广义Hamming重量的广义Griesmer界进一步分析

通过对q元线性码广义Hamming重量dr(·)的分析,应用支撑重量ωs(C)的性质,再次分析了q元[n,k]线性码广义Griesmer界n≥dr+sum from i=1 to k-r[(q-1)dr/qi(qr-1)].     

Weighted norm inequalities,off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights

This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace–Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian upper bounds.      

Ranking decision-making units using common weights in DEA

Data envelopment analysis (DEA) is a linear programming technique that is used to measure the relative efficiency of decision-making units (DMUs). Liu et al. (2008) [13] used common weights analysis (CWA) methodology to generate a CSW using linear programming. They classified the DMUs as CWA-efficient and CWA-inefficient DMUs and ranked the DMUs using CWA-ranking rules. The aim of this study is to show that the criteria used by Liu et al. are not theoretically strong enough to discriminate among the CWA-efficient DMUs with equal efficiency. Moreover, there is no guarantee that their proposed model can select one optimal solution from the alternative components. The optimal solution is considered to be the only unique optimal solution. This study shows that the proposal by Liu et al. is not generally correct. The claims made by the authors against the theorem proposed by Liu et al. are fully supported using two counter examples.     

Muckenhoupt weights with singularities on closed lower dimensional sets in spaces of homogeneous type

We give sufficient conditions on a real number β and on a closed set F   in a general space of homogeneous type (X,d,μ)$(X,d,\mu )$ in such a way that μ(B(x,d(x,F)))^β$\mu {(B(x,d(x,F)))}^{\beta }$ becomes a Muckenhoupt weight. In order to prove our result, we modify the underlying space so that it becomes 1-Ahlfors regular.     

本刊英文版Vol.30(2014),No.8论文摘要(英文)

<正>Weighted Estimates for Multilinear Pseudodifferential Operators Kang Wei LI;;Wen Chang SUN Abstract In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical A_p weights to multiple weights.Trigonometric Series With a Generalized Monotonicity Condition     

Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach

In a situation where imprecise attribute weights such as a rank order are captured, various approximate weighting methods have been proposed to aid multiattribute decision analysis. Among others, it is well known that the rank order centroid (ROC) weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights. In this paper, we aim to reinterpret the meaning of the ROC weights and to develop a compatible weighting method that is based on other well-established academic disciplines. The ordered weighted averaging (OWA) method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process. Some interesting semantics can be attached to the approximate weights in view of the measure developed in the OWA method. Furthermore, the weights generated by the maximum entropy method show equally compatible performance with the ROC weights under some condition, which is demonstrated by theoretical and simulation analysis.     

Function Spaces with Exponential Weights I

In this paper we define weighted function spaces of type B^s_pq(u) and F^s_pq(u) on the Euclidean space IRⁿ, where u is a weight function of at most exponential growth. In particular, u(x) = exp(±|χ|) is an admissible weight. We prove some basic properties of these spaces, such as completeness and density of the smooth functions.     

On the denominator values and barycentric weights of rational interpolants

We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341–348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355–370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole.     

Higher Integrability of the Gradient in Degenerate Elliptic Equations

We prove that under some global conditions on the maximum and the minimum eigenvalue of the matrix of the coefficients, the gradient of the (weak) solution of some degenerate elliptic equations has higher integrability than expected. Technically we adapt the Giaquinta–Modica regularity method in some degenerate cases. When the dimension is two, a consequence of our result is a new Hölder continuity result for the weak solution.     

Dependence of polarization mode dispersion of slotted core NZDF ribbon on cable design and environmental conditions

Non-zero dispersion fiber (NZDF) ribbon cable has recently become a considerable alternative in long-haul high-speed network construction. Since long-distance high-bit rate transmission requires low polarization mode dispersion (PMD), it is very important to know the PMD performance of this type of optical fiber cables. In this paper, we report experimental analysis of effects of the cable design and environmental parameters, in particular ribbon thickness, positions of fibers in the ribbon, flexing and vibration, on PMD performances of several slotted-core fiber ribbon cables. Results show that ribbon thickness and positions of fibers in the ribbon alter the PMD values of NZDF ribbon cables. Also, 23% and 11% PMD variations have been determined in flexing and vibration experiments, respectively. Moreover, it has been observed that vibration amplitude has significant effects and vibration frequency has little effects (14% and 6% variations, respectively) on fiber PMD. Results are important for understanding effects of installation conditions and wind, especially for aerial fibers, on PMD values of cables.