Log in

Relevant bibliographies by topics / Global submanifolds / Journal articles

To see the other types of publications on this topic, follow the link: Global submanifolds.

Journal articles on the topic 'Global submanifolds'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 42 journal articles for your research on the topic 'Global submanifolds.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

YANG, GUO-HONG, SHI-XIANG FENG, GUANG-JIONG NI, and YI-SHI DUAN. "RELATIONS OF TWO TRANSVERSAL SUBMANIFOLDS AND GLOBAL MANIFOLD." International Journal of Modern Physics A 16, no. 21 (2001): 3535–51. http://dx.doi.org/10.1142/s0217751x01005080.

Full text

Abstract:

In Riemann geometry, the relations of two transversal submanifolds and global manifold are discussed without any concrete models. By replacing the normal vector of a submanifold with the tangent vector of another submanifold, the metric tensors, Christoffel symbols and curvature tensors of the three manifolds are connected at the intersection points of the two submanifolds. When the inner product of the two tangent vectors of submanifolds vanishes, some corollaries of these relations give the most important second fundamental form and Gauss–Codazzi equation in the conventional submanifold theory. As a special case, the global manifold which is Euclidean is considered. It is pointed out that, in order to obtain the nonzero energy–momentum tensor of matter field in a submanifold, there must be the contributions of the above inner product and the other submanifold. Generally speaking, a submanifold is closely related to the matter fields of the other submanifold and the two submanifolds affect each other through the above inner product.

APA, Harvard, Vancouver, ISO, and other styles

2

Mondino, Andrea, and Huy T. Nguyen. "Global Conformal Invariants of Submanifolds." Annales de l'Institut Fourier 68, no. 6 (2018): 2663–95. http://dx.doi.org/10.5802/aif.3220.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Merkulov, Sergey A. "Moduli spaces of compact complex submanifolds of complex fibered manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 1 (1995): 71–91. http://dx.doi.org/10.1017/s0305004100073473.

Full text

Abstract:

In 1962 Kodaira[11] proved that ifX ↪ Y is a compact complex submanifold with normal bundle N such that H1(X, N) = 0, then X belongs to a locally complete family {Xt: t ∈ M} of complex submanifolds Xt of Y with the moduli space M being a (dimcH0(X, N))-dimensional complex manifold, and there exists a canonical isomorphismbetween the tangent space of M at a point t ∈ M and the space of all global sections of the normal bundle Nt of the embedding Xt ↪ Y.

APA, Harvard, Vancouver, ISO, and other styles

4

Dajczer, Marcos, and Lucio Rodríguez. "Substantial Codimension of Submanifolds: Global Results." Bulletin of the London Mathematical Society 19, no. 5 (1987): 467–73. http://dx.doi.org/10.1112/blms/19.5.467.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Cai, Kairen. "Global pinching theorems of submanifolds in spheres." International Journal of Mathematics and Mathematical Sciences 31, no. 3 (2002): 183–91. http://dx.doi.org/10.1155/s0161171202106247.

Full text

Abstract:

LetMbe a compact embedded submanifold with parallel mean curvature vector and positive Ricci curvature in the unit sphereS n+p(n≥2 ,p≥1). By using the Sobolev inequalities of P. Li (1980) toLpestimate for the square lengthσof the second fundamental form and the norm of a tensorΦ, related to the second fundamental form, we set up some rigidity theorems. Denote by‖σ‖ptheLpnorm ofσandHthe constant mean curvature ofM. It is shown that there is a constantCdepending only onn,H, andkwhere(n−1) kis the lower bound of Ricci curvature such that if‖σ‖ n/2<C, thenMis a totally umbilic hypersurface in the sphereS n+1.

APA, Harvard, Vancouver, ISO, and other styles

6

Cai, Kairen. "Global pinching theorems for minimal submanifolds in spheres." Colloquium Mathematicum 96, no. 2 (2003): 225–34. http://dx.doi.org/10.4064/cm96-2-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

SARDANASHVILY, G. "SUPERINTEGRABLE HAMILTONIAN SYSTEMS WITH NONCOMPACT INVARIANT SUBMANIFOLDS: KEPLER SYSTEM." International Journal of Geometric Methods in Modern Physics 06, no. 08 (2009): 1391–414. http://dx.doi.org/10.1142/s0219887809004260.

Full text

Abstract:

The Mishchenko–Fomenko theorem on superintegrable Hamiltonian systems is generalized to superintegrable Hamiltonian systems with noncompact invariant submanifolds. It is formulated in the case of globally superintegrable Hamiltonian systems which admit global generalized action-angle coordinates. The well known Kepler system falls into two different globally superintegrable systems with compact and noncompact invariant submanifolds.

APA, Harvard, Vancouver, ISO, and other styles

8

DAJCZER, MARCOS, and RUY TOJEIRO. "AN EXTENSION OF THE CLASSICAL RIBAUCOUR TRANSFORMATION." Proceedings of the London Mathematical Society 85, no. 1 (2002): 211–32. http://dx.doi.org/10.1112/s0024611502013552.

Full text

Abstract:

We extend the notion of Ribaucour transformation from classical surface theory to the theory of holonomic submanifolds of pseudo-Riemannian space forms with arbitrary dimension and codimension, that is, submanifolds with flat normal bundle admitting a global system of principal coordinates. Bianchi gave a positive answer to the question of whether among the Ribaucour transforms of a surface with constant mean or Gaussian curvature there exist other surfaces with the same property. Our main achievement is to solve the same problem for the class of holonomic submanifolds with constant sectional curvature. 2000 Mathematical Subject Classification: 53B25, 58J72.

APA, Harvard, Vancouver, ISO, and other styles

9

Forstneric, Franc, and Erik Low. "Global holomorphic equivalence of smooth submanifolds in C^n." Indiana University Mathematics Journal 46, no. 1 (1997): 0. http://dx.doi.org/10.1512/iumj.1997.46.1348.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

González-Dávila, J. C., M. C. González-Dávila, and L. Vanhecke. "Invariant submanifolds in flow geometry." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 62, no. 3 (1997): 290–314. http://dx.doi.org/10.1017/s1446788700001026.

Full text

Abstract:

AbstractWe begin a study of invariant isometric immersions into Riemannian manifolds (M, g) equipped with a Riemannian flow generated by a unit Killing vector field ξ. We focus our attention on those (M, g) where ξ is complete and such that the reflections with respect to the flow lines are global isometries (that is, (M, g) is a Killing-transversally symmetric space) and on the subclass of normal flow space forms. General results are derived and several examples are provided.

APA, Harvard, Vancouver, ISO, and other styles

11

Urban, Zbyněk, and Demeter Krupka. "Foundations of higher-order variational theory on Grassmann fibrations." International Journal of Geometric Methods in Modern Physics 11, no. 07 (2014): 1460023. http://dx.doi.org/10.1142/s0219887814600238.

Full text

Abstract:

A setting for higher-order global variational analysis on Grassmann fibrations is presented. The integral variational principles for one-dimensional immersed submanifolds are introduced by means of differential 1-forms with specific properties, similar to the Lepage forms from the variational calculus on fibred manifolds. Prolongations of immersions and vector fields to the Grassmann fibrations are defined as a geometric tool for the variations of immersions, and the first variation formula in the infinitesimal form is derived. Its consequences, the Euler–Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals are proved. Examples clarifying the meaning of the Noether theorem in the context of variational principles for submanifolds are given.

APA, Harvard, Vancouver, ISO, and other styles

12

Domitrz, Wojciech, and Pedro de M. Rios. "Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds." Geometriae Dedicata 169, no. 1 (2013): 361–82. http://dx.doi.org/10.1007/s10711-013-9861-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Kolasiński, Sławomir, Paweł Strzelecki, and Heiko von der Mosel. "Characterizing W 2,p Submanifolds by p -Integrability of Global Curvatures." Geometric and Functional Analysis 23, no. 3 (2013): 937–84. http://dx.doi.org/10.1007/s00039-013-0222-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Jost, J., and Y. L. Xin. "Some Aspects of the global Geometry of Entire Space-Like Submanifolds." Results in Mathematics 40, no. 1-4 (2001): 233–45. http://dx.doi.org/10.1007/bf03322708.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Wong, Willie Wai Yeung. "Singularities of axially symmetric time-like minimal submanifolds in Minkowski space." Journal of Hyperbolic Differential Equations 15, no. 01 (2018): 1–13. http://dx.doi.org/10.1142/s0219891618500017.

Full text

Abstract:

We prove that there does not exist global-in-time axisymmetric solutions to the time-like minimal submanifold system in Minkowski space. We further analyze the limiting geometry as the maximal time of existence is approached.

APA, Harvard, Vancouver, ISO, and other styles

16

Florit, Luis A., and Fangyang Zheng. "A local and global splitting result for real K�hler Euclidean submanifolds." Archiv der Mathematik 84, no. 1 (2005): 88–95. http://dx.doi.org/10.1007/s00013-004-1204-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Fiorani, E., and G. Sardanashvily. "Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds." Journal of Mathematical Physics 48, no. 3 (2007): 032901. http://dx.doi.org/10.1063/1.2713079.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

de la Llave, Rafael, and Florian Kogelbauer. "Global Persistence of Lyapunov Subcenter Manifolds as Spectral Submanifolds under Dissipative Perturbations." SIAM Journal on Applied Dynamical Systems 18, no. 4 (2019): 2099–142. http://dx.doi.org/10.1137/18m1210344.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Jun-min, Lin, and Xia Chang-yu. "Global pinching theorems for even dimensional minimal submanifolds in the unit spheres." Mathematische Zeitschrift 201, no. 3 (1989): 381–89. http://dx.doi.org/10.1007/bf01214903.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

CREACO, ANTHONY J., and NIKOS KALOGEROPOULOS. "THE GEODESIC RULE FOR HIGHER CODIMENSIONAL GLOBAL DEFECTS." Modern Physics Letters A 23, no. 25 (2008): 2053–66. http://dx.doi.org/10.1142/s0217732308027242.

Full text

Abstract:

We generalize the geodesic rule to the case of formation of higher codimensional global defects. Relying on energetic arguments, we argue that, for such defects, the geometric structures of interest are the totally geodesic submanifolds. On the other hand, stochastic arguments lead to a diffusion equation approach, from which the geodesic rule is deduced. It turns out that the most appropriate geometric structure that one should consider is the convex hull of the values of the order parameter on the causal volumes whose collision gives rise to the defect. We explain why these two approaches lead to similar results when calculating the density of global defects by using a theorem of Cheeger and Gromoll. We present a computation of the probability of formation of strings/vortices in the case of a system, such as nematic liquid crystals, whose vacuum is ℝP2.

APA, Harvard, Vancouver, ISO, and other styles

21

ALLEN, PAUL, LARS ANDERSSON, and JAMES ISENBERG. "TIMELIKE MINIMAL SUBMANIFOLDS OF GENERAL CO-DIMENSION IN MINKOWSKI SPACE TIME." Journal of Hyperbolic Differential Equations 03, no. 04 (2006): 691–700. http://dx.doi.org/10.1142/s0219891606000963.

Full text

Abstract:

We consider the timelike minimal surface problem in Minkowski spacetimes and show local and global existence of such surfaces having arbitrary dimension ≥ 2 and arbitrary co-dimension, provided they are initially close to a flat plane.

APA, Harvard, Vancouver, ISO, and other styles

22

Boumal, Nicolas, P.-A. Absil, and Coralia Cartis. "Global rates of convergence for nonconvex optimization on manifolds." IMA Journal of Numerical Analysis 39, no. 1 (2018): 1–33. http://dx.doi.org/10.1093/imanum/drx080.

Full text

Abstract:

Abstract We consider the minimization of a cost function f on a manifold $\mathcal{M}$ using Riemannian gradient descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality conditions within a tolerance ε. Specifically, we show that, under Lipschitz-type assumptions on the pullbacks of f to the tangent spaces of $\mathcal{M}$, both of these algorithms produce points with Riemannian gradient smaller than ε in $\mathcal{O}\big(1/\varepsilon ^{2}\big)$ iterations. Furthermore, RTR returns a point where also the Riemannian Hessian’s least eigenvalue is larger than −ε in $\mathcal{O} \big(1/\varepsilon ^{3}\big)$ iterations. There are no assumptions on initialization. The rates match their (sharp) unconstrained counterparts as a function of the accuracy ε (up to constants) and hence are sharp in that sense. These are the first deterministic results for global rates of convergence to approximate first- and second-order Karush-Kuhn-Tucker points on manifolds. They apply in particular for optimization constrained to compact submanifolds of ${\mathbb{R}^{n}}$, under simpler assumptions.

APA, Harvard, Vancouver, ISO, and other styles

23

Qiu, Qiang, and Qixin Cao. "Task constrained motion planning for 7-degree of freedom manipulators with parameterized submanifolds." Industrial Robot: An International Journal 45, no. 3 (2018): 363–70. http://dx.doi.org/10.1108/ir-01-2018-0004.

Full text

Abstract:

PurposeThis paper aims to use the redundancy of a 7-DOF (degree of freedom) serial manipulator to solve motion planning problems along a given 6D Cartesian tool path, in the presence of geometric constraints, namely, obstacles and joint limits.Design/methodology/approachThis paper describes an explicit expression of the task submanifolds for a 7-DOF redundant robot, and the submanifolds can be parameterized by two parameters with this explicit expression. Therefore, the global search method can find the feasible path on this parameterized graph.FindingsThe proposed planning algorithm is resolution complete and resolution optimal for 7-DOF manipulators, and the planned path can satisfy task constraint as well as avoiding singularity and collision. The experiments on Motoman SDA robot are reported to show the effectiveness.Research limitations/implicationsThis algorithm is still time-consuming, and it can be improved by applying parallel collision detection method or lazy collision detection, adopting new constraints and implementing more effective graph search algorithms.Originality/valueCompared with other task constrained planning methods, the proposed algorithm archives better performance. This method finds the explicit expression of the two-dimensional task sub-manifolds, so it’s resolution complete and resolution optimal.

APA, Harvard, Vancouver, ISO, and other styles

24

Cantarelli, Giancarlo. "Global existence in the future and boundedness of submanifolds of solutions of a scalar comparison equation." Rendiconti del Circolo Matematico di Palermo 44, no. 3 (1995): 401–16. http://dx.doi.org/10.1007/bf02844677.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

García Ariza, M. Á. "Degenerate Hessian structures on radiant manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 06 (2018): 1850087. http://dx.doi.org/10.1142/s0219887818500871.

Full text

Abstract:

We present a rigorous mathematical treatment of Ruppeiner geometry, by considering degenerate Hessian metrics defined on radiant manifolds. A manifold [Formula: see text] is said to be radiant if it is endowed with a symmetric, flat connection and a global vector field [Formula: see text] whose covariant derivative is the identity mapping. A degenerate Hessian metric on [Formula: see text] is a degenerate metric tensor that can locally be written as the covariant Hessian of a function, called potential. A function on [Formula: see text] is said to be extensive if its Lie derivative with respect to [Formula: see text] is the function itself. We show that the Hessian metrics appearing in equilibrium thermodynamics are necessarily degenerate, owing to the fact that their potentials are extensive (up to an additive constant). Manifolds having degenerate Hessian metrics always contain embedded Hessian submanifolds, which generalize the manifolds defined by constant volume in which Ruppeiner geometry is usually studied. By means of examples, we illustrate that linking scalar curvature to microscopic interactions within a thermodynamic system is inaccurate under this approach. In contrast, thermodynamic critical points seem to arise as geometric singularities.

APA, Harvard, Vancouver, ISO, and other styles

26

Musoke, Elle, Bernd Krauskopf, and Hinke M. Osinga. "A Surface of Heteroclinic Connections Between Two Saddle Slow Manifolds in the Olsen Model." International Journal of Bifurcation and Chaos 30, no. 16 (2020): 2030048. http://dx.doi.org/10.1142/s0218127420300487.

Full text

Abstract:

The Olsen model for the biochemical peroxidase-oxidase reaction has a parameter regime where one of its four variables evolves much slower than the other three. It is characterized by the existence of periodic orbits along which a large oscillation is followed by many much smaller oscillations before the process repeats. We are concerned here with a crucial ingredient for such mixed-mode oscillations (MMOs) in the Olsen model: a surface of connecting orbits that is followed closely by the MMO periodic orbit during its global, large-amplitude transition back to another onset of small oscillations. Importantly, orbits on this surface connect two one-dimensional saddle slow manifolds, which exist near curves of equilibria of the limit where the slow variable is frozen and acts as a parameter of the so-called fast subsystem. We present a numerical method, based on formulating suitable boundary value problems, to compute such a surface of connecting orbits. It involves a number of steps to compute the slow manifolds, certain submanifolds of their stable and unstable manifolds and, finally, a first connecting orbit that is then used to sweep out the surface by continuation. If it exists, such a surface of connecting orbits between two one-dimensional saddle slow manifolds is robust under parameter variations. We compute and visualize it in the Olsen model and show how this surface organizes the global return mechanism of MMO periodic orbits from the end of small oscillations back to a region of phase space where they start again.

APA, Harvard, Vancouver, ISO, and other styles

27

COATES, TOM, and HIROSHI IRITANI. "ON THE EXISTENCE OF A GLOBAL NEIGHBOURHOOD." Glasgow Mathematical Journal 58, no. 3 (2015): 717–26. http://dx.doi.org/10.1017/s0017089515000427.

Full text

Abstract:

AbstractSuppose that a complex manifoldMis locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, then they glue together to give a global neighbourhood ofM. As an application, we prove a global version of Hertling–Manin's unfolding theorem for germs of TEP structures; this has applications in the study of quantum cohomology.

APA, Harvard, Vancouver, ISO, and other styles

28

ASOREY, M., A. IBORT, and G. MARMO. "GLOBAL THEORY OF QUANTUM BOUNDARY CONDITIONS AND TOPOLOGY CHANGE." International Journal of Modern Physics A 20, no. 05 (2005): 1001–25. http://dx.doi.org/10.1142/s0217751x05019798.

Full text

Abstract:

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold M with regular boundary Γ=∂M. The space ℳ of self-adjoint extensions of the covariant Laplacian on M is shown to have interesting geometrical and topological properties which are related to the different topological closures of M. In this sense, the change of topology of M is connected with the nontrivial structure of ℳ. The space ℳ itself can be identified with the unitary group [Formula: see text] of the Hilbert space of boundary data [Formula: see text]. This description, is shown to be equivalent to the classical von Neumann's description in terms of deficiency index subspaces, but it is more efficient and explicit because it is given only in terms of the boundary data, which are the natural external inputs of the system. A particularly interesting family of boundary conditions, identified as the set of unitary operators which are singular under the Cayley transform, [Formula: see text] (the Cayley manifold), turns out to play a relevant role in topology change phenomena. The singularity of the Cayley transform implies that some energy levels, usually associated with edge states, acquire an infinity energy when by an adiabatic change the boundary conditions reaches the Cayley submanifold 𝒞_. In this sense topological transitions require an infinite amount of quantum energy to occur, although the description of the topological transition in the space ℳ is smooth. This fact has relevant implications in string theory for possible scenarios with joint descriptions of open and closed strings. In the particular case of elliptic self-adjoint boundary conditions, the space 𝒞_ can be identified with a Lagrangian submanifold of the infinite dimensional Grassmannian. The corresponding Cayley manifold 𝒞_ is dual of the Maslov class of ℳ. The phenomena are illustrated with some simple low dimensional examples.

APA, Harvard, Vancouver, ISO, and other styles

29

Kong, De-Xing, and Jinhua Wang. "Einstein's hyperbolic geometric flow." Journal of Hyperbolic Differential Equations 11, no. 02 (2014): 249–67. http://dx.doi.org/10.1142/s0219891614500076.

Full text

Abstract:

We investigate the Einstein's hyperbolic geometric flow, which provides a natural tool to deform the shape of a manifold and to understand the wave character of metrics, the wave phenomenon of the curvature for evolutionary manifolds. For an initial manifold equipped with an Einstein metric and assumed to be a totally umbilical submanifold in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric is Einstein if and only if the corresponding manifold is a totally umbilical hypersurface in the induced space-time. For an initial manifold which is equipped with an Einstein metric, assumed to be a totally umbilical submanifold with constant mean curvature in the induced space-time, we prove that, along the Einstein's hyperbolic geometric flow, the metric remains an Einstein metric, and the corresponding manifold is a totally umbilical hypersurface in the induced space-time. Moreover, the global existence and blowup phenomenon of the constructed metric is also investigated here.

APA, Harvard, Vancouver, ISO, and other styles

30

van der Schaft, Arjan, and Bernhard Maschke. "Geometry of Thermodynamic Processes." Entropy 20, no. 12 (2018): 925. http://dx.doi.org/10.3390/e20120925.

Full text

Abstract:

Since the 1970s, contact geometry has been recognized as an appropriate framework for the geometric formulation of thermodynamic systems, and in particular their state properties. More recently it has been shown how the symplectization of contact manifolds provides a new vantage point; enabling, among other things, to switch easily between the energy and entropy representations of a thermodynamic system. In the present paper, this is continued towards the global geometric definition of a degenerate Riemannian metric on the homogeneous Lagrangian submanifold describing the state properties, which is overarching the locally-defined metrics of Weinhold and Ruppeiner. Next, a geometric formulation is given of non-equilibrium thermodynamic processes, in terms of Hamiltonian dynamics defined by Hamiltonian functions that are homogeneous of degree one in the co-extensive variables and zero on the homogeneous Lagrangian submanifold. The correspondence between objects in contact geometry and their homogeneous counterparts in symplectic geometry, is extended to the definition of port-thermodynamic systems and the formulation of interconnection ports. The resulting geometric framework is illustrated on a number of simple examples, already indicating its potential for analysis and control.

APA, Harvard, Vancouver, ISO, and other styles

31

Duggal, K. L. "Space time manifolds and contact structures." International Journal of Mathematics and Mathematical Sciences 13, no. 3 (1990): 545–53. http://dx.doi.org/10.1155/s0161171290000783.

Full text

Abstract:

A new class of contact manifolds (carring a global non-vanishing timelike vector field) is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.

APA, Harvard, Vancouver, ISO, and other styles

32

Mihai, Adela, and Radu Rosca. "Skew-symmetric vector fields on aCR-submanifold of a para-Kählerian manifold." International Journal of Mathematics and Mathematical Sciences 2004, no. 10 (2004): 535–40. http://dx.doi.org/10.1155/s0161171204307143.

Full text

Abstract:

We deal with aCR-submanifoldMof a para-Kählerian manifoldM˜, which carries aJ-skew-symmetric vector fieldX. It is shown thatXdefines a global Hamiltonian of the symplectic formΩonM⊤andJXis a relative infinitesimal automorphism ofΩ. Other geometric properties are given.

APA, Harvard, Vancouver, ISO, and other styles

33

Piernicola, B., and C. Franco. "Lagrangian submanifold landscapes of necessary conditions for maxima in optimal control: Global parameterizations and generalized solutions." Journal of Mathematical Sciences 135, no. 4 (2006): 3125–44. http://dx.doi.org/10.1007/s10958-006-0149-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Bettiol, P., and F. Cardin. "Lagrangian submanifold landscapes of necessary conditions for maxima in optimum control: Global parameterizations and generalized solutions." Journal of Mathematical Sciences 135, no. 6 (2006): 3529. http://dx.doi.org/10.1007/s10958-006-0177-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Popovici, Dan. "L2 Extension for jets of holomorphic sections of a Hermitian line Bundle." Nagoya Mathematical Journal 180 (2005): 1–34. http://dx.doi.org/10.1017/s0027763000009168.

Full text

Abstract:

AbstractLet (X, ω) be a weakly pseudoconvex Kähler manifold, Y ⊂ X a closed submanifold defined by some holomorphic section of a vector bundle over X, and L a Hermitian line bundle satisfying certain positivity conditions. We prove that for any integer k > 0, any section of the jet sheaf which satisfies a certain L2 condition, can be extended into a global holomorphic section of L over X whose L2 growth on an arbitrary compact subset of X is under control. In particular, if Y is merely a point, this gives the existence of a global holomorphic function with an L2 norm under control and with prescribed values for all its derivatives up to order k at that point. This result generalizes the L2 extension theorems of Ohsawa-Takegoshi and of Manivel to the case of jets of sections of a line bundle. A technical difficulty is to achieve uniformity in the constant appearing in the final estimate. To this end, we make use of the exponential map and of a Rauch-type comparison theorem for complete Riemannian manifolds.

APA, Harvard, Vancouver, ISO, and other styles

36

Uschmajew, André, and Bart Vandereycken. "On critical points of quadratic low-rank matrix optimization problems." IMA Journal of Numerical Analysis 40, no. 4 (2020): 2626–51. http://dx.doi.org/10.1093/imanum/drz061.

Full text

Abstract:

Abstract The absence of spurious local minima in certain nonconvex low-rank matrix recovery problems has been of recent interest in computer science, machine learning and compressed sensing since it explains the convergence of some low-rank optimization methods to global optima. One such example is low-rank matrix sensing under restricted isometry properties (RIPs). It can be formulated as a minimization problem for a quadratic function on the Riemannian manifold of low-rank matrices, with a positive semidefinite Riemannian Hessian that acts almost like an identity on low-rank matrices. In this work new estimates for singular values of local minima for such problems are given, which lead to improved bounds on RIP constants to ensure absence of nonoptimal local minima and sufficiently negative curvature at all other critical points. A geometric viewpoint is taken, which is inspired by the fact that the Euclidean distance function to a rank-$k$ matrix possesses no critical points on the corresponding embedded submanifold of rank-$k$ matrices except for the single global minimum.

APA, Harvard, Vancouver, ISO, and other styles

37

Cao, Yinxia, Wei Zhou, Tong Chu, and Yingxiang Chang. "Global Dynamics and Synchronization in a Duopoly Game with Bounded Rationality and Consumer Surplus." International Journal of Bifurcation and Chaos 29, no. 11 (2019): 1930031. http://dx.doi.org/10.1142/s0218127419300313.

Full text

Abstract:

Based on the oligopoly game theory, a dynamic duopoly Cournot model with bounded rationality and consumer surplus is established. On the one hand, the type and the stability of the boundary equilibrium points and the stability conditions of the Nash equilibrium point are discussed in detail. On the other hand, the potential complex dynamics of the system is demonstrated by a set of 2D bifurcation diagrams. It is found that the bifurcation diagrams have beautiful fractal structures when the adjustment speed of production is taken as the bifurcation parameter. And it is verified that the area with scattered points in the 2D bifurcation diagrams is caused by the coexistence of multiple attractors. It is also found that there may be two, three or four coexisting attractors. It is even found the coexistence of Milnor attractor and other attractors. Moreover, the topological structure of the attracting basin and global dynamics of the system are investigated by the noninvertible map theory, using the critical curve and the transverse Lyapunov exponent. It is concluded that two different types of global bifurcations may occur. Because of the symmetry of the system, it can be concluded that the diagonal of the system is an invariant one-dimensional submanifold. And it is controlled by a one-dimensional map which is equivalent to the classical Logistic map. The bifurcation curve of the system on the adjustment speed and the weight of the consumer surplus is obtained based on the properties of the Logistic map. And the synchronization phenomenon along the invariant diagonal is discussed at the end of the paper.

APA, Harvard, Vancouver, ISO, and other styles

38

HUANG, HONG, JIAMIN LIU, and HAILIANG FENG. "UNCORRELATED LOCAL FISHER DISCRIMINANT ANALYSIS FOR FACE RECOGNITION." International Journal of Pattern Recognition and Artificial Intelligence 25, no. 06 (2011): 863–87. http://dx.doi.org/10.1142/s0218001411008889.

Full text

Abstract:

An improved manifold learning method, called Uncorrelated Local Fisher Discriminant Analysis (ULFDA), for face recognition is proposed. Motivated by the fact that statistically uncorrelated features are desirable for dimension reduction, we propose a new difference-based optimization objective function to seek a feature submanifold such that the within-manifold scatter is minimized, and between-manifold scatter is maximized simultaneously in the embedding space. We impose an appropriate constraint to make the extracted features statistically uncorrelated. The uncorrelated discriminant method has an analytic global optimal solution, and it can be computed based on eigen decomposition. As a result, the proposed algorithm not only derives the optimal and lossless discriminative information, but also guarantees that all extracted features are statistically uncorrelated. Experiments on synthetic data and AT&T, extended YaleB and CMU PIE face databases are performed to test and evaluate the proposed algorithm. The results demonstrate the effectiveness of the proposed method.

APA, Harvard, Vancouver, ISO, and other styles

39

BISCHI, GIAN-ITALO, LAURA GARDINI, and CHRISTIAN MIRA. "PLANE MAPS WITH DENOMINATOR. PART III: NONSIMPLE FOCAL POINTS AND RELATED BIFURCATIONS." International Journal of Bifurcation and Chaos 15, no. 02 (2005): 451–96. http://dx.doi.org/10.1142/s0218127405012314.

Full text

Abstract:

This paper continues the study of the global dynamic properties specific to maps of the plane characterized by the presence of a denominator that vanishes in a one-dimensional submanifold. After two previous papers by the same authors, where the definitions of new kinds of singularities, called focal points and prefocal sets, are given, as well as the particular structures of the basins and the global bifurcations related to the presence of such singularities, this third paper is devoted to the analysis of nonsimple focal points, and the bifurcations associated with them. We prove the existence of a one-to-one relation between the points of a prefocal curve and arcs through the focal point having all the same tangent but different curvatures. In the case of nonsimple focal points, such a relation replaces the one-to-one correspondence between the slopes of arcs through a focal point and the points along the associated prefocal curve that have been proved and extensively discussed in the previous papers. Moreover, when dealing with noninvertible maps, other kinds of relations can be obtained in the presence of nonsimple focal points or prefocal curves, and some of them are associated with qualitative changes of the critical sets, i.e. with the structure of the Riemann foliation of the plane.

APA, Harvard, Vancouver, ISO, and other styles

40

Wang, Xiaofei, Shuxin Wang, Jianmin Li, Guokai Zhang, and Chao He. "Easy Grasp: A novel hybrid-driven manual medical instrument for laparoscopic surgery." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 12 (2012): 2990–3001. http://dx.doi.org/10.1177/0954406212441568.

Full text

Abstract:

A novel compact manual instrument for laparoscopic surgery, Easy Grasp, is proposed and the prototype is developed. It is a hybridization of cable and link drives. The instrument conforms to the ergonomic engineering and it can realize roll, pitch, and yaw motions. Owing to the parallelograms and universal joints, the motions outside the abdomen can be mapped to the end-effector motions inside the abdomen exactly. The workspace of the wrist-like joint is a submanifold of special orthogonal group and is evaluated by the matrix exponential parameterization. The structure of the instrument is designed optimally on the basis of the kinematic analysis together with the global condition index. The instrument can not only satisfy the needs of basic tasks, but also be used to accomplish difficult tasks such as suturing and knot-tying. Experimental results show that the instrument works as well as commercial products. The ease of use will make the instrument effective in laparoscopic surgery. The structure of the instrument is a prototype for other manual instruments and provides a framework for instrument design.

APA, Harvard, Vancouver, ISO, and other styles

41

Fujii, Kanji, Naohisa Ogawa, Satoshi Uchiyama, and Nikolai Mikhailovich Chepilko. "Geometrically Induced Gauge Structure on Manifolds Embedded in a Higher-Dimensional Space." International Journal of Modern Physics A 12, no. 29 (1997): 5235–77. http://dx.doi.org/10.1142/s0217751x97002814.

Full text

Abstract:

We explain in a context different from that of Maraner the formalism for describing the motion of a particle, under the influence of a confining potential, in a neighborhood of an n-dimensional curved manifold Mn embedded in a p-dimensional Euclidean space Rp with p ≥ n + 2. The effective Hamiltonian on Mn has a (generally non-Abelian) gauge structure determined by the geometry of Mn. Such a gauge term is defined in terms of the vectors normal to Mn, and its connection is called the N connection. This connection is nothing but the connection induced from the normal connection of the submanifold Mn of Rp. In order to see the global effect of this type of connections, the case of M1 embedded in R3 is examined, where the relation of an integral of the gauge potential of the N connection (i.e. the torsion) along a path in M1 to the Berry phase is given through Gauss mapping of the vector tangent to M1. Through the same mapping in the case of M1 embedded in Rp, where the normal and the tangent quantities are exchanged, the relation of the N connection to the induced gauge potential (the canonical connection of the second kind) on the (p - 1)-dimensional sphere Sp - 1 (p ≥ 3) found by Ohnuki and Kitakado is concretely established; the former is the pullback of the latter by the Gauss mapping. Further, this latter which has the monopole-like structure is also proved to be gauge-equivalent to the spin connection of Sp - 1. Thus the N connection is also shown to coincide with the pullback of the spin connection of Sp - 1. Finally, by extending formally the fundamental equations for Mn to the infinite-dimensional case, the present formalism is applied to the field theory that admits a soliton solution. The resultant expression is in some respects different from that of Gervais and Jevicki.

APA, Harvard, Vancouver, ISO, and other styles

42

Izumiya, Shyuichi, Juan José Nuño Ballesteros, and María del Carmen Romero Fuster. "Global properties of codimension two spacelike submanifolds in Minkowski space." Advances in Geometry 10, no. 1 (2010). http://dx.doi.org/10.1515/advgeom.2009.034.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!