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Relevant bibliographies by topics / Geometry, Projective. Curves, Plane

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Academic literature on the topic 'Geometry, Projective. Curves, Plane'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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Journal articles on the topic "Geometry, Projective. Curves, Plane"

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DE BOBADILLA, J. FERNÁNDEZ, I. LUENGO-VELASCO, A. MELLE-HERNÁNDEZ, and A. NÉMETHI. "ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES." Proceedings of the London Mathematical Society 92, no. 1 (December 19, 2005): 99–138. http://dx.doi.org/10.1017/s0024611505015467.

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In 2002, L. Nicolaescu and the fourth author formulated a very general conjecture which relates the geometric genus of a Gorenstein surface singularity with rational homology sphere link with the Seiberg--Witten invariant (or one of its candidates) of the link. Recently, the last three authors found some counterexamples using superisolated singularities. The theory of superisolated hypersurface singularities with rational homology sphere link is equivalent with the theory of rational cuspidal projective plane curves. In the case when the corresponding curve has only one singular point one knows no counterexample. In fact, in this case the above Seiberg--Witten conjecture led us to a very interesting and deep set of `compatibility properties' of these curves (generalising the Seiberg--Witten invariant conjecture, but sitting deeply in algebraic geometry) which seems to generalise some other famous conjectures and properties as well (for example, the Noether--Nagata or the log Bogomolov--Miyaoka--Yau inequalities). Namely, we provide a set of `compatibility conditions' which conjecturally is satisfied by a local embedded topological type of a germ of plane curve singularity and an integer $d$ if and only if the germ can be realized as the unique singular point of a rational unicuspidal projective plane curve of degree $d$. The conjectured compatibility properties have a weaker version too, valid for any rational cuspidal curve with more than one singular point. The goal of the present article is to formulate these conjectured properties, and to verify them in all the situations when the logarithmic Kodaira dimension of the complement of the corresponding plane curves is strictly less than 2.

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Malara, Grzegorz, Piotr Pokora, and Halszka Tutaj-Gasińska. "On 3-syzygy and unexpected plane curves." Geometriae Dedicata 214, no. 1 (February 4, 2021): 49–63. http://dx.doi.org/10.1007/s10711-021-00602-5.

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AbstractIn this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study 3-syzygy curve arrangements and we present examples that admit unexpected curves.

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Kamel, Alwaleed, and Waleed Khaled Elshareef. "Weierstrass points of order three on smooth quartic curves." Journal of Algebra and Its Applications 18, no. 01 (January 2019): 1950020. http://dx.doi.org/10.1142/s0219498819500208.

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In this paper, we study the [Formula: see text]-Weierstrass points on smooth projective plane quartic curves and investigate their geometry. Moreover, we use a technique to determine in a very precise way the distribution of such points on any smooth projective plane quartic curve. We also give a variety of examples that illustrate and enrich the subject.

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Uchino, K. "Arnold's Projective Plane and -Matrices." Advances in Mathematical Physics 2010 (2010): 1–9. http://dx.doi.org/10.1155/2010/956128.

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We will explain Arnold's 2-dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular -matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.

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Taflin, Johan. "Invariant Elliptic Curves as Attractors in the Projective Plane." Journal of Geometric Analysis 20, no. 1 (August 18, 2009): 219–25. http://dx.doi.org/10.1007/s12220-009-9104-9.

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Pignoni, Roberto. "Integral relations for pointed curves in a real projective plane." Geometriae Dedicata 45, no. 3 (March 1993): 263–87. http://dx.doi.org/10.1007/bf01277967.

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ROUYER, JOËL. "A CHARACTERIZATION OF THE REAL PROJECTIVE PLANE." International Journal of Mathematics 21, no. 12 (December 2010): 1605–17. http://dx.doi.org/10.1142/s0129167x10006653.

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It is proved in this article, that in the framework of Riemannian geometry, the existence of large sets of antipodes (i.e. farthest points) for diametral points of a smooth surface has very strong consequences on the topology and the metric of this surface. Roughly speaking, if the sets of antipodes of diametral points are closed curves, then the surface is nothing but the real projective plane.

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WALL, C. T. C. "Geometry of projection-generic space curves." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 1 (July 2009): 115–42. http://dx.doi.org/10.1017/s0305004108002168.

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AbstractIn earlier work I defined a class of curves, forming a dense open set in the space of maps from S1 to P3, such that the family of projections of a curve in this class is stable under perturbations of C: we call the curves in the class projection-generic. The definition makes sense also in the complex case. The partition of projective space according to the singularities of the corresponding projection of C is a stratification. Its local structure outside C is the same as that of the versal unfoldings of the singularities presented.To study points on C we introduce the blow-up BC of P3 along C, and a family of plane curves, parametrised by z ∈ BC; we saw in the earlier work that this is a flat family.Here we show that near most z ∈ BC, the family gives a family of parametrised germs which versally unfolds the singularities occurring. Otherwise we find that the double point number δ of Γz drops by 1 for z ∉ EC. We establish a theory of versality for unfoldings of A or D singularities such that δ drops by at most 1, and show that in the remaining cases, we have an unfolding which is versal in this sense.This implies normal forms for the stratification of BC; further work allows us to derive local normal forms for strata of the stratification of P3.

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TSUKAMOTO, MASAKI. "Deformation of Brody curves and mean dimension." Ergodic Theory and Dynamical Systems 29, no. 5 (February 3, 2009): 1641–57. http://dx.doi.org/10.1017/s014338570800076x.

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AbstractThe main purpose of this paper is to show that ideas of deformation theory can be applied to ‘infinite-dimensional geometry’. We develop the deformation theory of Brody curves. A Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite-dimensional. As an application we prove a lower bound on the mean dimension of the space of Brody curves.

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Wennink, Thomas. "Counting the number of trigonal curves of genus 5 over finite fields." Geometriae Dedicata 208, no. 1 (January 9, 2020): 31–48. http://dx.doi.org/10.1007/s10711-019-00508-3.

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AbstractThe trigonal curves of genus 5 can be represented by projective plane quintics that have one singularity of delta invariant one. Combining this with a partial sieve method for plane curves we count the number of such curves over any finite field. The main application is that this gives the motivic Euler characteristic of the moduli space of trigonal curves of genus 5.

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Dissertations / Theses on the topic "Geometry, Projective. Curves, Plane"

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Cohen, Camron Alexander Robey. "CURVING TOWARDS BÉZOUT: AN EXAMINATION OF PLANE CURVES AND THEIR INTERSECTION." Oberlin College Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin159345184740689.

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Rimmasch, Gretchen. "Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2507.pdf.

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Cook, Gary Russell. "Arcs in a finite projective plane." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/7510/.

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The projective plane of order 11 is the dominant focus of this work. The motivation for working in the projective plane of order 11 is twofold. First, it is the smallest projective plane of prime power order such that the size of the largest (n, r)-arc is not known for all r ∈ {2,...,q + 1}. It is also the smallest projective plane of prime order such that the (n; 3)-arcs are not classified. Second, the number of (n, 3)-arcs is significantly higher in the projective plane of order 11 than it is in the projective plane of order 7, giving a large number of (n, 3)-arcs for study. The main application of (n, r)-arcs is to the study of linear codes. As a forerunner to the work in the projective plane of order eleven two algorithms are used to raise the lower bound on the size of the smallest complete n-arc in the projective plane of order thirty-one from 12 to 13. This work presents the classification up to projective equivalence of the complete (n, 3)- arcs in PG(2, 11) and the backtracking algorithm that is used in its construction. This algorithm is based on the algorithm used in [3]; it is adapted to work on (n, 3)-arcs as opposed to n-arcs. This algorithm yields one representative from every projectively inequivalent class of (n, 3)-arc. The equivalence classes of complete (n, 3)-arcs are then further classified according to their stabilizer group. The classification of all (n, 3)-arcs up to projective equivalence in PG(2, 11) is the foundation of an exhaustive search that takes one element from every equivalence class and determines if it can be extended to an (n′, 4)-arc. This search confirmed that in PG(2, 11) no (n, 3)-arc can be extended to a (33, 4)-arc and that subsequently m4(2, 11) = 32. This same algorithm is used to determine four projectively inequivalent complete (32, 4)-arcs, extended from complete (n, 3)-arcs. Various notions under the general title of symmetry are defined both for an (n, r)-arc and for sets of points and lines. The first of these makes the classification of incomplete (n; 3)- arcs in PG(2, 11) practical. The second establishes a symmetry based around the incidence structure of each of the four projectively inequivalent complete (32, 4)-arcs in PG(2, 11); this allows the discovery of their duals. Both notions of symmetry are used to analyze the incidence structure of n-arcs in PG(2, q), for q = 11, 13, 17, 19. The penultimate chapter demonstrates that it is possible to construct an (n, r)-arc with a stabilizer group that contains a subgroup of order p, where p is a prime, without reference to an (m < n, r)-arc, with stabilizer group isomorphic to ℤ1. This method is used to find q-arcs and (q + 1)-arcs in PG(2, q), for q = 23 and 29, supporting Conjecture 6.7. The work ends with an investigation into the effect of projectivities that are induced by a matrix of prime order p on the projective planes. This investigation looks at the points and subsets of points of order p that are closed under the right action of such matrices and their structure in the projective plane. An application of these structures is a restriction on the size of an (n, r)-arc in PG(2, q) that can be stabilized by a matrix of prime order p.

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Ellis, Amanda. "Classification of conics in the tropical projective plane /." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1104.pdf.

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Holanda, Felipe D'Angelo. "Introduction to differential geometry of plane curves." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=15052.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
A intenÃÃo desse trabalho serÃ de abordar de forma bÃsica e introdutÃria o estudo da Geometria Diferencial, que por sua vez tem seus estudos iniciados com as Curvas Planas. SerÃ necessÃrio um conhecimento de CÃlculo Diferencial, Integral e Geometria AnalÃtica para melhor compreensÃo desse trabalho, pois como seu prÃprio nome nos transparece Geometria Diferencial vem de uma junÃÃo do estudo da Geometria envolvendo CÃlculo. Assim abordaremos subtemas como curvas suaves, vetor tangente, comprimento de arco passando por fÃrmulas de Frenet, curvas evolutas e involutas e finalizaremos com alguns teoremas importantes, como o teorema fundamental das curvas planas, teorema de Jordan e o teorema dos quatro vÃrtices. O que, basicamente representa, o capÃtulo 1, 4 e 6 do livro IntroduÃÃo Ãs Curvas Planas de HilÃrio Alencar e Walcy Santos.
The intention of this work is to address in basic form and introductory study of Differential Geometry, which in turn has started his studies with Planas curves. It will require a knowledge of Differential Calculus, Integral and Analytic Geometry for better understanding of this work, because as its name says in Differential Geometry comes from the joint study of geometry involving Calculation. So we discuss sub-themes as smooth curves, tangent vector, arc length through formulas of Frenet, evolutas curves and involute and conclude with some important theorems, as the fundamental theorem of plane curves, Jordan 's theorem and the theorem of four vertices. What basically is, Chapter 1, 4 and 6 of the book Introduction to Plane Curves HilÃrio Alencar and Walcy Santos.

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Hønsen, Morten. "Compactifying locally Cohen-Macaulay projective curves." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-470.

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Mori, Izuru. "Some results on quantum projective planes /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5790.

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Nichols, Margaret E. "Intersection Number of Plane Curves." Oberlin College Honors Theses / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385.

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Hamed, Zainab Shehab. "Arcs of degree four in a finite projective plane." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/77816/.

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The projective plane, PG(2;q), over a Galois field Fq is an incidence structure of points and lines. A (k;n)-arc K in PG(2;q) is a set of k points such that no n+1 of them are collinear but some n are collinear. A (k;n)-arc K in PG(2;q) is called complete if it is not contained in any (k+1;n)-arc. The existence of arcs for particular values of k and n pose interesting problems in finite geometry. It connects with coding theory and graph theory, with important applications in computer science. The main problem, known as the packing problem, is to determine the largest size mn(2;q) of K in PG(2;q). This problem has received much attention. Here, the work establishes complete arcs with a large number of points. In contrast, the problem to determine the smallest size tn(2;q) of a complete (k;n)-arc is mostly based on the lower bound arising from theoretical investigations. This thesis has several goals. The first goal is to classify certain (k;4)-arcs for k = 6,...,38 in PG(2;13). This classification is established through an approach in Chapter 2. This approach uses a new geometrical method; it is a combination of projective inequivalence of (k;4)-arcs up to k = 6 and certain sdinequivalent (k;4)-arcs that have sd-inequivalent classes of secant distributions for k = 7,...,38. The part related to projectively inequivalent (k;4)-arcs up to k=6 starts by fixing the frame points f1;2;3;88g and then classify the projectively inequivalent (5;4)-arcs. Among these (5;4)-arcs and (6;4)-arcs, the lexicographically least set are found. Now, the part regarding sd-inequivalent (k;4)-arcs in this method starts by choosing five sd-inequivalent (7;4)-arcs. This classification method may not produce all sd-inequivalent classes of (k;4)-arcs. However, it was necessary to employ this method due to the increasing number of (k;4)-arcs in PG(2;13) and the extreme computational difficulty of the problem. It reduces the constructed number of (k;4)-arcs in each process for large k. Consequently, it reduces the executed time for the computation which could last for years. Also, this method decreases the memory usage needed for the classification. The largest size of (k;4)-arc established through this method is k = 38. The classification of certain (k;4)-arcs up to projective equivalence, for k = 34,35,36,37,38, is also established. This classification starts from the 77 incomplete (34;4)-arcs that are constructed from the sd-inequivalent (33;4)-arcs given in Section 2.29, Table 2.35. Here, the largest size of (k;4)-arc is still k = 38. In addition, the previous process is re-iterated with a different choice of five sd-inequivalent (7;4)-arcs. The purpose of this choice is to find a new size of complete (k;4)-arc for k > 38. This particular computation of (k;4)-arcs found no complete (k;4)-arc for k > 38. In contrast, a new size of complete (k;4)-arc in PG(2;13) is discovered. This size is k = 36 which is the largest complete (k;4)-arc in this computation. This result raises the second largest size of complete (k;4)-arc found in the first classification from k = 35 to k = 36. The second goal is to discuss the incidence structure of the orbits of the groups of the projectively inequivalent (6;4)-arcs and also the incidence structures of the orbits of the groups other than the identity group of the sd-inequivalent (k;4)-arcs. In Chapter 3, these incidence structures are given for k = 6,7,8,9,10,11,12,13,14,38. Also, the pictures of the geometric configurations of the lines and the points of the orbits are described. The third goal is to find the sizes of certain sd-inequivalent complete (k;4)-arcs in PG(2;13). These sizes of complete (k;4)-arcs are given in Chapter 4 where the smallest size of complete (k;4)-arc is at most k = 24 and the largest size is at least k = 38. The fourth goal is to give an example of an associated non-singular quartic curve C for each complete (k;4)-arc and to discuss the algebraic properties of each curve in terms of the number I of inflexion points, the number jC \K j of rational points on the corresponding arc, and the number N1 of rational points of C . These curves are given in Chapter 5. Also, the algebraic properties of complete arcs of the most interesting sizes investigated in this thesis are studied. In addition, there are two examples of quartic curves C (g0 1) and C (g0 2) attaining the Hasse-Weil- Serre upper bound for the number N1 of rational points on a curve over the finite field of order thirteen. This number is 32. The fifth goal is to classify the (k;4)-arcs in PG(2;13) up to projective inequivalence for k < 10. This classification is established in Chapter 6. It starts by fixing a triad, U1, on the projective line, PG(1;13). Here, the number of projectively inequivalent (k;4)-arcs are tested by using the tool given in Chapter 2. Then, among the number of the projectively inequivalent (10;4)-arcs found, the classification of sd-inequivalent (k;4)-arcs for k = 10 is made. The number of these sd-inequivalent arcs is 36. Then, the 36 sd-inequivalent arcs are extended. The aim here is to investigate if there is a new size of sd-inequivalent (k;4)-arc for k > 38 that can be obtained from these arcs. The largest size of sd-inequivalent (k;4)-arc in this process is the same as the largest size of the sd-inequivalent (k;4)-arc established in Chapter 2, that is, k = 38. In addition, the classification of (k;n)-arcs in PG(2;13) is extended from n = 4 to n = 6. This extension is given in Chapter 7 where some results of the classification of certain (k;6)-arcs for k = 9; : : : ;25 are obtained using the same method as in Chapter 2 for k = 7,...,38. This process starts by fixing a certain (8;6)-arc containing six collinear points in PG(2;13).

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Ellis, Amanda. "Classifcation of Conics in the Tropical Projective Plane." BYU ScholarsArchive, 2005. https://scholarsarchive.byu.edu/etd/697.

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This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.

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Books on the topic "Geometry, Projective. Curves, Plane"

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Horst, Knörrer, ed. Plane algebraic curves. Basel: Birkhäuser Verlag, 1986.

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Salmon, George. A treatise on conic sections. 6th ed. Providence, RI: AMS Chelsea Pub., 2005.

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Hulek, Klaus. Projective geometry of elliptic curves. Paris: Société Mathématique de France, 1986.

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Hulek, Klaus. Projective geometry of elliptic curves. Paris: Socie te Mathe matique de France, 1986.

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Ballico, Edoardo, and Ciro Ciliberto, eds. Algebraic Curves and Projective Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0085918.

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Hulek, Klaus. Projective geometry of elliptic curves. Paris: Société mathématique de France, 1986.

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The real projective plane. 3rd ed. New York: Springer-Verlag, 1993.

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Apéry, François. Models of the real projective plane: Computer graphics of Steiner and Boy surfaces. Braunschweig: Friedr. Vieweg, 1987.

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Fowler, R. H. The elementary differential geometry of plane curves. Mineola, N.Y: Dover Publications, 2005.

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Shaei kikagaku no kangaekata: An invitation to plane projective geometry. Tōkyō-to Bunkyō-ku: Kyōritsu Shuppan, 2013.

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Book chapters on the topic "Geometry, Projective. Curves, Plane"

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Brieskorn, Egbert, and Horst Knörrer. "The development of projective geometry." In Plane Algebraic Curves, 102–71. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5097-1_3.

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Brieskorn, Egbert, and Horst Knörrer. "3. The development of projective geometry." In Plane Algebraic Curves, 102–71. Basel: Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_3.

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Ciliberto, Ciro. "Projective Plane Curves." In UNITEXT, 247–66. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71021-7_17.

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Berger, Marcel. "Plane curves." In Geometry Revealed, 249–340. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-540-70997-8_5.

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Coxeter, H. S. M. "A Finite Projective Plane." In Projective Geometry, 91–101. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-6385-2_10.

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Musili, C. "Plane Curves." In Algebraic Geometry for Beginners, 187–270. Gurgaon: Hindustan Book Agency, 2001. http://dx.doi.org/10.1007/978-93-86279-05-7_5.

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Borceux, Francis. "Plane Curves." In A Differential Approach to Geometry, 55–138. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01736-5_2.

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Aarts, J. M., and R. Erne. "Curves." In Plane and Solid Geometry, 1–109. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-78241-6_4.

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Yang, Kichoon. "Projective Differential Geometry." In Meromorphic Functions and Projective Curves, 125–67. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9151-5_5.

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Coxeter, H. S. M., and George Beck. "Affine Geometry." In The Real Projective Plane, 105–25. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-2734-2_8.

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Conference papers on the topic "Geometry, Projective. Curves, Plane"

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Latecki, Longin J., and Azriel Rosenfeld. "Differentialless geometry of plane curves." In Optical Science, Engineering and Instrumentation '97, edited by Robert A. Melter, Angela Y. Wu, and Longin J. Latecki. SPIE, 1997. http://dx.doi.org/10.1117/12.279677.

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Ganter, M. A., and D. W. Storti. "Object Extent Determination for Algebraic Solid Models." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0176.

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Abstract This paper presents methods for determination of spatial extent of algebraic solid models. Algebraic solid models (ASM) are a variation of implicit solid models defined by implicit polynomial functions with rational coefficients. Spatial extent information, which can be used to enhance the performance of visualization and property evaluation, includes silhouettes, outlines and profiles. Silhouettes are curves on the surface of the solid which separate portions of the surface which face towards or away from a given viewpoint. The projection of the silhouette onto the viewing plane gives the outline of the solid, and the bivariate implicit function which defines the area enclosed by the outline is called the profile. A method for outline determination is demonstrated using concepts from algebraic geometry including polar surfaces and variable elimination via the Gröbner basis method and/or resultants. Examples of outline generation are presented and a sample profile function is constructed.

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Welke, Stefan. "Visualization of Real Projective Algebraic Curves on Models of the Real Projective Plane." In Proceedings of the Fifth International Mathematica Symposium. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2003. http://dx.doi.org/10.1142/9781848161313_0047.

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Miura, Kenjiro, Sho Suzuki, R. Gobithaasan, Shin Usuki, Jun-ichi Inoguchi, Masayuki Sato, Kenji Kajiwara, and Yasuhiro Shimizu. "Fairness Metric of Plane Curves Defined with Similarity Geometry Invariants." In CAD'17. CAD Solutions LLC, 2017. http://dx.doi.org/10.14733/cadconfp.2017.311-316.

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Tono, Keita. "The projective characterization of genus two plane curves which have one place at infinity." In Proceedings of the Conference. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814436700_0014.

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NAKAGAWA, Yasuhiro, and Hidekazu SATO. "PERIODIC SURFACES OF REVOLUTION in ℝ3 AND CLOSED PLANE CURVES." In 6th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789811206696_0013.

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Park, Jungseo, Seunghwan Mun, Chungmin Hyun, Byungkwon Kang, and Kwanghee Ko. "Similarity Assessment Method for Automated Curved Plate Forming." In SNAME 5th World Maritime Technology Conference. SNAME, 2015. http://dx.doi.org/10.5957/wmtc-2015-240.

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In this paper, a novel similarity estimation method for two shapes in the automated thermal forming is proposed. One shape is given as a CAD surface, and the other is given as a set of points measured points. These two shapes are registered with respect to a reference coordinate system so that they are aligned as closely as possible using the ICP based method. Three geometric properties are considered in the method. The first property is the distance between them. At each measured point, the closest distance to the CAD surface is computed, and the defined tolerance for the distances is used as a similarity measure. The second measure is the average distance of the minimum distances to the CAD surface at the measured points. The third one is the average of the bending strain values at the measured points and at the points on the CAD surface that are orthogonal projection points of the measured ones. The proposed similarity is computed as the linear combination of the three properties with weight values, which are determined empirically. Extensive experiments show that the proposed similarity method successfully computes the similarity of a plate to its CAD shape in the forming process.

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Lu, Chung-Chin, Chih-Yen Yang, and Ti-Chung Lee. "Syndrome calculation for the decoding of algebraic-geometry codes on plane Garcia-Stichtenoth curves." In Its Applications (Isita2010). IEEE, 2010. http://dx.doi.org/10.1109/isita.2010.5649521.

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Najar, F., S. Choura, E. M. Abdel-Rahman, S. El-Borgi, and A. H. Nayfeh. "Dynamics of Variable-Geometry Electrostatic Microactuators." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14017.

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This paper investigates the dynamic behavior of a microbeam-based electrostatic microactuator. The cross-section of the microbeam under consideration varies along its length. A mathematical model, accounting for the system nonlinearities due to mid-plane stretching and electrostatic forcing, is adopted and used to examine the microbeam dynamics. The Differential Quadrature Method (DQM) and Finite Difference Method (FDM) are used to discretize the partial-differential-integral equation representing the microbeam dynamics. The resulting nonlinear algebraic system is solved for the limit cycles of various microstructure geometries under combined DC-AC loads and the stability of these limit cycles is examined using Floquet theory. Results are presented to show the effect of variations in the geometry on the frequency-response curves of the microactuator. We examine the effect of varying the gap size and the microbeam thickness and width on the frequency-response curves for hardening-type and softening-type behaviors. We found that it is possible to tune the geometry of the microactuator to eliminate dynamic pull-in.

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Landi, Luca, and Damiano Amici. "Steel Sheets Impact Simulation for Safety Guards Design: Problems and Perspectives." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65181.

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The growing need of design of safety guards for industrial workers led to the need for experimentation in the field of ballistics, typically used in the military research. In the last few years some international standards for the safety of machine tools have been developed, such as the ISO 23125: 2010, improving the ballistic protection of safety guards. But it is still possible to find in the market a large quantity of machine tools with doubtful real protective characteristics of guards. The uncontrolled projection of parts of work piece or tools can often cause very dangerous perforations of the safety guards. In such a way specific experimental tests like the ones conducted in EU, have assured the possibility to write appendices of ISO standards for safety guards design of machine tools. These tests are based on impact between a particular standardized projectile, which exemplifies an impacting fragment of variable size and energy, and a flat plate placed in the trajectory of the projectile. The penetration or buckling of the target determines the non-suitability of a particular material of a given thickness, for the design and production of safety guards. However these tests, have the following limitations: they are valid only for: a limited type of thickness and materials, a perpendicular impact with flat plates of about 500 mm × 500 mm and when the standardized penetrator is a cylinder with a prismatic head. Moreover another limitation arises for the design of real safety guards: difficulties in taking into account curved design of guards such as the ones typically used in the spindles of machine tools. Moreover it is very difficult to take into account innovative materials different from the ones provided by the standards and also it is impossible to consider projected objects whose geometry is not regular, for example fragmented parts of tools, broken as a result of a wrong manoeuvre of the machine user. The main focus of this paper is to test the applicability of numerical methods for the simulation of impacts on steel sheets of standardized penetrators for the numerical design and validation of industrial safety guards. Correlation between experimental penetration tests found in international papers and optimized numerical tests will be presented.

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