相关论文: Integrable Models on Hyper-Elliptic Surfaces

General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…

This survey paper concerns elliptic surfaces with section. We give a detailed overview of the theory including many examples. Emphasis is placed on rational elliptic surfaces and elliptic K3 surfaces. To this end, we particularly review the…

It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.

We show several examples of integrable systems related to special K3 and rational surfaces (e.g., an elliptic K3 surface, a K3 surface given by a double covering of the projective plane, a rational elliptic surface, etc.). The construction,…

In this paper the full and exhaustive algorithm of formation of a smooth molecular Solvent Excluded Surface- SES, and also Solvent Accessible Surface- SAS is presented. These surfaces are a boundary between molecule and solvent. The basis…

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.

A generic surface in Euclidean 3-space is determined uniquely by its metric and curvature. Classification of all special surfaces where this is not the case, i.e. of surfaces possessing isometries which preserve the mean curvature, is known…

Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…

In this paper, we give smoe characterizations of relatively normal-slant helices and isophotic curves on a smooth surface immersed in Euclidean 3-space with respect to their position vevtor. We also introduce the methods for generating an…

We define ramified and split models of elliptic surfaces and study the relation between the two models. We focus on certain rational elliptic surfaces from these points of views and as an application, we give an observation on bitantgent…

A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…

The construction of Superintegrable models with rotational symmetry and two integrals of any integer degree greater than 3 was completed in [9] only for the so called simple case. It is extended here to a more general situation and several…

A general procedure is outlined which allows one to construct superintegrable models of Winternitz type. Some examples are presented.

The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system is described. For the standard two-fold elliptic coverings the…

This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

The paper discusses relations between the structure of the complex Fermi surface below the spectrum of a second order periodic elliptic equation and integral representations of certain classes of its solutions. These integral…

We give a self-contained introduction to the relations between Integrable Systems and the Geometry of Riemann Surfaces. We start from a historical introduction to the topic of integrable systems. Afterwards, we study the polynomial…

We discuss some applications of an intrinsic multipication in the space of simple loops in a surface.

The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…