An M∨ matrix has the form A = sI − B, where s ≥ ρ(B) ≥ 0 and B is eventually nonnegative; i.e., Bk is entrywise nonnegative for all sufficiently large integers k. A theory of M∨ matrices is developed here that parallels the theory of M-matrices, in particular as it regards exponential nonnegativity, spectral properties, semipositivity, monotonicity, inverse nonnegativity and diagonal dominance.

If every finitely generated subalgebra of an algebra A has a property P , then A is said to have P as a local property. In this paper we study classes L(K) and M(K), where K is a class of unary algebras, L(K) consists of all algebras such that every finitely generated subalgebra is in K, and M(K) is the class of all algebras with every monogenic subalgebra in K. In particular, the cases where K...

For positive integers m1, . . . ,mk, let f(m1, . . . ,mk) be the minimum order of a graph whose edges can be coloured with k colours such that every vertex is in a clique of cardinality mi all of whose edges have the i th colour for all i = 1, 2, . . . , k. The value for k = 2 was determined by Entringer et al. (J. Graph Theory 24 (1997), 21–23). We show that if k is fixed then f(m, . . . ,m) =...

We investigate some issues relating to recently proposed fractional superstring theories with Dcritical < 10. Using the factorization approach of Gepner and Qiu, we systematically rederive the partition functions of the K = 4, 8, and 16 theories and examine their spacetime supersymmetry. Generalized GSO projection operators for the K = 4 model are found. Uniqueness of the twist field, φ K/4 K/4...

We give a K-theory proof of the invariance under cobordism of the family index. We consider elliptic pseudodifferential families on a continuous fibre bundle with smooth fibres M →֒ M → B, and define a notion of cobordant families using K-groups on fibrations with boundary. We show that the index of two such families is the same using properties of the push-forward map in K-theory to reduce it t...

1. Shape Grammar Theory G. Stiny, MIT 2. Engineering Shape Grammars J. Cagan, CMU 3. Stochastic Optimization in MEMS Design E. K. Antonsson, Caltech 4. Topology optimization P. Papalambros, U. Michigan 5. Comparing Invention to Discovery, J. Cagan, K. Kotovksy, H. Simon, CMU 6. Evolutionary Synthesis M. Jakeila, Washington U. of St. Louis 7. AI-based synthesis T. Stahovich, CMU 8. Mechanical De...

Random discrete structures such as random graphs or matrices play an important role in several disciplines, including combinatorics, coding theory, computational complexity theory, and the theory of algorithms. Over the past about 20 years, non-rigorous techniques from statistical mechanics have been adapted for/applied to many of these problems. The monographs [3, 4, 8] provide an overview of ...

Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...

We find here another (not of the CROC-type) compactification of the Kontsevich spaces K(m,n). This compactification is a Stasheff-type compactification, in particular, it is exactly the Stasheff compactification when n = 1 or m = 1. The boundary strata of this compactification are products of the spaces K(m, n) and of the Stasheff polyhedra. Then we construct a dg Lie algebra naturally associat...