The dimension of a pairwise balanced design PBD(v,K) is the maximum positive integer d such that any d of its points are contained in a proper flat. The standard examples are affine and projective linear spaces. Also, Teirlinck provided a nearly complete existence theory for ‘Steiner spaces’, which is the case K = {3} and d = 3. A recent result of the first author and A.C.H. Ling says that ther...

For example, K. Künnemann [Ku] proved that if X is a projective space, then the conjecture is true. Here we fix a notation. We say a Hermitian line bundle (H, k) on X is arithmetically ample if (1) H is f -ample, (2) the Chern form c1(H∞, k∞) is positive definite on the infinite fiber X∞, and (3) there is a positive integer m0 such that, for any integer m ≥ m0, H(X, H) is generated by the set {...

In many applications it is desirable to cluster high dimensional data along various subspaces, which we refer to as projective clustering. We propose a new objective function for projective clustering, taking into account the inherent trade-off between the dimension of a subspace and the induced clustering error. We then present an extension of the -means clustering algorithm for projective clu...

We construct an obstruction theory for relative Hilbert schemes in the sense of [BF] and compute it explicitly for relative Hilbert schemes of divisors on smooth projective varieties. In the special case of curves on a surface V , our obstruction theory determines a virtual fundamental class [[Hilb m V ]] ∈ A m(m−k) 2 (Hilb m V), which we use to define Poincaré invariants These maps are invaria...

We investigate the structure of pure-syzygy modules in a pure-projective resolution of any right R-module over an associative ring R with an identity element. We show that a right R-module M is pure-projective if and only if there exists an integer n ≥ 0 and a pure-exact sequence 0 → M → Pn → · · · → P0 → M → 0 with pure-projective modules Pn, . . . , P0. As a consequence we get the following v...

In this paper, we principally explore flat modules over a commutative ring with identity. We do this in relation to projective and injective modules with the help of derived functors like Tor and Ext. We also consider an extension of the property of flatness and induce analogies with the “special cases” occurring in flat modules. We obtain some results on flatness in the context of a noetherian...

in this paper, we introduce the notion of an action $y_x$as a generalization of the notion of a module,and the notion of a norm $vt: y_xto f$, where $f$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: y_xto [0, 1]subseteq {bf r}$, with $bf r$  the set of all real numbers. a great many standard mappings on algebr...

1.1. Motivation. The aim of this paper is to develop a rigid-analytic theory of relative ampleness for line bundles, and to record some applications to rigid-analytic faithfully flat descent for morphisms and for proper geometric objects equipped with a relatively ample line bundle. (For coherent sheaves on rigid spaces, the theory of faithfully flat descent is established in [BG] via Raynaud’s...

in this paper, the accuracy of k- and k- turbulence models in super sonic boundary layer capturing of smooth/rough flat plates have been comprehensively investigated. among these investigations, some sorts of sensitivity analysis, including change in turbulence model, generated-grid density, near wall affects, c magnitude (for boundary layers generated on smooth flat plates), and change in c...