been the focus of quality and reliability research. However, a failure–rate curve of some products is a symmetrical function, the fault analysis result is not true because the failure period of the products cannot be judged accurately. In order to solve the problem of fault diagnosis, this paper proposes a new Takagi-Sugeno (T-S) dynamic fault tree analysis method based on a Bayesian network accompanying the Wiener process. Firstly, the top event, middle event, and bottom event of the product failure mode are determined, and the T-S dynamic fault tree is cons

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31

Spitzer, Emily R., and Michelle L. Hughes. "Effect of Stimulus Polarity on Physiological Spread of Excitation in Cochlear Implants." Journal of the American Academy of Audiology 28, no. 09 (2017): 786–98. http://dx.doi.org/10.3766/jaaa.16144.

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AbstractContemporary cochlear implants (CIs) use cathodic-leading, symmetrical, biphasic current pulses, despite a growing body of evidence that suggests anodic-leading pulses may be more effective at stimulating the auditory system. However, since much of this research on humans has used pseudomonophasic pulses or biphasic pulses with unusually long interphase gaps, the effects of stimulus polarity are unclear for clinically relevant (i.e., symmetric biphasic) stimuli.The purpose of this study was to examine the effects of stimulus polarity on basic characteristics of physiological spread-of-

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32

CONTOPOULOS, G., and M. HARSOULA. "STICKINESS IN CHAOS." International Journal of Bifurcation and Chaos 18, no. 10 (2008): 2929–49. http://dx.doi.org/10.1142/s0218127408022172.

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We distinguish two types of stickiness in systems of two degrees of freedom: (a) stickiness around an island of stability, and (b) stickiness in chaos, along the unstable asymptotic curves of unstable periodic orbits. In fact, there are asymptotic curves of unstable orbits near the outer boundary of an island that remain close to the island for some time, and then extend to large distances into the surrounding chaotic sea. But later the asymptotic curves return close to the island and contribute to the overall stickiness that produces dark regions around the islands and dark lines extending fa

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33

Klimenko, Stanislav, Igor Nikitin, and Lialia Nikitina. "Numerical solutions of Einstein field equations with radial dark matter." International Journal of Modern Physics C 28, no. 07 (2017): 1750096. http://dx.doi.org/10.1142/s0129183117500966.

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We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant velocities of circular motion, i.e. flat rotation curves. At smaller distances, the field switches to Newtonian regime, then to Schwarzschild regime. Deviations from Schwarzschild regime start below the gravitational radius. The dark matter prevents the creation of event horizon, instead, a spherical region possessing extremely large redshift is created. The stru

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34

Kęska, Sergiusz. "A Note on the Continuous and Nowhere Differentiable Function." Symmetry 17, no. 2 (2025): 269. https://doi.org/10.3390/sym17020269.

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We continue the studies of derivatives of the non-harmonic series ∑cnexp(iλnx). We consider replacing sinλnx with some step function fn:[0,1)→{0,1,2}. The purpose of this paper is to show that f(x)=∑fn(x)2n is continuous and nowhere differentiable in (0,1). All functions fn, used to construct f, are created from symmetrical blocks of type M: [0,1,0] and blocks of type L: [0,1,2] and R: [2,1,0], located symmetrically with respect to M. The function f1 takes the value zero in the intervals [0,1/3), [2/3,1) and the value one in the interval [1/3,2/3), i.e., it consists of the block of type M: [0,

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35

Wang, Yi, Baoying Wang, Yang Liu, and Yongtu Liang. "Study on Asymmetry Concentration of Mixed Oil in Products Pipeline." Energies 13, no. 23 (2020): 6398. http://dx.doi.org/10.3390/en13236398.

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Long-distance pipelines transporting multiple product oils such as gasoline, diesel and jet fuel, are important facilities for transporting fossil energy. One major concern in operation is the energy consumption of the pipeline. Energy consumption should be made optimized tracking batches of oils and cutting mixed oil, which requires an accurate prediction of concentration curve. In engineering, the concentration curve is usually assumed to be symmetric, but it is actually asymmetric, which may lead to estimation errors. Thus, the asymmetric concentration of mixed oil should be studied. The fo

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36

Glahn, Bob. "A Nonsymmetric Logit Model and Grouped Predictand Category Development." Monthly Weather Review 142, no. 8 (2014): 2991–3002. http://dx.doi.org/10.1175/mwr-d-13-00300.1.

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Abstract Logistic regression is an alternative to regression estimation of event probabilities (REEP) and other techniques for estimating weather event probabilities based on NWP output or other predictors. Logistic regression has the advantage over REEP in that the probability estimates are constrained between zero and unity, whereas REEP can “overshoot” these values. It may be a detriment in some applications that the curves developed, one for each of several predictand categories (events), are symmetric. This paper shows how the logit curve can easily be made nonsymmetric as a function of a

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37

Capuano, Ana W., Robert S. Wilson, Sue E. Leurgans, Jeffrey D. Dawson, David A. Bennett, and Donald Hedeker. "Sigmoidal mixed models for longitudinal data." Statistical Methods in Medical Research 27, no. 3 (2016): 863–75. http://dx.doi.org/10.1177/0962280216645632.

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Linear mixed models are widely used to analyze longitudinal cognitive data. Often, however, the trajectory of cognitive function is nonlinear. For example, some participants may experience cognitive decline that accelerates as death approaches. Polynomial regression and piecewise linear models are common approaches used to characterize nonlinear trajectories, although both have assumptions that may not correspond with the actual trajectories. An alternative is to use a flexible sigmoidal mixed model based on the logistic family of curves. We describe a general class of such a model, which has

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38

Landi, Giovanni, Luca La Notte, Alessandro Lorenzo Palma, Andrea Sorrentino, Maria Grazia Maglione, and Giovanni Puglisi. "A Comparative Evaluation of Sustainable Binders for Environmentally Friendly Carbon-Based Supercapacitors." Nanomaterials 12, no. 1 (2021): 46. http://dx.doi.org/10.3390/nano12010046.

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Environmentally friendly energy storage devices have been fabricated by using functional materials obtained from completely renewable resources. Gelatin, chitosan, casein, guar gum and carboxymethyl cellulose have been investigated as sustainable and low-cost binders within the electrode active material of water-processable symmetric carbon-based supercapacitors. Such binders are selected from natural-derived materials and industrial by-products to obtain economic and environmental benefits. The electrochemical properties of the devices based on the different binders are compared by using cycl

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39

Zhou, Jianhui, Chuanshuang Hu, Xiaoying Ma, and Xingwei Guo. "Finite element modeling and experimental validation of radio frequency heating (RFH) of curved laminated wood-based panels." Holzforschung 68, no. 6 (2014): 699–705. http://dx.doi.org/10.1515/hf-2013-0199.

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Abstract Thin medium-density fiberboards (MDF) are often used for the production of curved laminated furniture components by post-hot pressing with radiofrequency heating (RFH). Dimensional instability is one of the major quality problems of these products, and inappropriate heating process was discussed as the main reason for this. In the present study, a finite element model (FEM) was developed in this context, and the temperature distribution within laminated MDF panels was predicted aiming at optimizing the hot-pressing process with RFH. The time-dependent temperatures were collected by te

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40

Qiu, L. P., En Chun Zhu, Hua Zhang Zhou, and L. Y. Liu. "Fracture Toughness of Northeast China Larch." Key Engineering Materials 517 (June 2012): 661–68. http://dx.doi.org/10.4028/www.scientific.net/kem.517.661.

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Wood, as a green and environment-friendly building material, is widely used in building engineering. Naturally grown, wood has various defects like knots, cracks and inclined grain. Fracture Mechanics is thus an efficient tool to investigate the mechanical behavior of wood and wood-based composite products. According to Linear-elastic Fracture Mechanics (LEFM), fracture toughness can be introduced to measure the resistance to crack propagation. Crack was assumed to occur when the stress intensity factorKreached a critical valueKC.Fracture in wood usually involves not only the Mode I type (open

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41

Jang, Changuk, Juhong Han, Akshita Maradapu Vera Venkata Sai, Yingshu Li, and Okyeon Yi. "A Study on Scalar Multiplication Parallel Processing for X25519 Decryption of 5G Core Network SIDF Function for mMTC IoT Environment." Wireless Communications and Mobile Computing 2022 (June 6, 2022): 1–17. http://dx.doi.org/10.1155/2022/4087816.

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When 5G telecommunication becomes a standardized and widely used communication medium, it must be implemented in coherence with certain 5G network standards and requirements. One such requirement is a Subscription Concealed Identifier called SUCI. SUCI prevents the exposure of international mobile subscriber identity (IMSI), which was a vulnerability in previous generation mobile telecommunication networks. Unlike IMSI, SUCI is encrypted and transmitted using a symmetric key cryptographic algorithm, to prevent the aforementioned vulnerabilities. However, for the first terminal to be encrypted,

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42

Prodan, Maria, Emilian Ghicioi, Robert Laszlo, Irina Nalboc, Sonia Suvar, and Aurelian Nicola. "Experimental and Numerical Study of Ignition and Flame Propagation for Methane–Air Mixtures in Small Vessels." Processes 9, no. 6 (2021): 998. http://dx.doi.org/10.3390/pr9060998.

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Methane is one of the most common gaseous fuels that also exist in nature as the main part of the natural gas, the flammable part of biogas or as part of the reaction products from biomass pyrolysis. In this respect, the biogas and biomass installations are always subjected to explosion hazards due to methane. Simple methods for evaluating the explosion hazards are of great importance, at least in the preliminary stage. The paper describes such a method based on an elementary analysis of the cubic law of pressure rise during the early stages of flame propagation in a symmetrical cylindrical ve

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43

RAY, KUMAR S., and BIMAL KUMAR RAY. "POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT." International Journal of Image and Graphics 13, no. 04 (2013): 1350017. http://dx.doi.org/10.1142/s0219467813500174.

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This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

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44

Mukai, Shigeru. "Curves and symmetric spaces." Proceedings of the Japan Academy, Series A, Mathematical Sciences 68, no. 1 (1992): 7–10. http://dx.doi.org/10.3792/pjaa.68.7.

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45

van Opstall, Michael, and Răzvan Veliche. "Maximally symmetric stable curves." Michigan Mathematical Journal 55, no. 3 (2007): 513–34. http://dx.doi.org/10.1307/mmj/1197056455.

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46

Ozawa, Fumisato, Kazuki Koyama, Shota Azuma, Tatsuo Horiba, and Morihiro Saito. "Analysis of Li Dissolution/Deposition Behavior in LiNO₃ Electrolytic Solution for Li-Air Battery." ECS Meeting Abstracts MA2022-02, no. 4 (2022): 551. http://dx.doi.org/10.1149/ma2022-024551mtgabs.

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Li-air batteries (LAB) have been attracting much attention because of their theoretical energy density of 3500 Wh kg−1, which is five times as high as that of Li-ion batteries. However, many problems remain to be challenged in every component of the battery: air electrodes, electrolytic solutions, Li electrodes, etc. As for the Li electrode, we have reported some results on the reversibility of the Li dissolution/deposition reaction by using Li | Li symmetric cells with tetraglyme (G4) -based electrolytic solution [1, 2]. In particular, it has been confirmed that in the 1.0 M LiNO3/G4 electrol

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47

Contreras Ramírez, Jesús Miguel, and Meribary Monsalve. "Synthesis and characterization of poly(1-methyltrimethylene carbonate) (PMTMC) by mean ring-opening polymerization." Revista Bases de la Ciencia. e-ISSN 2588-0764 5, no. 3 (2020): 21. http://dx.doi.org/10.33936/rev_bas_de_la_ciencia.v5i3.1863.

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 In this work, the activity of samarium (III) acetate (Sm(OAc)3) was evaluated as a possible initiator in the ring opening polymerization (ROP) of 1-methyltrimethylene carbonate (MTMC). The effects of temperature (Tr) and monomer-initiator molar ratio (M/I) on the molecular characteristics (conversion, dispersity, and molar mass) of the polymers obtained were analyzed. The reaction temperature was varied between 90 and 160 °C and the molar ratio M/I between 200 and 1000. The molar mass of the products was obtained by size exclusion chromatography (SEC), while its structure was analyzed u

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48

Gaskell, P. H., F. Gürcan, M. D. Savage, and H. M. Thompson. "Stokes flow in a double-lid-driven cavity with free surface side walls." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 212, no. 5 (1998): 387–403. http://dx.doi.org/10.1243/0954406981521312.

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Stokes flow is considered in a rectangular double-lid-driven cavity with free surface side walls, aspect ratio A and speed ratio S= U1/ U2, where U1 and U2 are lid velocities, as an idealized model for two-dimensional viscous flow in the ‘bead’ of a two-roll, meniscus coating system. For S ≤ 0 (> 0) there is one (two) large eddy (eddies) within the cavity with one (two) stagnation points on the centre-line between the free surfaces. Various transformations of flow structure arising as a result of flow bifurcations at these stagnation points are identified as the two control parameters A and

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Farnsworth, David L. "Axes for symmetric convex curves." Mathematical Gazette 102, no. 553 (2018): 23–30. http://dx.doi.org/10.1017/mag.2018.4.

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Abstract:

Curves are given in polar coordinates (r, θ)by equations of the form r = f (θ), where for f (θ) > 0 all θ. Consider curves which are symmetric about the origin O, so that, f(θ + π) = f (θ) for all θ. For such a curve, its interior is the set {(r, θ) : 0 ≤ r ≤ f (θ)}. Further, assume that the curve is convex. Recall that a closed curve is convex if a line segment between any two of its points has no points exterior to the curve [1], [2, pp. 198-203]. We call these curves M-curves, because the curves are fundamental objects in Minkowski geometry, where they are called Minkowski circles or sim

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50

Mukai, Shigeru. "Curves and Symmetric Spaces, I." American Journal of Mathematics 117, no. 6 (1995): 1627. http://dx.doi.org/10.2307/2375032.

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