Peter Sin

Fusion Product Planning: A Market Offering Perspective

Devices that integrate multiple functions together are popular in consumer electronic markets. We describe these multifunction devices as fusion products as they fuse together products that traditionally stand alone in the marketplace. In this article, we investigate the manufacturers fusion product planning decision, adopting a market offering perspective that allows us to address the design and product portfolio decisions simultaneously. The general approach adopted is to develop and analyze a profit-maximizing model for a single firm that integrates product substitution effects in identifying an optimal market offering. In the general model, we demonstrate that the product design and portfolio decisions are analytically difficult to characterize because the number of possible portfolios can be extremely large. The managerial insight from a stylized all-in-one model and numerical analysis is that the manufacturer should, in most cases, select only a subset of fusion and single-function products to satisfy the markets multidimension needs. This may explain why the function compositions available in certain product markets are limited. In particular, one of the key factors driving the product portfolio decision is the margin associated with the fusion products. If a single all-in-one fusion product has relatively high margins, then this product likely dominates the product portfolio. Also, the congruency of the constituent single-function products is an important factor. When substitution effects are relatively high (i.e., the product set is more congruent), a portfolio containing a smaller number of products is more likely to be optimal.

On the Dimensions of Certain LDPC Codes Based on

An explicit construction of a family of binary low-density parity check (LDPC) codes called LU(3,q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a four-dimensional (4-D) symplectic vector space and the action of the symplectic group and its subgroups

q

We compute the first cohomology group with coefficients in a simple module for the algebraic group and related finite groups

-Regular Bipartite Graphs

INTRODUCTION In this paper we investigate representations of simple algebraic groups over an algebraically closed field of characteristic 2 and of their Lie algebras. For the groups of rank 4 or less, we shall determine all of the extensions of simple modules. The central theme will be the study of some intimate connections among the groups of types Bl, C l and Dl (and F 4 when l = 4). We also give calculations for those other groups of rank 4 or less which have not already been treated elsewhere ([1], [18]), but this is primarily for the sake of completeness.

On the 1-Cohomology of the Groups

Let V be a vector space of dimension n+1 over a field of pt elements. A d-dimensional subspace and an e-dimensional subspace are considered to be incident if their intersection is not the zero subspace. The rank of these incidence matrices, modulo p, are computed for all n, d, e and t. This result generalizes the well-known formula of Hamada for the incidence matrices between points and subspaces of given dimensions in a finite projective space. A generating function for these ranks as t varies, keeping n, d and e fixed, is also given. In the special case where the dimensions are complementary, i.e., d+e=n+ 1, our formula improves previous upper bounds on the size of partial m-systems (as defined by Shult and Thas).

ON REPRESENTATIONS OF ALGEBRAIC GROUPS IN CHARACTERISTIC TWO

This paper studies the permutation representation of the symplectic group Sp(2m,Fq), where q is odd, on the 1-spaces of its natural module. The complete submodule lattice for the modulo l reduction of this permutation module is known for all odd primes l not dividing q. In this paper we determine the complete submodule lattice for the mod2 reduction. Similar results are then obtained for the orthogonal group O(5,Fq).

The p -Rank of the Incidence Matrix of Intersecting Linear Subspaces

We determine the Smith normal forms of the incidence matrices of points and projective (r - 1)-dimensional subspaces of PG(n, q) and of the incidence matrices of points and r-dimensional affine subspaces of AG(n, q) for all n, r, and arbitrary prime power q.

The modulo 2 structure of rank 3 permutation modules for odd characteristic symplectic groups

Abstract Each symplectic group over the field of two elements has two exceptional doubly transitive actions on sets of quadratic forms on the defining symplectic vector space. This paper studies the associated 2-modular permutation modules. Filtrations of these modules are constructed which have subquotients which are modules for the symplectic group over an algebraically closed field of characteristic 2 and which, as such, have filtrations by Weyl modules and dual Weyl modules having fundamental highest weights. These Weyl modules have known submodule structures. It is further shown that the submodule structures of the Weyl modules are unchanged when restricted to the finite subgroups Sp(2 n ,2) and O ± (2 n ,2).

The invariant factors of the incidence matrices of points and subspaces in (,) and (,)

We study modular representations of the Hall-Janko group and its double cover in characteristics 2, 3 and 5. In particular, we determine all extensions of simple modules. Results on the group G 2(2) ≅ PSU(3,3), which is isomorphic to a maximal subgroup of the Hall-Janko group, are also included.

On the doubly transitive permutation representations of Sp(2n,F2)

We consider the action of the