Open sets with the Runge property in Banach spaces

We show that every pseudoconvex open subset of a Banach space with an unconditional Schauder basis has the F-valued Runge property for every Banach space F.     

Fractional set systems with few disjoint pairs

Ahlswede (1980) [1] and Frankl (1977) [5] independently found a result about the structure of set systems with few disjoint pairs. Bollobás and Leader (2003) [3] gave an alternate proof by generalizing to fractional set systems and noting that the optimal fractional set systems are {0,1}-valued. In this paper we show that this technique does not extend to t-intersecting families. We find optimal fractional set systems for some infinite classes of parameters, and we point out that they are strictly better than the corresponding {0,1}-valued fractional set systems. We prove some results about the structure of an optimal fractional set system, which we use to produce an algorithm for finding such systems. The run time of the algorithm is polynomial in the size of the ground set.     

Iron(III) tosylate-catalyzed deprotection of aromatic acetals in water

The deprotection of aromatic as well as conjugated acetals and ketals in water is catalyzed by iron(III) tosylate (1.0-5.0 mol %). Iron(III) tosylate is an inexpensive and readily available catalyst. The use of water, the most environmentally benign solvent, makes this procedure especially attractive for acetal deprotection.     

Nonparametric analysis of doubly truncated data

One of the principal goals of the quasar investigations is to study luminosity evolution. A convenient one-parameter model for luminosity says that the expected log luminosity, T*, increases linearly as θ ₀· log(1  +  Z*), and T*(θ ₀) = T*  −  θ ₀· log(1  +  Z*) is independent of Z*, where Z* is the redshift of a quasar and θ ₀ is the true value of evolution parameter. Due to experimental constraints, the distribution of T* is doubly truncated to an interval (U*, V*) depending on Z*, i.e., a quadruple (T*, Z*, U*, V*) is observable only when U* ≤ T* ≤ V*. Under the one-parameter model, T*(θ ₀) is independent of (U*(θ ₀), V*(θ ₀)), where U*(θ ₀) = U*  −  θ ₀· log(1  +  Z*) and V*(θ ₀) = V*  −  θ ₀· log(1  +  Z*). Under this assumption, the nonparametric maximum likelihood estimate (NPMLE) of the hazard function of T*(θ ₀) (denoted by ĥ) was developed by Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999). In this note, we present an alternative derivation of ĥ. Besides, the NPMLE of distribution function of T*(θ ₀), [^(F)]{\hat F} , will be derived through an inverse-probability-weighted (IPW) approach. Based on Theorem 3.1 of Van der Laan (1996), we prove the consistency and asymptotic normality of the NPMLE [^(F)]{\hat F} under certain condition. For testing the null hypothesis H_q0: T^*(q₀) = T^*-q₀·log(1 + Z^*){H_{\theta_0}: T^{\ast}(\theta_0) = T^{\ast}-\theta_0\cdot \log(1 + Z^{\ast})} is independent of Z*, (Efron and Petrosian in J Am Stat Assoc 94:824–834, 1999). proposed a truncated version of the Kendall’s tau statistic. However, when T* is exponential distributed, the testing procedure is futile. To circumvent this difficulty, a modified testing procedure is proposed. Simulations show that the proposed test works adequately for moderate sample size.     

Confidence intervals for the regression parameter based on weighted log-rank estimating functions

In this paper construction of a confidence interval for the regression parameter under the accelerated life regression model is discussed. The confidence interval is based on the distribution of the regression estimator, approximated by a resampling method. The procedures are incorporated with some weight functions which have mass at censored data points as well as non-censored data points. Numerical studies show that for some weight functions, the proposed confidence interval performs well. We illustrate the procedures in a real data example.     

Environmentally friendly organic synthesis using bismuth compounds: bismuth(III) iodide catalyzed deprotection of acetals in water

The chemoselective deprotection of a wide range of acetals and ketals in water is catalyzed by bismuth(III) iodide. Bismuth(III) compounds are remarkably nontoxic and hence are attractive as environmentally friendly catalysts.     

Discriminant Bounds for Spinor Regular Ternary Quadratic Lattices

The main goals of the paper are to establish a priori boundsfor the prime power divisors of the discriminants of spinorregular positive definite primitive integral ternary quadraticlattices, and to describe a procedure for determining all suchlattices.     

Bismuth compounds in organic synthesis. Synthesis of resorcinarenes using bismuth triflate

Bismuth triflate (5 mol%) smoothly catalyzes the condensation of aromatic and aliphatic aldehydes with resorcinol to give tetrameric cyclic products, resorcinarenes. With benzaldehyde, the product is obtained as a mixture of two diastereomers and the ratio of the diastereomers depends on reaction time. On the other hand, a single diastereomer is obtained with aliphatic aldehydes. The low toxicity and ease of handling of bismuth compounds coupled with fast reaction times make this method an attractive alternative to the existing methods for resorcinarene formation.     

一对普遍的级数变换公式（英）

利用Krasnoselskii-Zabreiko不动点定理获得了非线性三点边值问题{u″（t）＋a（t）u′（t）＋b（t）u（t）＋h（t）f（t）=0,t∈（0,1） u（0）=0,u（1）=αu（η）解的—个新的存在定理．     

ON ABEL-GONTSCHAROFF-GOULD＇S POLYNOMIALS

In this paper a connective study of Gould‘s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould‘s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff‘s remainder and a new form of it are demonstrated, and also illustrated with several examples.