考虑分布式电源不确定性的配电网鲁棒动态重构

间歇性分布式电源并网使得配电网网络重构过程需要考虑更多的不确定因素。在利用仿射数对分布式电源出力的不确定性进行合理分析与建模基础上,建立以重构周期内开关动作耗费与网络有功损耗等综合成本最低为目标函数,以网络安全运行为约束条件的配电网鲁棒动态重构模型。为精确求解该数学模型,引入基于最佳等距思想的分段线性逼近方法将原目标函数松弛为线性可解形式,并根据对偶定理将模型进一步等效转化为双层混合整数线性规划问题;最后采用列约束生成算法对模型进行高效求解。修改的PG＆E 69节点系统测试分析结果表明,与现有的配电网确定性动态重构方法比较,所提鲁棒动态重构方法在抗系统不确定性扰动方面具有明显的优势。

Hamiltonian Formalism of mKdV Equation with Non-vanishing Boundary Values

Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform.

A new method to estimate wave height of specified return period

In this paper, we propose a new method to estimate the wave height of a specifi c return period based on the Hurst rule and a self-affi ne fractal formula. A detailed description of our proposed model is presented in this paper. We use the proposed model to analyze wave height data recorded along the coast of Chaolian Island from 1963 to 1989. The results show that the performance of our proposed model in estimating design wave heights is superior to traditional models.

Find Better Boolean Functions in the Affine Equivalence Class

The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.

Realization of Vertex Operators of 7-Twisted Affine Lie Algebra ■[θ]

In this paper, we construct a new algebra structure 7-twisted atone Lie algebra sl（3,C）[θ] and study its vertex operator representations.

P-Twisted Affine Lie Algebras and Their Associated Vertex Algebras

For any finite-dimensional semisimple Lie algebra g, a Z＋-graded vertex algebra is construsted on the vacuum representation Vk（g[θ]of g[θ]）,which is a one-dimentionM central extension of 8-invariant subspace on the loop algebra Lg=g C（（t^1/p））.

New Mathematical Model Based on Affine ransformation for Remote Sensing Image with High Resolution

This paper calculates the parameters of image position and orientation,proposes a mathematical model and adopts a new method with three steps of transformations based on parallel ray projection.Every step of the model is strict,and the map function of each transformation is the first order polynomials and other simple function.The final calculation of the parameters is for the linear equations with good status.As a result,the problem of the relativity of image parameter calculation is solved completely.Some experiments are carried out.

Numerical Simulation on the Extraction of Modal Back-Scattering Matrix from Reverberation Data for High Frequency Cases

The modal back-scattering matrix can be extracted from reverberation data. For high frequency cases the ’window smoothed’ processing has been proposed by E. C. Shang, T. F. Gao and D. J. Tang (2002) to extract the ’window averaged’ back-scattering matrix. It is pointed out in this paper that in order to inverse the ’window averaged’ back-scattering matrix by changing the source depth data we have to assume that the matrix is not related to the source depth, and the numerical simulation on the question has been conducted.

Dynamic simulation research on injection and withdrawal performance of underground salt cavern natural gas storage

Owing to perfect impermeability,dynamics stability,flexible and efficient operation mode and strong adjustment,underground salt cavern natural gas storage is especially adapted to be used for short-term dispatch.Based on characteristics of gas flow and heat transfer,dynamic mathematic models were built to simulate the injection and withdrawal performance of underground salt cavern gas storage.Temperature and pressure variations of natural gas in gas storage were simulated on the basis of building models during withdrawal operation,and factors affecting on the operation of gas storage were also analyzed.Therefore,these models can provide theore-tic foundation and technology support for the design,building and operation of salt cavern gas storage.

AN IMPROVED RADIAL BASIS FUNCTION BASED METHOD FOR IMAGE WARPING

A new image warping method is proposed in this letter, which can warp a given image by some manual defined features. Based on the radial basis interpolation function algorithm, the proposed method can transform the original optimized problem into nonsingular linear problem by adding one-order term and affine differentiable condition. This linear system can get the steady unique solution by choosing suitable kernel function. Furthermore, the proposed method demonstrates how to set up the radial basis function in the target image so as to achieve supports to adopt the backward re-sampling technology accordingly which could gain the very slippery warping image. Theexperimental result shows that the proposed method can implement smooth and gradual image warping with multi-anchor points' accurate interpolation.

Nonparametric VSS-APA based on precise background noise power estimate

The adaptive algorithm used for echo cancellation(EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm(APA) is a better alternative than normalized least mean square(NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA(VSS-APA) provides a more reliable solution. A nonparametric VSS-APA(NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power(BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.

工件粗糙度在线检测的试验研究

采用分形几何与图形图像学等交叉学科理论，基于分形布朗函数，本文提出了用于描述工件表面粗糙度的灰度图像自仿射维数计算新方法。在提出上述理论的基础上，采用高速摄像机拍摄工件车削的实时过程，计算工件的灰度图像自仿射维数，评估不同时刻工件表面粗糙度变化，进而提出可实现在线检测工件表面粗糙度的新技术。研究显示：（1）工件表面图像揭示了其表面存在清晰可见的切痕和纹理，但粗糙度不大，同时计算出的对应灰度图像自仿射维数较小，这与描述表面粗糙度的维数定义是吻合的，因而，灰度图像自仿射维数能很好地描述工件表面的粗糙度特征。（2）在初始车削不稳定状态时，灰度图像自仿射维数较大，灰度图像自仿射维数随着进刀量增加而增大，这些结论与传统检测技术所得结论是一致的，由此充分表明，本文所提的灰度图像自仿射维数计算理论是正确的，基于该理论所提的在线检测技术也是实用可行的。

Spectrality of a class of self-affine measures with decomposable digit sets

The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measures have some surprising connections with a number of areas in mathematics, and have been received much attention in recent years. In the present paper, we shall determine the spectrality and non-spectrality of a class of self-aiffine measures with decomposable digit sets. We present a method to deal with such case, and clarify the spectrality and non-spectrality of a class of self-affine measures by applying this method.

Affine groups and flag-transitive triplanes

Let D be a nontrivial 2-(v, k, 3) symmetric design (triplane) and let G≤Aut(D) be flag-transitive and point-primitive. In this paper, we prove that if G is an affine group, then G≤AΓL1(q), where q is some power of a prime p and p≥5.

Some conjectures on modular representations of affine sl_2 and Virasoro algebra

We conjecture an explicit bound on the prime characteristic of a field, under which the Weyl modules of affine sl_2 and the minimal series modules of Virasoro algebra remain irreducible, and Goddard-Kent-Olive coset construction for affine sl_2 is valid.

A class of irreducible modules for the extended affne Lie algebra ■

We construct a class of modules for extended affine Lie algebra gl l（Cq） by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.

The spectrum of Bergman Toeplitz operators with some harmonic symbols

In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .

A necessary and sufficient condition for the finite μM,D-orthogonality

The self-affine measure μM,D associated with an expanding matrix M ∈ Mn(Z) and a finite digit set D ? Znis uniquely determined by the self-affine identity with equal weight. The set of orthogonal exponential functions E(Λ) := {e2πiλ,x : λ∈Λ} in the Hilbert space L2(μM,D) is simply called μM,D-orthogonal exponentials. We consider in this paper the finiteness of μM,D-orthogonality. A necessary and sufficient condition is obtained for the set E(Λ) to be a finite μM,D-orthogonal exponentials. The research here is closely connected with the non-spectrality of self-affine measures.

Efficiently Counting Affine Roots of Mixed Trigonometric Polynomial Systems

Estimating the number of isolated roots of a polynomial system is not only a fundamental study theme in algebraic geometry but also an important subproblem of homotopy methods for solving polynomial systems. For the mixed trigonometric polynomial systems, which are more general than polynomial systems and rather frequently occur in many applications, the classical B6zout number and the multihomogeneous Bezout number are the best known upper bounds on the number of isolated roots. However, for the deficient mixed trigonometric polynomial systems, these two upper bounds are far greater than the actual number of isolated roots. The BKK bound is known as the most accurate upper bound on the number of isolated roots of a polynomial system. However, the extension of the definition of the BKK bound allowing it to treat mixed trigonometric polynomial systems is very difficult due to the existence of sine and cosine functions. In this paper, two new upper bounds on the number of isolated roots of a mixed trigonometric polynomial system are defined and the corresponding efficient algorithms for calculating them are presented. Numerical tests are also given to show the accuracy of these two definitions, and numerically prove they can provide tighter upper bounds on the number of isolated roots of a mixed trigonometric polynomial system than the existing upper bounds, and also the authors compare the computational time for calculating these two upper bounds.