Using the Donsker Delta Function to Compute Hedging Strategies

We use white noise calculus and the Donsker Delta Function to find explicit formulas for the replicating portfolios in a Black–Scholes market for a class of contingent T-claims.     

Metallorganische Verbindungen des Kupfers XIII. Kupfer(I)-chlorid-Komplexe winkelgespannter Cycloheptine Synthesen und Röntgenstrukturanalysen

The strained cycloheptynes 2a, 2b and 2c react with copper(I) chloride to form the dinuclear complexes [CuCl(cycloheptyne)]₂ 3a, 3b and 3c respectively. X-ray diffraction studies on all three compounds 3 show an increase in strength of the copper-alkyne bond with increasing deformation of the alkyne moiety from the ideal 180°. Thus going from the least strained alkyne (2c) to the most strained one (2a), the Cu-C bond lengths in the corresponding complexes decrease from 197.5 pm (3c) to 194.9 pm (3a). The C≡C-C angles increase from 145.6° (3a) over 147.4° (3b) to 151.6° (3c).

Zusammenfassung

Die gespannten Cycloheptine 2a, 2b und 2c reagieren mit Kupfer(I)—chlorid unter Bildung der zweikernigen Komplexe [CuCl(cycloheptin)]₂ 3a, 3b und 3c. Röntgenstrukturanalysen von allen drei Verbindungen 3 zeigen, daβ die Stärke der Kupfer—Alkin-Bindung zunimmt je mehr das ganze Alkinsystem vom idealen 180°-Winkel abweicht. Geht man vom am wenigsten gespannten Alkin (2c) zum gespanntesten (2a), so nehmen die Cu-C-Bindungslängen in den entsprechenden Komplexen von 197.5 pm (3c) auf 194.9 pm (3a) ab. Die C≡C-C-Winkel werden von 145.6° (3a) über 147.4° (3b) nach 151.6° (3c) hin gröβer.     

ATR-IR studies of CO adsorption from solutions

The formation of strongly bonded carbonaceous species from simple fuels on platinum metal electrodes at open circuit at potentials in the hydrogen region is widely accepted. Attenuated total reflection (ATR)-IR spectroscopy was used in this work to investigate the adsorption of such particles. A platinum film sufficiently stable for such studies in acid solution could be obtained on a germanium reflection element with a 0.5 nm layer of chromium and a 5 nm layer of platinum. The adsorption of CO leads to a strong band at 2000 cm⁻¹ assigned to linearly bonded CO, a broad band at 1800 cm⁻¹ assigned to bridge-bonded and possibly multiple bonded CO and a weak band at 1430 cm⁻. Clearly, the reaction of methanol, formaldehyde or formic acid produces the strong CO band.     

A standardised test environment to compare aircraft noise calculation programs

A new standardised test environment for aircraft noise calculation programs is presented. By means of this test environment different programs for aircraft noise calculation can be compared systematically. For this purpose a complete data set was developed, containing all relevant information needed to perform unambiguous aircraft noise calculations in the vicinity of an artificial airport. The input data is provided in a generic, non-program-specific form in order to be applicable to programs based on different calculation methods and data structures. In addition to the input data, guidelines on the file format of the results of calculations performed with different programs are specified to facilitate direct comparisons. The test environment and its data structure are outlined and examples of calculations according to this scheme are presented.     

Kinetic roughening of laser deposited polymer films: crossover from single particle character to continuous growth

The crossover in kinetic roughening of thin films from a particle-character-dominated regime to continuous growth behavior has been observed in this work. This has been accomplished by atomic force microscopy investigations of pulsed laser deposited amorphous organic films with thicknesses ranging from several nanometers to more than 4 microm. The early-stage random-deposition-like processes end once a closed layer is formed, which grows without saturation on the characteristic length scales. In addition, the influence of oblique film deposition has been examined and interpreted.     

A stochastic maximum principle for processes driven by fractional Brownian motion

We prove a stochastic maximum principle for controlled processes X(t)=X^(u)(t) of the form

dX(t)=b(t,X(t),u(t)) dt+σ(t,X(t),u(t)) dB^(H)(t),

where B^(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter . As an application we solve a problem about minimal variance hedging in an incomplete market driven by fractional Brownian motion.     

Alternativ-Liganden. XXXII [1]. Neue Tetraphosphan-Nickelkomplexe mit Tripod-Liganden des Typs XM′ (OCH2PMe2)n(CH2CH2PR2)3 – n (M′ = Si,Ge; n = 0 – 3)

Alternative Ligands. XXXII [1]. Novel Tetraphosphane Nickel Complexes with Tripod-Ligands of the Type XM′(OCH₂PMe₂)_n(CH₂CH₂PR₂)_{3 – n} (M′ = Si, Ge; n = 0 – 3) Tripod Ligands of the type XM′(OCH₂PMe₂)_n(CH₂CH₂PMe_{23 – n} (M′ = Si, Ge; n = 0 – 3) ( 1 – 6 , Table 1) have been used together with PPh₃ or PMe₃ for the preparation of novel tetraphosphane complexes of Nickel. The representatives LNiPPh₃ ( 7 – 12 ) are obtained by reaction of Ni(COD)₂ (COD = 1,5-cyclooctadiene) with the corresponding ligands and PPh₃ in toluene in moderate yields. The synthesis of the derivatives LNiPMe₃ ( 13 – 18 ) is partly ( 16 – 18 ) accomplished in analogy to the Ph₃P-complexes; compounds 13 – 16 are obtained in higher yields by reaction of Ni(PMe₃)₄ with the respective ligand. As a rule, 13 – 18 cannot be separated from by-products. The trinuclear complex FSi(CH₂CH₂PMe₂)₃[Ni(PMe₂CH₂CH₂)₃SiF]₃ ( 19 ) is formed together with 18 in the reaction of Ni(COD)₂ with 6 and PMe₃. The new compounds have been characterized (if possible) by analytical (C, H), but in general by spectroscopic investigations (IR; ¹H-, ¹³C-, ¹⁹F-, ³¹P-NMR; MS). A weak, but significant Ni → Si interaction through the cage is indicated by the following results: (i) Large low-field shifts δδ_F of 35.2 ppm ( 12 ), 38.3 ppm ( 18 ) and 37.7 ppm ( 19 ); (ii) ⁶J(PF) coupling constants [or ³J(PNiSiF) through the cage] of 6.0 Hz ( 12 ) and 7.6 Hz ( 18 ) together with a low-field shift δδ_Si of 12.8 ppm ( 12 ); (iii) NiSi distances of 3.95 Å in 7 and 3.92 Å in 12 , accompanied by a compression of the cage along the Ni ··· Si axis. An additional release from the high charge density on Ni results from π-backbonding to the phosphane ligands.     

A p-version finite element method for nonlinear elliptic variational inequalities in 2D

This article introduces and analyzes a p-version FEM for variational inequalities resulting from obstacle problems for some quasi-linear elliptic partial differential operators. We approximate the solution by controlling the obstacle condition in images of the Gauss–Lobatto points. We show existence and uniqueness for the discrete solution u _p from the p-version for the obstacle problem. We prove the convergence of u _p towards the solution with respect to the energy norm, and assuming some additional regularity for the solution we derive an a priori error estimate. In numerical experiments the p-version turns out to be superior to the h-version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation.     

Intramolecular and intermolecular kinetic isotope effects (KIE) in the nitrosoarene ene reaction: experimental evidence for reversible intermediate formation

The intramolecular and intermolecular kinetic isotope effects (KIE) have been determined for the nitrosoarene ene reaction with deuterium-stereolabeled 2,3-dimethyl-2-butenes (TME). trans-TME-d(6) (k(H)/k(D) = 3.0) and gem-TME-d(6) (k(H)/k(D) = 4.0) show large intramolecular primary isotope effects. In contrast, the intramolecular competition in cis-TME-d(6) (k(H)/k(D) = 1.5) and the intermolecular competition for the TME-d(0)/TME-d(12) pair (k(H)/k(D) = 1.98) show considerably smaller, but mechanistically significant kinetic isotope effects. The latter fact is rationalized in terms of reversible formation of a three-membered-ring intermediate, namely the aziridine N-oxide, or a similar unsymmetrical, polarized diradical in the first step of the reaction. Such reversibility has also been implied earlier for triazolinedione (TAD) and singlet oxygen ((1)O(2)) with deuterium-stereolabeled 2-butenes, but of the three enophiles, ArNO is the most sensitive toward reversibility, which is due to its moderate reactivity and its high steric demand.