The Limits of Horn Logic Programs

Given a sequence $\{\Pi_n\}$ of Horn logic programs, the limit $\Pi$ of $\{\Pi_n\}$ is the set of the clauses such that every clause in $\Pi$ belongs to almost every $\Pi_n$ and every clause in infinitely many $\Pi_n$'s belongs to $\Pi$ also. The limit program $\Pi$ is still Horn but may be infinite. In this paper, we consider if the least Herbrand model of the limit of a given Horn logic program sequence $\{\Pi_n\}$ equals the limit of the least Herbrand models of each logic program $\Pi_n$. It is proved that this property is not true in general but holds if Horn logic programs satisfy an assumption which can be syntactically checked and be satisfied by a class of Horn logic programs. Thus, under this assumption we can approach the least Herbrand model of the limit $\Pi$ by the sequence of the least Herbrand models of each finite program $\Pi_n$. We also prove that if a finite Horn logic program satisfies this assumption, then the least Herbrand model of this program is recursive. Finally, by use of the concept of stability from dynamical systems, we prove that this assumption is exactly a sufficient condition to guarantee the stability of fixed points for Horn logic programs.Comment: 11 pages, added new results. Welcome any comments to [email protected]

Analysis of programmable molecular electronic systems

The continuing scaling down in size of microelectronics devices has motivated the development of molecular electronic devices, often called moletronics, which use molecules to function as electronic devices. One of the moletronics is the programmable molecular array. In this device, disordered arrays of metallic islands are interlinked by molecules. It is addressed by a small number of input/output leads located on the periphery of the device. In this dissertation, a thorough investigation of the programmable molecular array is performed. First, theoretical calculations for single molecules are carried out. The effect of bias voltage on the electron transmission through the molecule is reported. Next, electrical measurements are conducted on programmable molecular arrays. Negative differential resistance and memory phenomena are found. The electrical characteristics of the programmable molecular array populated with different molecules indicate that the metallic islands contribute to the above phenomena. The electrical conductance through the metallic islands is investigated, and conformational change of the metallic islands under bias is reported. Furthermore, a scenario is proposed to use molecular vibronics and electrostatic potential to transport and process signals inside the programmable molecular array. Simulated results are presented

Adaptive Robust Actuator Fault Accommodation for a Class of Uncertain Nonlinear Systems with Unknown Control Gains

An adaptive robust fault tolerant control approach is proposed for a class of uncertain nonlinear systems with unknown signs of high-frequency gain and unmeasured states. In the recursive design, neural networks are employed to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unknown sign of the virtual control direction. By incorporating the switching function σ algorithm, the adaptive backstepping scheme developed in this paper does not require the real value of the actuator failure. It is mathematically proved that the proposed adaptive robust fault tolerant control approach can guarantee that all the signals of the closed-loop system are bounded, and the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples

CFD analysis and optimization of axial flow fans

The axial fan plays a vital role in the safe production of the mine, and in this paper, a mine axial flow ventilator is designed through numerical simulation to meet the demand of air exchange inside and outside of the mine, so as to maintain the oxygen supply of the mine and discharge the harmful gases. Finite element analysis of four structural factors of axial fan blade installation angle, number of blades, deflector plate, rotational speed, drawing fan wind pressure and rotational speed cloud diagram, calculation of axial power, by analyzing the distribution of the cloud diagram to design the shape of the fan blade, and derive the change rule of the wind pressure when changing the structure of the fan. By using gradient descent method to control the percentage of imported mass flow rate, the P-Q performance curve of the fan is obtained, which optimizes its aerodynamic performance, improves efficiency, and extends its service life