Three-step iterative methods with eighth-order convergence for solving nonlinear equations

A family of eighth-order iterative methods for the solution of nonlinear equations is presented. The new family of eighth-order methods is based on King’s fourth-order methods and the family of sixth-order iteration methods developed by Chun et al. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based on n$n$ evaluations could achieve optimal convergence order 2ⁿ⁻¹$2^{n-1}$. Thus we provide a new example which agrees with the conjecture of Kung–Traub for n=4$n=4$. Numerical comparisons are made to show the performance of the presented methods.     

A cryptographic watermarking technique for multimedia signals

Digital watermarking has been widely used in digital rights management and copyright protection. In this paper, new cryptographic watermark schemes are proposed. Compare to the existing watermarking techniques, our proposed watermark schemes combine both security and efficiency that none of the existing schemes can do. We first develop an algorithm to randomly generate the watermark indices based on the discrete logarithm problem (DLP) and the Fermat’s little theorem. Then we embed watermark signal into the host image in both time domain and frequency domain at the indices. Our security analysis and simulation demonstrate that our proposed schemes can achieve excellent transparency and robustness under the major security attacks and common signal degradations. The novel approaches provided in this paper are ideal for general purpose commercial digital media copyright protection.     

Ship-pack optimization in a two-echelon distribution system

In large distribution systems, distribution centers (DC) deliver some merchandize to their retail stores in size-specific packages, also called ship-packs. These ship-packs include cases (e.g., cartons containing 24 or 48 units), inners (packages of 6 or 8 units) or eaches (individual units). For each Stock Keeping Unit (SKU), a retailer can decide which of these ship-pack options to use when replenishing its retail stores. Working with a major US retailer, we have developed a cost model that balances DC handling costs, store handling costs and inventory-related costs at both the DC and the stores, and therefore can help to determine the optimum warehouse ship-pack for each SKU. We implement our model for a sample of 529 SKUs, and show that by changing ship-pack size for about 30 SKUs, the retailer can reduce its total cost by 0.3% - 0.4%. Interestingly, we find that most of the cost savings occurs at the DC level.     

An Approach to Shape Optimization with State Constraints

We introduce a new approach to solve shape optimization problems with state constraints. The problem is reformulated on a fixed reference domain using conformal pull-back. The shape dependence is then hidden in the conformal parameter. The problem is discretized using FEM and solved as an NLP. Finally the optimal shape can be reconstructed from the optimal conformal parameter. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Freidlin-Wentzell's large deviations for homeomorphism flows of non-Lipschitz SDEs

We prove a Freidlin-Wentzell large deviation principle for multi-dimensional stochastic differential equations with non-Lipschitz coefficients and apply it to the Brownian motion on the diffeomorphism group of the disc constructed recently by Airault, Malliavin and Thalmaier.     

Nucleation in the FitzHugh-Nagumo system: Interface-spike solutions

We find nucleation solutions of N interfaces and K spikes to the one-dimensional FitzhHugh-Nagumo system. Each spike sits asymptotically in the middle between two interfaces. We use the Lyapunov-Schmidt reduction method, in which the problem is split into a finite-dimensional problem related to the translation of the K spikes and an infinite-dimensional complement problem. However the complement problem remains near degenerate due to the translation of the N interfaces. To overcome this difficulty we move the interfaces by a small distance and solve the complement problem with the help of a Newton iteration argument.     

压电复合材料层合板自适应结构的振动控制

本文针对板壳型自适应结构,研究了压电材料作为作动器的自适应结构的振动控制。利用四节点压电复合材料层合板单元进行自适应结构的有限元动力分析;采用模态控制方法,将结构的各阶模态的阻尼比作为控制目标,并以此计算出各压电片的控制电压,达到控制结构振动的目的。算例给出了数值计算的结果。     

S-polar sets of super-brownian motions and solutions of nonlinear differential equations

This paper gives probabilistic expressions of the minimal and maximal positive solutions of the partial differential equation -1/2△v(x) γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 < α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.     

两类广义Petersen 图的Euler亏格

广义 Petersen 图 P(n, m) 是这样的一个图:它的顶点集是{u_i, v_i | i=0,1, ^… , n-1}, 边集是 {u_iu_i+1, v_iv_i+m, u_iv_i | i=0,1, ^…, n-1}, 这里 m, n 是正整数、加法是在模n 下且 m<|n/2| . 这篇文章证明了P(2m+1, m)(m≥ 2) 的 Euler 亏格是1, 并且 P(2m+2, m)(m≥ 5) 的 Euler 亏格是2.     

Regression analysis of right-censored failure time data with missing censoring indicators

This paper discusses regression analysis of right-censored failure time data when censoring indicators are missing for some subjects. Several methods have been developed for the analysis under different situations and especially, Goetghebeur and Ryan considered the situation where both the failure time and the censoring time follow the proportional hazards models marginally and developed an estimating equation approach. One limitation of their approach is that the two baseline hazard functions were assumed to be proportional to each other. We consider the same problem and present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An EM algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided.