Estimation of integrated volatility in stochastic volatility models

In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the pth power variation (i.e. the sum of pth absolute powers of the log‐returns). We derive consistency and distributional results for the estimators given high‐frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.     

Vector-Orthogonality and Lanczos-Type Methods

A method for solving a linear system is defined. It is a Lanczos-type method, but it uses formal vector orthogonality instead of scalar orthogonality. Moreover, the dimension of vector orthogonality may vary which gives a large freedom in leading the algorithm, and controlling the numerical problems. The ideas of truncated and restarted methods are revisited. The obtained residuals are exactly orthogonal to a space of increasing dimension. Some experiments are done, the problem of finding automaticaly good directions of projection remains partly open.     

GnRH binding RNA and DNA Spiegelmers: a novel approach toward GnRH antagonism

Mirror-image oligonucleotide ligands (Spiegelmers) that bind to the pharmacologically relevant target gonadotropin-releasing hormone I (GnRH) with high affinity and high specificity have been identified using the Spiegelmer technology. GnRH is a decapeptide that plays an important role in mammalian reproduction and sexual maturation and is associated with several benign and malignant diseases. First, aptamers that bind to D-GnRH with dissociation constants of 50-100 nM were isolated out of RNA and DNA libraries. The respective enantiomers of the DNA and RNA aptamers were synthesized, and their binding to L-GnRH was shown. These Spiegelmers bind to L-GnRH with similar affinity to that of the corresponding aptamers that bind to D-GnRH. We further demonstrated dose-dependent inhibition of GnRH-induced Ca(2+) release in Chinese hamster ovary cells that were stably transfected with the human GnRH receptor.     

Electronic Structure of [Ta(5)(NH)(4)Cl(17)](6-): A Cluster with a Distorted Square Pyramidal Ta(5) Core

We report approximate molecular orbital calculations on the [Ta(5)(NH)(4)Cl(17)](6-) cluster synthesized by Simon and Meyer. The cluster is based on a "flattened" square pyramid of tantalum atoms, basal bridging imides, and terminal chlorides. This cluster was of interest to us due to the unusual presence of imide ligands, the distorted nature of the metal core, and the possible resemblance to B(5)H(9). Our calculations indicate that metal-metal bonding is limited to Ta(apical)-Ta(basal) bonding, with no significant bonding between the basal metal atoms. The imide ligands, which bridge the base of the pyramid, were found to have a significant amount of capping character. The metal-metal bonding orbitals have some unusual features due to the pyramid's distortion. Additionally, the flattened nature of the pyramid leads to an interesting energy ordering of the metal-metal bonding orbitals.     

Ditungsten Siloxide Hydrides, [(silox)(2)WH(n)()](2) (n = 1, 2; silox = (t)BuSiO), and Related Complexes

The addition of 4.0 equiv of Na(silox) to Na[W(2)Cl(7)(THF)(5)] afforded (silox)(2)ClW&tbd1;WCl(silox)(2) (1, 65%). Treatment of 1 with 2.0 equiv of MeMgBr in Et(2)O provided (silox)(2)MeW&tbd1;WMe(silox)(2) (2, 81%). In the presence of 1 atm of H(2), reduction of 1 with 2.0 equiv of Na/Hg in DME provided (silox)(2)HW&tbd1;WH(silox)(2) (3, 70%), characterized by a hydride resonance at delta 19.69 (J(WH) = 325 Hz, (1)H NMR). Exposure of 2 to 1 atm of H(2) yielded 3 and CH(4) via (silox)(2)HW&tbd1;WMe(silox)(2) (4); use of D(2) led to [(silox)(2)WD](2) (3-d(2)). Exposure of 3 to ethylene ( approximately 1 atm, 25 degrees C) in hexanes generated (silox)(2)EtW&tbd1;WEt(silox)(2) (5), but solutions of 5 reverted to 3 and free C(2)H(4) upon standing. NMR spectral data are consistent with a sterically locked, gauche, C(2) symmetry for 1-5. Thermolysis of 3 at 100 degrees C (4 h) resulted in partial conversion to (silox)(2)HW&tbd1;W(OSi(t)Bu(2)CMe(2)CH(2))(silox) (6a, approximately 60%) and free H(2), while extended thermolysis with degassing (5 d, 70 degrees C) produced a second cyclometalated rotational isomer, 6b (6a:6b approximately 3:1). When left at 25 degrees C (4 h) in sealed NMR tubes, 6 and free H(2) regenerated 3. Reduction of 1 with 2.0 equiv of Na/Hg in DME also afforded 6a (25%). When 3 was exposed to approximately 3 atm of H(2), equilibrium amounts of [(silox)(2)WH(2)](2) (7) were observed by (1)H NMR spectroscopy (3 + H(2) right harpoon over left harpoon 7; 25.9-88.7 degrees C, DeltaH = -9.6(4) kcal/mol, DeltaS = -21(2) eu). Benzene solutions of 3 and 1-3 atm of D(2) revealed incorporation of deuterium into the silox ligands, presumably via intermediate 6. In sealed tubes containing [(silox)(2)WCl](2) (1) and dihydrogen (1-3 atm), (1)H NMR spectral evidence for [(silox)(2)WCl](2)(&mgr;-H)(2) (8) was obtained, suggesting that formation of 3 from 1 proceeded via reduction of 8. Alternatively, 3 may be formed from direct reduction of 1 to give [(silox)(2)W](2) (9), followed by H(2) addition. Hydride chemical shifts for 7 are temperature dependent, varying from delta 1.39 (-70 degrees C, toluene-d(8)), to delta 3.68 (90 degrees C). (29)Si{(1)H} NMR spectra revealed a similar temperature dependence of the silox (delta 12.43, -60 degrees C, to delta 13.64, 45 degrees C) resonances. These effects may arise from thermal population of a low-lying, deltadelta, paramagnetic excited state of D(2)(d)() [(silox)(2)W](2)(&mgr;-H)(4) (DeltaE approximately 2.1 kcal/mol, chi(7a) approximately 0.03), an explanation favored over thermal equilibration with an energetically similar but structurally distinct isomer (e.g., [(silox)(2)WH(2)](2)(&mgr;-H)(2), DeltaG degrees approximately 0.69 kcal/mol, chi(7b) approximately 0.25) on the basis of spectral arguments. Extended Hückel and ab initio molecular orbital calculations on model complexes [(H(3)SiO)(2)W](2)(&mgr;-H)(4) (staggered bridged 7a', EHMO), [(H(3)SiO)(2)WH(2)](2) (all-terminal 7b', EHMO), [(H(3)SiO)(2)W](2) (9', EHMO), (HO)(4)W(2)(H(4)) (staggered-bridged 7", ab initio), and (HO)(4)W(2)(H(4)) (bent-terminal 7, ab initio) generally support the explanation of a thermally accessible excited state and assign 7 a geometry intermediate between the all-terminal and staggered-bridged forms.     

Preparation and spectroscopic properties of 2-benzothiazolyl araldehyde hydrazones

Notwithstanding its tendency toward air oxidation in solution, 2-hydrazinobenzothiazole I reacted with aromatic aldehydes in ethanol to give the corresponding hydrazones III-XV in high yields and analytical purity. In related examples, acylation took place under similar conditions to produce hydrazides XVI-XX . The near-infrared bands of the absorption spectra of the araldehyde hydrazones have been associated with charge transfer and appeared to correlate with structural elements of the compounds in a way suggesting that the charge transfer was intermolecular.     

Matroid intersection algorithms

LetM ₁ = (E, 9₁),M ₂ = (E, 9₂) be two matroids over the same set of elementsE, and with families of independent sets 9₁, 9₂. A setI 9₁ 9₂ is said to be anintersection of the matroidsM ₁,M ₂. An important problem of combinatorial optimization is that of finding an optimal intersection ofM ₁,M ₂. In this paper three matroid intersection algorithms are presented. One algorithm computes an intersection containing a maximum number of elements. The other two algorithms compute intersections which are of maximum total weight, for a given weighting of the elements inE. One of these algorithms is primal-dual, being based on duality considerations of linear programming, and the other is primal. All three algorithms are based on the computation of an augmenting sequence of elements, a generalization of the notion of an augmenting path from network flow theory and matching theory. The running time of each algorithm is polynomial inm, the number of elements inE, and in the running times of subroutines for independence testing inM ₁,M ₂. The algorithms provide constructive proofs of various important theorems of matroid theory, such as the Matroid Intersection Duality Theorem and Edmonds' Matroid Polyhedral Intersection Theorem.Research sponsored by the Air Force Office of Scientific Research Grant 71-2076.     

On the use of x-ray-excited optical luminescence (XEOL) for the analysis of multisite rare-earth systems

The realization of a XEOL (X-ray-excited optical luminescence) spectrometer is reported. The aim of the present paper is to show that a comparison between UV-excited emission spectra and XEOL spectra can be helpful in the assignment of some weak transitions for multiple site rare-earth compounds. The case of c-Y₂O₃ doped with Eu³⁺ cations is considered in some detail, as in the XEOL spectrum three lines to be assigned to transitions occurring at the centrosymmetrical Eu³⁺ (C_3i) site are strongly enhanced. Additional site-selective UV-excited emission spectra are also reported supporting the present discussion.