Sensitivity analysis of initial value problems with mixed odes and algebraic equations

An efficient method is described for sensitivity analysis of nonlinear initial value problems, which may include algebraic equations as well as ordinary differential equations.The linearity of the sensitivity equations is utilized to solve them directly via the local Jacobian of the state equations. The method is implemented with the implicit integrator DASSL and is demonstrated on a stiff industrial reaction model.     

Optimal tool replacement with asymmetric quadratic loss

In this paper, an analysis of a tool replacement problem with asymmetric quadratic loss function is presented. The expected average cost per unit time is derived and it is shown that the optimal initial setting and the optimal replacement time can be found by solving two nonlinear equations. The paper generalizes and improves on previous work in the area.     

Pairs of Complementary Unary Languages with “Balanced” Nondeterministic Automata

For each sufficiently large n, there exists a unary regular language L such that both L and its complement L ^c are accepted by unambiguous nondeterministic automata with at most n states, while the smallest deterministic automata for these two languages still require a superpolynomial number of states, at least \(e^{\Omega(\sqrt[3]{n\cdot\ln^{2}n})}\). Actually, L and L ^c are “balanced” not only in the number of states but, moreover, they are accepted by nondeterministic machines sharing the same transition graph, differing only in the distribution of their final states. As a consequence, the gap between the sizes of unary unambiguous self-verifying automata and deterministic automata is also superpolynomial.     

The E3 architecture: enabling future cellular networks with cognitive and self‐x capabilities

Future mobile networks are expected to be complex heterogeneous systems. On the one hand this will enable users to take advantage of a number of different access technologies. On the other hand it will seriously affect network management procedures since more extensive operations and decisions will have to be dealt with. To tackle these challenges a number of new dynamic mechanisms need to be designed. It is imperative that certain network management tasks have to be performed without human intervention to reduce the OPEX costs and achieve faster responses in different events. To achieve this goal, the introduction of self‐x functionalities, combined with cognitive mechanisms and the ability to reconfigure network entities and terminals, is required. Moreover, the introduction of a new pilot channel needs to be considered to assist the terminals in selecting the most suitable radio access technology according to their requirements. We present the functional architecture of an evolved network that was designed in the context of the EU‐funded IP project ‘E³: End‐to‐End Efficiency’. This architecture aims to enhance existing procedures usually performed in traditional operation and maintenance systems (e.g. spectrum management, network planning, configuration actions). We explain the rationale of our design and provide specific examples to illustrate the role of the different functional entities and their interfaces. A considerable part of this architecture has recently been approved as a feasibility study by the ETSI Committee Reconfigurable Radio System. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

Most maintenance optimization models of gear systems have considered single failure mode. There have been very few papers dealing with multiple failure modes, considering mostly independent failure modes. In this paper, we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks. The system failures include degradation failure and catastrophic failure. A three‐state continuous‐time–homogeneous hidden Markov model (HMM), namely the model with unobservable healthy and unhealthy states, and an observable failure state, describes the deterioration process of the gear system. The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy. The objective is to maximize the long‐run expected average system availability per unit time. The maintenance optimization model is formulated and solved in a semi‐Markov decision process (SMDP) framework. The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development. The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results. A comparison with the Bayesian control chart based on the previously published HMM and the age‐based replacement policy is given to illustrate the superiority of the proposed approach. The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.     

Two-way unary automata versus logarithmic space

We show that if L=NL (the classical logarithmic space classes), then each unary 2nfa (a two-way nondeterministic finite automaton) can be converted into an equivalent 2dfa (a deterministic two-way automaton), keeping the number of states polynomial. (Unlike other results of this kind, here the deterministic simulation is valid for inputs of all lengths, not only polynomially long ones.) This shows a connection between the standard logarithmic space complexity and the state complexity of two-way unary automata: it indicates that L could be separated from NL by proving a superpolynomial gap, in the number of states, for the conversion from unary 2nfas to 2dfa. Moreover, without any unproven assumptions, we show that each n-state unary 2nfa can be simulated by an equivalent 2ufa (an unambiguous 2nfa) with a polynomial number of states.     

Hot-Ball Method for Measuring Thermal Conductivity

This article deals with the theory and performance of a sensor for measuring thermal conductivity. The sensor, in the form of a small ball, generates heat and simultaneously measures its temperature response. An ideal model of the hollow sphere in an infinite medium furnishes a working equation of the hot-ball method. A constant heat flux through the surface of the ball generates the temperature field. The thermal conductivity of the surrounding medium is to be determined by the stabilized value of the temperature response, i.e., when the steady-state regime is attained. Error components of the sensor are discussed due to analysis of the deviations of the real hot-ball construction from the ideal model. The functionality of a set of hot balls has been tested, and the calibration for a limited range of thermal conductivities was performed. A working range of thermal conductivities of tested materials has been estimated to be from 0.06 W· m⁻¹ · K⁻¹ up to 1 W· m⁻¹ · K⁻¹.