On the Differential Polynomial of a Graph

We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x) :=∑?(G)k=-nB_k(G) x~(n+k), where B_k(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G;x) and its coefficients.In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G.     

Multi-Model Communication and Data Assimilation for Mitigating Model Error and Improving Forecasts

Models for weather and climate prediction are complex, and each model typi-cally has at least a small number of phenomena that are poorly represented, such as perhaps the Madden-Julian Oscillation (MJO for short) or El Ni\~{n}o-Southern Oscillation (ENSO for short) or sea ice. Furthermore, it is often a very challenging task to modify and improve a complex model without creating new deficiencies. On the other hand, it is sometimes possible to design a low-dimensional model for a particular phenomenon, such as the MJO or ENSO, with significant skill, although the model may not represent the dynamics of the full weather-climate system. Here a strategy is proposed to mitigate these model errors by taking advantage of each model''s strengths. The strategy involves inter-model data assimilation, during a forecast simulation, whereby models can exchange information in order to obtain more faithful representations of the full weather-climate system. As an initial investigation, the method is examined here using a simplified scenario of linear models, involving a system of stochastic partial differential equations (SPDEs for short) as an imperfect tropical climate model and stochastic differential equations (SDEs for short) as a low-dimensional model for the MJO. It is shown that the MJO prediction skill of the imperfect climate model can be enhanced to equal the predictive skill of the low-dimensional model. Such an approach could provide a route to improving global model forecasts in a minimally invasive way, with modifications to the prediction system but without modifying the complex global physical model itself.     

L~p INEQUALITIES AND ADMISSIBLE OPERATOR FOR POLYNOMIALS

Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of p(Rz)-βp(rz) + α (R+1/r+1)n-|β | p(rz) s on p(z) s for every α, β∈ C with |α|≤ 1, |β | ≤ 1, R > r 1, and s > 0. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.     

Pole placement controllers for linear time-delay systems with commensurate point delays

This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delaydependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer‘s choice of a (delay-dependent) arbitrary spectrum assignment objective.     

X射线荧光光谱法分析玻璃纤维中主、次量元素成分

采用粉末压片-波长色散X射线荧光光谱法分析了中碱及无碱玻璃纤维中硅、铝、钙、镁、铁、钛、钾、钠、砷、氟等10种主、次量元素成分含量。以6个标准样品并结合两个参考样品建立校准曲线,采用DeJongh模式方程有效校正玻璃基体中元素间的吸收增强效应和重叠效应。该方法测定10个元素的精密度和准确度均较好,其相对标准偏差在0．35％～2．86％之间,对实际样品的分析结果与化学法相吻合,可应用于玻璃纤维中多元素成分的快速分析。     

基于深度学习的柔性直流线路单端量波形特征保护

多端柔性直流电网是未来智能电网的一种重要发展趋势,但对线路保护性能提出了更严苛的要求.针对现有柔性直流线路保护四性协调困难、阈值整定繁杂、耐受过渡电阻能力不足等问题,该文指出反行波波形特征蕴含丰富的故障位置信息,并以此为基础提出了基于深度学习的柔性直流线路单端量波形特征保护方案.该方案首先经极模变换、基于线路依频参数计...     

On the Generalized Strongly Nil-Clean Property of Matrix Rings

Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n × n matrix A over R is expressible as a sum A =E1 +…+ Es + N of (commuting) idempotent matrices Ei and a nilpotent matrix N.     

双离子(40Ar+, C2H+6)辐照合成金刚石纳米晶颗粒

用双离子(⁴⁰Ar⁺，C₂H⁺₆)辐照实验完成了从多壁碳纳米管向金刚石纳米晶颗粒的转变.对转变机理进行了初步探讨.这一探索有望能成为一种金刚石纳米晶合成的新途径.由此可知，多重荷能离子辐照用于其他材料纳米结构的制备也不是凭空设想. 关键词： 金刚石纳米晶 离子辐照 透射电子显微镜