Computing integrals over polynomially defined regions and their boundaries in 2 and 3 dimensions

We use the cylindrical algebraic decomposition algorithms implemented in Mathematica to produce procedures to analytically compute integrals over polynomially defined regions and their boundaries in two and three dimensions. Using these results, we can implement the divergence theorem in three dimensions or the Green's theorems in two dimensions. These theorems are of central importance in the applications of multidimensional integration. They also provide a strong correctness test for the implementation of our results in a computer algebra system. The resulting software can solve many of the two and some of the three dimensional integration problems in vector calculus textbooks. The three dimensional results are being extended. The results in this paper are being included in an automated student assistant for vector calculus.     

The efficiency of identifying timed automata and the power of clocks

We develop theory on the efficiency of identifying (learning) timed automata. In particular, we show that: (i) deterministic timed automata cannot be identified efficiently in the limit from labeled data and (ii) that one-clock deterministic timed automata can be identified efficiently in the limit from labeled data. We prove these results based on the distinguishability of these classes of timed automata. More specifically, we prove that the languages of deterministic timed automata cannot, and that one-clock deterministic timed automata can be distinguished from each other using strings in length bounded by a polynomial. In addition, we provide an algorithm that identifies one-clock deterministic timed automata efficiently from labeled data.Our results have interesting consequences for the power of clocks that are interesting also out of the scope of the identification problem.     

Information transmittal, Newton’s law of gravitation, and tensor approach to general relativity

The special relativity considered in [A. Einstein, Zur Elektrodynamik der bewegte Körper. Ann. Physik, 17 (1905) 891-921] is based on the concept of finite speed of information transmittal by the available signals (rays of light). It is demonstrated that the same concept applies to Newton’s law of universal gravitation since the magnitude of distances between attracting masses can be physically defined (carried, accounted in acting forces of gravity) only by signals (physical processes) propagating at finite velocities. It follows that the speed of propagation of gravity is finite. The linear transformations of special relativity are applied to Newton’s law of gravitation to take into account the relativistic effects of information transmittal in a field of central forces of attraction. Relativistic representations of Newton’s law are obtained with respect to the center of gravity exposing illusory effects that appear at high velocities. It is verified that in atomic physics the effect of Newtonian gravitation on the motion of elementary particles at high velocities is negligible also in relativistic consideration. Computational methods are developed to measure the intensity of gravitation at a distant space-time location using a body that travels in space, emitting uniform pulses of light that are received by the observer at a different space-time location. It is demonstrated that the tensor approach to the general relativity and the united theory of space, time and gravitation in which the geometrical properties (metric) of the four-dimensional space-time continuum depend on the distribution of gravitating masses in space and their motion represent a transformed Lorentz invariant with a new type of inertia in the field of forces changing in space and time. Real physical processes evolve according to the forces represented in the tensor form by this invariant which is equivalent to the coordinate-free local invariant of relativistic dynamics that defines the field and the motion of a body whose velocities and accelerations can be measured by relativistic identification methods at a point, time and direction of interest. The results open new avenues for research in the general relativity and can be used for software development, field measurements and experimental studies in application to distant or fast moving systems.     

Effect of La2CuO4 electrode area on potentiometric NOx sensor response and its implications on sensing mechanism

The intent of this work is to look at the effects of varying the La₂CuO₄ electrode area and the asymmetry between the sensing and counter electrode in a solid state potentiometric sensor with respect to NO_x sensitivity. NO₂ sensitivity was observed at 500-600 °C with a maximum sensitivity of ∼22 mV/decade [NO₂] observed at 500 °C for the sensor with a La₂CuO₄ electrode area of ∼30 mm². The relationship between NO₂ sensitivity and area is nearly parabolic at 500 °C, decreases linearly with increasing electrode area at 600 °C, and was a mixture of parabolic and linear behavior 550 °C. NO sensitivity varied non-linearly with electrode area with a minima (maximum sensitivity) of ∼−22 mV/decade [NO] at 450 °C for the sensor with a La₂CuO₄ electrode area of 16 mm². The behavior at 400 °C was similar to that of 450 °C, but with smaller sensitivities due to a saturation effect. At 500 °C, NO sensitivity decreases linearly with area.We also used electrochemical impedance spectroscopy (EIS) to investigate the electrochemical processes that are affected when the sensing electrode area is changed. Changes in impedance with exposure to NO_x were attributed to either changes in La₂CuO₄ conductivity due to gas adsorption (high frequency impedance) or electrocatalysis occurring at the electrode/electrolyte interface (total electrode impedance). NO₂ caused a decrease in high frequency impedance while NO caused an increase. In contrast, NO₂ and NO both caused a decrease in the total electrode impedance. The effect of area on both the potentiometric and impedance responses show relationships that can be explained through the mechanistic contributions included in differential electrode equilibria.     

动态节点质心定位改进算法

为降低无线传感器网络的定位误差,提高动态节点的定位精度和定位覆盖度,使节点定位能够应用于动态环境下,基于传统的定位算法,提出了一种新的动态节点定位改进算法。该算法通过未知节点接收、保存的分组信息来循环组成虚拟三角形,同时依靠内点测试方法来判断未知节点自身位置,最后根据质心算法来进行最终定位。将仿真结果与传统算法进行比较,结果表明,改进算法可以大大提高无线传感器网络的定位精度和覆盖度。     

木马隐藏技术与防范方法

为加固网络安全、防范木马攻击,结合实例研究了一种木马隐藏技术,实现了基于加载三级跳和线程守护的隐藏技术,增强了木马的隐蔽性与抗毁性,并提出了该技术相应的防范措施和清除方法。实验结果表明,融入该隐藏技术的木马程序完成了预期的隐藏功能并可以穿透最新的瑞星杀毒软件、瑞星防火墙及硬件防火墙,表明了该隐藏技术的可行性与有效性。     

复杂高炉炼铁过程的数据驱动建模及预测算法

高炉炼铁过程的控制意味着控制高炉铁水温度及成份在指定的范围. 本文以高炉炉内热状态的重要指示剂---高炉铁水硅含量为研究对象, 针对机理建模难以准确预测、控制高炉铁水硅含量的发展变化, 利用数据驱动建模的思想, 建立了基于多元时间序列的高炉铁水硅含量数据驱动预测模型. 实例分析表明, 建立的数据驱动预测模型能够很好地预测高炉铁水硅含量, 连续预测167炉高炉铁水硅含量, 命中率高达83.23%, 预测均方根误差为0.07260. 这些指标均优于基于单一硅时间序列所建立的数据驱动模型, 对实际生产具有很好的指导作用.     

基于数据挖掘的入侵防御系统研究

针对传统异构安全设备的广泛应用而产生的海量不可靠安全事件和难以有效管理的现状,提出了一种基于数据挖掘的深度入侵防御系统模型。其中,以统一网络安全管理平台为核心,采用在线检测和离线数据挖掘相结合的方式分析网络和主机数据。