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 ...

A Group Labeled Graph is a pair (G,Λ) where G is an oriented graph and Λ is a mapping from the arcs of G to elements of a group. A (not necessarily directed) cycle C is called non-null if for any cyclic ordering of the arcs in C, the group element obtained by ‘adding’ the labels on forward arcs and ‘subtracting’ the labels on reverse arcs is not the identity element of the group. Non-null cycle...

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....

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...

In this paper, we try to give a classification of spacelike hypersurfaces the Lorentz-Minkowski space-time E1n+1, whose mean curvature vector field order (k+ 1) is an eigenvector kth linearized operator Lk, for non-negative integer k less than n. The Lk defined as linear part first variation (k + 1)th hypersurface arising from its normal variations. We show that any E1n+1 satisfying condition L...