Asymptotic bias of the least squares estimator for multivariate autoregressive models

Summary The asymptotic bias of the least squares estimator for the multivariate autoregressive models is derived. The formulas for the low order univariate autoregressive models are given in terms of the simple functions of parameters. Our results are useful to the bias correction method of the least squares estimation. This work was supported by National Science Foundation Grant SES79-13976 at the Institute for Mathematical Studies in the Social Sciences, Stanford University. This paper is a revision of Discussion Paper No. 504, The Center for Mathematical Studies in Economics and Management Science, Northwestern University, October 1981.     

Shear response of Fe-bearing MgSiO3 post-perovskite at lower mantle pressures

We investigate the shear response of possible slip systems activated in pure and Fe-bearing MgSiO₃ post-perovskite (PPv) through ab initio generalized stacking fault (GSF) energy calculations. Here we show that the [100](001) slip system has the easiest response to plastic shear among ten possible slip systems investigated. Incorporation of Fe²⁺ decreases the strength of all slip systems but does not change the plastic anisotropy style. Therefore, pure and Fe-bearing MgSiO₃ PPv should demonstrate similar LPO patterns with a strong signature of the [100](001) slip system. An aggregate with this deformation texture is expected to produce a V_SH > V_SV type polarization anisotropy, being consistent with seismological observations.     

Archimedean zeta integrals on GL n × GL m and SO2n+1 × GL m

In this paper, we evaluate archimedean zeta integrals for automorphic L-functions on GL _n × GL _n-1+? and on SO_2n+1 × GL _n+? , for ? = ?1, 0, and 1. In each of these cases, the zeta integrals in question may be expressed as Mellin transforms of products of class one Whittaker functions. Here, we obtain explicit expressions for these Mellin transforms in terms of Gamma functions and Barnes integrals. When ? = 0 or ? = 1, the archimedean zeta integrals amount to integrals over the full torus. We show that, as has been predicted by Bump for such domains of integration, these zeta integrals are equal to the corresponding local L-factors—which are simple rational combinations of Gamma functions. (In the cases of GL _n × GL _n-1 and GL _n × GL _n this has, in large part, been shown previously by the second author of the present work, though the results here are more general in that they do not require the assumption of trivial central characters. Our techniques here are also quite different. New formulas for GL(n, R) Whittaker functions, obtained recently by the authors of this work, allow for substantially simplified computations). In the case ? = ?1, we express our archimedean zeta integrals explicitly in terms of Gamma functions and certain Barnes-type integrals. These evaluations rely on new recursive formulas, derived herein, for GL(n, R) Whittaker functions. Finally, we indicate an approach to certain unramified calculations, on SO_2n+1 × GL _n and SO_2n+1 × GL _n+1, that parallels our method herein for the corresponding archimedean situation. While the unramified theory has already been treated using more direct methods, we hope that the connections evoked herein might facilitate future archimedean computations.     

Adhesion of binary giant vesicles containing negative spontaneous curvature lipids induced by phase separation

We report the adhesion of binary giant vesicles composed of two types of phospholipids, one has negative spontaneous curvature which tends to bend toward the head group and the other has zero spontaneous curvature. In a homogeneous one-phase region, the giant vesicles do not adhere to each other, whereas in a coexisting two-phase region, the giant vesicles show adhesion. A fluorescence microscope observation reveals that the adhesion takes place through the domains rich in phospholipids having negative spontaneous curvature. We propose a phase separation induced hemifusion model where two apposed monolayers of adjacent vesicles are hemifused in order to reduce the bending energy of monolayers with negative spontaneous curvature and the boundary energy between the domains and matrix. We provide a strong evidence for the hemifusion model by lipid transfer experiments.     

Reactions in Water Involving the “On-Water” Mechanism

Ever-evolving catalyst advances in synthetic protocols using water as a reaction medium have enriched the understanding of sustainable organic chemistry. Because conventional classification and definitions were ambivalent, it is proposed here that catalytic reactions using water be collectively called to be “in water”, with further classification into seven types. When accelerated in water as heterogeneous mixtures, the reactions can be regarded as following an “on-water” mechanism. The original term “on water” coined by Sharpless is incongruous with catalytic reactions, whereas on-water used in this review covers all the interfaces involving water where chemical reactions are accelerated. As a result of the unconcluded dispute on the antiquated catalyst-free “on water” model, the modified model defines three water layers: water molecules that are oriented to extrude protons toward the oil phase in the inner layer, those enwrapped by a secondary layer, and finally the bulk water layer. In light of the latitudinous outlook on the role of water at the interface, selected examples of reactions, in particular those reported over the past decade, that follow an “on-water” mechanism are reviewed herein.     

Three-dimensional visualization of columnar vortices in rotating Rayleigh–Bénard convection

Journal of Visualization -  To enrich the three-dimensional experimental details of vortex structures in rotating Rayleigh–Bénard convection, we established a technique...     

Biphenyl ether and biphenyl quinolizidine lactone alkaloids from Heimia salicifolia

Three new biphenyl ether quinolizidine lactone alkaloids (1–3) and 13 new biphenyl quinolizidine lactone alkaloids (4–16) were isolated from Heimia salicifolia (Lythraceae) together with seven known alkaloids. Their structures were determined by spectroscopic analyses and chemical conversions.     

Synthesis and photophysical properties of azuleno[1′,2′:4,5]pyrrolo[2,1-b]quinazoline-6,14-diones: Azulene analogs of tryptanthrin

Azulene analog of tryptanthrin, azuleno[1′,2′:4,5]pyrrolo[2,1-b]quinazoline-6,14-dione, was successfully prepared by the condensation reaction of azuleno[2,1-b]pyrrole-2,3-dione with isatoic anhydride in the presence of sodium hydride or diisopropylethylamine (DIPEA). Its 2-halo derivatives were also obtained in high yields by the condensation reaction with 5-haloisatoic anhydrides in the presence of DIPEA. Reactivity toward electrophilic reagents was revealed by halogenation with N-bromosuccinimide (NBS) or N-iodosuccinimide (NIS) to afford 12-halo derivatives in high yields. Among the halo derivatives, 2-iodo and 12-iodo derivatives were reactive enough to afford phenylethynyl derivatives under Pd-catalyzed Sonogashira cross-coupling conditions. Within the phenylethynyl derivatives, only 12-phenylethynyl derivative was transformed into its 1,1,4,4-tetracyanobutadiene (TCBD) derivative by the reaction with TCNE. Amphoteric redox properties of the novel azulene analogs of tryptanthrin were characterized by spectroscopic and voltammetric analyses.