Con(u>i)

We prove here the consistency of u>i where: u=Min{|X|:XP() generates a non-principle ultrafilter}, i=Min{|A|:A is a maximal independent family of subsets of }In this we continue Goldstern and Shelah [G1Sh388] where Con(r>u) was proved using a similar but different forcing. We were motivated by Vaughan [V] (which consists of a survey and a list of open problems). For more information on the subject see [V] and [G1Sh388].     

Computation ofg(1,5; 10)

It is established that the exact covering numberg(1,5; 10) is 102. It is further shown that this configuration is unique. It can be obtained from the unique Steiner systemS(5, 6, 12).     

Excursions of a BES0 (d) and its drift term (0<d<1)

Summary LetX be a BES₀(d) (0<d<1) with canonical decompositionX=B+(d–1)H, whereB is a brownian motion andH locally of zero energy. The process (X; H) is shown to have a local time at (0; 0), and the characteristic measure of its excursions (in Itô's sense) is described. This study leads us to new determinations of the-space variable-process defined by the occupation densities ofH taken at some optional times.     

Generalized quadrangles admitting PSL(2,q) × PSL(2,q)

In this paper, we classify the generalized quadrangles of order (s,t), s ≠ 1 ≠ t, which admit the natural action of PSL(2,s) × PSL(2,s) on a subGQ of order (s,1). This generalizes a recent result of J. De Kaey and H. Van Maldeghem 3 , by whom the classification was obtained for the case s = t. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

Groups G2(p) as quotients of (2,3,7;2p)

It is proved that for any prime the group is a quotient of      

Polynomial approximation inL p (0<p<1)

We prove that forf∈L _p , 0<p<1, andk a positive integer, there exists an algebraic polynomialP _n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω _k ^? (f,t)p is the Ditzian-Totik modulus of smoothness off inL _p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP _n can also be taken to be nondecreasing.     

GPBi‐CGstab(L): A Lanczos‐type product method unifying Bi‐CGstab(L) and GPBi‐CG

Lanczos‐type product methods (LTPMs), in which the residuals are defined by the product of stabilizing polynomials and the Bi‐CG residuals, are effective iterative solvers for large sparse nonsymmetric linear systems. Bi‐CGstab(L) and GPBi‐CG are popular LTPMs and can be viewed as two different generalizations of other typical methods, such as CGS, Bi‐CGSTAB, and Bi‐CGStab2. Bi‐CGstab(L) uses stabilizing polynomials of degree L, while GPBi‐CG uses polynomials given by a three‐term recurrence (or equivalently, a coupled two‐term recurrence) modeled after the Lanczos residual polynomials. Therefore, Bi‐CGstab(L) and GPBi‐CG have different aspects of generalization as a framework of LTPMs. In the present paper, we propose novel stabilizing polynomials, which combine the above two types of polynomials. The resulting method is referred to as GPBi‐CGstab(L). Numerical experiments demonstrate that our presented method is more effective than conventional LTPMs.