Showing papers by "University of Newcastle published in 1968"

A simplified viewpoint of hyperstability

Abstract: The definition of a hyperstable system according to Popov is given a network theoretic interpretation, and proofs are presented outlining the connection between passive and hyperstable systems.

A generalization of the Popov criterion

Abstract: A criterion for the stability of control systems which contain an arbitrary finite number of memoryless nonlinearities is considered. The criterion is such that the degree of stability may be specified, and such that for the case when the absolute stability of a control system having one memoryless nonlinearity is considered, it reduces to the original Popov criterion.

The reliability of behavioural measures obtained in the open-field

Abstract: Seven open-field measures (defecation, urination, ambulation, washing, rearing, latency, and inner circle activity) were obtained using a number of different scoring methods for albino and hooded rats. The albino Ss were tested on 3 different occasions. The first test session was conducted when Ss were 90 days old, the second test session was held 63 days later and a third test session was conducted 154 days after the second. The hooded rats were subjected to 1 test session when Ss were 90 days old. The reliability of these measures was examined using test-retest and odd-even day correlations. The obtained results suggested that defecation, ambulation and rearing can be considered as providing reliable measures of behaviour in the open-field.

Impedance synthesis via state-space techniques

Abstract: The paper deals with the synthesis of passive networks and relies on general systems theory and control concepts. The network-synthesis problem is first interpreted in state-variable terminology, solved as a control problem and the solution is then translated back into network-theory terms. After a review of state-space formulations, an algebraic theory of synthesis is developed, beginning with a minimal state-space realisation, perhaps obtained through control-theory procedures, from which a synthesis of rational positive-real impedance matrices is obtained through a transformation on the state. The method rests upon an appropriate basis change, in the state-space, obtained by factoring the Pmatrix of the control-theory positive real lemma. The minimum number of resistors and reactive elements is used. The paper also serves as a review of the ‘state-of-the-art’ for formal nport synthesis; the results lead to new methods of attacking open problems, as well as to methods of analysis and synthesis via digital computers.

Extensions of quadratic minimization theory I. Finite time results

Abstract: Necessary and sufficient conditions are developed for the existence and calculation of well-defined Riccati differential equation solutions associated with quadratic loss minimization problems. Of particular interest is the fact that a. covariance condition is involved. The disclosure of this condition not only extends the range of optimal control problems for which a solution, guaranteed to be well defined, may be calculated, but also introduces an approach for establishing the existence of well-defined solutions in other problems involving covariance conditions, as for example, in a time-varying spectral factorization procedure. This paper is concerned with finite time results, whilo a companion paper considers tho infinite time case.

Nitrogenous chelate complexes of transition metals. V. Binuclear hydroxybridged copper(II) complexes of 1,10-phenanthroline and 2,2'-bipyridyl

Abstract: A series of compounds of the type OH [chelate Cu ' \Cu chelate]X,,nH20 \OH/ [where chelate = 1,lO-phenanthroline; X = 01 (n = 3), Br (n = 4), I (n = 2), NCS (n = 2), C10, (n = 1); 2X = SO, (n = 5), PtCl, (n = 4), and where chelate = 22'-bipyridyl; X = C1 (n = 3), Br (n = 4), I (n = 3), NCS (n = l), PF6 (n = 2), C10, (n = 1); 2X = SO4 (n = 5) and PtC1, (n = 3)] have been prepared and their properties investigated. In dilute aqueous solution the compounds are ionized forming the solvated [chelate Cu(OH,)Cu chelateI2+ species which exhibit similar visible absorption spectra (where chelate = p,h, ,eAn, = 630 mp and 6 = 97, and where chelate = b ,i,p,Ay, = 620 mp and E = 105). In nitrobenzene solution some of these compounds have been shown from electrical conductivity and spectrophotometric measurements to involve coordination of the anion to the copper(11) atoms. This effect has also been verified in the solid state by the measurement of diffuse reflectance spectra. The compounds all exhibit room temperature magnetic moments of the order of 2.0 B.&I. per copper atom. A study of the magnetic susceptibility of the sulphate [bipy Cu(OH),Cu bipy]S04,5H,0 over the temperature range 83-293'~ showed no antiferromagnetic interaction between pairs of hydroxy-bridged copper atoms, and the results obey a Curie-Weiss law (8 -13'~). The average value of the corrected moment is 1.91 B.M. per copper atom. A value for g of 2.20 was estimated from these data, and is in agreement with the average g value of 2.19 obtained from an e.s.r. measurement.

Nilpotent Subgroups of Finite Soluble Groups

Abstract: The general problem, with a particular instance of which the present paper is concerned, is to obtain a description of the local structure of a group from information about the global structure. The aspect of local structure investigated here is the embedding of subgroups, especially of nilpotent subgroups in finite soluble groups. A classification of embeddings of subgroups in finite groups by means of an arithmetic function called abnormal depth was proposed in [6]. Let H be a subgroup of a finite group G. Then a(G:H), the abnormal depth of H in G, is the least number of abnormal links appearing in any balanced chain of subgroups connecting H to G, that is a chain for which each link is either normal or abnormal. Thus a (G:H)= 0 if and only if H is subnormal in G; and a(G:P)__< 1 for every subgroup P of G of prime power order. It was shown in [6] that if H is a nilpotent subgroup of a finite soluble group G, of nilpotent length n, then a (G: H) =< n - 1. Here in w 1 we examine in greater detail the easiest non-trivial case, in which n = 2, and then in w 2 prove certain supplementary results for n = 3 and n = 4. Some simple wreath product properties are established in w 3 and used in w 4 for the construction of examples showing that the embedding results obtained cannot be improved in various obvious ways. Notation and terminology follow common usage. If t; and ~ are classes of groups, then 3s ~ denotes the class of all groups G having a normal subgroup X such that X e 3~ and G/X e ~. This defines a composition of classes of groups which in general is not associative. However, we shall deal only with classes of which the composition is associatNe, and we may therefore omit brackets from products of more than two classes. Since we shall be concerned exclusively with finite groups, we take 91 to denote the class of finite nilpotent groups and 9.1 the class of finite abelian groups. Then for any positive integer n, 9l" is the class of finite soluble groups of nilpotent lengths <__ n; and 9.I" is the class of finite soluble groups of derived lengths __< n. Henceforth the term group is understood to mean finite group. Then any group G has a unique smallest normal subgroup L such that G/L is nilpotent: G/L is called the 91-residual ofG. IfH is any subgroup of G, then there is a unique smallest normal subgroup of G containing H, called the normal closure of H in G and denoted by Ha; and a unique smallest subnormal subgroup of G containing H, called the subnormal closure of H in G and (following Wielandt [8]) denoted by H'" a. If H a = G, we shall say that H is contranormal in G. Then, for any subgroup H of G, it is clear that H is contranormal in H'" a. (This is to be compared with the fact that the hypernormalizer NE(H ) of H in G is self-normalizing in G.) An abnormal subgroup is both self-normalizing and

Simulation of stationary stochastic processes

Abstract: A ‘spectral-factorisation’ procedure involving the solution of a Riccati matrix differential equation is considered to determine systems which, with white-noise input signals, may be used in the simulation of stochastic processes having prescribed stationary covariances. More spe$itically, the specification of a system is made so that the covariance of the system output is a prescribed stationary covariance R(t – ~) for all t and -r greater than or equal to the ‘switch-on’ time of the system. The advantage of the ‘spectralfactorisation’ procedure described compared with those previously given is that, assuming an initial-state mean of zero, a suitable initial-state covariance is calculated as an intermediate result in the procedure. The calculation of an appropriate initial-state covariance is of interest since, if zero initial conditions are used in an attempted simulation, an undesirable time lapse may be necessary for the output covariance to be acceptable as a simulation of the prescribed stationary covariance. For the case when the system is given or is determined using alternative procedures to those described in the paper, the initial-state covariance is calculated from the solution of a linear matrix equation. The problem considered in the paper is the simulation of stationary stochastic processes with prescribed covariances using linear, finite-dimensional, time-invariant systems with white-noise input. Of particular interest is the selection of an initial-state covariance, so that the covariance of the outputs will be indistinguishable from that observed over the same time interval for the hypothetical limiting case as the initial time approaches – m. Systems which may be used in the simulation of stationary stochastic processes with prescribed covariances may be determined from any of a number of spectral-factorisation procedures, ] z,* With regard to the initial conditions, Cttrrent practice is to set these to zero and ignore the outputs for a period corresponding to a few time constants of the system. The inadequacy of this procedure has been recognised.3 In the paper two results are presented. The first is a method for selecting an initial-state covariance for a given system, so that the application of white noise at the input results in outputs that may be considered, after the switch-on, as sample functions of a stationary stochastic process; this is the best possible real-time simulation for a stationary stochastic process. All that is required in order to obtain the result is the solution of a linear matrix equation. The second result of the paper is a spectral factorisation of a specified covariance matrix using theorems from Anderson. t The procedure gives a system having a stable transferfunction matrix with a stable inverse (often required in certain optimisation problems), together with the initial-state covariance; the advantage of the particular approach presented is that all the information necessary for the simulation is given in one procedure. The key step in the procedure is the solution of a quadratic matrix equation which satisfies certain constraints. This solution, which is unique, may be found using algebraic means similar to those of Reference 4 or by determining the steadystate solution of a Riccati matrix differential equation. t The method avoids the need to carry out any of the procedures in References 1, 2 or *, which prove very complex in cases where the covariance is a matrix rather than scalar.

Pre-tectonic metamorphic crystallization in the Mt. Lofty Ranges, South Australia

Abstract: Evidence for the growth of andalusite and staurolite porphyroblasts prior to the first penetrative movements in the rocks of the Mt Lofty ranges is presented The implications of this unusual observation are discussed

Effects of Density Ratio on Sedimentary Similitude

Abstract: The question of whether or not significant similarity can be achieved in a movable bed model with a different value of density ratio from that in the prototype is examined. The equation of motion of a particle falling in a vertically oscillating column of fluid is made dimensionless by a linear scale which minimizes the effect of density ratio. It is shown that the average fall velocity of the particle in such circumstances is less than its terminal settling velocity in still fluid. By a combination of dimensional analysis and physical reasoning, scale ratios are derived which give better correlation for various density ratios in the particular case of the scour phenomenon considered than those suggested previously.

Expectancy waves and other complex cerebral events in dyslexic and normal subjects

Abstract: Slow cortical waves were studied in a small group of adult and child Ss. A peculiarity in the brain response under conditions, of uncertainty was noted. Cerebral responses of dyslexics to semantic stimuli differed from those of normal Ss. A reinterpretation of slow positive waves is suggested, and proposals are made for the study of complex brain responses under varying conditions of arousal and set, especially in relation to remedial programs for dyslexic children.

Development and Reproduction of Parathemisto Gracilipes (Norman) (Amphipoda, Hyperiidea) in the North Sea

Abstract: [Parathemisto gracilipes se reproduit dans la mer du Nord presque tout au long de l'annee, sauf pendant une periode creuse au milieu de l'hiver. L'espece est annuelle et presente deux centres de reproduction, l'un en ete, l'autre au printemps. Les reproducteurs du printemps sont deux fois plus longs que les reproducteurs de l'ete et se reproduisent pour la deuxieme et derniere fois. Leurs jeunes, s'unissant a une population de jeunes de l'ete precedent, se developpent pour former les reproducteurs de petite taille de l'ete. Ceux-ci a leur tour engendrent une generation de jeunes, qui passera l'hiver, tandis qu'eux-memes mueront avant de se developper pendant l'hiver et de former les reproducteurs de grande taille du printemps suivant. Les embryons, au nombre de neuf environ, sortent des lamelles incubatrices de la femelle quand ils atteignent 1 mm de longueur, alors qu'il y a trois segments a l'exopodite du premier pleopode. Apres avoir mue quatre ou cinq fois, ils atteignent leur premiere maturite a la taille de 3 mm environ., Parathemisto gracilipes se reproduit dans la mer du Nord presque tout au long de l'annee, sauf pendant une periode creuse au milieu de l'hiver. L'espece est annuelle et presente deux centres de reproduction, l'un en ete, l'autre au printemps. Les reproducteurs du printemps sont deux fois plus longs que les reproducteurs de l'ete et se reproduisent pour la deuxieme et derniere fois. Leurs jeunes, s'unissant a une population de jeunes de l'ete precedent, se developpent pour former les reproducteurs de petite taille de l'ete. Ceux-ci a leur tour engendrent une generation de jeunes, qui passera l'hiver, tandis qu'eux-memes mueront avant de se developper pendant l'hiver et de former les reproducteurs de grande taille du printemps suivant. Les embryons, au nombre de neuf environ, sortent des lamelles incubatrices de la femelle quand ils atteignent 1 mm de longueur, alors qu'il y a trois segments a l'exopodite du premier pleopode. Apres avoir mue quatre ou cinq fois, ils atteignent leur premiere maturite a la taille de 3 mm environ.]

Convergence properties of Riccati equation solutions

Abstract: Existence results are developed for Riccati equations. In particular, it is shown that the existence of one solution to a Riccati equation implies the existence of a whole family of solutions whose initial condition lies in a cone determined by the initial condition associated with the known solution.

Auditory vigilance: The effects of costs and values on signals

Abstract: The effects on signal detection performance of the value of correctly detecting a signal and the costs of a miss and false detection were examined for auditory vigilance behaviour. Results suggested that poorer detection performance was obtained with increased costs for misses and false detections, while the value placed on the correct detection of a signal had little effect. The d' statistic of signal detection theory was invariant with both signal costs and time, while β varied with both factors. These results were interpreted to mean that the performance decrement during the vigil was due to an increased strictness in the criterion (β) which the S used for deciding whether or not a signal was present. The cost factors were effective in manipulating performance during the watch by causing changes in the S's decision criteria. Findings from this study unanimously support those predicted by Swets et al's (1961) “Decision Theory” this is suggested as perhaps being the best available basis for a th...

The relationship between chemical constitution and antifungal activity in arylhydrazono-isoxazolone compounds.

Abstract: SUMMARY From a study of compounds related to the mildew fungicide, 4-o-chloro-phenylhydrazono-3-methyl-5-isoxazolone, it is apparent that high antifungal activity is associated with the arylhydrazonoisoxazolone structure. Differences in the relative effectiveness of o-chlorophenylhydrazono-, m-chlorophenyl-hydrazono- and phenylhydrazono- derivatives against Botrytis fabae on beans and Podosphaera leucotricha on apples may be due to different modes of action. Several possible mechanisms of action are discussed.

A circle criterion generalization for relative stability

Abstract: It is shown that the circle criterion for linear systems containing a single time-varying element corresponds to a specialization of the Popov stability theory. The circle criteria are generalized using the Popov theory to give some measure of the degree of the system stability.