ONE LINEAR ANALYTIC APPROXIMATION FOR STOCHASTIC INTEGRODIFFERENTIAL EQUATIONS

This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L^p-th norm, uniformly on the time interval. The convergence with probability one is also given.

Cancellation of nonlinear distortion based on integration of FCM clustering algorithm and adaptive-two-stage linear approximation

A hybrid system of the fuzzy c-means （FCM） clustering algorithm and adaptive-two-stage linear approximation was presented for nonlinear distortion cancellation of radio frequency （RF） power amplifier （PA）. This mechanism can effectively eliminate noise, adaptively model PA＇s instantaneous change, and efficiently correct nonlinear distortion. This article puts forward the FCM clustering algorithm for clustering received signals to eliminate white noise, and then uses the adaptive-two-stage linear approximation to fit the inverse function of the amplitude＇s and phase＇s nonlinear mapping during the training phase. Parameters of the linear function and similarity function are trained using the gradient-descent and minimum mean-square error criteria. The proposed approach＇s training results is directly employed to eliminate sampling signal＇s nonlinear distortion. This hybrid method is realized easier than the multi-segment linear approximation and could reduce the received signal＇s bit error rate （BER） more efficiently.

Estimation of Nonlinear Roll Damping by Analytical Approximation of Experimental Free-Decay Amplitudes

Damping is critical for the roll motion response of a ship in waves. A common method for the assessment of damping in a ship’s rolling motion is to perform a free-decay experiment in calm water. In this paper, we propose an approach for estimating nonlinear damping that involves a linear exponential analytical approximation of the experimental roll free-decay amplitudes, fol- lowed by parametric identification based on the asymptotic method. The restoring moment can be strongly nonlinear. To validate this method, we first analyzed numerically simulated roll free-decay data using rolling equations with two alternative parametric forms: linear-plus-quadratic and linear-plus-cubic damping. By doing so, we obtained accurate estimates of nonlinear damping coefficients, even for large initial roll amplitudes. Then, we applied the proposed method to real free-decay data obtained from a scale model of a bulk barrier, and found the simulated results to be in good agreement with the experimental data. Using only free-decay peak data, the proposed method can be used to estimate nonlinear roll-damping coefficients for conditions with a strongly nonlinear restoring moment and large initial roll amplitudes.

Linear Momentum Approximation and Frontogenesis Caused by Baroclinic Ekman Momentum Flow

A method of linear momentum approximation is proposed that deals with weak nonlinear problems in an approximate manner. A motion of nonlinear nature is obtained in the system by assuming the motion to be in the form of linear momentum flow in the corresponding space introduced, followed by the transformation from the specified into a physical space. Significant results have been thereby derived in examining the effects of baroclinic Ekman momentum flow upon Eady-type baroclinic waves and frontogenesis. Also, this technique can be applied to investigate the dynamic characteristics of the weak nonlinear boundary layer including topography, stratification and non-Ekmantype friction for gaining further insight into the influence on the boundary layer inner parameters of terrain, baroclinicity and inhomogeneous process so that the classic theory is revised.

ON CONSERVATIVE APPROXIMATION BY LINEAR POLYNOMIAL OPERATORS AN EXTENSION OF THE BERNSTEIN'S OPERATOR

In this work we slwly linear polynomial operators preserving some consecutive i-convexities and leaving in-verant the polynomtals up to a certain degree. First we study the existence of an incompatibility between the conservation of cenain i-cotivexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DcVore about the Bernstein's operator ts extended. Finally, from these results a genera'ized Bernstein's operator is obtained.

Piecewise linear detection for direct superposition modulation

Considering high-order digital modulation schemes, the bottleneck in consumer products is the detector rather than the modulator. The complexity of the optimal a posteriori probability （APP） detector increases exponentially with respect to the number of modulated bits per data symbol. Thus, it is necessary to develop low-complexity detection algorithms with an APP-like performance, especially when performing iterative detection, for example in conjunction with bit interleaved coded modulation. We show that a special case of superposition modulation, dubbed Direct Superposition Modulation （DSM）, is particularly suitable for complexity reduction at the receiver side. As opposed to square QAM, DSM achieves capacity without active signal shaping. The main contribution is a low-cost detection algorithm for DSM, which enables iterative detection by taking a priori information into account. This algorithm exploits the approximate piecewise linear behavior of the soft outputs of an APP detector over the entire range of detector input values. A theoretical analysis and simulation results demonstrate that at least max-log APP performance can be reached, while the complexity is significantly reduced compared to classical APP detection.

Study on High-Speed Magnitude Approximation for Complex Vectors

High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.

Optimal Perturbations Triggering Weather Regime Transitions:Onset of Blocking and Strong Zonal Flow

In this paper, the approach proposed by Mu and Jiang （2008） to obtain the optimal perturbations for triggering blocking （BL） onset is generalized to seek the optimal perturbations triggering onset of the strong zonal flow （SZF） regime. The BL and SZF regimes are characterized by the same dipole-like anomaly pattern superposed on the climatological flow, but with opposite sign. The results show that this method is also superior at finding the initial optimal perturbations triggering onset of the SZF regime, especially in the medium range. Furthermore, by comparing the two kinds of conditional nonlinear optimal perturbations （CNOPs） trig-gering onset of BL and SZF regimes, we find that in the linear approximation, there is symmetry in the sensitivities for BL and SZF onset, and the perturbations that optimally trigger onset of BL and SZF regimes at times when linear approximation is valid are also characterized by the same spatial pattern but with opposite sign. Whereas when the optimization time is extended to 6 days, the two kinds of CNOPs lose their out-of-phase behavior. The nonlinearity results in an asymmetry between the sensitivity for BL and SZF onset. Additionally, we find that the optimal perturbations have one common property, which is that the second baroclinic mode contributes more to the initial perturbations while the barotropic mode dominates the final structures.

Theory of gas extraction from coal seams and its use

Gas extraction is one of the main measures of control and use of gas of coal mines. At present, the design method is under the experimental period and do not satisfy the need of practice. In this paper, the theory of gas extraction of coal seams based upon Darcy law was studied. Mathematical model of gas extraction of coal seams was established and two kinds of solv- ing approaches based on computer software and linear approximation were given. The rightness and the validities of the model were examined with a practical example. Results obtained can be used to determine and optimize the parameters related etc.

Stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal. A new linear approximation approach is advanced to calculate the signal-to-noise ratio. In the linear approximation only the drift term is linearized, the multiplicative noise term is unchangeable. It is found that there appears not only the standard form of stochastic resonance but also the broad sense of stochastic resonance, especially stochastic multiresonance appears in the curve of signal-to-noise ratio as a function of coupling strength A between the real and imaginary parts of the pump noise.

Viewing the noise propagation mechanism in a unidirectional transition cascade from the perspective of stability

Noise and noise propagation are inevitable and play a constructive role in various biological processes.The stability of cell homeostasis is also a critical issue.In the unidirectional transition cascade of colon cells,stem cells(SCs)are the source.They differentiate into transit-amplifying cells(TACs),and TACs differentiate into fully differentiated cells(FDCs).Two differentiation processes are irreversible.The stability factor is introduced so that the noise propagation mechanism from the perspective of stability is studied according to the noise propagation formulas.It is found that the value of the stability factor corresponding to the minimum noise in FDCs may be the best choice to enable colon cells to maintain high stability and low noise of the cascade.Moreover,for the source cell,the total noise only includes intrinsic noise;for the downstream cell with self-proliferation capability,the total noise mainly depends on its intrinsic noise and transmitted noise from upstream cells,and its intrinsic noise is dominant.For the downstream cell without self-proliferation capability,the total noise is mainly determined by transmitted noises from upstream cells,and there is a minimum value.This work provides a new approach for studying the mechanism of noise propagation while considering the stability of cell homeostasis in biological systems.

Effect on Intensity Correlation Time by Input Signal in a Single-Mode Laser with Bias Signal Modulation

The effect on intensity correlation time T by input signal is studied for gain-noise model of a single-mode laser driven by colored pump noise and colored quantum noise with colored cross-correlation with a bias signal modulation in this paper. By using the linear approximation method, we detect that there exists maximum （i.e., resonance） in the curve of the intensity correlation time T upon bias current io when the noise correlation coefficient λ is positive; and there exists minimum （i.e., suppression） in the T-io curve when λ is negative. And whenλ is zero, T increases monotonously with increasing io. Furthermore, the curve of T upon the signal frequency Ω is also studied. Our study shows that no matter what the value of λ is, there exists minimum （i.e., suppression） in the T-Ω curve.

Intensity Correlation Function of a Single-Mode Laser Driven by Colored Cross-Correlation Noises in Modulation of a Bias Signal

By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlation. We found that, when the correlation time between the two noises is very short, the behavior of the intensity correlation function versus the time, in addition to decreasing monotonously, also exhibits several cases, such as one maximum, one minimum, and two extrema. When the correlation time between the two noises is very long, the behavior of the intensity correlation function exhibits oscillation and the envelope is similar to the case of short cross-correlation time.

A statistical RCL interconnect delay model taking account of process variations

As the feature size of the CMOS integrated circuit continues to shrink, process variations have become a key factor affecting the interconnect performance. Based on the equivalent Elmore model and the use of the polynomial chaos theory and the Galerkin method, we propose a linear statistical RCL interconnect delay model, taking into account process variations by successive application of the linear approximation method. Based on a variety of nano-CMOS process parameters, HSPICE simulation results show that the maximum error of the proposed model is less than 3.5%. The proposed model is simple, of high precision, and can be used in the analysis and design of nanometer integrated circuit interconnect systems.

Influences of quantum noises on direct-modulated properties of 1.3-μm InGaAsP/InP laser diodes

Due to the zero dispersion point at 1.3μm in optical fibres, 1.3-μm InGaAsP/InP laser diodes have become main light sources in fibre communication systems recently. Influences of quantum noises on direct-modulated properties of single-mode 1.3-μm InGaAsP/InP laser diodes are investigated in this article. Considering the carrier and photon noises and the cross-correlation between the two noises, the power spectrum of the photon density and the signal-to-noise ratio （SNR） of the direct-modulated single-mode laser system are calculated using the linear approximation method. We find that the stochastic resonance （SR） always appears in the dependence of the SNR on the bias current density, and is strongly affected by the cross-correlation coefficient between the carrier and photon noises, the frequency of modulation signal, and the photon lifetime in the laser cavity. Hence, it is promising to use the SR mechanism to enhance the SNR of direct-modulated InGaAsP/InP laser diodes and improve the quality of optical fibre communication systems.

Stochastic resonance in a gain-noise model of a single-mode laser driven by pump noise and quantum noise with cross-correlation between real and imaginary parts under direct signal modulation

Stochastic resonance （SR） is studied in a gain-noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio （SNR） separately with the pump noise self-correlation time τ, the noise correlation coefficient between the real part and the imaginary part of the quantum noise λq, the attenuation coefficient γ＇ and the deterministic steady-state intensity I0. In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of and λq, but also by the dependence of SNR on the laser system variables of γ and I0. Thus our investigation extends the characteristic quantity of SR proposed before.

An Extension of the Dimension-Reduced Projection 4DVar

This paper extends the dimension-reduced projection four-dimensional variational assimilation method(DRP-4DVar) by adding a nonlinear correction process,thereby forming the DRP-4DVar with a nonlinear correction, which shall hereafter be referred to as the NC-DRP-4DVar. A preliminary test is conducted using the Lorenz-96 model in one single-window experiment and several multiple-window experiments. The results of the single-window experiment show that compared with the adjoint-based traditional 4DVar, the final convergence of the cost function for the NC-DRP-4DVar is almost the same as that using the traditional 4DVar, but with much less computation. Furthermore, the 30-window assimilation experiments demonstrate that the NC-DRP-4DVar can alleviate the linearity approximation error and reduce the root mean square error significantly.

Improved response surface method based on sample point selection strategies

In the reliability analysis of complex structures,response surface method(RSM)has been suggested as an efficient technique to estimate the actual but implicit limit state function.A set of sample points are needed to fit to the implicit function.It has been noted that the accuracy of RSM depends highly on the so-called sample points.However,the technique for point selection has had little attention.In the present study,an improved response surface method(IRSM)based on two sample point selection techniques,named the direction cosines projected strategy(DCS)and the limit step length iteration strategy(LSS),is investigated.Since it uses the sampling points selected to be located in the region close to the original failure surface,and since it needs only one response surface,the IRSM should be accurate and simple in practical structural problems.Applications to several typical examples have helped to elucidate the successful working of the IRSM.

Alternative Method for Concrete Structures Compressive Strength Estimation with Small-Scale Destruction

To estimate a compressive strength from existing concrete structures by core drilling are usually gathered with a diameter specimen of 100 mm or three times of maximum coarse aggregate size and examined by uniaxial compressive strength （UCS）. It is relatively difficult to gather a large sized core, and a pit place will be limited by main members. To get an alternative solution with smaller specimen, point load test （PLT） has been sele,：ted which is a simple test and widely accepted in rock materials research, but relatively new in concrete. The reliability of PLT is evaluated by extracting a lot of core drilled specimen from ready mixed concrete blocks with maximum coarse aggregate size, G of 20 mm in representative of architectural structures and 40 mm in representative of civil structures on the range of concrete grade from 16 to 50. Compressive strengths were classified into general categories, conversion factors were determined, and scattering characteristics were also investigated. The relationship between point load index （Is） and compressive strength of concrete core specimen （fcc） can be written as linear approximation as fcc = k.Is- C.

基于两部模型的组合惩罚似然估计方法研究及其应用

在统计学中,多借助零膨胀模型研究零膨胀数据潜在的模型结构及变量选择问题。然而,在多数情况下,响应变量的非零部分为定量数据,简单的零膨胀模型无法刻画这类数据的模型结构,对应的参数估计方法也不再适用。鉴于此,学者提出处理零膨胀半连续数据的两部模型。本文将组合惩罚似然估计方法引入两部模型,研究其变量选择问题。提出一种新的处理高维统计分析问题的惩罚似然估计方法:NCPM (New Combined Punishment Method),并将该方法应用于太原市降水量数据,分析其影响因素。模拟及实例分析结果均表明本文的方法行之有效,较传统的惩罚似然估计方法具有更高的预测精度。