Journal articles: 'Holonomy map for curve'

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Massa, Enrico, Danilo Bruno, Gianvittorio Luria, and Enrico Pagani. "Geometric constrained variational calculus I: Piecewise smooth extremals." International Journal of Geometric Methods in Modern Physics 12, no. 05 (May 2015): 1550061. http://dx.doi.org/10.1142/s0219887815500619.

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A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic constraints. Special attention is paid to the tensorial aspects of the theory. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The standard classification of the extremals into normal and abnormal ones is discussed, pointing out the existence of an algebraic algorithm assigning to each admissible curve a corresponding abnormality index, related to the co-rank of a suitable linear map. Attention is then shifted to the study of the first variation of the action functional. The analysis includes a revisitation of Pontryagin's equations and of the Lagrange multipliers method, as well as a reformulation of Pontryagin's algorithm in Hamiltonian terms. The analysis is completed by a general result, concerning the existence of finite deformations with fixed endpoints.

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Bhosle, Usha N., and A. J. Parameswaran. "Holonomy group scheme of an integral curve." Mathematische Nachrichten 287, no. 17-18 (April 25, 2014): 1937–53. http://dx.doi.org/10.1002/mana.201300117.

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Langerock, B. "Leafwise holonomy of connections over a bundle map." Differential Geometry and its Applications 20, no. 2 (March 2004): 125–43. http://dx.doi.org/10.1016/j.difgeo.2003.10.002.

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KLEPTSYN, VICTOR, and YURY KUDRYASHOV. "A curve in the unstable foliation of an Anosov diffeomorphism with globally defined holonomy." Ergodic Theory and Dynamical Systems 35, no. 3 (October 8, 2013): 935–43. http://dx.doi.org/10.1017/etds.2013.71.

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WANG, SHUGUANG. "GERBES, HOLONOMY FORMS AND REAL STRUCTURES." Communications in Contemporary Mathematics 11, no. 01 (February 2009): 109–30. http://dx.doi.org/10.1142/s0219199709003302.

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We study geometry on real gerbes in the spirit of the Cheeger–Simons theory. The concepts of adaptations and holonomy forms are introduced for flat connections on real gerbes. Their relations to complex gerbes with connections are presented, as well as results in loop and map spaces.

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Baba, Shinpei, and Subhojoy Gupta. "Holonomy map fibers of ℂP1-structures in moduli space." Journal of Topology 8, no. 3 (June 26, 2015): 691–710. http://dx.doi.org/10.1112/jtopol/jtv013.

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7

Giovannardi, Gianmarco. "Higher Dimensional Holonomy Map for Rules Submanifolds in Graded Manifolds." Analysis and Geometry in Metric Spaces 8, no. 1 (July 1, 2020): 68–91. http://dx.doi.org/10.1515/agms-2020-0105.

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AbstractThe deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of coordinates, which allows to deeply simplify the formal expression of the system, and to reduce it to a system of ODEs along a characteristic direction. We introduce a notion of higher dimensional holonomy map in analogy with the one-dimensional case [29], and we provide a characterization for singularities as well as a deformability criterion.

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ELSTON, GILLIAN Z., and CHRYSTOPHER L. NEHANIV. "HOLONOMY EMBEDDING OF ARBITRARY STABLE SEMIGROUPS." International Journal of Algebra and Computation 12, no. 06 (December 2002): 791–810. http://dx.doi.org/10.1142/s0218196702001206.

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We show how the Rhodes expansion Ŝ of any stable semigroup S embeds into the cascade integral (a natural generalization of the wreath product) of permutation-reset transformation semigroups with zero adjoined. The permutation groups involved are exactly the Schützenberger groups of the [Formula: see text]-classes of S. Since S ←← Ŝ is an aperiodic map via which all subgroups of S lift to Ŝ, this results in a strong Krohn–Rhodes–Zeiger decomposition for the entire class of stable semigroups. This class includes all semigroups that are finite, torsion, finite [Formula: see text]-above, compact Hausdorff, or relatively free profinite, as well as many other semigroups. Even if S is not stable, one can expand it using Henckell's expansion and then apply our embedding. This gives a simplified proof of the Holonomy Embedding theorem for all semigroups.

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Kohno, Toshitake. "Higher holonomy of formal homology connections and braid cobordisms." Journal of Knot Theory and Its Ramifications 25, no. 12 (October 2016): 1642007. http://dx.doi.org/10.1142/s0218216516420074.

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We construct a representation of the homotopy 2-groupoid of a manifold by means of Chen’s formal homology connections. By using the idea of this 2-holonomy map, we describe a method to obtain a representation of the category of braid cobordisms.

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HEINTZE, E., C. OLMOS, and G. THORBERGSSON. "SUBMANIFOLDS WITH CONSTANT PRINCIPAL CURVATURES AND NORMAL HOLONOMY GROUPS." International Journal of Mathematics 02, no. 02 (April 1991): 167–75. http://dx.doi.org/10.1142/s0129167x91000107.

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A submanifold has by definition constant principal curvatures if the eigenvalues of the shape operators Aξ are constant for any parallel normal field ξ along any curve. It is shown that a submanifold of Euclidean space has constant principal curvatures if and only if it is an isoparametric or a focal manifold of an isoparametric submanifold. Furthermore a "homogeneous slice theorem" is proved which says that the fibres of the projection of an isoparametric submanifold onto a full focal manifold are homogeneous isoparametric. To this end it is shown that any two points of an isoparametric submanifold can be connected by a piecewise differentiable curve whose pieces are tangent to one of the simultaneous eigenspaces Ei, i ∈ I, of the shape operators provided that the corresponding reflections generate the Weyl group of the isoparametric submanifold.

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11

Fine, B., P. Kirk, and E. Klassen. "A local analytic splitting of the holonomy map on flat connections." Mathematische Annalen 299, no. 1 (May 1994): 171–89. http://dx.doi.org/10.1007/bf01459778.

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12

Fried, David. "Anosov foliations and cohomology." Ergodic Theory and Dynamical Systems 6, no. 1 (March 1986): 9–16. http://dx.doi.org/10.1017/s0143385700003266.

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AbstractThe cohomology action of an Anosov diffeomorphism on a nilmanifold resembles that of a Cartesian product map. Corresponding results hold for infranilmanifolds, giving an invariant bigrading of the cohomology and a fourfold symmetry that extends Poincaré duality. Holonomy invariant cocycles are applied to the action on first cohomology.

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Lee, Jong Bum, and Kyung Bai Lee. "Averaging Formula for Nielsen Numbers of Maps on Infra-Solvmanifolds of Type (R)." Nagoya Mathematical Journal 196 (2009): 117–34. http://dx.doi.org/10.1017/s0027763000009818.

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We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-solvmanifolds of type (R): Let M be such a manifold with holonomy group Ψ and let f: M → M be a continuous map. The averaging formula for Nielsen numbersis proved. This is a workable formula for the difficult number N(f).

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DESENONGES, NICOLAS HUSSENOT. "Analytic continuation of holonomy germs of Riccati foliations along Brownian paths." Ergodic Theory and Dynamical Systems 37, no. 6 (April 11, 2016): 1887–914. http://dx.doi.org/10.1017/etds.2015.132.

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Consider a Riccati foliation whose monodromy representation is non-elementary and parabolic and consider a non-invariant section of the fibration whose associated developing map is onto. We prove that any holonomy germ from any non-invariant fibre to the section can be analytically continued along a generic Brownian path. To prove this theorem, we prove a dual result about complex projective structures. Let $\unicode[STIX]{x1D6F4}$ be a hyperbolic Riemann surface of finite type endowed with a branched complex projective structure: such a structure gives rise to a non-constant holomorphic map ${\mathcal{D}}:\tilde{\unicode[STIX]{x1D6F4}}\rightarrow \mathbb{C}\mathbb{P}^{1}$, from the universal cover of $\unicode[STIX]{x1D6F4}$ to the Riemann sphere $\mathbb{C}\mathbb{P}^{1}$, which is $\unicode[STIX]{x1D70C}$-equivariant for a morphism $\unicode[STIX]{x1D70C}:\unicode[STIX]{x1D70B}_{1}(\unicode[STIX]{x1D6F4})\rightarrow \mathit{PSL}(2,\mathbb{C})$. The dual result is the following. If the monodromy representation $\unicode[STIX]{x1D70C}$ is parabolic and non-elementary and if ${\mathcal{D}}$ is onto, then, for almost every Brownian path $\unicode[STIX]{x1D714}$ in $\tilde{\unicode[STIX]{x1D6F4}}$, ${\mathcal{D}}(\unicode[STIX]{x1D714}(t))$ does not have limit when $t$ goes to $\infty$. If, moreover, the projective structure is of parabolic type, we also prove that, although ${\mathcal{D}}(\unicode[STIX]{x1D714}(t))$ does not converge, it converges in the Cesàro sense.

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BISKAMP, MORITZ. "ABSOLUTE CONTINUITY THEOREM FOR RANDOM DYNAMICAL SYSTEMS ON Rd." Stochastics and Dynamics 13, no. 02 (March 4, 2013): 1250018. http://dx.doi.org/10.1142/s0219493712500189.

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In this paper we provide a proof of the so-called absolute continuity theorem for random dynamical systems on Rd which have an invariant probability measure. First we present the construction of local stable manifolds in this case. Then the absolute continuity theorem basically states that for any two transversal manifolds to the family of local stable manifolds, the induced Lebesgue measures on these transversal manifolds are absolutely continuous under the map that transports every point on the first manifold along the local stable manifold to the second manifold, the so-called Poincaré map or holonomy map. In contrast to known results, we have to deal with the non-compactness of the state space and the randomness of the random dynamical system.

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Koike, Takayuki. "Plurisubharmonic functions on a neighborhood of a torus leaf of a certain class of foliations." Forum Mathematicum 31, no. 6 (November 1, 2019): 1457–66. http://dx.doi.org/10.1515/forum-2018-0228.

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AbstractLet C be a smooth elliptic curve embedded in a smooth complex surface X such that C is a leaf of a suitable holomorphic foliation of X. We investigate the complex analytic properties of a neighborhood of C under some assumptions on the complex dynamical properties of the holonomy function. As an application, we give an example of {(C,X)} in which the line bundle {[C]} is formally flat along C, however it does not admit a {C^{\infty}} Hermitian metric with semi-positive curvature. We also exhibit a family of embeddings of a fixed elliptic curve for which the positivity of normal bundles does not behave in a simple way.

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Alghanemi, Azeb, and Peter Giblin. "On geometry of the midlocus associated to a smooth curve in plane and space." Filomat 32, no. 8 (2018): 2977–90. http://dx.doi.org/10.2298/fil1808977a.

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The singularities of the midpoint map associated to a smooth plane curve, which is a map from the plane to the plane, are classified. The midlocus associated to a regular space curve is introduced. The geometric conditions for the midlocus of a space curve to have a crosscap or an S?1 singularities are investigated. A more general map, the ?-point map, associated to a space curve is introduced and many known surface singularities are realized as a special cases of this construction.

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Ito, T., B. Scárdua, and Y. Yamagishi. "On holomorphic flows on Stein surfaces: Transversality, dicriticalness and stability." International Journal of Mathematics 25, no. 10 (September 2014): 1450093. http://dx.doi.org/10.1142/s0129167x14500931.

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We study the classification of the pairs (N, X) where N is a Stein surface and X is a ℂ-complete holomorphic vector field with isolated singularities on N. We describe the role of transverse sections in the classification of X and give necessary and sufficient conditions on X in order to have N biholomorphic to ℂ2. As a sample of our results, we prove that N is biholomorphic to ℂ2 if H2(N, ℤ) = 0, X has a finite number of singularities and exhibits a singularity with three separatrices or, equivalently, a singularity with first jet of the form [Formula: see text] where λ1/λ2 ∈ ℚ+. We also study flows with many periodic orbits (i.e. orbits diffeomorphic to ℂ*), in a sense we will make clear, proving they admit a meromorphic first integral or they exhibit some special periodic orbit, whose holonomy map is a non-resonant nonlinearizable diffeomorphism map.

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Guo, Xin Cheng, Xiao Yan Tang, Zi Hui Song, and Feng Li Gao. "Transformation of the Glyph Curve in Map Publishing." Advanced Materials Research 341-342 (September 2011): 883–87. http://dx.doi.org/10.4028/www.scientific.net/amr.341-342.883.

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In the case of complete information, it is of great significance that use cubic Bezier curves which used as primitive form standard in graphic system to express the spatial data for data processing and transmission. In the text fonts of map, it is customary to use straight lines and the set of quadratic Bezier curves to describe the glyph outlines,but it is inconvenient in the process because the quadratic Bezier curves are non-standard curves. Based on this situation, in this paper,it is proposed the method of quadratic curves fitting using cubic Bezier curves and derive corresponding computing formula. The method is that remove the characters glyph outlines which are described by curve edges from the font and fit the curve edges with quadratic Bezier curves, finally the curve edges are fitted by cubic Bezier curves segment by segment. Through the result of the experiment, it proves that the differences between fitted cubic Bezier curves and quadratic Bezier curves to be fitted are small. The text graphics curves expressed by the method represent the geographical features effectively and provide an effective way of the transformation from font text to the map text.

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Binous, Housam. "Residue curve map for homogeneous reactive quaternary mixtures." Computer Applications in Engineering Education 15, no. 1 (2007): 73–77. http://dx.doi.org/10.1002/cae.20099.

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SAYGILI, K. "TOPOLOGICALLY MASSIVE GAUGE THEORY: A LORENTZIAN SOLUTION." International Journal of Modern Physics A 22, no. 16n17 (July 10, 2007): 2961–76. http://dx.doi.org/10.1142/s0217751x07036361.

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We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space [Formula: see text] by means of an SU (1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map [Formula: see text] including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of [Formula: see text] as a trivial [Formula: see text] bundle over the upper portion of the pseudosphere [Formula: see text] which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto [Formula: see text] using a global section of the solution on [Formula: see text]. Then we discuss the integration of the field equation using the Archimedes map [Formula: see text]. We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on [Formula: see text].

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VETRO, FRANCESCA. "On approximating curves associated with nonexpansive mappings." Carpathian Journal of Mathematics 27, no. 1 (2011): 142–47. http://dx.doi.org/10.37193/cjm.2011.01.01.

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Let X be a Banach space with metric d. Let T, N : X → X be a strict d-contraction and a d-nonexpansive map, respectively. In this paper we investigate the properties of the approximating curve associated with T and N. Moreover, following [3], we consider the approximating curve associated with a holomorphic map f : B → α B and a ρ-nonexpansive map M : B → B, where B is the open unit ball of a complex Hilbert space H, ρ is the hyperbolic metric defined on B and 0 ≤ α < 1. We give conditions on f and M for this curve to be injective, and we show that this curve is continuous.

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Andriulli, Francesco. "Maxwell Ahead of the Curve [Editor’s Comments]." IEEE Antennas and Propagation Magazine 64, no. 3 (June 2022): 4. http://dx.doi.org/10.1109/map.2022.3162922.

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Polat, Burak. "Space-Curve Types of Distributions and Sources." IEEE Antennas and Propagation Magazine 54, no. 3 (June 2012): 68–85. http://dx.doi.org/10.1109/map.2012.6293953.

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Irmak, Elmas. "Edge-preserving maps of the nonseparating curve graphs, curve graphs and rectangle preserving maps of the Hatcher–Thurston graphs." Journal of Knot Theory and Its Ramifications 29, no. 11 (October 2020): 2050078. http://dx.doi.org/10.1142/s0218216520500789.

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Let [Formula: see text] be a compact, connected, orientable surface of genus [Formula: see text] with [Formula: see text] boundary components with [Formula: see text], [Formula: see text]. Let [Formula: see text] be the nonseparating curve graph, [Formula: see text] be the curve graph and [Formula: see text] be the Hatcher–Thurston graph of [Formula: see text]. We prove that if [Formula: see text] is an edge-preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We prove that if [Formula: see text] is an edge-preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We prove that if [Formula: see text] is closed and [Formula: see text] is a rectangle preserving map, then [Formula: see text] is induced by a homeomorphism of [Formula: see text]. We also prove that these homeomorphisms are unique up to isotopy when [Formula: see text].

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Wang, Ping, and Fangguo Zhang. "Computing elliptic curve discrete logarithms with the negation map." Information Sciences 195 (July 2012): 277–86. http://dx.doi.org/10.1016/j.ins.2012.01.044.

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Mora, Leonardo. "Birkhoff-Hénon attractors for dissipative perturbations of area-preserving twist maps." Ergodic Theory and Dynamical Systems 14, no. 4 (December 1994): 807–15. http://dx.doi.org/10.1017/s0143385700008166.

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AbstractWe prove that an area-preserving twist map having an invariant curve, can be approximated by a twist map exhibiting a Birkhoff-Hénon attractor. This is done by showing that the invariant curve can be perturbed into a saddle-node cycle with criticalities and by using a recent result reported by Diaz, Rocha and Viana.

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Gültepe, Funda, Christopher Leininger, and Witsarut Pho-on. "A universal Cannon-Thurston map and the surviving curve complex." Transactions of the American Mathematical Society, Series B 9, no. 3 (February 17, 2022): 99–143. http://dx.doi.org/10.1090/btran/99.

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Using the Birman exact sequence for pure mapping class groups, we construct a universal Cannon-Thurston map onto the boundary of a curve complex for a surface with punctures we call surviving curve complex. Along the way we prove hyperbolicity of this complex and identify its boundary as a space of laminations. As a corollary we obtain a universal Cannon-Thurston map to the boundary of the ordinary curve complex, extending earlier work of the second author with Mj and Schleimer [Comment. Math. Helv. 86 (2011), pp. 769–816].

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Yang, Fangwei, Fei Chen, Mingping Zhu, Aiqing Chen, and Dingchang Zheng. "Significantly Reduced Blood Pressure Measurement Variability for Both Normotensive and Hypertensive Subjects: Effect of Polynomial Curve Fitting of Oscillometric Pulses." BioMed Research International 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/5201069.

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This study aimed to compare within-subject blood pressure (BP) variabilities from different measurement techniques. Cuff pressures from three repeated BP measurements were obtained from 30 normotensive and 30 hypertensive subjects. Automatic BPs were determined from the pulses with normalised peak amplitude larger than a threshold (0.5 for SBP, 0.7 for DBP, and 1.0 for MAP). They were also determined from cuff pressures associated with the above thresholds on a fitted curve polynomial curve of the oscillometric pulse peaks. Finally, the standard deviation (SD) of three repeats and its coefficient of variability (CV) were compared between the two automatic techniques. For the normotensive group, polynomial curve fitting significantly reduced SD of repeats from 3.6 to 2.5 mmHg for SBP and from 3.7 to 2.1 mmHg for MAP and reduced CV from 3.0% to 2.2% for SBP and from 4.3% to 2.4% for MAP (all P<0.01). For the hypertensive group, SD of repeats decreased from 6.5 to 5.5 mmHg for SBP and from 6.7 to 4.2 mmHg for MAP, and CV decreased from 4.2% to 3.6% for SBP and from 5.8% to 3.8% for MAP (all P<0.05). In conclusion, polynomial curve fitting of oscillometric pulses had the ability to reduce automatic BP measurement variability.

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Zhao, Yehui, Lijun Xue, Guangming Wang, Fanglei Zou, Yue Song, and Hongjian Zhang. "TGA-based solutions map method for four-position synthesis of planar 4R linkage." Mechanical Sciences 13, no. 2 (September 28, 2022): 771–90. http://dx.doi.org/10.5194/ms-13-771-2022.

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Abstract. In this study, the authors propose a solutions map based on a telomere genetic algorithm (TGA) to improve the efficiency of 4R-linkage synthesis. First, the points on the center curve are obtained by using projective geometry, and those of the circle curve are obtained by vector elimination. Second, the definition of the linkage type, assessment of linkage performance, and a method to identify defects in the linkage are introduced. Third, the solutions map method is proposed that can map the linkage solutions obtained by all combinations of the points on the center curve to a 3D color-coded surface to represent the distribution of solutions with different attributes of linkages in the solution domain. Fourth, we use the proposed telomere operator and pseudo-histogram method to improve the traditional genetic algorithm, and expand the domain of solutions of the solutions map by using the TGA. Finally, the linkage synthesis software BurLink is developed based on the solutions map method. The results show that the TGA-based solutions map can quickly locate the required 4R-linkage solution in the solution domain, and provides engineers with more candidate solutions than traditional methods.

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Li, Xue Bin, and Xiao Ling Yu. "Composite Linkage Mapping Using Back-Propagation Artificial Neural Networks." Advanced Materials Research 108-111 (May 2010): 285–90. http://dx.doi.org/10.4028/www.scientific.net/amr.108-111.285.

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With the completion of the HapMap project, largescale, high-density single-nucleotide polymorphism (SNP) markers and information on haplotype structure and frequencies become available. Although meta-analysis could combine the data by placing markers on a common genetic map and performing linkage analysis on the whole sample jointly, how to adjust the map distance of those markers with no crossover data sets in available databases is still an important problem. In this paper, back-propagation artificial neural network was be used to combine the linkage mapping. The results showed composite genetic map can be got after adjusted the small sample map distance curve with a criteria curve, a large sample size curve or a map got from meta-analysis, and the composite genetic map with more precise and dense markers could also be got using an appropriate networks trained with crossover marker data. The small genetic maps could also be spliced by using an appropriate networks trained with crossover marker data, the network structure with different hidden neurons was also very important for splicing the genetic maps from different literatures. The meta-analysis combining appropriate networks trained with crossover marker data was a good selection for composite mapping.

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CARCASSES, JEAN-PIERRE. "SINGULARITIES OF THE PARAMETRIC PLANE OF AN n-DIMENSIONAL MAP." International Journal of Bifurcation and Chaos 05, no. 02 (April 1995): 419–47. http://dx.doi.org/10.1142/s0218127495000351.

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This paper uses the notion of “contour lines” in a parameter plane. A given contour line is related to a constant value of a “reduced multiplier” constructed from the elements of the Jacobian matrix associated with a given periodic point. The singularities type of such lines permit to determine a point of intersection of two bifurcation curves of same nature (flip or fold) and a point of tangency between a fold bifurcation curve and a flip bifurcation curve. When a third parameter varies, these singularities permit to determine the appearance (or disappearance) of a closed fold or flip bifurcation curve. Three different configurations of fold and flip bifurcation curves, centred round a cusp point of a fold curve, are considered. They are called saddle area, spring area, and crossroad area. The singularities type of the contour lines define the configuration types of these areas and, when a third parameter varies, the qualitative changes of such areas are directly identified.

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Li, Kang, Han-Shue Tan, James Misener, and J. Karl Hedrick. "Digital map as a virtual sensor - dynamic road curve reconstruction for a curve speed assistant." Vehicle System Dynamics 46, no. 12 (December 2008): 1141–58. http://dx.doi.org/10.1080/00423110701837110.

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DEVANEY, ROBERT L. "Cantor sets of circles of Sierpiński curve Julia sets." Ergodic Theory and Dynamical Systems 27, no. 5 (October 2007): 1525–39. http://dx.doi.org/10.1017/s0143385707000156.

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AbstractOur goal in this paper is to give an example of a one-parameter family of rational maps for which, in the parameter plane, there is a Cantor set of simple closed curves consisting of parameters for which the corresponding Julia set is a Sierpiński curve. Hence, the Julia sets for each of these parameters are homeomorphic. However, each of the maps in this set is dynamically distinct from (i.e. not topologically conjugate to) any other map in this set (with only finitely many exceptions). We also show that, in the dynamical plane for any map drawn from a large open set in the connectedness locus in this family, there is a Cantor set of invariant simple closed curves on which the map is conjugate to the product of certain subshifts of finite type with the maps $z \mapsto \pm z^n$ on the unit circle.

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Liu, Zonghua, and Shigang Chen. "Control of Coupled Standard Map." International Journal of Bifurcation and Chaos 08, no. 06 (June 1998): 1355–62. http://dx.doi.org/10.1142/s0218127498001054.

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In this work, we extend the periodic impulsive method to high-dimensional conservative system, and use the coupled standard map as an example to illustrate how to control the high-dimensional Hamiltonian chaos. When the periodic pulse is applied to one variable of the system, different periodic windows, quasiperiodic orbit and some special structure can be stabilized, even the approximate KAM curve. And the largest Lyapunov exponent spectra corresponding to different initial points are given.

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AVILA, ARTUR, and BASSAM FAYAD. "Non-differentiable irrational curves for twist map." Ergodic Theory and Dynamical Systems 42, no. 2 (December 2, 2021): 491–99. http://dx.doi.org/10.1017/etds.2021.117.

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He, Qiang, and Jiawei Yu. "A Depth Map Generation Method for Path Planning of Mobile Robot." Journal of Physics: Conference Series 2095, no. 1 (November 1, 2021): 012074. http://dx.doi.org/10.1088/1742-6596/2095/1/012074.

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Abstract Recently, the unmanned mobile robots have received broad applications, such as industrial and security inspection, disinfection and epidemic prevention, warehousing logistics, agricultural picking, etc. In order to drive autonomously from departure to destination, an unmanned mobile robot mounts different sensors to collect information around it and further understand its surrounding environment based on the perceptions. Here we proposed a method to generate high-resolution depth map for given sparse LiDAR point cloud. Our method fits the point cloud into a 3D curve and projects LiDAR data onto the curve surface, and then we make appropriate interpolations of the curve and finally implement the Delaunay triangulation algorithm to all the data points on the 3D curve. The experimental results show that our approach can effectively improve the resolution of depth maps from sparse LiDAR measurements.

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Li, Luchang, Mengting Li, Zhaoning Zhang, and Zhen-Li Huang. "Assessing low-light cameras with photon transfer curve method." Journal of Innovative Optical Health Sciences 09, no. 03 (May 2016): 1630008. http://dx.doi.org/10.1142/s1793545816300081.

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Low-light camera is an indispensable component in various fluorescence microscopy techniques. However, choosing an appropriate low-light camera for a specific technique (for example, single molecule imaging) is always time-consuming and sometimes confusing, especially after the commercialization of a new type of camera called sCMOS camera, which is now receiving heavy demands and high praise from both academic and industrial users. In this tutorial, we try to provide a guide on how to fully access the performance of low-light cameras using a well-developed method called photon transfer curve (PTC). We first present a brief explanation on the key parameters for characterizing low-light cameras, then explain the experimental procedures on how to measure PTC. We also show the application of the PTC method in experimentally quantifying the performance of two representative low-light cameras. Finally, we extend the PTC method to provide offset map, read noise map, and gain map of individual pixels inside a camera.

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Fan, Jing, Xuejun Fan, Ningning Song, and Long Wang. "Hyperelliptic Covers of Different Degree for Elliptic Curves." Mathematical Problems in Engineering 2022 (July 4, 2022): 1–11. http://dx.doi.org/10.1155/2022/9833393.

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In elliptic curve cryptography (ECC) and hyperelliptic curve cryptography (HECC), the size of cipher-text space defined by the cardinality of Jacobian is a significant factor to measure the security level. Counting problems on Jacobians of elliptic curve can be solved in polynomial time by Schoof–Elkies–Atkin (SEA) algorithm. However, counting problems on Jacobians of hyperelliptic curves are solved less satisfactorily than those on elliptic curves. So, we consider the construction of the cover map from the hyperelliptic curves to the elliptic curves to convert point counting problems on hyperelliptic curves to those on elliptic curves. We can also use the cover map as a kind of cover attacks. Given an elliptic curve over an extension field of degree n , one might try to use the cover attack to reduce the discrete logarithm problem (DLP) in the group of rational points of the elliptic curve to DLPs in the Jacobian of a curve of genus g ≥ n over the base field. An algorithm has been proposed for finding genus 3 hyperelliptic covers as a cover attack for elliptic curves with cofactor 2. Our algorithms are about the cover map from hyperelliptic curves of genus 2 to elliptic curves of prime order. As an application, an example of an elliptic curve whose order is a 256-bit prime vulnerable to our algorithms is given.

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HAN, Jiafu, Hongsheng LI, and Zhong ZHANG. "Classification Method of Population Density Map Based on Lorenz Curve." Geo-information Science 11, no. 6 (March 19, 2010): 833–38. http://dx.doi.org/10.3724/sp.j.1047.2009.00833.

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Spaak, Jonas, Patrik Sundblad, and Dag Linnarsson. "Human carotid baroreflex during isometric lower arm contraction and ischemia." American Journal of Physiology-Heart and Circulatory Physiology 275, no. 3 (September 1, 1998): H940—H945. http://dx.doi.org/10.1152/ajpheart.1998.275.3.h940.

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Our aim was to determine the roles of somatomotor activation and muscle ischemia for the tachycardia and hypertension of isometric arm contraction. Carotid-cardiac and carotid-mean arterial pressure (MAP) baroreflex response curves were determined in 10 men during rest, during isometric arm contraction at 30% of maximum, and during postcontraction ischemia. Carotid distending pressure (CDP) was changed by applying pressure and suction in a neck chamber. Pressures ranged from +40 to −80 mmHg and were applied repeatedly for 15 s during the three conditions. Maximum slopes and ranges of the response curves did not differ among conditions. The heart rate (HR) curve was shifted to a 14 ± 1.8 (mean ± SE) beats/min higher HR and a 9 ± 5.7 mmHg higher CDP during contraction and to a 14 ± 5.9 mmHg higher CDP during postcontraction ischemia with no change of HR compared with rest. The MAP curve was shifted to a 20 ± 2.8 mmHg higher MAP and to a 18 ± 5.4 mmHg higher CDP during contraction, and the same shifts were recorded during postcontraction ischemia. We conclude that neither somatomotor activation nor muscle ischemia changes the sensitivity of arterial baroreflexes. The upward shift of the MAP response curve, with no shift of the HR response curve during postexercise ischemia, supports the notion of parallel pathways for MAP and HR regulation in which HR responses are entirely caused by somatomotor activation and the pressor response is mainly caused by muscle ischemia.

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LEVI, MARK. "GEOMETRY OF VIBRATIONAL STABILIZATION AND SOME APPLICATIONS." International Journal of Bifurcation and Chaos 15, no. 09 (September 2005): 2747–56. http://dx.doi.org/10.1142/s0218127405013745.

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This paper gives a short overview of various applications of stabilization by vibration, along with the exposition of the geometrical mechanism of this phenomenon. More specifically, the following observation is described: a rapidly vibrated holonomic system can be approximated by a certain associated nonholonomic system. It turns out that effective forces in some rapidly vibrated (holonomic) systems are the constraint forces of an associated auxiliary nonholonomic constraint. In particular, we review a simple but remarkable connection between the curvature of the pursuit curve (the tractrix) on the one hand and the effective force on the pendulum with vibrating support. The latter observation is a part of a recently discovered close relationship between two standard classical problems in mechanics: (1) the pendulum whose suspension point executes fast periodic motion along a given curve, and (2) the Chaplygin skate (known also as the Prytz planimeter, or the "bicycle"). The former is holonomic, the latter is nonholonomic. The holonomy of the skate shows up in the effective motion of the pendulum. This relationship between the pendulum with a twirled pivot and the Chaplygin skate has somewhat unexpected physical manifestations, such as the drift of suspended particles in acoustic waves. Finally, a higher-dimensional example of "geodesic motion" on a vibrating surface is described.

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STRUCHKOV, I. N. "PERMANENT TRANSIENT CHAOS IN A TWO-DIMENSIONAL NON-INVERTIBLE MAP." International Journal of Bifurcation and Chaos 05, no. 02 (April 1995): 409–18. http://dx.doi.org/10.1142/s021812749500034x.

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We study unusual chaotic transients towards the zero fixed point in the DAOD-map derived from differential equations of the delayed aperiodic oscillator [Rozhdestvensky et al., 1992; Struchkov, 1993], which is one of the simplest models of the radiophysical autogenerator with chaotic transients [Rozhdestvensky et al., 1992]. Unusual character of the observed chaotic transients manifests itself in near-linear increase of the Ln[τ(p)]-curve for its average lifetime τ(p) as a function of system’s parameter p. Parameter p is corresponding to the amplifying coefficient of the radio-physical autogenerator [Rozhdestvensky et al., 1992]. This curve includes lacunas when p belongs to the periodic windows (when p∈∆n). In small enough neighborhood of ∆nLn[τ(p)]-curve behaves itself like as in boundary crisis due to intermittency. Permanent presence of the transient chaos in the DAOD-map (even when p∈∆n) is caused by the existence in phase space of the Monotonous Descent Channel (MDCh), which is coming in a zero fixed point from infinity.

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Chen, Meng, Bing Wei, and Xinbo He. "FDTD Complex Terrain Modeling Method Based on Papery Contour Map." International Journal of Antennas and Propagation 2023 (January 30, 2023): 1–10. http://dx.doi.org/10.1155/2023/6986225.

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This study aims to develop a finite difference time-domain (FDTD) modeling method for complex terrain using a paper contour map. First, the image preprocessing technology is employed to segment, denoise, and number the drawing area to arrive at independent figures and curve matrices. Subsequently, the support vector machine (SVM) classifier is implemented to identify the number and obtain the elevation value pertinent to the curve in the figure. Finally, the scattered points in the curve matrix are meshed by the Delaunay triangulation algorithm, and a three-dimensional triangular mesh model is established according to the recognition results. The FDTD calculation model is established by the method of intersection of Yee cell grid lines and triangle projection. The simulation results reveal that the recognition rate of the SVM classification model in this study is close to 100% for printed numerals. This approach is capable of quickly and accurately establishing the FDTD-based calculation model for complex terrain on the basis of the paper contour map.

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Nishida, Y., and V. S. Bishop. "Vasopressin-induced suppression of renal sympathetic outflow depends on the number of baroafferent inputs in rabbits." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 263, no. 6 (December 1, 1992): R1187—R1194. http://dx.doi.org/10.1152/ajpregu.1992.263.6.r1187.

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We tested the hypothesis that the inhibitory action of arginine vasopressin (AVP) on renal sympathetic nerve activity (RSNA) is related to the number of baroreceptor stations. The role of baroreceptor afferents was determined by comparing the effects of AVP on the baroreflex function curves [mean arterial pressure (MAP) vs. %RSNA] obtained in intact conscious rabbits with those obtained in rabbits with one carotid sinus and one aortic nerve intact (1CSN + 1AoN) and in rabbits with only a single carotid sinus nerve intact (1CSN). Baroreflex curves were obtained by relating %RSNA to MAP during ramp increases and decreases in MAP. MAP was increased with phenylephrine and decreased with caval occlusion. In the intact state (n = 7), AVP infusions (0.4, 1.5, and 3.0 mU.kg-1 x min-1) produced dose-dependent reduction in the maximum %RSNA (97 +/- 1 to 85 +/- 6, 68 +/- 6, and 57 +/- 5%, respectively) at minimum MAP and the gain of the baroreflex curve (5.7 +/- 0.2 to 3.9 +/- 0.2, 3.2 +/- 0.3, and 2.2 +/- 0.2 mmHg, respectively) and shifted the midrange of the curves (72 +/- 3 to 68 +/- 4, 68 +/- 2, and 63 +/- 3 mmHg, respectively). However, in the 1CSN + 1AoN state (n = 6), the medium dose of AVP (1.5 mU.kg-1 x min-1) did not significantly alter the maximum %RSNA, the gain of the curve, or the midrange of the curve. The highest dose of AVP (3.0 mU.kg-1 x min-1) still reduced the maximum %RSNA (98 +/- 3 to 75 +/- 3) and the gain of the curve (4.1 +/- 0.4 to 2.7 +/- 0.2).(ABSTRACT TRUNCATED AT 250 WORDS)

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Xu, Ling, John P. Collister, John W. Osborn, and Virginia L. Brooks. "Endogenous ANG II supports lumbar sympathetic activity in conscious sodium-deprived rats: role of area postrema." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 275, no. 1 (July 1, 1998): R46—R55. http://dx.doi.org/10.1152/ajpregu.1998.275.1.r46.

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This study tests the hypothesis that the area postrema (AP) is necessary for endogenous ANG II to chronically maintain lumbar sympathetic nerve activity (LSNA) and heart rate (HR) in conscious sodium-deprived rats. The effect of the ANG II type 1-receptor antagonist, losartan, on LSNA and HR was determined in rats that were either AP lesioned (APX) or sham lesioned. The sham rats were divided into groups, with (SFR) or without (SAL) food restriction, to control for the decreased food intake of APX rats. Before losartan, basal mean arterial pressure (MAP), HR, and baroreflex control of LSNA and HR were similar between groups, with the exception of lower maximal reflex LSNA and higher maximal gain of the HR-MAP curve in APX rats. In all groups, losartan similarly shifted ( P < 0.01) the LSNA-MAP curve to the left without altering maximal gain. Losartan also decreased ( P < 0.05) minimal LSNA in all groups, and suppressed ( P < 0.01) maximal LSNA (% of control) in SFR (240 ± 13 to 205 ± 15) and SAL (231 ± 21 to 197 ± 26) but not APX (193 ± 10 to 185 ± 8) rats. In general, losartan similarly shifted the HR-MAP curve to a lower MAP in all groups. The results suggest that the AP is not necessary for endogenous ANG II to chronically support LSNA and HR at basal and elevated MAP levels in sodium-deprived rats. However, the AP is required for endogenous ANG II to increase maximal reflex LSNA at low MAP levels.

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Tan, Guo Guo, Xi Sheng Gu, Shu Wen Chen, Qi Kui Man, Chun Tao Chang, Run Wei Li, Fa Shen Li, and Xin Min Wang. "Dependence of Peak Frequency of Microwave Absorption for Co₂Z Composite on the Thickness." Materials Science Forum 898 (June 2017): 1631–37. http://dx.doi.org/10.4028/www.scientific.net/msf.898.1631.

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A map displaying the reflection loss (RL) properties including the frequency and intensity for Co2Z barium ferrite composite was developed based on the matching model. In quarter-wavelength matching map, the number and the frequency positions of absorbing peaks presenting in RL curve for Co2Z barium ferrite composite with a certain thickness could be approximately predicted by quarter-wavelength matching model. From impedance map, the intensity of absorbing peaks in measured RL curves was analyzed. Moreover, the presence of absorbing peak in RL curve could be illustrated and understood physically and clearly using a picture of interference cancellation of two EM waves reflected by the absorber layer interface and a backed metal plate.

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Nurdin, Putri Fatimah, and Tetsuya Kubota. "GIS-BASED LANDSLIDE SUSCEPTIBILITY ASSESSMENT AND FACTOR EFFECT ANALYSIS BY CERTAINTY FACTOR IN UPSTREAM OF JENEBERANG RIVER, INDONESIA." Geoplanning: Journal of Geomatics and Planning 5, no. 1 (April 25, 2018): 75. http://dx.doi.org/10.14710/geoplanning.5.1.75-90.

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This study aimed to assess landslide susceptibility by employing certainty factors model (CF) to select the causative factors for landslide susceptibility mapping in Upstream of Jeneberang River, South Sulawesi. Indonesia. The landslide causative factors were: soil, slope angle, aspect, elevation, lithology, land use, distance to the river, drainage density, and precipitation. For validation purpose, landslide inventory map was randomly partition into two groups, 30% for the validation and 70% for the training. Landslide susceptibility maps were produced by logistic regression using original factor (all nine factors) and selected factor (four factors with positive CF value). The result of certainty factor analysis shows CF value is positive for elevation, land use, slope and drainage density. The accuracy of two landslide susceptibility maps were evaluated by calculating the area under the curve of Receiver Operating Characteristic (ROC) curves. The result shows the the success rate curve for nine factor map (80.2%) is higher than four factor map (78%). But in case of closeness between success rate curve and predictive rate curve, certainty factors model has a closer distance. In this study, effect analysis studies show how the accuracy changes when the input factors are changed.

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Li, Yanlin, Kemal Eren, Kebire Hilal Ayvacı, and Soley Ersoy. "The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space." AIMS Mathematics 8, no. 1 (2022): 2226–39. http://dx.doi.org/10.3934/math.2023115.

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<abstract><p>In this study, the ruled developable surfaces with pointwise 1-type Gauss map of Frenet-type framed base (Ftfb) curve are introduced in Euclidean 3-space. The tangent developable surfaces, focal developable surfaces, and rectifying developable surfaces with singular points are considered. Then the conditions for the Gauss map of these surfaces to be pointwise 1-type are obtained separately. In order to form a basis for the study, first, the basic concepts related to the Ftfb curve and the Gauss map of a surface are recalled. Later, the necessary and sufficient conditions are found for these surfaces to be of the pointwise 1-type of the Gauss map. Finally, examples for each type of these surfaces are given, and their graphics are illustrated.</p></abstract>

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Persona, Paolo, Tommaso Tonetti, Ilaria Valeri, Emanuele Pivetta, Francesco Zarantonello, Tommaso Pettenuzzo, Alessandro De Cassai, and Paolo Navalesi. "Dynamic Arterial Elastance to Predict Mean Arterial Pressure Decrease after Reduction of Vasopressor in Septic Shock Patients." Life 13, no. 1 (December 22, 2022): 28. http://dx.doi.org/10.3390/life13010028.

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After fluid status optimization, norepinephrine infusion represents the cornerstone of septic shock treatment. De-escalation of vasopressors should be considered with caution, as hypotension increases the risk of mortality. In this prospective observational study including 42 patients, we assess the role of dynamic elastance (EaDyn), i.e., the ratio between pulse pressure variation and stroke volume variation, which can be measured noninvasively by the MostCare monitoring system, to predict a mean arterial pressure (MAP) drop > 10% 30 min after norepinephrine reduction. Patients were divided into responders (MAP falling > 10%) and non-responders (MAP falling < 10%). The receiver-operating-characteristic curve identified an area under the curve of the EaDyn value to predict a MAP decrease > 10% of 0.84. An EaDyn cut-off of 0.84 predicted a MAP drop > 10% with a sensitivity of 0.71 and a specificity of 0.89. In a multivariate logistic regression, EaDyn was significantly and independently associated with MAP decrease (OR 0.001, 95% confidence interval 0.00001–0.081, p < 0.001). The nomogram model for the probability of MAP decrease > 10% showed a C-index of 0.90. In conclusion, in a septic shock cohort, EaDyn correlates well with the risk of decrease of MAP > 10% after norepinephrine reduction.

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Journal articles on the topic 'Holonomy map for curve'

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