Статті в журналах: "Transversal set of vector fields"

1

ANDRADE, Plácido. "The set of vector fields with transverse foliations." Journal of the Mathematical Society of Japan 45, no. 1 (January 1993): 21–35. http://dx.doi.org/10.2969/jmsj/04510021.

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2

Ройтенберг, Владимир Шлеймович. "Planar vector fields with central symmetry: roughness and first degree of non-roughness." Вестник Адыгейского государственного университета, серия «Естественно-математические и технические науки», no. 2(281) (September 28, 2021): 27–40. http://dx.doi.org/10.53598/2410-3225-2021-2-281-27-40.

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Рассматривается пространство гладких векторных полей, заданных в замкнутой области D на плоскости, инвариантных относительно центральной симметрии и трансверсальных границе D. Описано множество векторных полей, грубых относительно этого пространства; показано, что оно открыто и всюду плотно. Во множестве всех негрубых векторных полей выделено открытое всюду плотное подмножество, состоящее из векторных полей первой степени негрубости. We consider the space of smooth vector fields defined in a closed domain D on the plane, invariant under the central symmetry and transversal to the boundary D. The set of vector fields that are rough with respect to this space is described; it is shown that it is open and everywhere dense. In the set of all non-rough vector fields, an open everywhere dense subset consisting of vector fields of the first degree of non-roughness is distinguished.

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3

DEGIOVANNI, L., and G. MAGNANO. "TRI–HAMILTONIAN VECTOR FIELDS, SPECTRAL CURVES AND SEPARATION COORDINATES." Reviews in Mathematical Physics 14, no. 10 (October 2002): 1115–63. http://dx.doi.org/10.1142/s0129055x0200151x.

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We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P0,P1,P2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which generalise those considered by E. Sklyanin in his algebro-geometric approach, are obtained from the knowledge of: (i) a common Casimir function for the two Poisson pencils (P1-λP0) and (P2-μP0); (ii) a suitable set of vector fields, preserving P0 but transversal to its symplectic leaves. The framework is applied to Lax equations with spectral parameter, for which not only it establishes a theoretical link between the separation techniques of Sklyanin and of Magri, but also provides a more efficient "inverse" procedure to obtain separation variables, not involving the extraction of roots.

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4

Goodman, Sue. "Vector fields with transverse foliations, II." Ergodic Theory and Dynamical Systems 6, no. 2 (June 1986): 193–203. http://dx.doi.org/10.1017/s0143385700003400.

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AbstractWhen does a non-singular flow on a 3-manifold have a 2-dimensional foliation everywhere transverse to it? A complete answer is given for a large class of flows, those with 1-dimensional hyperbolic chain recurrent set. We find a simple necessary and sufficient condition on the linking of periodic orbits of the flow.

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5

Vavryčuk, Václav. "Calculation of the slowness vector from the ray vector in anisotropic media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2067 (January 10, 2006): 883–96. http://dx.doi.org/10.1098/rspa.2005.1605.

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The wave quantities needed in constructing wave fields propagating in anisotropic elastic media are usually calculated as a function of the slowness vector, or of its direction called the wave normal. In some applications, however, it is desirable to calculate the wave quantities as a function of the ray direction. In this paper, a method of calculating the slowness vector for a specified ray direction is proposed. The method is applicable to general anisotropy of arbitrary strength with arbitrary complex wave surface. The slowness vector is determined by numerically solving a system of multivariate polynomial equations of the sixth order. By solving the equations, we obtain a complete set of slowness vectors corresponding to all wave types and to all branches of the wave surface including the slowness vectors along the acoustic axes. The wave surface can be folded to any degree. The system of equations is further specified for rays shot in the symmetry plane of an orthorhombic medium and for a transversely isotropic medium. The system is decoupled into two polynomial equations of the fourth order for the P –SV waves, and into equations for the SH wave, which yield an explicit closed-form solution. The presented approach is particularly advantageous in constructing ray fields, ray-theoretical Green functions, wavefronts and wave fields in strong anisotropy.

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6

Ramachandra, L. S., and D. Roy. "A New Method for Nonlinear Two-Point Boundary Value Problems in Solid Mechanics." Journal of Applied Mechanics 68, no. 5 (May 17, 2001): 776–86. http://dx.doi.org/10.1115/1.1387444.

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A local and conditional linearization of vector fields, referred to as locally transversal linearization (LTL), is developed for accurately solving nonlinear and/or nonintegrable boundary value problems governed by ordinary differential equations. The locally linearized vector field is such that solution manifolds of the linearized equation transversally intersect those of the nonlinear BVP at a set of chosen points along the axis of the only independent variable. Within the framework of the LTL method, a BVP is treated as a constrained dynamical system, which in turn is posed as an initial value problem. (IVP) In the process, the LTL method replaces the discretized solution of a given system of nonlinear ODEs by that of a system of coupled nonlinear algebraic equations in terms of certain unknown solution parameters at these chosen points. A higher order version of the LTL method, with improved path sensitivity, is also considered wherein the dimension of the linearized equation needs to be increased. Finally, the procedure is used to determine post-buckling equilibrium paths of a geometrically nonlinear column with and without imperfections. Moreover, deflections of a tip-loaded nonlinear cantilever beam are also obtained. Comparisons with exact solutions, whenever available, and other approximate solutions demonstrate the remarkable accuracy of the proposed LTL method.

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7

Li, Yuanjin, Tao Chen, and Defu Liu. "Path Planning for Laser Cladding Robot on Artificial Joint Surface Based on Topology Reconstruction." Algorithms 13, no. 4 (April 15, 2020): 93. http://dx.doi.org/10.3390/a13040093.

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Artificial joint surface coating is a hot issue in the interdisciplinary fields of manufacturing, materials and biomedicine. Due to the complex surface characteristics of artificial joints, there are some problems with efficiency and precision in automatic cladding path planning for coating fabrication. In this study, a path planning method for a laser cladding robot for artificial joints surface was proposed. The key of this method was the topological reconstruction of the artificial joint surface. On the basis of the topological relation, a set of parallel planes were used to intersect the CAD model to generate a set of continuous, directed and equidistant surface transversals on the artificial joint surface. The arch height error method was used to extract robot interpolation points from surface transversal lines according to machining accuracy requirements. The coordinates and normal vectors of interpolation points were used to calculate the position and pose of the robot tool center point (TCP). To ensure that the laser beam was always perpendicular to the artificial joint surface, a novel laser cladding set-up with a robot was designed, of which the joint part clamped by a six-axis robot moved while the laser head was fixed on the workbench. The proposed methodology was validated with the planned path on the surface of an artificial acetabular cup using simulation and experimentation via an industrial NACHI robot. The results indicated that the path planning method based on topological reconstruction was feasible and more efficient than the traditional robot teaching method.

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8

Shi, Peng, Luping Du, Congcong Li, Anatoly V. Zayats, and Xiaocong Yuan. "Transverse spin dynamics in structured electromagnetic guided waves." Proceedings of the National Academy of Sciences 118, no. 6 (February 1, 2021): e2018816118. http://dx.doi.org/10.1073/pnas.2018816118.

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Spin–momentum locking, a manifestation of topological properties that governs the behavior of surface states, was studied intensively in condensed-matter physics and optics, resulting in the discovery of topological insulators and related effects and their photonic counterparts. In addition to spin, optical waves may have complex structure of vector fields associated with orbital angular momentum or nonuniform intensity variations. Here, we derive a set of spin–momentum equations which describes the relationship between the spin and orbital properties of arbitrary complex electromagnetic guided modes. The predicted photonic spin dynamics is experimentally verified with four kinds of nondiffracting surface structured waves. In contrast to the one-dimensional uniform spin of a guided plane wave, a two-dimensional chiral spin swirl is observed for structured guided modes. The proposed framework opens up opportunities for designing the spin structure and topological properties of electromagnetic waves with practical importance in spin optics, topological photonics, metrology and quantum technologies and may be used to extend the spin-dynamics concepts to fluid, acoustic, and gravitational waves.

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9

Lee, Manseob, and Seunghee Lee. "Robust chain transitive vector fields." Asian-European Journal of Mathematics 08, no. 02 (June 2015): 1550026. http://dx.doi.org/10.1142/s1793557115500266.

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Let M be a closed n(≥2)-dimensional smooth Riemannian manifold and let X be a vector field on M. In this paper, we show that the robust chain transitive set is hyperbolic if and only if there are a C1-neighborhood [Formula: see text] of X and a compact neighborhood U of the chain transitive set such that for any [Formula: see text], the index of the continuation on ΛY(U) = ⋂t∈ℝYt(U) of every critical point does not change.

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10

Ciaglia, F. M., F. Di Cosmo, A. Ibort, M. Laudato, and G. Marmo. "Dynamical Vector Fields on the Manifold of Quantum States." Open Systems & Information Dynamics 24, no. 03 (September 2017): 1740003. http://dx.doi.org/10.1142/s1230161217400030.

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In this paper we shall consider the stratified manifold of quantum states and the vector fields which act on it. In particular, we show that the infinitesimal generator of the GKLS evolution is composed of a generator of unitary transformations plus a gradient vector field along with a Kraus vector field transversal to the strata defined by the involutive distribution generated by the former ones.

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11

Vera, Jaime. "Stability of quasi-transversal bifurcation of vector fields on 3-manifolds." Nonlinearity 9, no. 4 (July 1, 1996): 943–72. http://dx.doi.org/10.1088/0951-7715/9/4/008.

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12

Li, Bang-He, and Gui-Song Li. "Immersions with non-zero normal vector fields." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (September 1992): 281–85. http://dx.doi.org/10.1017/s0305004100070961.

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Let M be a smooth n-manifold, X be a smooth (2n − 1)-manifold, and g:M → X be a map. It was proved in [6] that g is always homotopic to an immersion. The set of homotopy classes of monomorphisms from TM into g*TX, which is denoted by Sg, may be enumerated either by the method of I. M. James and E. Thomas or by the singularity method of U. Koschorke (see [1] and references therein). When the natural action of π1(XM, g) on Sg is trivial, for example, if X is euclidean, the set Sg is in one-to-one correspondence with the set of regular homotopy classes of immersions homotopic to g (see e.g. [4]).

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13

Gubatenko, Valeriy Petrovich. "Criteria Affiliation of the Vector Fields to the Set of Electromagnetic Fields." Izvestiya of Saratov University. New Series. Series: Earth Sciences 14, no. 2 (2014): 63–72. http://dx.doi.org/10.18500/1819-7663-2014-14-2-63-72.

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14

Braga, Denis de Carvalho, Luis Fernando Mello, and Antonio Carlos Zambroni de Souza. "Nonhyperbolic Periodic Orbits of Vector Fields in the Plane Revisited." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/212340.

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The main goal of this paper is to present a theory of approximation of periodic orbits of vector fields in the plane. From the theory developed here, it is possible to obtain an approximation to the curve of nonhyperbolic periodic orbits in the bifurcation diagram of a family of differential equations that has a transversal Hopf point of codimension two. Applications of the developed theory are made in Liénard-type equations and in Bazykin’s predator-prey system.

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15

Labarca, R., and S. Plaza. "Global stability of families of vector fields." Ergodic Theory and Dynamical Systems 13, no. 4 (December 1993): 737–66. http://dx.doi.org/10.1017/s0143385700007641.

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16

Llibre, Jaume, Rafael Ramírez, and Natalia Sadovskaia. "Planar Vector Fields with a Given Set of Orbits." Journal of Dynamics and Differential Equations 23, no. 4 (July 13, 2011): 885–902. http://dx.doi.org/10.1007/s10884-011-9219-0.

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17

Prishlyak, A. O. "Vector fields with a given set of singular points." Ukrainian Mathematical Journal 49, no. 10 (October 1997): 1548–58. http://dx.doi.org/10.1007/bf02487440.

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18

Legendre, Eveline. "Existence and non-uniqueness of constant scalar curvature toric Sasaki metrics." Compositio Mathematica 147, no. 5 (July 27, 2011): 1613–34. http://dx.doi.org/10.1112/s0010437x1100529x.

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AbstractWe study compatible toric Sasaki metrics with constant scalar curvature on co-oriented compact toric contact manifolds of Reeb type of dimension at least five. These metrics come in rays of transversal homothety due to the possible rescaling of the Reeb vector fields. We prove that there exist Reeb vector fields for which the transversal Futaki invariant (restricted to the Lie algebra of the torus) vanishes. Using an existence result of E. Legendre [Toric geometry of convex quadrilaterals, J. Symplectic Geom. 9 (2011), 343–385], we show that a co-oriented compact toric contact 5-manifold whose moment cone has four facets admits a finite number of rays of transversal homothetic compatible toric Sasaki metrics with constant scalar curvature. We point out a family of well-known toric contact structures on S2×S3 admitting two non-isometric and non-transversally homothetic compatible toric Sasaki metrics with constant scalar curvature.

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19

VASSILEVICH, D. V. "QUANTUM GRAVITY ON CP2." International Journal of Modern Physics D 02, no. 02 (June 1993): 135–47. http://dx.doi.org/10.1142/s021827189300012x.

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20

Dorosiewicz, Slawomir, and Kazimierz Napiórkowski. "Vector fields generating more than one flow." International Journal of Mathematics and Mathematical Sciences 18, no. 1 (1995): 185–96. http://dx.doi.org/10.1155/s0161171295000238.

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Vector fields generating more than one flow on a manifold are constructed. For one-dimensional case a complete description of the set of flows is given. For dimensions larger than one a method of constructing vector fields with dense or open branched sets sets is given. Density of vector fields with nonempty sets of branched points is studied.

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21

Feng, Huitao. "Holomorphic Equivariant Cohomology via a Transversal Holomorphic Vector Field." International Journal of Mathematics 14, no. 05 (July 2003): 499–514. http://dx.doi.org/10.1142/s0129167x03001879.

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In this paper an analytic proof of a generalization of a theorem of Bismut [1, Theorem 5.1] is given, which says that, when v is a transversal holomorphic vector field on a compact complex manifold X with a zero point set Y, the embedding j:Y→ X induces a natural isomorphism between the holomorphic equivariant cohomology of X via v with coefficients in ξ and the Dolbeault cohomology of Y with coefficients in ξ|Y, where ξ→ X is a holomorphic vector bundle over X.

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22

Muciño-Raymundo, Jesús, and Carlos Valero-Valdés. "Bifurcations of meromorphic vector fields on the Riemann sphere." Ergodic Theory and Dynamical Systems 15, no. 6 (December 1995): 1211–22. http://dx.doi.org/10.1017/s0143385700009883.

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AbstractLet {Xθ} be a family of rotated singular real foliations in the Riemann sphere which is the result of the rotation of a meromorphic vector field X with zeros and poles of multiplicity one. We prove that the set of bifurcation values, in the circle {θ}, is for each family a set with at most a finite number of accumulation points. A condition which implies a finite number of bifurcation values is given. We also show that the property of having an infinite set of bifurcation values defines open but not dense sets in the space of meromorphic vector fields with fixed degree.

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23

Litvinenko, Yuriy, Maria Litvinenko, and Mikhail Katasonov. "Experimental Investigation of an Acoustic Field Influence on a Development of the Plane Microjet by Particle Image Velocimetry (PIV)." Siberian Journal of Physics 6, no. 4 (December 1, 2011): 42–50. http://dx.doi.org/10.54362/1818-7919-2011-6-4-42-50.

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An acoustic field influence on a development of the plane microjet at low Reynolds numbers were investigated experimentally employing Particle Image Velocimetry (PIV). Measurements were performed at synchronization of an acoustic signal phase with a laser flash. Instantaneous velocity fields of different cross- and longitudinal sections are occurred. Receptivity of the plane microjet to transversal acoustic disturbances is shown. PIV-images, correspond to them vector fields and vorticity fields are presented

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24

Narmanov, A. Ya, and S. S. Saitova. "On the geometry of the reachability set of vector fields." Differential Equations 53, no. 3 (March 2017): 311–16. http://dx.doi.org/10.1134/s001226611703003x.

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25

Li, Chong, Genaro López, Victoria Martín-Márquez, and Jin-Hua Wang. "Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds." Set-Valued and Variational Analysis 19, no. 3 (November 19, 2010): 361–83. http://dx.doi.org/10.1007/s11228-010-0169-1.

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26

Guckenheimer, John, and Philip Holmes. "Structurally stable heteroclinic cycles." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 1 (January 1988): 189–92. http://dx.doi.org/10.1017/s0305004100064732.

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This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of Cr vector fields equivariant with respect to a symmetry group. In the space X(M) of Cr vector fields on a manifold M, there is a residual set of vector fields having no trajectories joining saddle points with stable manifolds of the same dimension. Such heteroclinic connections are a structurally unstable phenomenon [4]. However, in the space XG(M) ⊂ X(M) of vector fields equivariant with respect to a symmetry group G, the situation can be quite different. We give an example of an open set U of topologically equivalent vector fields in the space of vector fields on ℝ3 equivariant with respect to a particular finite subgroup G ⊂ O(3) such that each X ∈ U has a heteroclinic cycle that is an attractor. The heteroclinic cycles consist of three equilibrium points and three trajectories joining them.

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27

Boyd, Colin. "On the structure of the family of Cherry fields on the torus." Ergodic Theory and Dynamical Systems 5, no. 1 (March 1985): 27–46. http://dx.doi.org/10.1017/s014338570000273x.

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AbstractA class of vector fields on the 2-torus, which includes Cherry fields, is studied. Natural paths through this class are defined and it is shown that the parameters for which the vector field is unstable is the closure ofhas irrational rotation number}, where ƒ is a certain map of the circle andRtis rotation throught. This is shown to be a Cantor set of zero Hausdorff dimension. The Cherry fields are shown to form a family of codimension one submanifolds of the set of vector fields. The natural paths are shown to be stable paths.

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28

Janeczko, S. "On quasicaustics and their logarithmic vector fields." Bulletin of the Australian Mathematical Society 43, no. 3 (June 1991): 365–76. http://dx.doi.org/10.1017/s0004972700029208.

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Suppose F: (Cn+1 × Cp, 0) → (C, 0) is a germ of a holomorphic function, and (S, 0) ⊂ (Cn+1, 0) is a germ of some hypersurface in (Cn+1, 0). The quasicaustic Q(F) of F is defined as Q(F) = {a ∈ Cp; F(•, a) has a critical point on S}. We investigate the structure of quasicaustics corresponding to boundary singularities. The procedure for calculating the modules of logarithmic vector fields is given. The minimal set of generators for the Whitney's cross-cap singular variety is explicitly calculated.

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29

Shah, Firdous Ahmad, and M. Younus Bhat. "Vector-valued nonuniform multiresolution analysis on local fields." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 04 (July 2015): 1550029. http://dx.doi.org/10.1142/s0219691315500290.

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A multiresolution analysis (MRA) on local fields of positive characteristic was defined by Shah and Abdullah for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis (VNUMRA) where the associated subspace V0 of L2(K, ℂM) has an orthonormal basis of the form {Φ (x - λ)}λ∈Λ where Λ = {0, r/N} + 𝒵, N ≥ 1 is an integer and r is an odd integer such that r and N are relatively prime and 𝒵 = {u(n) : n ∈ ℕ0}. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of VNUMRA on local fields starting from a vector refinement mask G(ξ) with appropriate conditions. Further, these results also hold for Cantor and Vilenkin groups.

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30

SAVVIDY, GEORGE. "EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS." International Journal of Modern Physics A 25, no. 31 (December 20, 2010): 5765–85. http://dx.doi.org/10.1142/s0217751x10051050.

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In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

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31

VASCONCELOS DOS SANTOS, R. J., and S. COUTINHO. "ANTIFERROMAGNETIC ISING MODEL DECORATED WITH D-VECTOR SPINS: TRANSVERSAL AND LONGITUDINAL LOCAL FIELDS EFFECTS." International Journal of Modern Physics B 09, no. 26 (November 30, 1995): 3387–400. http://dx.doi.org/10.1142/s0217979295001336.

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The effect of a local field acting on decorating classical D-vector bond spins of an antiferromagnetic Ising model on the square lattice is studied for both the annealed isotropic and the axial decorated cases. In both models the effect on the phase diagrams of the transversal and the longitudinal components of the local field acting on the decorating spins are fully analyzed and discussed.

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32

Arai, Kenichi, and Hiroyuki Okazaki. "N-Dimensional Binary Vector Spaces." Formalized Mathematics 21, no. 2 (June 1, 2013): 75–81. http://dx.doi.org/10.2478/forma-2013-0008.

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Summary The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields and n-dimensional binary vector spaces are very important in proving the security of cryptographic systems [13]. In this article we define the n-dimensional binary vector space Vn. Moreover, we formalize some facts about the n-dimensional binary vector space Vn.

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33

Kato, Yoshifumi. "Vector fields on some class of complete symmetric varieties." Nagoya Mathematical Journal 103 (October 1986): 85–94. http://dx.doi.org/10.1017/s0027763000000593.

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In the previous papers [6], [7], we show that the set of an algebraic homogeneous space G/P fixed under the action of a maximal torus T can be canonically identified with the coset W1 = W/W1 of Weyl group W. We find a T invariant Zariski open set near each element w ∊ W1 and introduce a very nice local coordinate system such that we can express the maximal torus action explicitly. As a result, we become able to apply the study of J. B. Carrell and D. Lieberman [2], [3] to the space G/P and investigate the numerical properties of its characteristic classes and cycles.

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34

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 (August 20, 2001): 3535–51. http://dx.doi.org/10.1142/s0217751x01005080.

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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.

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35

LI, CHENGZHI, ZHIHUA REN, and JIAZHONG YANG. "MODULI-FREE NORMAL FORMS AND LINEARIZATION OF VECTOR FIELDS." International Journal of Bifurcation and Chaos 16, no. 12 (December 2006): 3759–64. http://dx.doi.org/10.1142/s0218127406017154.

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In this paper we study C1 linearization and classification of germs of hyperbolic vector fields on Rn. Two sets of algebraic conditions imposed on the eigenvalues of vector fields are given, under either of which strict similarity of the linear parts is necessary and sufficient for C1 conjugacy of two vector fields. Furthermore, one set of the algebraic conditions together with strict similarity also imply linearization.

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36

Sdika, Michaël. "Diffeomorphic B-spline vector fields with a tractable set of inequalities." Mathematics of Computation 88, no. 320 (March 5, 2019): 2827–56. http://dx.doi.org/10.1090/mcom/3419.

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37

McLachlan, Robert I. "The structure of a set of vector fields on Poisson manifolds." Journal of Physics A: Mathematical and Theoretical 42, no. 14 (March 13, 2009): 142001. http://dx.doi.org/10.1088/1751-8113/42/14/142001.

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38

Nomizu, Katsumi, and Fabio Podestà. "On the Cartan-Norden theorem for affine Kähler immersions." Nagoya Mathematical Journal 121 (March 1991): 127–35. http://dx.doi.org/10.1017/s002776300000341x.

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In [N-Pi-Po] the notion of affine Kähler immersion for complex manifolds has been introduced: if Mn is an n-dimensional complex manifold and f: Mn -→ Cn+1 is a holomorphic immersion together with an anti-holomorphic transversal vector field ζ, we can induce a connection ▽ on Mn which is Kähler-like, that is, its curvature tensor R satisfies R(Z, W) = 0 as long as Z, W are (1, 0) complex vector fields on M.

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39

Shandra and Mikeš. "Geodesic Mappings of Vn(K)-Spaces and Concircular Vector Fields." Mathematics 7, no. 8 (August 1, 2019): 692. http://dx.doi.org/10.3390/math7080692.

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In the present paper, we study geodesic mappings of special pseudo-Riemannian manifolds called V n ( K ) -spaces. We prove that the set of solutions of the system of equations of geodesic mappings on V n ( K ) -spaces forms a special Jordan algebra and the set of solutions generated by concircular fields is an ideal of this algebra. We show that pseudo-Riemannian manifolds admitting a concircular field of the basic type form the class of manifolds closed with respect to the geodesic mappings.

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40

Epureanu, Bogdan I., and Ali Hashmi. "Parameter Reconstruction Based on Sensitivity Vector Fields." Journal of Vibration and Acoustics 128, no. 6 (June 20, 2006): 732–40. http://dx.doi.org/10.1115/1.2346692.

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A novel approach to determine very accurately multiple parameter variations by exploiting the geometric shape of dynamic attractors in state space is presented. The approach is based on the analysis of sensitivity vector fields. These sensitivity vector fields describe changes in the state space attractor of the dynamics and system behavior when parameter variations occur. Distributed throughout the attractor in state space, these fields form a collection of snapshots for known parameter changes. Proper orthogonal decomposition of the parameter space is then employed to distinguish multiple simultaneous parametric variations. The parametric changes are reconstructed by analyzing the deformation of attractors which are characterized by means of the sensitivity vector fields. A set of basis functions in the vector space formed by the sensitivity fields is obtained and is used to successfully identify test cases involving multiple simultaneous parametric variations. The method presented is shown to be robust over a wide range of parameter variations and to perform well in the presence of noise. One of the main applications of the proposed technique is detecting multiple simultaneous damage in vibration-based structural health monitoring.

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41

Khan, Suhail, Amjad Mahmood, and Ahmad T. Ali. "Concircular vector fields for Kantowski–Sachs and Bianchi type-III spacetimes." International Journal of Geometric Methods in Modern Physics 15, no. 08 (June 22, 2018): 1850126. http://dx.doi.org/10.1142/s0219887818501268.

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This paper intends to obtain concircular vector fields (CVFs) of Kantowski–Sachs and Bianch type-III spacetimes. For this purpose, ten conformal Killing equations and their general solution in the form of conformal Killing vector fields (CKVFs) are derived along with their conformal factors. The obtained conformal Killing vector fields are then placed in Hessian equations to obtain the final form of concircular vector fields. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that Kantowski–Sachs and Bianchi type-III spacetimes admit four-, six-, or fifteen-dimensional concircular vector fields. It is established that for Einstein spaces, every conformal Killing vector field is a concircular vector field. Moreover, it is explored that every concircular vector field obtained here is also a conformal Ricci collineation.

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42

Khatsymovsky, V. M. "Some minisuperspace model for the Faddeev formulation of gravity." Modern Physics Letters A 29, no. 27 (September 3, 2014): 1450141. http://dx.doi.org/10.1142/s0217732314501417.

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We consider Faddeev formulation of General Relativity (GR) in which the metric is composed of ten vector fields or a 4 ×10 tetrad. This formulation reduces to the usual GR upon partial use of the field equations. A distinctive feature of the Faddeev action is its finiteness on the discontinuous fields. This allows to introduce its minisuperspace formulation where the vector fields are constant everywhere on ℝ4 with exception of a measure zero set (the piecewise constant fields). The fields are parametrized by their constant values independently chosen in, e.g. the 4-simplices or, say, parallelepipeds into which ℝ4 can be decomposed. The form of the action for the vector fields of this type is found. We also consider the piecewise constant vector fields approximating the fixed smooth ones. We check that if the regions in which the vector fields are constant are made arbitrarily small, the minisuperspace action and equations of motion tend to the continuum Faddeev ones.

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43

Mittmann, Katrin, and Ingo Steinwart. "On the Existence of Continuous Modifications of Vector-Valued Random Fields." gmj 10, no. 2 (June 2003): 311–17. http://dx.doi.org/10.1515/gmj.2003.311.

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Abstract We consider vector-valued random fields on a general index set in and show the existence of continuous modifications if some Kolmogorov type condition is satisfied. Furthermore, we prove an extension result for Hölder continuous vector valued mappings.

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44

Chen, Xiu-Wu, Wei-Qiang Zheng, and Ji-Yan Chen. "Localization and mass spectra of bulk bosonic fields on de Sitter thick branes." International Journal of Modern Physics A 30, no. 26 (September 18, 2015): 1550151. http://dx.doi.org/10.1142/s0217751x15501511.

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A thick de Sitter brane constructed by a canonical or phantom scalar field and localization mass spectra of the bulk scalar and vector fields on the de Sitter brane is investigated. It is found that the scalar and vector zero modes are always localized on the de Sitter brane. For the de Sitter brane generated by a canonical scalar field, the spectrum of the scalar (vector) KK modes consists of one or two bound modes (one bound mode) and a set of continuous modes. However, for the de Sitter brane generated by a phantom scalar field, the spectrum of the scalar (vector) KK modes consists of two (one) or more bound KK modes as well as a set of continuous modes. The continuous spectrum on both branes starts with a same value for the scalar (vector) KK modes.

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45

LIU, Yu. "Point Set Surface Reconstruction Method Based on Energy Functions and Vector Fields." Journal of Mechanical Engineering 54, no. 5 (2018): 179. http://dx.doi.org/10.3901/jme.2018.05.179.

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46

Enciso, Alberto, and Daniel Peralta-Salas. "Existence and vanishing set of inverse integrating factors for analytic vector fields." Bulletin of the London Mathematical Society 41, no. 6 (November 18, 2009): 1112–24. http://dx.doi.org/10.1112/blms/bdp090.

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47

Amit, Yali. "Ergodic properties of markov processes driven by a set of vector fields." Stochastics and Stochastic Reports 27, no. 4 (August 1989): 235–47. http://dx.doi.org/10.1080/17442508908833577.

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48

Albano, Paolo, and Antonio Bove. "Wave Front Set of Solutions to Sums of Squares of Vector Fields." Memoirs of the American Mathematical Society 221, no. 1039 (2012): 1. http://dx.doi.org/10.1090/s0065-9266-2012-00663-0.

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49

Liu, Guoqi, Lin Sun, and Shangwang Liu. "Efficient and Enhanced Diffusion of Vector Field for Active Contour Model." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/343159.

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Gradient vector flow (GVF) is an important external force field for active contour models. Various vector fields based on GVF have been proposed. However, these vector fields are obtained with many iterations and have difficulty in capturing the whole image area. On the other hand, the ability to converge to deep and complex concavity with these vector fields is also needed to improve. In this paper, by analyzing the diffusion equation of GVF, a normalized set is defined and a dynamically normalized constraint of vector fields is used for efficient diffusion, which makes the edge vector diffusing rapidly to the entire image region. In order to improve the ability to converge to concavity, an enhanced diffusion term is integrated into the original energy functional. With the dynamically normalized constraint and enhanced diffusion term, new vector fields of EDGVF (efficient and enhanced diffusion for GVF) and EDNGVF (efficient and enhanced diffusion of NGVF) are obtained. Experimental results demonstrate that vector fields with proposed method capture the entire image and are obtained with less iterations and computational times. In particular, EDNGVF greatly improves the ability to converge to concavity.

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50

CORBERA, MONTSERRAT, and JAUME LLIBRE. "SYMMETRIC PERIODIC ORBITS NEAR HETEROCLINIC LOOPS AT INFINITY FOR A CLASS OF POLYNOMIAL VECTOR FIELDS." International Journal of Bifurcation and Chaos 16, no. 11 (November 2006): 3401–10. http://dx.doi.org/10.1142/s0218127406016884.

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For polynomial vector fields in ℝ3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

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