A Laplace-like method for solving linear difference equations

This paper is concerned with the problem of solving linear difference equations of ordern with constant coefficients and with given initial conditions in which the variable runs not only through the integers but over . The main idea is the introduction of a suitable commutative ring of functions with discrete convolution as multiplication rule which works, although it is not a field. The existence of inverses is studied and, after the introduction of suitable functions, the problem is reduced by means of a Laplace-like relation to an algebraic equation. Examples of application are given. Finally some remarks make the connection with the Operational Calculus of Mikusinski and with the Operational Calculus of Fenyö. The advantages of this method lie in the fact that it is applicable to functions others than the step functions, in its simplicity from the theoretical point of view, in its usefulness even when computation is required and in its formal similarity to the classical treatment of linear differential equations with constant coefficients.     

硝酸银及其产物银对六角相液晶流变性影响

用偏光显微镜测定了硝酸银及其产物银对NP－10／水六角相区的影响，用动态 （应力和频率扫描）和稳态（蠕变－恢复）方法研究了硝酸银的加入和银的生成对 该体系粘弹性的影响。无机前驱物硝酸银和银的生成能使六角相区略缩，动态流变 实验表明，无机物引入纯六角相液晶体系中会使其抗剪切的能力降低，对相区两侧 影响与振荡所采用的频率有关。生成的银原子会在胶束表面聚集，增加了胶束内部 不同EO链之间的交联，造成松弛时间变长，粘弹性指数降低，稳态实验所得到的结 果与动态实验一致，并将粘性和弹性定量化。用弹簧－粘壶模型和液晶的空间构型 及作用力解释了实验结果。     

Synthesis and Crystal Structure of 3,3‘—（Hexane—1,6—diyl）bis（1—acetyl—5,5—dimethylhydantoin）,a New Inducer of Differentiation

The title compound C20H30N4O6, Mr = 422.48)was synthesized and its crystal structure was determined by X-ray diffraction method. It crystallizes in the triclinic system, space group P ī with cell parameters: a = 8.330(2), b = 8.468(2), c = 16.017(3) A, α = 97.30(3), β = 92.33(3), γ = 103.94(3)o, V = 1084.7(4) A3, Dc = 1.294 g/cm3, Z = 2, F(000) = 452 and μ = 0.096 mm-1. The structure was refined to R = 0.0483 for 3732 observed reflections with I>2(I) and wR = 0.1335 for 4828 unique reflections. The hydantoin rings are planar and the two ring planes of one molecule are paralleled to each other.     

On two methods for accelerating convergence of series

Summary The Euler-Knopp transformation and a recently considered transformation, effective for entire function of order 1, are applied to series involving completely monotonic coefficients. Some properties of the resulting series are analyzed; these include uniform convergence with respect to the index, a priori and a posteriori estimates of the remainder. For the latter transformation a compact recursive algorithm is established which enables one to make effective use of the transformation. To illustrate the effectiveness of the transformations three applications, with examples, are included.     

Approximation under an arc length constraint

Let f C[a, b]. LetP be a subset ofC[a, b], L b – a be a given real number. We say thatp P is a best approximation tof fromP, with arc length constraintL, ifA[p] _b ^a [1 + (p(x)) ²]dx L andp – f q – f for allq P withA[q] L. represents an arbitrary norm onC[a, b]. The constraintA[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755.     

Symmetrische Permutationsmengen

A permutation set (M, I) consisting of a setM and a set of permutations ofM, is calledsymmetric, if for any two permutations, the existence of anx M with (x) (x) and ^–1 (x) = ^–1 (x) implies ^–1 = ^–1 , andsharply 3-transitive, if for any two triples (x ₁,x ₂,x ₃), (y ₁,y ₂,y ₃) M ³ with|{x ₁,x ₂,x ₃ }| = |{y ₁,y ₂,y ₃ }| = 3 there is exactly one permutation with(x ₁) =y ₁,(x ₂) =y ₂,(x ₃) =y ₃. The following theorem will be proved.THEOREM.Let (M, ) be a sharply 3-transitive symmetric permutation set with |M|3, such that contains the identity. Then is a group and there is a commutative field K such that and the projective linear group PGL(2, K) are isomorphic.     

Characterization of the normal distribution by constant regression of quadratic statistics on linear statistics

This paper contains applications of theorems of [1] for quadratic statistics which have constant regression on linear statistics. Two theorems are proved. The first is a sufficient condition which assumes that the characteristic function of a sample is an entire function. The second gives a new characterization of the normal distribution.     

On the divergence of certain Hermite-Fejér interpolation

Summary In his paper [1]P. Turán discovers the interesting behaviour of Hermite-Fejér interpolation (based on the ebyev roots) not describing the derivative values at exceptional nodes {_n} _n=1 . Answering to his question we construct such exceptional node-sequence for which the mentioned process is bounded for bounded functions whenever –1<x<1 but does not converge for a suitable continuous function at any point of the whole interval [–1, 1].     

Crystal Structure, Thermal Stability and Luminescence of Coordination Polymer [Cd（BBP）（p-PDOA）]n

Hydrothermal reaction of Cd（NO3）2·4H2O with bbp and p-PDOAH2 at 140 ℃ yielded a novel 1D cadmium（Ⅱ） coordination polymer, [Cd（bbp）（p-PDOA）]n （bbp=2,6-bis（benzimidazol-2-yl）pyridine, p-PDOA=p-phenylenedioxydiacetate dianion）, in which CdN3O4 pentagonal bipyramids were linked by p-PDOA ligands in a bis-bidentate mode to construct a zigzag chain with the adjacent Cd…Cd distance of 1.14（1） nm, There exists a 2D supramolecular network linked by π-π stacking with a face-to-face distance of 0.35（1） nm between the 2,6-bis（benzimidazol-2-yl） pyridine ligands and hydrogen-bonding interactions （0.27（4） nm）. A 3D supramolecular network was further constructed by these non-covalent interactions between the zippers. The TG/DTG showed that its chain skeleton was thermally stable up to 389 ℃ and the blue fluorescent emission of the complex was determined at 428 nm in a solid state with its long decay lifetime of 7.24 ns.     

Synthesis and Crystal Structure of (2S,2'S,4'R)-2-(1-Hydroxy-1-ethylpropyl)-1-[(1'-p-tosyl-4'-hydroxypyrrolidin-2'-yl)methyl]pyrrolidine

1 INTRODUCTION In recent years, chiral β-amino alcohols have attracted much attention due to their special bio- logical functions and catalytic activities. Chiral β- amino alcohol moieties are usually found not only in natural products (e.g., cinchona alkaloids, ephe- drine, toxal, etc.) with special biological activities[1, 2], but also critical structural segments of some syn- thesized biologically active compounds, such as adrenergic agonists or antagolist[3, 4] and inhibitors for HI…