Lifting Bailey pairs to WP-Bailey pairs

A pair of sequences such that and

     

Pointwise van der Corput lemma for functions of several variables

A multidimensional version of the well-known van der Corput lemma is presented. A class of phase functions is described for which the corresponding oscillatory integrals satisfy a multidimensional decay estimate. The obtained estimates are uniform with respect to parameters on which the phases and amplitudes may depend.     

Degenerate Crossing Numbers

Let G be a graph with n vertices and e≥4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p, then they properly cross one another at p. It is shown that the number of crossing points, counted without multiplicity, is at least constant times e and that the order of magnitude of this bound cannot be improved. If, in addition, two edges are allowed to cross only at most once, then the number of crossing points must exceed constant times (e/n)⁴. The research of J. Pach was supported by NSF grant CCF-05-14079 and by grants from NSA, PSC-CUNY, BSF, and OTKA-K-60427. The research of G. Tóth was supported by OTKA-K-60427.     

Abel’s lemma on summation by parts and partial <Emphasis Type="Italic">q</Emphasis>-series transformations

The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established. This work was partially supported by National Natural Science Foundation for the Youth (Grant No. 10801026)     

A rotation method which gives linear estimates for powers of the Ahlfors–Beurling operator

In [O. Dragičević, A. Volberg, Sharp estimate of the Ahlfors–Beurling operator via averaging martingale transforms, Michigan Math. J. 51 (2) (2003) 415–435] the Ahlfors–Beurling operator T was represented as an average of two-dimensional martingale transforms. The same result can be proven for powers Tⁿ. Motivated by [T. Iwaniec, G. Martin, Riesz transforms and related singular integrals, J. Reine Angew. Math. 473 (1996) 25–57], we deduce from here that Tⁿ_p are bounded from above by Cnp^*, . We further improve this estimate to obtain the optimal behaviour of the L^p norms in question.     

Unavoidable topological minors of infinite graphs

A graph G is loosely-c-connected, or ?-c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite component and a graph containing at most d vertices. In this paper, we give the structure of a set of ?-c-connected infinite graphs that form an unavoidable set among the topological minors of ?-c-connected infinite graphs. Corresponding results for minors and parallel minors are also obtained.     

Non-commutative generalisations of Urysohn's lemma and hereditary inner ideals

We establish several generalisations of Urysohn's lemma in the setting of JB^∗-triples which provide full answers to Problems 1.12 and 1.13 in Fernández-Polo and Peralta (2007) [22]. These results extend the previous generalisations obtained by C.A. Akemann, G.K. Pedersen and L.G. Brown in the setting of C^∗-algebras. A generalised Kadison's transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in JBW^∗-triples. We introduce the notion of positively open tripotent in the bidual of a JB^∗-triple as an extension of a concept which was already considered in the setting of ternary rings of operators. We investigate the connections appearing between positively open tripotents and hereditary inner ideals.     

Star-critical Ramsey numbers for large generalized fans and books

In this paper, we show that for any fixed integers $m\ge 2$ and $t\ge 2$, the star-critical Ramsey number $r_1(K_1+n{K}_t,K_{m+1})=(m?1)tn+t$ for all sufficiently large $n$. Furthermore, for any fixed integers $p\ge 2$ and $m\ge 2$, $r_1(K_p+n{K}_1,K_{m+1})=(m?1+o\left(1\right))n$ as $n\to \infty$.     

L(V)是无限维中心代数的初等证明

研究域F上无限维线性空间V的任一子空间W的线性变换在V上的扩张,用初等方法可证明V的线性变换代数L(V)是无限维的中心代数.在一定意义上推广了域F上的n级矩阵代数是中心代数这一结果.