Positivity and divisibility of enumerators of alternating descents

The Ramanujan Journal - The alternating descent statistic on permutations was introduced by Chebikin as a variant of the descent statistic. We show that the alternating descent polynomials on...     

Ammonium Iodide–Promoted Cyclization of Aryl-Substituted Carboxylic Acids

An efficient procedure was developed for direct preparation of aryl-substituted lactones from corresponding aryl carboxylic acids, which was promoted by ammonium iodide. In this protocol, aryl carboxylic acids were treated with ammonium iodide, potassium bromide, and oxidant Oxone in a mixture of acetonitrile and 2,2,2-trifluoroethanol (6:4) at room temperature for 12 h, resulting in corresponding aryl lactones in moderate to good yields.     

随机删失下光滑的Bahadur—Kiefer过程的渐近分布

本文在随机删失数据下讨论了由核光滑的ＰＬ过程和它的分位点过程所构成的Ｂａ－ｈａｄｕｒ－Ｋｉｅｆｅｒ过程的渐近分布，证明了在不同的窗宽选择下，所得到的渐近分布可以完全不同，并由此得出了它的所有可能渐近分布。     

Congruences for 5-regular partitions modulo powers of 5

Let \(b_{5}(n)\) denote the number of 5-regular partitions of n. We find the generating functions of \(b_{5}(An+B)\) for some special pairs of integers (A, B). Moreover, we obtain infinite families of congruences for \(b_{5}(n)\) modulo powers of 5. For example, for any integers \(k\ge 1\) and \(n\ge 0\), we prove that

$$\begin{aligned} b_{5}\left( 5^{2k-1}n+\frac{5^{2k}-1}{6}\right) \equiv 0 \quad (\mathrm{mod}\, 5^{k}) \end{aligned}$$

and

$$\begin{aligned} b_{5}\left( 5^{2k}n+\frac{5^{2k}-1}{6}\right) \equiv 0 \quad (\mathrm{mod}\, 5^{k}). \end{aligned}$$

     

New proofs of Ramanujan’s identities on false theta functions

The Ramanujan Journal - We show that for any positive integer N, there are only finitely many holomorphic eta quotients of level N, none of which is a product of two holomorphic eta quotients other...     

Novel α-tosyloxylation of ketones catalyzed by the in situ generated hypoiodous acid from alkyl iodide

Using a catalytic amount of 1-iodopropane, a novel and efficient procedure has been developed for direct preparation of α-tosyloxyketones from ketones. In this protocol, 1-iodopropane is first oxidized into iodosylpropane, which decomposes to form the key catalyst hypoiodous acid. With this method, not only α-tosyloxyketones, but also other α-sulfonyloxyketones have been prepared in moderate to good yields, which extends the application of alkyl substituted hypervalent iodine reagents in organic synthesis.     

Regression analysis of multivariate recurrent event data with time-varying covariate effects

Recurrent event data occur in many fields and many approaches have been proposed for their analyses (Andersen et al. (1993) [1]; Cook and Lawless (2007) [3]). However, most of the available methods allow only time-independent covariate effects, and sometimes this may not be true. In this paper, we consider regression analysis of multivariate recurrent event data in which some covariate effects may be time-dependent. For the problem, we employ the marginal modeling approach and, especially, estimating equation-based inference procedures are developed. Both asymptotic and finite-sample properties of the proposed estimates are established and an illustrative example is provided.     

BIVARIATE ESTIMATION WITH LEFT-TRUNCATED DATA

1. Introductionffendomly truncated data frequently arise in medical studies; other application areas include economics, insurance and astronomy in a broad senses random truncation correspondsto biased sampling, where only partial or incomplete data are aVailable about the variableof interest. A typical realization. can occur as follows: Suppose that individuals/items experience tWO consecutive events in time, an initiating eveal at t and a terminating eveal ats. Usuajly, statistical niterest …     

Using modulated DSC to investigate the origin of multiple thermal transitions in frozen 10% sucrose solutions

Modulated differential scanning calorimetry (MDSC) was used to investigate the effect of annealing on multiple thermal transitions in frozen aqueous sucrose solutions. Two thermal transitions were detected from the reversing heat flow. Here, to maintain consistency with terminology used in the practice of freeze-drying [1], the higher temperature is denoted, T^′g, and the lower transition is given the symbol, T^″g. The transition at low temperature is usually believed to be a true glass transition. However, the origin of the transition at high temperature is still highly controversial. Based upon a study of 10% sucrose solutions with different cooling histories and annealing conditions, we suggest that the transition at high temperature is also a glass transition. We conclude that the lower transition is a glass transition of a phase plasticized by a higher than equilibrium amount of unfrozen water, and the higher transition, T^′g, corresponds to a glass transition in a maximally freeze-concentrated solute phase.