let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.

Relations between multiple dimensions of family involvement in early childhood education and classroom outcomes were examined. Participants included 144 urban, Head Start children. Parental report of family involvement was gathered in late fall using a multidimensional assessment. Relations between family involvement dimensions and end of the year outcomes of approaches to learning, conduct pro...

We present a new family of binary codes derived from the family of classical Goppa codes. We generalize properties of Goppa codes to this family and deduce bounds on the dimension and on the minimum distance, and the existence of a polynomial-time decoding algorithm up to a constructed error-correcting capability. Asymptotically these codes have the same parameters as Goppa codes.

Let H be a cosemisimple Hopf algebra over an algebraically closed field k. Assume that H contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with order 2 or 3, a Hopf subalgebra of dimension 75, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. I...

We give a complete characterization of receptive field codes realizable by connected receptive fields and their minimal embedding dimensions. In particular, we show that all connected codes are realizable in dimension at most three. To our knowledge, this is the first family of receptive field codes for which the exact characterization and minimal embedding dimension is known.

We generalize the Hadwiger(-Danzer-Grünbaum-Klee) theorem on line transversals for an unbounded family of compact convex sets to the case of transversal planes of arbitrary dimension. This is the first Helly-type theorem known for transversals of dimension between 1 and d− 1.

We present two families of exterior differential systems (EDS) for causal embeddings of orthonormal frame bundles over Riemannian spaces of dimension q = 2, 3, 4, 5.... into orthonormal frame bundles over flat spaces of higher dimension. We calculate Cartan characters showing that these EDS are dynamical field theories. The first family includes a nonisometric embedding EDS for classical Einste...

We extend the notion of Iitaka dimension of a line bundle, and deene a family of dimensions indexed by weights, for vector bundles of arbitrary ranks on complex varieties. In the case of the cotangent bundle, we get a family of birational invariants, including the Kodaira dimension and the cotangent genus introduced by Sakai. We treat in detail several classes of examples, such as complete inte...

In this paper the geometric dimension of an oriented matroid is introduced. It is the minimal euclidian dimension where its separoid (to be defined) can be realized as a family of convex sets. We show that in the uniform case, it is enough to know this invariant to decide if the oriented matroid is linear .

We compute all Hirzebruch invariants χq for D5, E6, E7 and E8 elliptic fibrations of every dimension. A single generating series χ(t, y) is produced for each family of fibrations such that the coefficient of tkyq encodes χq over a base of dimension k, solely in terms of invariants of the base of the fibration. ♣Email: jfullwoo at math.fsu.edu, hoeij at math.fsu.edu