In the common polynomial regression of degree m we determine the design which max imizes the minimum of the D e ciency in the model of degree m and the D e ciencies in the models of degree m j m k j k given The resulting designs allow an e cient estimation of the parameters in the chosen regression and have reasonable e ciencies for checking the goodness of t of the assumed model of degree m by...

Let G be a compact connected Lie group, and (M,ω) a compact Hamiltonian Gspace with moment map μ. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the original manifold M , under certain technical conditions on μ. This result is a natural K-theoretic analogue of the Kirwan surjectivity theorem in symplectic geomet...

We call a module M , quasi-catenary if for each pair of quasi-prime submodules K and L of M with K L all saturated chains of quasi-prime submodules of M from K to L have a common finite length. We show that any homomorphic image of a quasi-catenary module is quasi-catenary. We prove that if M   is a module with following properties: (i) Every quasi-prime submodule of M has finite quasi-height;...

We provide an M theory interpretation of the recently discovered N=8 supersymmetric Chern-Simons theory with SO(4) gauge symmetry. The theory is argued to describe two membranes moving in the orbifold R8/Z2. At level k=1 and k=2, the classical moduli space M coincides with the infrared moduli space of SO(4) and SO(5) super Yang-Mills theory, respectively. For higher Chern-Simons level, the modu...

‎We say that a module $M$ is a emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{'}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove tha...

The ideal I 1 generated by the 2 2 quantum minors in the coordinate algebra of quantum matrices, O q (M m;n (k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I 1 is a completely prime ideal, that is, O q (M m;n (k))=I 1 is an integral domain, and that O q (M m;n (k))=I 1 is the ring of coinvariants of a ...

In this paper, our aim is to introduce the notion of a composition (m,n, k)-hyperring and to analyze its properties. We also consider the algebraic structure of (m,n, k) hyperrings which is a generalization of composition rings and composition hyperrings. Also, the isomorphism theorems of ring theory are derived in the context of composition (m,n, k)-hyperrings.