The uncertainty relation expressed by means of a new entropic function

In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.      

Models for the size distribution of businesses in a price driven market

A microscopic model of aggregation and fragmentation is introduced to investigate the size distribution of businesses. In the model, businesses are constrained to comply with the market price, as expected by the customers, while customers can only buy at the prices offered by the businesses. We show numerically and analytically that the size distribution scales like a power-law. A mean-field version of our model is also introduced and we determine for which value of the parameters the mean-field model agrees with the microscopic model. We discuss to what extent our simple model and its results compare with empirical data on company sizes in the US and debt sizes in Japan. Finally, possible extensions of the mean-field model are discussed, to cope with other empirical data. Received 10 January 2001 and Received in final form 12 March 2001     

Measurement of the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame by means of a laser-based interferometer technique

With a view to measuring the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame, a thin laser beam is sent into the flame perpendicular to the flow direction. The laser beam generally undergoes fluctuations of direction, phase, and amplitude. Only the random deflections of the laser beam may be taken into account. After having traversed the flame, the perturbed laser beam enters into an interferometric system. Materials and experimental procedure are described. In the unperturbed interference pattern, the zones only sensitive to fluctuations of the angle-of-arrival of the laser beam are detected. From the random displacements of the central bright fringe, the structure coefficient of refractive index fluctuations in the flame is measured. To prove that the method of measurement is satisfactory, the result obtained is applied for computing the power spectral density of the angle-of-arrival of the laser beam from the formula of correlations of the laser beam deflection angles which we have demonstrated in previous works. This computed power spectral density is compared to that measured from the effective position of the detector. A good agreement is observed between the two results.     

Acoustic nonlinearity parameter B/A determined by means of thermodynamic method under elevated pressures for alkanediols

The so-called Beyer nonlinearity parameter B/A is calculated for 1,2- and 1,3-propanediol, 1,2-, 1,3-, and 1,4-butanediol, as well as 2-methyl-2,4-pentanediol by means of a thermodynamic method. The calculations are made for temperatures from (293.15 to 318.15) K and pressures up to 100 MPa. The decrease in B/A values with the increasing pressure is observed. In the case of 1,3-butanediol, the results are compared with corresponding literature data. The consistency is very satisfactory. A simple relationship between the internal pressure and B/A nonlinearity parameter has also been studied.     

基于高斯伪谱方法的混沌系统最优控制

针对混沌系统最优控制问题,提出一种基于高斯伪谱方法的数值求解新算法. 首先在勒让德-高斯点上构造Lagrange插值多项式并近似表示混沌系统最优控制中的状态变量和控制变量;接着将连续空间的最优控制问题转化为非线性规划问题;然后通过序列二次规划（SQP）算法获得最优解;最后对三个典型混沌系统的仿真实验结果表明,新方法能有效和快速地实现混沌系统的最优控制. 关键词： 混沌系统 最优控制 高斯伪谱法 非线性规划     

Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T _c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T _c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T _c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.      

Analysis of Excitations for a Groove Guide Resonator at 10 GHz by means of the FDTD Method

Various excitations of a new groove guide resonator working in the X-band (8 GHz – 12 GHz) are investigated by means of numerical simulations. For the numerical simulations the Finite-Difference Time-Domain method is used. The groove guide resonator, modelled both with and without excitation structures, is discretised in space. The results in the time domain are then transformed into the frequency domain in order to obtain the resonance frequency spectrum. Comparison between simulations with and without excitations shows the effect of the excitations on the resonance frequency spectrum. The results are compared with those of previous analytical methods.     

An exact limit for the Peierls distortion energy in an antiferromagnetic chain by means of a renormalization procedure

A renormalization procedure gives a rigorous upper bound for the ground-state energy per spin for a Peierls-distorted antiferromagnetic chain with Heisenberg interaction.     

Conditions for the harmonic-like and efficient amplitude modulation of the cw gaussian laser beam by means of a mechanical chopper

The values of the chopping disc slot and mark space widths relative to the radius of the Gaussian beam are found, which achieve optimum harmonic-like and efficient amplitude modulation of the cw laser beam. The simple approximation for the waveform of the modulated laser power valid for these optimum or near optimum values of the chopping disc parameters is presented.     

Maximum entropy: a complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR

Tikhonov regularization (TIKR) has been demonstrated as a powerful and valuable method for the determination of distance distributions of spin-pairs in bi-labeled biomolecules directly from pulsed ESR signals. TIKR is a direct method, which requires no iteration, and, therefore, provides a rapid and unique solution. However, the distribution obtained tends to exhibit oscillatory excursions with negative portions in the presence of finite noise, especially in the peripheral regions of the distribution. The Shannon-Jaynes entropy of a probability distribution provides an intrinsic non-negativity constraint on the probability distribution and an unbiased way of obtaining information from incomplete data. We describe how the maximum entropy regularization method (MEM) may be applied to solve the ill-posed nature of the dipolar signal in pulsed ESR. We make use of it to suppress the negative excursions of the distance distribution and to increase the tolerance to noise in the dipolar signal. Model studies and experimental data are investigated, and they show that, with the initial or "seed" probability distribution that is required for MEM taken as the TIKR result, then MEM is able to provide a regularized solution, subject to the non-negativity constraint, and it is effective in dealing with noise that is problematic for TIKR. In addition we have incorporated into our MEM method the ability to extract the intermolecular dipolar component, which is embedded in the raw experimental data. We find that MEM minimization, which is implemented iteratively, is greatly accelerated using the TIKR result as the seed, and it converges more successfully. Thus we regard the MEM method as a complement to TIKR by securing a positive pair distance distribution and enhancing the accuracy of TIKR.     

A theoretical model for the evaluation of measurement uncertainty of a sound level meter calibration by comparison method in an anechoic room

A theoretical model for the evaluation of measurement uncertainty of a sound level meter (hereafter as `SLM') calibration by comparison method in an anechoic room was developed. Through this model, the uncertainties in the semi-automatic calibration and that in the full-automatic calibration were estimated for the recently developed SLM calibration system. In order to estimate the standard uncertainty against the SLM positioning, which is a significant uncertainty component, the sound field curve-fitting formulae were adopted. The validity of the curve-fitting method was proven by the similarity of the spatial distributions of radiation sound field produced by the plane circular piston source and that by the cone shape source. A linear equation was used to fit the measurements of the sound field distribution along the radiation axis. A quadratic equation was used to fit the measurements along the radial axis normal to the radiation axis. The fitting parameters gave us the sensitivity coefficients of the propagation of the uncertainty. In addition, one of the quadratic fitting parameters was found to be a positional uncertainty itself. Using this model, the expanded uncertainties were evaluated for the semi-automatic and full-automatic calibration of SLM.     

Engineering design and prototype development of a full scale ultrasound system for virgin olive oil by means of numerical and experimental analysis

The aim of the virgin olive oil extraction process is mainly to obtain the best quality oil from fruits, by only applying mechanical actions while guaranteeing the highest overall efficiency. Currently, the mechanical methods used to extract virgin oils from olives are basically of two types: the discontinuous system (obsolete) and the continuous one. Anyway the system defined as “continuous” is composed of several steps which are not all completely continuous, due to the presence of the malaxer, a device that works in batch. The aim of the paper was to design, realize and test the first full scale sono-exchanger for the virgin olive oil industry, to be placed immediately after the crusher and before the malaxer. The innovative device is mainly composed of a triple concentric pipe heat exchanger combined with three ultrasound probes. This mechanical solution allows both the cell walls (which release the oil droplets) along with the minor compounds to be destroyed more effectively and the heat exchange between the olive paste and the process water to be accelerated. This strategy represents the first step towards the transformation of the malaxing step from a batch operation into a real continuous process, thus improving the working capacity of the industrial plants. Considering the heterogeneity of the olive paste, which is composed of different tissues, the design of the sono-exchanger required a thorough fluid dynamic analysis. The thermal effects of the sono-exchanger were monitored by measuring the temperature of the product at the inlet and the outlet of the device; in addition, the measurement of the pigments concentration in the product allowed monitoring the mechanical effects of the sono-exchanger. The effects of the innovative process were also evaluated in terms of extra virgin olive oil yields and quality, evaluating the main legal parameters, the polyphenol and tocopherol content. Moreover, the activity of the polyphenol oxidase enzyme in the olive paste was measured.