A Rejoinder to Notes on a ‘Constructive Proof of the Existence of a Collateral Equilibrium’

This rejoinder contains a few remarks on my paper published in this journal with the title ‘A Constructive Proof of the Existence of Collateral Equilibrium for a Two-Period Exchange Economy Based on a Smooth Interior-Point Path’ and Ragupathy and Velupillai’s notes on a ‘Constructive Proof of the Existence of Collateral Equilibrium’ published recently in the same journal.     

Effects of the ‘spring structure’ on the performance of a vibrating plate of the piezoelectric inkjet print-head

Microsystem Technologies - One of the core components of piezoelectric inkjet print-head is the piezoelectric vibrating plate which directly affects the jet performance of a print-head. In the...     

Proof Pearl: Mechanizing the Textbook Proof of Huffman’s Algorithm

Huffman’s algorithm is a procedure for constructing a binary tree with minimum weighted path length. Our Isabelle/HOL proof closely follows the sketches found in standard algorithms textbooks, uncovering a few snags in the process. Another distinguishing feature of our formalization is the use of custom induction rules to help Isabelle’s automatic tactics, leading to very short proofs for most of the lemmas. This work was supported by the DFG grant NI 491/11-1.     

Chaos emerged on the ‘edge of chaos’

Rule 110 is a complex cellular automaton (CA) in Wolfram's system of identification, capable of supporting universal computation. It has been suggested that a universal CA should be on the ‘edge of chaos’, which means that the dynamical behaviour of such a system is neither simple nor chaotic. There is no doubt that the dynamical property of Rule 110 is extremely complex and still not well understood. This paper proves the existence of subsystems on which this rule is chaotic in the sense of Devaney.     

Comments on ‘ Properties of the system matrix of a generalized state-space system’†

The purpose of this correspondence is to draw attention to significant extensions of the results presented by Verghese, et al. (1979). These extensions were obtained after the above paper was written, and are described in more detail in Verghese (1978) and Verghese and Kailath (1979).     

Note on ‘ On the definition of transfer function ’

An algorithm for directly obtaining the canonical state-space model corresponding to the Cauer third form of continued fraction expansion (CFE) from a given general state-space model is presented. The algorithm can be used to determine the transfer function of linear time-invariant system from its state-space model as well as to obtain the reduced order models..Two new similarity matrices, one transforms a state-space equation from a general form to a Cauer third CFE canonical form, and the other transforms a state-space model in phase-variable form to a state-space model in a Cauer third CFE canonical form, are derived. Using these matrices an approximate relationship between the original state vector and the state-vector of reduced model obtained by the method of Cauer third CFE is established     

Systemic analysis of so-called ‘accidents on the level’ in a multi trade company

Slips, trips and falls on the level are considered commonplace and are rarely subjected to in-depth analysis. They occur in highly varied circumstances in an occupational situation. In-depth analysis of these accidents was conducted within a company with the aim of understanding them better, to be able to discuss prevention field possibilities and priorities for the company concerned. Firstly, available data on ‘accidents on the level’ occurring over the last 4 years were analysed and a typology for these accidents was derived, based on individual activity at the time of the accident and accident location. The three most serious accident-causing situations were analysed in-depth from interviews with injured persons, as well as from activity observation and activity-related verbal information obtained from operatives. These most serious situations involved accidents occurring when climbing down from trucks or when walking either in surroundings outside company premises or from (to) a vehicle to (from) a work location. In-depth accident analysis and characterization of accident-causing situations as a whole enhance our understanding of the accident process and allow us to envisage priorities for action in the prevention field, in operational terms. Each accident-causing situation reveals environmental factors that in fact constitute accident factors (obstacle, stone, etc.), when the individual walks or climbs down from a truck. Analysis shows that other events are necessary for accident occurrence. For example, the individual may be subjected to a time constraint or may be preoccupied. Results obtained here, in a company integrating different trades, are discussed and compared with those referred to in the literature. Generalization of some of these results is also considered.     

Optimal Control of the Mean Field Equilibrium for a Pedestrian Tourists’ Flow Model

Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the historic center of a heritage city. We initially present a mean field game model, where both continuous and switching decisional variables are introduced to respectively describe the position of a tourist and the point of interest that he/she may visit. We prove the existence of a mean field equilibrium. A mean field equilibrium is Nash-type equilibrium in the case of infinitely many players. Then, we study an optimization problem for an external controller who aims to induce a suitable mean field equilibrium.

     

Comments on ‘Stabilization of a class of singularly perturbed bilinear systems’

Asamoah and Jamshidi (1987) investigated a stabilizing controller for singularly perturbed bilinear systems. We point out that their result is incorrect unless another assumption is employed.     

Comments on ‘Stabilization of a class of singularly perturbed bilinear systems’

In some particular cases, the application of the singular perturbations method to singularly perturbed systems leads to reduced-order bilinear models. The simplification in the analysis of Asamoah and Jamshidi (1987) is then only valid in those cases.     

Proof Pearl—A Mechanized Proof of GHC’s Mergesort

We present our Isabelle/HOL formalization of GHC’s sorting algorithm for lists, proving its correctness and stability. This constitutes another example of applying a state-of-the-art proof assistant to real-world code. Furthermore, it allows users to take advantage of the formalized algorithm in generated code.     

Comments on ‘ A note on the calculation and placing of finite zeros ’

A novel dual adaptive controller for extremum control of stochastic and uncertain nonlinear Hammerstein systems is proposed. The design is based on the innovations dual control cost function originally developed for conventional adaptive control of linear systems. However, the design process is extensively modified and developed so as to cater for the extremum control scenario. This is a more challenging problem because the reference input is itself a nonlinear function of the unknown system parameters, rather than an independent and predefined external reference signal. As in all dual adaptive schemes, it leads to a control law that balances out the need for caution, due to parameter uncertainty, with the conflicting requirement of probing that acts to quickly reduce parameter uncertainty. The proposed controller's performance is analysed through extensive Monte Carlo simulation trials and compared with several other non-dual adaptive extremum controllers. It is shown that the novel extremum innovations dual controller is superior to other types of adaptive control systems that are based on a certainty equivalence assumption. In addition, a novel statistical measure is introduced that yields a more objective evaluation of the Monte Carlo simulation results.     

Comments on the ‘ fuzzy max ’ operator of Dubois and Prade

The aim of this paper is to study controllability for systems described by first-order evolution equations and for systems described by second-order evolution equations in the case of discrete-time controls. For systems with finite-dimensional controls we present necessary and sufficient conditions for controllability. We show that distributed parameter systems are never finite-step controllable. We also investigate the relations between systems with discrete-time controls and systems with continuous -time controls from the view-point of controllability. Moreover we see the essential difference between the parabolic case and the hyperbolic case.     

Additional considerations concerning the effects of ‘warm’ and ‘cool’ wall colours on energy conservation

The possibility of wall colours mediating thermal comfort was examined. Potential colour constancy problems in previous research were eliminated by painting laboratory walls either red, blue, or white. A total of 72 male and 72 female undergraduate college students were used in the study; each subject was exposed in a carrel to one of the possible combinations of the three colours and four room temperatures, 18, 22, 29 and 35°C. Data from forms completed by subjects under these conditions indicated that temperature influenced personal comfort, arousal, and perceived ambient temperature, and that colour influenced personal comfort and perceived environmental quality. However, colour did not influence perceived temperature, suggesting that energy conservation may not be facilitated by selected wall colours.     

Comments on the reply to comments on ‘State observers and state-feedback controllers for a class of non-linear systems’

Some further remarks seem necessary on the reply of Hauksdottir and Fenton (1990) to the present author's original comment (Birk 1990) on their paper (Hauksdottir and Fenton 1988).     

Comment on ‘Stability of interval matrices’

Liao Xiao Xin (1987) gave necessary and sufficient conditions for the stability of a class of interval matrices. It can easily be shown that these results follow directly from a theorem relating stable Metzler matrices and quasidominant negative diagonal matrices by McKenzie (1966) which states (see also Siljak 1978)

A Metzler matrix A is stable if and only if it is quasidominant negative diagonal.

As the author considers Metzler matrices, Theorems 1,2 and 3 are obvious. Also, a theorem by Fiedler and Ptak (1962) concerning a pair of Minkowski matrices (see also Siljak 1978) leads to the same results.     

Why ‘GSA: a gravitational search algorithm’ is not genuinely based on the law of gravity

This letter highlights a fundamental inconsistency in the formulation of the Gravitational search algorithm (GSA) (Rashedi et al., Inf Sci 2232?C48, 2009). GSA is said to be based on the law of gravity, that is, candidate solutions attract each other in the search space based on their relative distances and ??masses?? (qualities). We show that, contrary to what is claimed, GSA does not take the distances between solutions into account, and therefore cannot be considered to be based on the law of gravity.     

Comment on ‘On sufficient conditions for the stability of interval matrices’

Some new sufficient conditions for the stability of interval matrices were given by Argoun (1986). These conditions, however, are incorrect.