Bounds on the inverses of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.     

Almost maximal spaces

A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents.     

Hölder exponents and box dimension for self-affine fractal functions

We consider some self-affine fractal functions previously studied by Barnsleyet al. The graphs of these functions are invariant under certain affine scalings, and we extend their definition to allow the use of nonlinear scalings. The Hölder exponent,h, for these fractal functions is calculated and we show that there is a larger Hölder exponent,h , defined at almost every point (with respect to Lebesgue measure). For a class of such functions defined using linear affinities these exponents are related to the box dimensionD _B of the graph byh2–D _Bh .Communicated by Michael F. Barnsley.     

Lower bound of overall exponential sums for polynomialsϕ(x d )

LetS ⁽¹⁾ (n, Q) denote the maximum module of exponential sums for polynomials of degree n over the Galois fieldF _Q . In a previous paper the transition to the multiple exponential sums allowed us to obtain a good lower bound of the valueS ⁽¹⁾ (n, Q), which coincides with Weil's bound whenn = q ^(m-1)/2 + 1, whereq, m are odd andm 3. Here the same approach is used for the estimation of the valueS ^(d) (n, Q), which corresponds to polynomials(x ^d ) overF _Q , whered is any divisor ofq – 1.     

Solutions rationnelles de certaines équations fonctionnelles

Dans cet article, nous démontrons essentiellement les deux résultats suivants, qui montrent que les solutions séries formelles à coefficients dans de certaines équations fonctionnelles sont rationnelles. Soient tout d'abords un entier naturel non nul, eta _i ,b _i ,(i = 1, , s), 2s nombres complexes, lesa _i étant non nuls. On définit l'ensembleA comme étant l'intersection des parties de , contenant l'origine et stables par toutes les applicationsg _i (x) = a _i x + b _i . On a alors le résultat suivant: Théorème 1.Soient f, R ₁, ,R _s s + 1 fractions rationnelles de (x), régulières à l'origine, et a_i, b_i (i = 1,, s), 2s éléments de . On suppose que les a_i sont non nuls et de module strictement inférieur à un pour tout i = 1,, s. Soit y(x) un élément de [[x]], vérifiant l'équation fonctionnelle

Dual vectors and lower bounds for the nearest lattice point problem

We prove that given a point outside a given latticeL then there is a dual vector which gives a fairly good estimate for how far from the lattice the vector is. To be more precise, there is a set of translated hyperplanesH _i, such thatL _iH_i andd( _iH_i)(6n ²+1)^–1 d( ,L).Supported by an IBM fellowship.     

大环二萜类化合物的研究(Ⅳ)——Isosarcophytol—A前体化合物的合成

Isosarcophytol-A(1)是1982年首次从澳大利亚软珊瑚(Nephthea brassica)中分离鉴定的西松烷型(Cembrane)大环二萜类化合物,其结构为6,10,14-三甲基-3-异丙基-3E,5E,9E,13E-环十四碳四烯-1-醇,是Sarcophytol—A(2)的异构体,但有关1的生物活性试验和全合成研究尚未见报道.我们在前文报道了以低价钛诱导的分子内二羰基偶联为环化方法,完成了天然大环二萜类化合物Cembrene—C的全合成和Sarcophytol—A(2)苄醚衍生物(3)的合成.本文报道以天然法呢醇4为起始原料,经区域选择性氧化、羟醛缩合等六步反应,合成了1的前体化合物11.合成路线如下:     

亚运会兴奋剂检测

本文建立了检查IOC禁用的五大类100种药物的筛选和确证方法。对药物检查机构及资格认可,药物检验的一般步骤,第十一届亚运会兴奋剂的检测均作了简要的介绍。     

SAPO－5，－11和－34分子筛模板剂的脱除及其结构的热致变化

用水热法合成了ＳＡＰＯ－５，－１１和－３４硅磷酸铝类分子筛。并对经不同温度焙烧处理的样品进行表征，结果表明：分子筛中模块剂的热分解过程与其结构和孔大小有较大的关系。在ＳＡＰＯ－５和ＳＡＰＯ－３４分子筛中，外部联接的Ｔ－Ｏ－Ｔ键的反对称伸缩振动峰（１２４０ｃｍ~（－１）－１０３８ｃｍ~（－１））和其对称伸缩振动（７３４ｃｍ~（－１）－６００ｃｍ~（－１））及双环的变形振动（６００－５００ｃｍ~（－１））的吸收峰对样品的结晶度比较敏感。但在ＳＡＰＯ－１１中，分子筛骨架中Ｔ－Ｏ－Ｔ反对称伸缩振动（１２２５ｃｍ~（－１）和１０３８ｃｍ~（－１））随结晶度的下降而基本保持不变，但内四面体（ＴＯ_４）的对称伸缩振动，反对称伸缩振动峰及Ｔ－Ｏ弯曲振动峰随样品焙烧温度的升高而减弱并分裂。红外吸收带向低频方向移动。ＳＥＭ－ＥＤＡＸ结果表明：随样品焙烧温度的升高，结晶度下降，分子筛晶形变得不规则，晶面越来越粗糙，但结晶度的下降并非由于其中ＰＯ_４四面体的热分解所引起，而是由外部联结的Ｔ－Ｏ－Ｔ键的断裂，双环被破坏及骨架元素间的重排所引起。