Further improvements on the designed minimum distance of algebraic geometry codes

In the literature about algebraic geometry codes one finds a lot of results improving Goppa’s minimum distance bound. These improvements often use the idea of “shrinking” or “growing” the defining divisors of the codes under certain technical conditions. The main contribution of this article is to show that most of these improvements can be obtained in a unified way from one (rather simple) theorem. Our result does not only simplify previous results but it also improves them further.     

The early exercise region for Bermudan options on two underlyings

This paper investigates the early exercise region for Bermudan options on two underlying assets. We present a set of analytical validation results for the early exercise region which can be used as a means of validating pricing techniques. When all strike prices are identical we show the existence of an intersection point such that for any asset price pair below this point early exercise is always optimal. We develop an approximation to this point in the two asset put case. When the strike prices are not all equal, we show that three separate cases exist for the early exercise region. For a Bermudan put on two assets we present these cases and show that there exists a critical point in which the boundaries of the two asset early exercise region bifurcate. Comparisons are drawn between the Bermudan results presented and the corresponding American option results.     

Domination number in graphs with minimum degree two

A set D of vertices of a graph G = （V, E） is called a dominating set if every vertex of V not in D is adjacent to a vertex of D. In 1996, Reed proved that every graph of order n with minimum degree at least 3 has a dominating set of cardinality at most 3n/8. In this paper we generalize Reed＇s result. We show that every graph G of order n with minimum degree at least 2 has a dominating set of cardinality at most （3n ＋IV21）/8, where V2 denotes the set of vertices of degree 2 in G. As an application of the above result, we show that for k ≥ 1, the k-restricted domination number rk （G, γ） ≤ （3n＋5k）/8 for all graphs of order n with minimum degree at least 3.     

On ramification in the compositum of function fields

The aim of this paper is twofold: Firstly, we generalize well-known formulas for ramification and different exponents in cyclic extensions of function fields over a field K (due to H. Hasse) to extensions E = F(y), where y satisfies an equation of the form f(y) = u · g(y) with polynomials f(y), g(y) ∈ K[y] and u ∈ F. This result depends essentially on Abhyankar’s Lemma which gives information about ramification in a compositum E = E ₁ E ₂ of finite extensions E ₁, E ₂ over a function field F. Abhyankar’s Lemma does not hold if both extensions E ₁/F and E ₂/F are wildly ramified. Our second objective is a generalization of Abhyankar’s Lemma if E ₁/F and E ₂/F are cyclic extensions of degree p = char(K). This result may be useful for the study of wild towers of function fields over finite fields.     

Control Strategy of Hardware-in-the-Loop Simulator EPOS 2.0 for Autonomous Docking Verification

This paper briefly describes the hybrid simulator system called European Proximity Operation Simulator (EPOS 2.0) and the development of the hardware-in-the-loop (HIL) docking simulation concept. A critical requirement for the docking simulation of this HIL simulator is that the 6-DOF robots in the loop have to exactly mimic the dynamic response of the two satellites during a contact operation. The main challenges to meet this requirement are in the stiffness of the robots, which is unlike that of the satellites, as well as the time delay in the HIL simulator. The paper mainly presents the impedance parameter identification concept for matching the impedance between the satellites impact model and the EPOS robots. Finally it presents the preliminary results and future work. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electronic spectroscopy of the 3d Rydberg states of NO-Rg (Rg=Ne,Ar,Kr,Xe) van der Waals complexes

We have employed (2+1) resonance-enhanced multiphoton ionization spectroscopy to record electronic absorption spectra of NO-Rg (Rg=Ne,Ar,Kr) van der Waals complexes. The nitric oxide molecule is the chromophore, and the excitation corresponds to an electron being promoted from the 2ppi* orbital to 3dsigma, 3dpi, and 3ddelta Rydberg states. We review the ordering of the 3dlambda states of NO and use this as a basis for discussing the 3d components in the NO-Rg complexes, in terms of the interactions between the Rydberg electron, the core, and the Rg atom. Predissociation of the H' 2Pi state occurs through the F2Delta state for NO-Ar and NO-Kr, and this will be considered. We shall also outline problems encountered when trying to record similar spectra for NO-Xe, related to the presence of atomic Xe resonances.     

Crystal structure, physical properties and HRTEM investigation of the new oxonitridosilicate EuSi2O2N2

The new layered oxonitridosilicate EuSi₂O₂N₂ has been synthesized in a radio‐frequency furnace at temperatures of about 1400 °C starting from europium(III ) oxide (Eu₂O₃) and silicon diimide (Si(NH)₂). The structure of the yellow material has been determined by single‐crystal X‐ray diffraction analysis (space group P1 (no. 1), a=709.5(1), b=724.6(1), c=725.6(1) pm, α=88.69(2), β=84.77(2), γ=75.84(2)°,V=360.19(9)×10⁶ pm³, Z=4, R1=0.0631, 4551 independent reflections, 175 parameters). Its anionic Si₂O₂N₂^2? layers consist of corner‐sharing SiON₃ tetrahedra with threefold connecting nitrogen and terminal oxygen atoms. High‐resolution transmission electron micrographs indicate both ordered and disordered crystallites as well as twinning. Magnetic susceptibility measurements of EuSi₂O₂N₂ exhibit Curie–Weiss behavior above 20 K with an effective magnetic moment of 7.80(5) μ_B Eu^?1, indicating divalent europium. Antiferromagnetic ordering is detected at 4.5(2) K. EuSi₂O₂N₂ shows a field‐induced transition with a critical field of 0.50(5) T. The four crystallographically different europium sites cannot be distinguished by ¹⁵¹Eu Mössbauer spectroscopy. The room‐temperature spectrum is fitted by one signal at an isomer shift of δ=?12.3(1) mm s^?1 subject to quadrupole splitting of ΔE_Q=?2.3(1) mm s^?1 and an asymmetry parameter of 0.46(3). Luminescence measurements show a narrow emission band with regard to the four crystallographic europium sites with an emission maximum at λ=575 nm.     

Investigation of the ionisation and fragmentation behaviour of different nitroaromatic compounds occurring as polar metabolites of explosives using electrospray ionisation tandem mass spectrometry

In order to develop a liquid chromatography/electrospray ionisation tandem mass spectrometry (LC/ESI-MS/MS) method for identification and quantification of polar metabolites of explosives using a triple quadrupole system, the mass spectrometric ionisation and fragmentation behaviour of different nitrophenols, nitro- and aminonitrobenzoic acids, nitrotoluenesulfonic acids, and aminonitrotoluenes was investigated. Due to their different molecular structures, the substances concerned showed a very different ionisation efficiency in the ESI process. Interestingly, 2,4-dinitrobenzoic acid yielded no mass signals in the Q1 scan suggesting a thermal decarboxylation in the ion source, whereas the corresponding 3,5-isomer showed a high ionisation yield. Using negative ionisation polarity, carboxylic, phenolic, and sulfonic acid groups were deprotonated resulting in molecular anions, which could be fragmented in a collision cell. A pronounced dependency of the produced fragment ion series on the kind and position of substituents at the nitrobenzene ring (ortho effects) was observed and exploited for the development of substance-specific detection methods in the multiple reaction monitoring mode. In case of benzoic and sulfonic acids, decarboxylation and desulfonation, respectively, were observed as the most frequent fragmentation reactions. Furthermore, besides loss of NO(2), NO fragmentation occurred and preceded a decarbonylation of the benzene ring. The expulsion of the open-shell molecules NO and NO(2) led to a variety of distonic radical anions.     

Thermodynamic evaluation and optimization of the (Na2SO4 + K2SO4 + Na2S2O7 + K2S2O7) system

A complete, critical evaluation of all phase diagram and thermodynamic data was performed for all phases of the (Na₂SO₄ + K₂SO₄ + Na₂S₂O₇ + K₂S₂O₇) system and optimized model parameters were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range ordering, where the cations (Na⁺ and K⁺) are assumed to mix on a cationic sublattice, while anions were assumed to mix on an anionic sublattice. The Compound Energy Formalism was used for modelling the solid solutions of (Na,K)₂SO₄ and (Na,K)₂S₂O₇. The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature were reproduced within experimental error limits.