Group path covering and distance two labeling of graphs

For a positive integer d, an L(d,1)-labeling f of a graph G is an assignment of integers to the vertices of G such that |f(u)−f(v)|?d if uv∈E(G), and |f(u)−f(v)|?1 if u and u are at distance two. The span of an L(d,1)-labeling f of a graph is the absolute difference between the maximum and minimum integers used by f. The L(d,1)-labeling number of G, denoted by λd,1(G), is the minimum span over all L(d,1)-labelings of G. An L^′(d,1)-labeling of a graph G is an L(d,1)-labeling of G which assigns different labels to different vertices. Denote by the L^′(d,1)-labeling number of G. Georges et al. [Discrete Math. 135 (1994) 103-111] established relationship between the L(2,1)-labeling number of a graph G and the path covering number of Gc, the complement of G. In this paper we first generalize the concept of the path covering of a graph to the t-group path covering. Then we establish the relationship between the L^′(d,1)-labeling number of a graph G and the (d−1)-group path covering number of Gc. Using this result, we prove that and for bipartite graphs G can be computed in polynomial time.     

Necessary optimality conditions for fuzzy variational problems

The main aims of this study are to derive the fuzzy Euler-Lagrange conditions for both fuzzy unconstrained and constrained variational problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its α-level sets.     

Entropic component analysis and its application in geological data

We present an entropic component analysis for identifying key parameters or variables and the joint effects of various parameters that characterize complex systems. This approach identifies key parameters through solving the variable selection problem. It consists of two steps. First, a Bayesian approach is utilized to convert the variable selection problem into the model selection problem. Second, the model selection is achieved uniquely by evaluating the information difference of models by relative entropies of these models and a reference model. We study a geological sample classification problem, where a brine sample from Texas and Oklahoma oil field is considered, to illustrate and examine the proposed approach. The results are consistent with qualitative analysis of the lithology and quantitative discriminant function analysis. Furthermore, the proposed approach reveals the joint effects of the parameters, while it is unclear from the discriminant function analysis. The proposed approach could be thus promising to various geological data analysis.     

Strong stability of the mono-tubular heat exchanger equation with output feedback

We investigate asymptotic behavior of the C₀-semigroup T(t) associated with the mono-tubular heat exchanger equation with output feedback by a perturbation method. It is shown that T(t) is bounded if a constraint is satisfied by the parameters and the spatial distribution function. Further, applying the Arendt-Batty-Lyubich-Vu theorem, a criterion is established to judge strong stability of T(t).     

Input-output properties of the Page-Hinkley detector

We consider the stochastic input-output properties of a simple non-linear dynamical system, the so-called Page-Hinkley detector, playing a key role in change detection, and also in queuing theory. We show that for L-mixing inputs with negative expectation the output process of this system is L-mixing. The result is applied to get an upper bound for the false alarm rate. The proof is then adapted to get a similar result for the case of random i.i.d. inputs. Possible extensions and open problems are given in the discussion.     

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.     

Rectangle packing with additional restrictions

We formulate a generalization of the NP-complete rectangle packing problem by parameterizing it in terms of packing density, the ratio of rectangle areas, and the aspect ratio of individual rectangles. Then we show that almost all restrictions of this problem remain NP-complete and identify some cases where the answer to the decision problem can be found in constant time.     

Patterns for multigrid equidistributed functions: Application to general parabolas and length estimation

We show that for some special functions (called k-multigrid equidistributed functions), we can compute the limit of the frequency of patterns in the discretization of their graph, when the resolution tends to zero. This result is applied to parabolas. We deduce also that local length estimators almost never converge to the length for the parabolas.     

对DAG-MAP算法的研究

DAG－MAP是一个面向延迟优化的FPGA工艺映射算法,其中的标记过程是该算法的核心.文章对原算法中的标记过程进行了研究,并且提出了一个改进的标记方法.通过对MCNC标准测试电路的实验结果表明该算法比原算法更为有效,并且算法所用时间没有明显的增加.     

基于OpenGL的虚拟海洋环境生成技术

文章提出了一种海洋环境的三维图像生成方法,该方法基于OpenGL图形库,采用计算机图形技术和多媒体技术,能够快速、逼真地建立水下虚拟场景,并已应用在水下制导仿真系统中,仿真实验表明该方法有良好的视觉效果.