## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (198.174 recursos)

Proceedings of the International Conference on Geometry, Integrability and Quantization

1. #### Quantification of Image Data and a Kinetic Model for the Integrin Receptor Movement on the Surface of Living Cells

Zlatanov, Ivaylo; Groth, Thomas; Altankov, George
Living human fibroblasts were attached on fibronectin coated surfaces and stained with FITC labeled anti-$\beta_{1}$ integrin monoclonal antibody. The dynamic behaviour of these integrin–antibody complexes were then observed within 2.5 hours by periodic scans using confocal laser scanning microscope. Obtained data were used for analyzing the initial $\beta_{1}$ integrin reorganizations during fibroblasts spreading on fibronectin. Pursuing this aim, a specific physical model and mathematical algorithm was created that permit the corrections of the noise and the fluorescence photobleaching during the scanning. Using specific image analyzing software were defined three “regions of interest” (ROI) and the kinetic changes of integrin densities,...

2. #### Compatible Poisson Tensors Related to Bundles of Lie Algebras

Yanovski, Alexander B.
We consider some recent results about the Poisson structures, arising on the co-algebra of a given Lie algebra when we have on it a structure of a bundle of Lie algebras. These tensors have applications in the study of the Hamiltonian structures of various integrable nonlinear models, among them the O(3)-chiral fields system and Landau–Lifshitz equation

3. #### On Special Types of Minimal and Totally Geodesic Unit Vector Fields

Yampolsky, Alexander
We present a new equation with respect to a unit vector field on Riemannian manifold $M^n$ such that its solution defines a totally geodesic submanifold in the unit tangent bundle with Sasakian metric and apply it to some classes of unit vector fields. We introduce a class of covariantly normal unit vector fields and prove that within this class the Hopf vector field is a unique global one with totally geodesic property. For the wider class of geodesic unit vector fields on a sphere we give a new necessary and sufficient condition to generate a totally geodesic submanifold in $T_{1}S^{n}$.

4. #### Painlevé Analysis and Exact Solutions of Nonintegrable Systems

Vernov, Sergey Yu.
Here we consider the cubic complex Ginzburg–Landau equation. Applying the Hone’s method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has no elliptic standing wave solutions. This result supplements Hone’s result, that this equation has no elliptic travelling wave solutions. It has been shown that the Hone’s method can be applied to a system of polynomial differential equations more effectively than to an equivalent differential equation.

5. #### Symmetry Groups, Conservation Laws and Group–Invariant Solutions of the Membrane Shape Equation

Vassilev, Vassil M.; Djondjorov, Peter A.; Mladenov, Ivaïlo M.
The six-parameter group of three dimensional Euclidean motions is recognized as the largest group of point transformations admitted by the membrane shape equation in Mongé representation. This equation describes the equilibrium shapes of biomembranes being the Euler-Lagrange equation associated with the Helfrich curvature energy functional under the constraints of fixed enclosed volume and membrane area. The conserved currents of six linearly independent conservation laws that correspond to the variational symmetries of the membrane shape equation and hold on its smooth solutions are obtained. All types of non-equivalent group-invariant solutions of the membrane shape equation are identified via an optimal system...

6. #### The Relativistic Hyperbolic Parallelogram Law

Ungar, Abraham A.
A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed segments that add according to the parallelogram law. In the “gyrolanguage” of this paper one attaches the prefix “gyro” to a classical term to mean the analogous term in hyperbolic geometry. The prefix stems from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Gyrolanguage turns out to be the language one needs to articulate novel analogies that the classical and the modern in this paper...

7. #### Variational Problems In Elastic Theory of Biomembranes, Smectic-A Liquid Crystals, and Carbon Related Structures

Tu, Zhanchun; Ou-Yang, Zhongcan
After a brief introduction to several variational problems in the study of shapes of thin structures, we deal with variational problems on two-dimensional surface in three-dimensional Euclidian space by using exterior differential forms and the moving frame method. The morphological problems of lipid bilayers and stabilities of cell membranes are also discussed. The key point is that the first and the second order variations of the free energy determine equilibrium shapes and mechanical stabilities of structures

8. #### On the Inverse Problem of the Scattering Theory for a Boundary-Value Problem

Menken, Hamza; Mamedov, Khanlar R.
In the present work the inverse problem of the scattering theory for Sturm-Liouville differential equation with a spectral parameter in the boundary condition is investigated. The Gelfand–Marchenko–Levitan fundamental equation is obtained, the uniqueness of the solution of the inverse problem is proved and some properties of the scattering data are given.

9. #### On a Basic Problem for a Second Order Differential Equation With a Discontinuous Coefficient and a Spectral Parameter in the Boundary Conditions

Mamedov, Khanlar R.
In the present paper we investigate the completeness, minimality and basic properties of the eigenfunctions of one discontinuous Sturm–Liouville problem with a spectral parameter in boundary conditions and transmission conditions.

10. #### Manev Problem and Its Real Form Dynamics: Superintegrability and Symmetry Algebras

Kyuldjiev, Assen; Gerdjikov, Vladimir; Marmo, Giuseppe; Vilasi, Gaetano
The Manev model is known to possess Ermanno–Bernoulli type invariants similar to the Laplace–Runge–Lenz vector of the ordinary Kepler model. If the orbits are bounded these invariants exist only when a certain rationality condition is met and consequently we have superintegrability only on a subset of initial values. On the contrary, real form dynamics of the Manev model is superintegrable for all initial values. Using these additional invariants, we demonstrate here that both Manev model and its real Hamiltonian form have $\mathfrak{su}(2) \simeq \mathfrak{so}(3)$ (or $\mathfrak{so}(2,1)$ depending on the value of a parameter in the potential) symmetry algebra in addition...

11. #### Nambu Dynamics, $n$-Lie Algebras and Integrability

Vilasi, Gaetano
We present a generalized formulation of Poisson dynamics suitable to describe the n-bodies interactions. Examples are given of physical systems endowed with such a general structure.

12. #### Nambu Dynamics, $n$-Lie Algebras and Integrability

Vilasi, Gaetano
We present a generalized formulation of Poisson dynamics suitable to describe the n-bodies interactions. Examples are given of physical systems endowed with such a general structure.

13. #### Nambu Dynamics, $n$-Lie Algebras and Integrability

Vilasi, Gaetano
We present a generalized formulation of Poisson dynamics suitable to describe the n-bodies interactions. Examples are given of physical systems endowed with such a general structure.

14. #### Nambu Dynamics, $n$-Lie Algebras and Integrability

Vilasi, Gaetano
We present a generalized formulation of Poisson dynamics suitable to describe the n-bodies interactions. Examples are given of physical systems endowed with such a general structure.

15. #### Defects in Four-Dimensional Continua: A Paradigm for the Expantion of the Universe?

Tartaglia, Angelo
The presence of defects in material continua is known to produce internal permanent strained states. Extending the theory of defects to four dimensions and allowing for the appropriate signature, it is possible to apply these concepts to space-time. In this case a defect would induce a non-trivial metric tensor, which can be interpreted as a gravitational field. The image of a defect in space-time can be applied to the description of the Big Bang. A review of the four-dimensional generalisation of defects and an application to the expansion of the universe will be presented.

16. #### Defects in Four-Dimensional Continua: A Paradigm for the Expantion of the Universe?

Tartaglia, Angelo
The presence of defects in material continua is known to produce internal permanent strained states. Extending the theory of defects to four dimensions and allowing for the appropriate signature, it is possible to apply these concepts to space-time. In this case a defect would induce a non-trivial metric tensor, which can be interpreted as a gravitational field. The image of a defect in space-time can be applied to the description of the Big Bang. A review of the four-dimensional generalisation of defects and an application to the expansion of the universe will be presented.

17. #### Defects in Four-Dimensional Continua: A Paradigm for the Expantion of the Universe?

Tartaglia, Angelo
The presence of defects in material continua is known to produce internal permanent strained states. Extending the theory of defects to four dimensions and allowing for the appropriate signature, it is possible to apply these concepts to space-time. In this case a defect would induce a non-trivial metric tensor, which can be interpreted as a gravitational field. The image of a defect in space-time can be applied to the description of the Big Bang. A review of the four-dimensional generalisation of defects and an application to the expansion of the universe will be presented.

18. #### Defects in Four-Dimensional Continua: A Paradigm for the Expantion of the Universe?

Tartaglia, Angelo
The presence of defects in material continua is known to produce internal permanent strained states. Extending the theory of defects to four dimensions and allowing for the appropriate signature, it is possible to apply these concepts to space-time. In this case a defect would induce a non-trivial metric tensor, which can be interpreted as a gravitational field. The image of a defect in space-time can be applied to the description of the Big Bang. A review of the four-dimensional generalisation of defects and an application to the expansion of the universe will be presented.

19. #### Noncommutative Deformation of Instantons and Vortexes

Sako, Akifumi
We study noncommutative (NC) instantons and vortexes. At first, we construct instanton solutions which are deformations of instanton solutions on commutative Euclidean four-space. We show that the instanton numbers of these NC instanton solutions coincide with the commutative solutions. Next, we also deform vortex solutions similarly and we show that their vortex numbers are unchanged under the NC deformation.

20. #### Noncommutative Deformation of Instantons and Vortexes

Sako, Akifumi
We study noncommutative (NC) instantons and vortexes. At first, we construct instanton solutions which are deformations of instanton solutions on commutative Euclidean four-space. We show that the instanton numbers of these NC instanton solutions coincide with the commutative solutions. Next, we also deform vortex solutions similarly and we show that their vortex numbers are unchanged under the NC deformation.

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