Approximate Similarity Reduction for Perturbed Kaup-Kupershmidt Equation via Lie Symmetry Method and Direct Method

The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbationmethod and the approximate direct method.The similarity reduction solutions of different orders are obtainedfor both methods, series reduction solutions are consequently derived.Higher order similarity reduction equations arelinear variable coefficients ordinary differential equations.By comparison, it is find that the results generated from theapproximate direct method are more general than the results generated from the approximate symmetry perturbationmethod.

等体积不同纵横比水滴粒子的光学特性计算

不同重力场环境中水滴粒子的形状会偏离球形,为了研究水滴粒子非球形化程度对其光学特性的影响,本文计算了不同方向取向下,等体积不同纵横比水滴粒子在3.0~5.0 μm波段的光学特性。研究发现虽然不同纵横比水滴粒子的光学特性在3.0~5.0 μm波段的变化趋势相似,但具体数值仍然明显依赖于水滴粒子的空间取向和偏离球形程度。总体而言,水滴粒子的吸收截面只在方位角θ较小和波长较短时随其纵横比显著变化;而散射截面、不对称因子和散射相函数则在任意方位角和波长下都对水滴粒子的纵横比有较明显的依赖。因此,由于光学特性对水滴粒子的纵横比有较强的依赖性,由水滴粒子所组成的水雾的辐射传输特性会强烈依赖于水滴粒子的形状。

Soft spectral clustering ensemble applied to image segmentation

An unsupervised learning algorithm, named soft spectral clustering ensemble （SSCE）, is proposed in this paper. Until now many proposed ensemble algorithms cannot be used on image data, even images of a mere 256 × 256 pixels are too expensive in computational cost and storage. The proposed method is suitable for performing image segmentation and can, to some degree, solve some open problems of spectral clustering （SC）. In this paper, a random scaling parameter and Nystrǒm approximation are applied to generate the individual spectral clusters for ensemble learning. We slightly modify the standard SC algorithm to aquire a soft partition and then map it via a centralized logcontrast transform to relax the constraint of probability data, the sum of which is one. All mapped data are concatenated to form the new features for each instance. Principal component analysis （PCA） is used to reduce the dimension of the new features. The final aggregated result can be achieved by clustering dimension-reduced data. Experimental results, on UCI data and different image types, show that the proposed algorithm is more efficient compared with some existing consensus functions.

L-fuzzy Roughness of n-ary Polygroups

In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ~）-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called （normal） TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the （strong） homomorphism of θ-lower and T-upper L-fuzzy rough approximation operators is studied.

An 11-bit 22-MS/s 0.6 mW SAR ADC with parasitic capacitance compensation

： This paper presents an l 1-bit 22-MS/s 0.6-mW successive approximation register （SAR） analog-to- digital converter （ADC） using SMIC 65-nm low leakage （LL） CMOS technology with a 1.2 V supply voltage. To reduce the total capacitance and core area the split capacitor architecture is adopted. But in high resolution ADCs the parasitic capacitance in the LSB-side would decrease the linearity of the ADC and it is hard to calibrate. This paper proposes a parasitic capacitance compensation technique to cancel the effect with no calibration circuits. Moreover, dynamic circuits are used to minimize the switching power of the digital logic and also can reduce the latency time. The prototype chip realized an 11-bit SAR ADC fabricated in SMIC 65-nm CMOS technology with a core area of 300 × 200 μm2. It shows a sampling rate of 22 MS/s and low power dissipation of 0.6 mW at a 1.2 V supply voltage. At low input frequency the signal-to-noise-and-distortion ratio （SNDR） is 59.3 dB and the spurious-free dynamic range is 72.2 dB. The peak figure-of-merit is 36.4 fJ/conversion-step.

LOW RANK APPROXIMATION SOLUTION OF A CLASS OF GENERALIZED LYAPUNOV EQUATION

In this paper, we consider the low rank approximation solution of a generalized Lya- punov equation which arises in the bilinear model reduction. By using the variation prin- ciple, the low rank approximation solution problem is transformed into an unconstrained optimization problem, and then we use the nonlinear conjugate gradient method with ex- act line search to solve the equivalent unconstrained optimization problem. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

Fluid approximation for generalized Jackson network with vacations

Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.