相关论文: The CR geometry of the three-segment snake

The Cartan $(2,3,5)$-distribution is a tangent distribution of rank~$2$ on a $5$-dimensional manifold satisfying certain generic conditions. The necessary and sufficient condition for a manifold to admit such a structure is established in…

Faced with complex and unstructured construction environments, wheeled and tracked robots exhibit significant limitations in terrain adaptability and flexibility, making it difficult to meet the requirements of autonomous operation.…

The paper presents a new formal way of modeling and designing reconfigurable robots, in which case the robots are allowed to reconfigure not only structurally but also functionally. We call such kind of robots "self-evolvable", which have…

We study the following three fundamental problems about ridge regression: (1) what is the structure of the estimator? (2) how to correctly use cross-validation to choose the regularization parameter? and (3) how to accelerate computation…

We describe recent work on the Bergman kernel of the (non-smooth) worm domain in several complex variables. An asymptotic expansion is obtained for the Bergman kernel. Mapping properties of the Bergman projection are studied. Irregularity…

With the recent advances in machine learning, problems that traditionally would require accurate modeling to be solved analytically can now be successfully approached with data-driven strategies. Among these, computing the inverse…

The goal of this note is to explore, from a geometric and probabilistic point of view, the dynamics of cone structures adapted to open book decompositions. This is inspired by the picture which arises in the study of the circular restricted…

In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior…

The RAVE survey, combined with proper motions and distance estimates, can be used to study in detail stellar kinematics in the extended solar neighbourhood (solar suburb). Using the red clump, we examine the mean velocity components in 3D…

We show a duality which arises from distributions of Cartan type, having growth (2, 3, 5), from the view point of geometric control theory. In fact we consider the space of singular (or abnormal) paths on a given five dimensional space…

Cosmic ray (CR) protons are an important component in many astrophysical systems. Processes like CR injection, cooling, adiabatic changes as well as active CR transport through the medium strongly modify the CR momentum distribution and…

An extension of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force distribution. The method extends the regularized Stokeslet segment methodology used for…

An oval $O$ of a plane real algebraic quartic curve $S$ is called a snake coiling around a real curve $C_k$ of degree $k$ if $O\cup\mathbb{R}C_k$ is isotopic to $O'\cup\mathbb{R}C_k$, where $O'$ is the boundary of a thickening of the…

We investigate three-dimensional surfaces where the normal vector forms a constant angle with the radius vector. These surfaces naturally extend equiangular (logarithmic) spirals in the plane.

Object manipulation has been extensively studied in the context of fixed base and mobile manipulators. However, the overactuated locomotion modality employed by snake robots allows for a unique blend of object manipulation through…

In the frame of the Kerr-Schild approach, we consider the complex structure of Kerr geometry which is determined by a complex world line of a complex source. The real Kerr geometry is represented as a real slice of this complex structure.…

Every open and orientable three manifold has a CR structure which is locally equivalent to the standard CR structure on $S^3$.

Correlated random walks (CRW) have been used for a long time as a null model for animal's random search movement in two dimensions (2D). An increasing number of studies focus on animals' movement in three dimensions (3D), but the key…

In subarctic and arctic areas, large and heavy skid-steered robots are preferred for their robustness and ability to operate on difficult terrain. State estimation, motion control and path planning for these robots rely on accurate odometry…

We study the hyperkaehler geometry of a regular semisimple adjoint orbit of SL(k,C) via the algebraic geometry of the corresponding reducible spectral curve.