Central limit theorems for realized volatility under hitting times of an irregular grid

We consider a continuous semi-martingale sampled at hitting times of an irregular grid. The goal of this work is to analyze the asymptotic behavior of the realized volatility under this rather natural observation scheme. This framework strongly differs from the well understood situations when the sampling times are deterministic or when the grid is regular. Indeed, neither Gaussian approximations nor symmetry properties can be used. In this setting, as the distance between two consecutive barriers tends to zero, we establish central limit theorems for the normalized error of the realized volatility. In particular, we show that there is no bias in the limiting process.     

SYNTHESIS AND CHARACTERIZATION OF KINETICALLY STABILIZED 1,3-DIPHOSPHACYCLOBUTENE DERIVATIVES

1-(2,4,6-Tri-tert-butylphenyl)-2-phosphaethyne (1) was allowed to react with 0.5 equiv of an alkyllithium and subsequently with an alcohol to afford a bulky 1,3-diphosphacyclobutene, and its structure and coordination properties on transition metals were investigated. On the other hand, 1 was allowed to react with an alkyllithium and iodomethane to form a stable biradical, 1,3-diphosphacyclobutane-2,4-diyl.     

On the classification of weighing matrices and self‐orthogonal codes

We provide a classification method of weighing matrices based on a classification of self‐orthogonal codes. Using this method, we classify weighing matrices of orders up to 15 and order 17, by revising some known classification. In addition, we give a revised classification of weighing matrices of weight 5. A revised classification of ternary maximal self‐orthogonal codes of lengths 18 and 19 is also presented. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:40–57, 2012     

Synthesis and Self‐Assembly of Cyclic 2,7‐Anthrylene Ethynylene 1,3‐Phenylene Ethynylene Trimer with a Planar Conformation

Cyclic arylene ethynylene hexamer 1 , composed of alternating 2,7‐anthrylene ethynylene units and meta‐phenylene ethynylene units, was synthesized. It shows C₃ symmetry and possesses a flat and rigid conformation with a large equilateral triangle‐like cavity. Macrocycle 1 self‐associates through π–π stacking interactions between the anthracene‐containing macrocyclic aromatic cores with indefinite‐association constant K_E=6980 m ^?1 in CDCl₃ at 303 K. Macrocycle 1 also self‐assembles into π‐stacked nanofibers in the drop‐cast film.     

Construction of binary LCD codes,ternary LCD codes and quaternary Hermitian LCD codes

We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and quaternary Hermitian LCD codes, which improve the previously known lower bounds on the largest minimum weights.

     

Reactions of Sterically Protected 1-Halo- and 1-Pseudohalo-2-Phosphaethenyl-Lithiums

Abstract

Phosphorus analogs of alkylidenecarbenoid, Ar-P=C(X)Li, where X equals halogen or pseudohalogen atom, such as C1, Br, or SPh, have been generated by use of the 2,4,6-tri-t-butylphenyl group (abbreviated to Ar in the Scheme) as a protecting group for low coordinated organophosphorus compounds. The reaction with methyl iodide and with some aldehydes or ketones, at low temperature, gave the corresponding alkylation products^[l]. The reaction with copper salts gave 1,4-diphosphabutadiene (1) or 1,4-diphosphabutatriene (2), depending upon the substituent X^[2,3], as well as reaction conditions, such as reaction tenlperature and time, solvent, presence or absence of oxygen. Upon warming the phosphaethenyllithiun1s, thus generated, the chloro derivative of E-configuration gave a phosphaalkyne (3) via [1,2]-aromatic migration^[4], whereas the bromo derivative of Z-configuration gave a l-phospha-3,4-dihydronaphthalene derivative (4), that is a formal C-H insertion product of a phosphinidenecarbene intermediate^[5].     

Some reactions of diphosphenes and related species

Abstract

Some reactions of diphosphenes and the related species involving oxidation, reduction, alkylation, sulfurization, and ⁶η-coordination are described.