The generalized Schoenflies theorem asserts that if φ ∶ Sn−1 → S is a topological embedding and A is the closure of a component of Sn∖φ(Sn−1), then A ≅ D as long as A is a manifold. This was originally proved by Barry Mazur and Morton Brown using rather different techniques. We give both of these proofs.

Following systematically the generalized Hamiltonian approach of Batalin and Fradkin, we demonstrate the equivalence of a self-dual model with the Maxwell-Chern-Simons theory by embedding the former second-class theory into a first-class theory. On sabbatical leave from S.N. Bose National Centre for Basic Sciences, DB-17, Sec 1, Salt Lake, Calcutta-700064, India

We present embeddings of generalized ladders as subgraphs into the hypercube. By embedding caterpillars into ladders, we obtain embeddings of caterpillars into the hypercube. In this way we obtain almost all known results concerning the em-beddings of caterpillars into the hypercube. In addition we construct embeddings for some new types of caterpillars.

We describe a natural action on the Quot scheme, Rd compactifying the space of degree d maps from P to the Grassmannian of lines. We identify the fixed points components for this action and the weights of the normal bundle of these components. We compute the degree of this Quot scheme under the generalized Plücker embedding by applying Atiyah-Bott localization formula.

A Halin graph is a graph H = T ∪ C , where T is a tree with no vertex of degree two, and C is a cycle connecting the end-vertices of T in the cyclic order determined by a plane embedding of T. In this paper, we define classes of generalized Halin graphs, called k-Halin graphs, and investigate their Hamiltonian properties.

In this paper we formulate the Vertex Congestion Lemma leading to a new technique in computing the exact wirelength of an embedding. We compute the circular wirelength of generalized Petersen graphs by partitioning the vertices as well as the edges of cycles. Further we obtain the linear wirelength of circular ladders. Our algorithms produce optimal values in linear time.

Following systematically the generalized Hamiltonian approach of Batalin and Fradkin, we demonstrate the equivalence of a self-dual model with the Maxwell-Chern-Simons theory by embedding the former second-class theory into a rst-class theory. On sabbatical leave from S.N. Bose National Centre for Basic Sciences, DB-17, Sec 1, Salt Lake, Calcutta-700064, India

It is shown that, by a suitable embedding in the standard H1-optimal control problem, the generalized H1-optimal control problem can be recast as a 1-block Nehari problem. Since an explicit solution exists for the latter, there appears to be little need for the iterative polynomial-based solution procedures recently presented in the literature.

Some old and new constructions of the tilde geometry (the flag transitive connected triple cover of the unique generalized quadrangle W(2) of order (2, 2)) are discussed. Using them, we prove some properties of that geometry. In particular, we compute its generating rank, we give an explicit description of its universal projective embedding and we determine its homogeneous embeddings.

A robust data hiding method is proposed. A generalized wavelet transform domain is used to design a private-key embedding scheme. Specifically, a binary mask is created in the Tree Structured Haar Transform (TSH) to select the most perceptually significant coefficients using leveladaptive thresholding. Experimental results show the effectiveness of the proposed approach.