For the mean curvature vector field H and the Laplace operator ∆ of a submanifold in the Minkowski space, a submanifold satisfying the condition ∆H = f H + gC is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper...

The problem of determining shortest paths in the presence of polyhedral obstacles between two points in Euclidean 3-space stems from the general problem of obtaining optimal coliision free paths in robot systems. For the special case when paths are constrained to the surfaces of 3-dimensional objects, simple planar unfoldings are used to obtain the shortest path. For the general case wben paths...

We present two algorithms for computing the geodesic distance between phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann (2001). We show that the possible combinatorial types of shortest paths between two trees can be compactly represented by a partially ordered set. We calculate the shortest distance along each candidate path by converting the problem into one of ...

In this paper, we study different types of non-additive set multifunctions (such as: uniformly autocontinuous, null-additive, null-null-additive), presenting relationships among them and some of their properties regarding atoms and pseudo-atoms. We also study non-atomicity and non-pseudo-atomicity of regular null-additive set multifunctions defined on the Baire (Borel respectively) δ-ring of a ...

Consider the problem of sequentially testing a null hypothesis vs an alternative hypothesis when the risk function is a linear combination of probability of error in the terminal decision and expected sample size (i.e., constant cost per observation.) Assume that the parameter space is the union of null and alternative, the parameter space is convex, the intersection of null and alternative is ...

In a coor cross-polarized channel, the polarization states of the transmitting and receiving antennas are the same or orthogonal, and the corresponding target nulls (i.e., the CO-POL Nulls or X-POL Nulls) are defined as the polarization states of the transmitting antenna such that the received power equals zero. However, no systematic studies have been carried out to solve the problem of the co...

The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which  wea...

The null space of the within-class scatter matrix is found to express most discriminative information for the small sample size problem (SSSP). The null space-based LDA takes full advantage of the null space while the other methods remove the null space. It proves to be optimal in performance. From the theoretical analysis, we present the NLDA algorithm and the most suitable situation for NLDA....

| This paper addresses dynamic trajectory planning which is deened as trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace, i.e. with moving obstacles. To begin with, we propose the novel concept of state-time space as a tool to formulate dynamic trajectory planning problems. The state-time space of a robot is its state space augmented of the time dim...

The paper considers the influence of external forces, which can act anywhere on the body of the manipulator, on the behavior of the manipulator. For these forces the equivalent generalized forces in the task space and in the null space were defined. Next, a compliant motion controller is proposed, which ensures stiff behavior in the task space and compliant behavior in the null space. Two guide...