A long-range memory stochastic model of the return in financial markets

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE.     

Empirical regularities of opening call auction in Chinese stock market

We study the statistical regularities of an opening call auction using the ultra-high-frequency data of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. The distribution of the relative price, defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day, is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price. The detrended fluctuation analysis (DFA) method is adopted to investigate the long-term memory of relative order prices. We further study the statistical regularities of order sizes in the opening call auction, and observe a phenomenon of number preference, known as order size clustering. The probability density function (PDF) of order sizes could be well fitted by a q-Gamma function, and the long-term memory also exists in order sizes. In addition, both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit-order book (LOB) established immediately after the opening call auction, and a price clustering phenomenon is observed.     

Dependence of Curie temperature on surface strain in InMnAs epitaxial structures

Pairs of self-assembled InMnAs quantum dot structures and reference epitaxial layers (0 < x < 0.13) were prepared on GaAs substrates by low-pressure metal organic vapour phase epitaxy. Magnetic moment measurements indicated that reference epitaxial layer had a Curie temperature of 343 K independent on the composition. On the other hand, the quantum dots prepared under Stranski-Krastanov growth mode from the identical gas phase composition showed a lower value of Curie temperature. This value varied from 41 to 235 K in relation to the material composition. Moiré fringes at transmission electron microscopy plan view were used for characterization of strain in InMnAs quantum dot structures.     

Effects of O2 and H2O plasma immersion ion implantation on surface chemical composition and surface energy of poly vinyl chloride

Oxygen and water plasma immersion ion implantation (PIII) was used to modify poly vinyl chloride (PVC) to enhance oxygen-containing surface functional groups for more effective grafting. The modified surfaces were characterized by X-ray photoelectron spectroscopy (XPS), attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR), and contact angle measurements. Our experimental results show that both oxygen and water PIII can greatly improve the O to C ratios on the surface. The optimal plasma processing conditions differ for the two treatments. The hydrophilicity and surface energy of the plasma-implanted PVC are also improved significantly. Our results indicate that O₂ and H₂O PIII increase both the polar and dispersion interactions and consequently the surface energy. It can be explained by the large amount of oxygen introduced to the surface and that many CC bonds are transformed into more polar oxygen containing functional groups.     

Renormalizing the Lippmann-Schwinger equation for the one-pion exchange potential

We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one-pion exchange potential plus local (δ-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires, in the limit when the cut-off is taken to infinity, such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial-wave mixing. We argue that this is an indication that this term must be treated perturbatively. Received: 7 October 2002 / Accepted: 15 January 2003 / Published online: 5 May 2003     

The mass renormalization of nonperturbative light-front Hamiltonian theory: an illustration using truncated, Pauli-Villars-regulated Yukawa interactions

We obtain analytic, nonperturbative, approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli-Villars scalar and fermion fields, each with negative norm. In order to obtain a directly soluble problem, fermion-pair creation and annihilation are neglected, and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution, including its endpoint behavior and spin and orbital angular momentum content. The limit of infinite Pauli-Villars mass receives special scrutiny.     

Fusion cross-section of the 7Li + 11B reaction

The ⁷Li + ¹¹B reaction has been investigated in the energy range 5.5 MeV < E _lab < 19MeV, by detecting γ-ray resulting from the de-excitation of evaporation residues. Statistical compound-nucleus calculations have been performed in order to extract both the cross-sections of individual exit channels and the fusion cross-section of the system. The total angular momentum that the compoundn ucleus ¹⁸O can support has been deduced and is seen to exhibit saturation for a limiting value of 8.5ħ at the high-energy extreme. The results are discussed in terms of the entrance channel and statistical yrast line limitations.     

Controlled Evolution of Silicon Nanocone Arrays Induced by Ar+ Sputtering at Room Temperature

Controlled evolution of silicon nanocone arrays induced by Ar^＋ sputtering at room temperature, using the coating carbon as a mask, is demonstrated. The investigation of scanning electron microscopy indicates that the morphology of silicon nanostructures can be controlled by adjusting the thickness of the coating carbon film. Increasing the thickness of the coating carbon film from 50-60 nm, 250-300 nm and 750-800 nm to 1500 nm, the morphologies of silicon nanostructures are transformed from smooth surface ripple, coarse surface ripple and surface ripple with densely distributed nanocones to nanocone arrays with a high density of about 1 × 10^9- 2 × 10^9 cm^-2.     

Precise numerical results for limit cycles in the quantum three-body problem

The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930s. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems (e.g., few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.     

Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings

We present a new efficient analytical approximation scheme to two-point boundary value problems of ordinary differential equations (ODEs) adapted to the study of the derivative expansion of the exact renormalization group equations. It is based on a compactification of the complex plane of the independent variable using a mapping of an angular sector onto a unit disc. We explicitly treat, for the scalar field, the local potential approximations of the Wegner–Houghton equation in the dimension d=3$d=3$ and of the Wilson–Polchinski equation for some values of d∈]2,3]$d\in ]2,3]$. We then consider, for d=3$d=3$, the coupled ODEs obtained by Morris at the second order of the derivative expansion. In both cases the fixed points and the eigenvalues attached to them are estimated. Comparisons of the results obtained are made with the shooting method and with the other analytical methods available. The best accuracy is reached with our new method which presents also the advantage of being very fast. Thus, it is well adapted to the study of more complicated systems of equations.