A 2.5n lower bound on the monotone network complexity of T 3 n

Summary The k-th threshold function, T _k ⁿ , is defined as: where x _i{0,1} and the summation is arithmetic. We prove that any monotone network computing T _3/n(x ₁,...,x _n) contains at least 2.5n-5.5 gates.This research was supported by the Science and Engineering Research Council of Great Britain, UK     

Determinants of off-road vehicle transmission 'shift quality'

This study was conducted to determine the relationship between factors associated with a tractor transmission shift and the tractor operator's judgement of the quality of the shift. The specific objective was to measure experienced tractor operators' ratings of shift 'acceptability' as peak acceleration, peak jerk and direction of initial acceleration were varied at two levels of background vibration. A six-degree-of-freedom vehicle motion simulator in the Deere & Company Technical Center's human factors laboratory was used to simulate the background vibration and to control the experimental variables. The key results are: (1) The most important factor influencing 'shift quality' is the peak acceleration experienced during the shift. (2) Background vehicle vibration experienced by the tractor operator affects his perception of 'shift quality'. Higher background vibration masks the acceleration experienced during a shift and makes the shift more acceptable than when experienced at a low level of background vibration. (3) Peak jerk experienced during a shift has a negligible effect on 'shift quality'. (4) Upshifts and downshifts of the same peak acceleration, peak jerk, and background vibration receive the same general rating of 'shift quality'.     

Lever controls on specialised farm equipment: some control/response stereotypes

Linearly arranged banks of hydraulic control levers constitute common control layouts on many specialized pieces of equipment used in agriculture, especially in California. Such controls are used to control multi-function equipment with various types of articulating mechanisms performing both linear and rotary translations in order to effect pitch, roll and yaw movements; also other movements such as clamping and encircling. Stereotypes regarding the control of the motion of a cube with six degrees of freedom by a single control lever were assessed. Results generally were consistent with previous work except for the case of the up/down motion of the cube for which a strongly anomalous phenomenon was found. Stereotypes for the assignment of cube motions to sets of multiple control levers were found to be weak or non-existent.     

Silicon carbide filaments: Microstructure

The microstructure of chemically vapour deposited silicon carbide filaments has been examined using transmission electron microscopy. The filament bulk consisted of heavily faulted columnar subgrains of-SiC which were preferentially oriented such that {1 1 1} planes were parallel to the surface of the carbon fibre substrate. The protective coating on the filament surface was characterized by several microstructurally distinct layers, all of which consisted primarily of carbon. The first layers of the coating contained small crystallites of SiC in addition to turbostratic carbon, while the outer layers showed no evidence of SiC. Implications of the filament microstructure with respect to mechanical properties are discussed.     

True stabilization: the behaviour of lead compounds against the thermal decomposition of polyvinyl chloride

Investigations which have been conducted within the last two decades into the behaviour of basic lead compounds as stabilizers against the thermal dehydrochlorination of polyvinyl chloride are summarized. It is shown that the results can be explained satisfactorily in terms of a free radical dehydrochlorination mechanism and a regenerative exchange process which interferes with the dehydrochlorination. This may be regarded as true stabilization in contrast to hydrogen chloride scavenging. In true stabilization it is proposed that aliphatic carboxylate groups (such as the stearate ion) react with reservoirs of basic lead compounds (such as white lead) to form relatively mobile salts (such as stearates of lead). Also, it is proposed that these salts take part in exchange reactions with chlorine atoms released by the PVC during free radical decomposition, to give innocuous chlorides of lead and the corresponding aliphatic carboxylate free radicals. Hence the chlorine atoms are trapped and no longer able to propagate dehydrochlorination of the polymer. Further, it is proposed that the aliphatic carboxylate free radicals can esterify PVC chains at sites where prior attack by chlorine atoms has abstracted methylenic hydrogen atoms leaving unpaired electrons. This step eliminates the stimulus for loss of chlorine atoms from the PVC, thereby also interfering with the free radical propagation mechanism. Subsequently, the pendant aliphatic carboxylate groups dissociate from the polymer chains with neighbouring chloromethylenic hydrogen atoms to form the corresponding acids, and leaving the chlorine atoms adjacent to carbon-carbon double bonds in relatively stable vinyl-type positions. The aliphatic carboxylic acids so formed can react with the basic lead compounds reservoir to regenerate mobile salts so that the stabilizing process is therefore continuous and cyclic. It is demonstrated that ionic and unimolecular mechanisms which normally are put forward to explain the behaviour of primary stabilizers in PVC are not satisfactory because they do not account for all observations made with basic lead stabilizing regimes. Other evidence which favours the free radical decomposition and stabilization mechanisms is cited, and a suggestion is made for further work.     

A boundary element method for two dimensional linear elastic fracture analysis

A boundary element method is developed for the analysis of fractures in two-dimensional solids. The solids are assumed to be linearly elastic and isotropic, and both bounded and unbounded domains are treated. The development of the boundary integral equations exploits (as usual) Somigliana's identity, but a special manipulation is carried out to regularize certain integrals associated with the crack line. The resulting integral equations consist of the conventional ordinary boundary terms and two additional terms which can be identified as a distribution of concentrated forces and a distribution of dislocations along each crack line. The strategy for establishing the integral equations is first outlined in terms of real variables, after which complex variable techniques are adopted for the detailed development. In the numerical implementation of the formulation, the ordinary boundary integrals are treated with standard boundary element techniques, while a novel numerical procedure is developed to treat the crack line integrals. The resulting numerical procedure is used to solve several sample problems for both embedded and surface-breaking cracks, and it is shown that the technique is both accurate and efficient. The utility of the method for simulating curvilinear crack propagation is also demonstrated.