Use of portable ladders – field observations and self-reported safety performance in the cable TV industry

Abstract

Portable ladders incidents remain a major cause of falls from heights. This study reported field observations of environments, work conditions and safety behaviour involving portable ladders and their correlations with self-reported safety performance. Seventy-five professional installers of a company in the cable and other pay TV industry were observed for 320 ladder usages at their worksites. The participants also filled out a questionnaire to measure self-reported safety performance. Proper setup on slippery surfaces, correct method for ladder inclination setup and ladder secured at the bottom had the lowest compliance with best practices and training guidelines. The observation compliance score was found to have significant correlation with straight ladder inclined angle (Pearson’s r = 0.23, p < 0.0002) and employees’ self-reported safety participation (r = 0.29, p < 0.01). The results provide a broad perspective on employees’ safety compliance and identify areas for improving safety behaviours.

Practitioner Summary: A checklist was used while observing professional installers of a cable company for portable ladder usage at their worksites. Items that had the lowest compliance with best practices and training guidelines were identified. The results provide a broad perspective on employees’ safety compliance and identify areas for improving safety behaviours.     

Unsafe acts and unsafe outcomes in aircraft maintenance

Road safety studies using the Driver Behaviour Questionnaire (DBQ) have provided support for a three-way distinction between violations, skill-based errors and mistakes, and have indicated that a tendency to commit driving violations is associated with an increased risk of accident involvement. The aims of this study were to examine whether the three-way distinction of unsafe acts is applicable in the context of aircraft maintenance, and whether involvement in maintenance safety occurrences can be predicted on the basis of self-reported unsafe acts. A Maintenance Behaviour Questionnaire (MBQ) was developed to explore patterns of unsafe acts committed by aircraft maintenance mechanics. The MBQ was completed anonymously by over 1300 Australian aviation mechanics, who also provided information on their involvement in workplace accidents and incidents. Four factors were identified: routine violations, skill-based errors, mistakes and exceptional violations. Violations and mistakes were related significantly to the occurrence of incidents that jeopardized the quality of aircraft maintenance, but were not related to workplace injuries. Skill-based errors, while not related to work quality incidents, were related to workplace injuries. The results are consistent with the three-way typology of unsafe acts described by Reason et al. (1990) and with the DBQ research indicating an association between self-reported violations and accidents. The current findings suggest that interventions addressed at maintenance quality incidents should take into account the role of violations and mistakes, and the factors that promote them. In contrast, interventions directed at reducing workplace injury are likely to require a focus on skill-based errors.     

Unsafe acts and unsafe outcomes in aircraft maintenance

Road safety studies using the Driver Behaviour Questionnaire (DBQ) have provided support for a three-way distinction between violations, skill-based errors and mistakes, and have indicated that a tendency to commit driving violations is associated with an increased risk of accident involvement. The aims of this study were to examine whether the three-way distinction of unsafe acts is applicable in the context of aircraft maintenance, and whether involvement in maintenance safety occurrences can be predicted on the basis of self-reported unsafe acts. A Maintenance Behaviour Questionnaire (MBQ) was developed to explore patterns of unsafe acts committed by aircraft maintenance mechanics. The MBQ was completed anonymously by over 1300 Australian aviation mechanics, who also provided information on their involvement in workplace accidents and incidents. Four factors were identified: routine violations, skill-based errors, mistakes and exceptional violations. Violations and mistakes were related significantly to the occurrence of incidents that jeopardized the quality of aircraft maintenance, but were not related to workplace injuries. Skill-based errors, while not related to work quality incidents, were related to workplace injuries. The results are consistent with the three-way typology of unsafe acts described by Reason et al. (1990) and with the DBQ research indicating an association between self-reported violations and accidents. The current findings suggest that interventions addressed at maintenance quality incidents should take into account the role of violations and mistakes, and the factors that promote them. In contrast, interventions directed at reducing workplace injury are likely to require a focus on skill-based errors.     

Errors and violations on the roads: a real distinction?

In considering the human contribution to accidents, it seems necessary to make a distinction between errors and violations; two forms of aberration which may have different psychological origins and demand different modes of remediation. The present study investigated whether this distinction was justified for self-reported driver behaviour. Five hundred and twenty drivers completed a driver behaviour questionnaire (DBQ) which asked them to judge the frequency with which they committed various types of errors and violations when driving. Three fairly robust factors were identified: violations, dangerous errors, and relatively harmless lapses, respectively. Violations declined with age, errors did not. Men of all ages reported more violations than women. Women, however, were significantly more prone to harmless lapses (or more honest) than men. These findings were consistent with the view that errors and violations are indeed mediated by different psychological mechanisms. Violations require explanation in terms of social and motivational factors, whereas errors (slips, lapses, and mistakes) may be accounted for by reference to the information-processing characteristics of the individual.     

Increasing surfboard volume reduces energy expenditure during paddling

Abstract

The purpose of this study was to investigate how altering surfboard volume (BV) affects energy expenditure during paddling. Twenty surfers paddled in a swim flume on five surfboards in random order twice. All surfboards varied only in thickness and ranged in BV from 28.4 to 37.4 L. Measurements of heart rate (HR), oxygen consumption (VO₂), pitch angle, roll angle and paddling cadence were measured. VO₂ and HR significantly decreased on thicker boards [VO₂: r = ?0.984, p = 0.003; HR: r = ?0.972, p = 0.006]. There was also a significant decrease in pitch and roll angles on thicker boards [Pitch: r = ?0.995, p < 0.001; Roll: r = ?0.911, p = 0.031]. Results from this study suggest that increasing BV reduces the metabolic cost of paddling as a result of lower pitch and roll angles, thus providing mechanical evidence for increased paddling efficiency on surfboards with more volume.

Practioner Summary: This study investigated the impact of surfboard volume on energy expenditure during paddling. Results from this study suggest that increasing surfboard volume reduces the metabolic cost of paddling as a result of lower pitch and roll angles, thus providing mechanical evidence for increased paddling efficiency on surfboards with more volume.     

Multidirectional manual arm strength and its relationship with resultant shoulder moment and arm posture

Previous work has quantified manual force capabilities for ergonomics design, but the number of studies and range of conditions tested are limited in scope. Therefore, the aims of this study were to collect seated manual arm strength (MAS) data from 24 females in several unique exertion directions (n = 26) and hand locations relative to the shoulder (n = 8), and to investigate the associations between MAS and shoulder/elbow moments. MAS was generally highest when the direction of force application was oriented parallel to the vector from the shoulder to knuckle, and weakest when oriented orthogonal to that vector. Moderate correlations were found between MAS and: (1) resultant shoulder moment (r = 0.34), (2) resultant moment arms (r = ?0.545) and (3) elbow flexion/extension moment (r = 0.481). Our strength data will be used in the development of a comprehensive MAS predictive method, so that strength capabilities can be predicted to help design acceptable tasks in the workplace.

Practitioner Summary: This study sought to enhance our understanding of one-handed manual arm strength capabilities for ergonomics task evaluations. Our findings provide researchers and practitioners with manual strength data for off-axis force directions, as well as hand locations not previously measured. These data will contribute to future methods for predicting strength capabilities.     

Aberrant driving behaviour: errors and violations

The present study was a replication of the research of Reason et al. (1990). Its aim was to confirm the distinction between driving errors and violations in a Western Australian driving population. Sixty-one male drivers and 74 female drivers completed a questionnaire containing items on driver demographics, driving penalties incurred, driving convictions and accident history and driver behavioural aberrations drawn from the Driver Behaviour Questionnaire (DBQ). In agreement with Reason et al. factor analysis revealed three factors; in the present study these were general errors, dangerous errors, and dangerous violations. Young drivers committed more dangerous errors and dangerous violations than older drivers. Females reported more dangerous errors than males. Males reported more dangerous violations than females. Drivers who reported a high level of road exposure and those who reported having been convicted for speeding reported more dangerous violations. Differences in the results of the two studies can largely by accounted for by differences in the representation of age and gender in the two populations studied.     

Using Neural Networks to predict HFACS unsafe acts from the pre-conditions of unsafe acts

Abstract

Human Factors Analysis and Classification System (HFACS) is based upon Reason’s organizational model of human error which suggests that there is a ‘one to many’ mapping of condition tokens (HFACS level 2 psychological precursors) to unsafe act tokens (HFACS level 1 error and violations). Using accident data derived from 523 military aircraft accidents, the relationship between HFACS level 2 preconditions and level 1 unsafe acts was modelled using an artificial neural network (NN). This allowed an empirical model to be developed congruent with the underlying theory of HFACS. The NN solution produced an average overall classification rate of ca. 74% for all unsafe acts from information derived from their level 2 preconditions. However, the correct classification rate was superior for decision- and skill-based errors, than for perceptual errors and violations.

Practitioner Summary: A model to predict unsafe acts (HFACS level 1) from their preconditions (HFACS level 2) was developed from the analysis of 523 military aircraft accidents using an artificial NN. The results could correctly predict approximately 74% of errors.     

Comparison of measured and self-reported anthropometric information among firefighters: implications and applications

This study evaluated the accuracy of self-reported body weight and height compared to measured values among firefighters and identified factors associated with reporting error. A total of 863 male and 88 female firefighters in four US regions participated in the study. The results showed that both men and women underestimated their body weight ( ? 0.4 ± 4.1, ? 1.1 ± 3.6 kg) and overestimated their height (29 ± 18 , 17 ± 16 mm). Women underestimated more than men on weight (p = 0.022) and men overestimated more than women on height (p < 0.001). Reporting errors on weight were increased with overweight status (p < 0.001) and were disproportionate among subgroups. About 27% men and 24% women had reporting errors on weight greater than ± 2.2 kg, and 59% men and 28% women had reporting errors on height greater than 25 mm.

Practitioner Summary: This study along with literature revealed that the self-reported approach is not a sustainable option for anthropometric surveys, even for gathering data from physically active professional groups, such as firefighters, who presumably are knowledgeable of their body dimensions. Self-reported anthropometric information is undependable in important population subgroups.     

Evaluating multiple colour-producing agents in Case II waters from Lake Erie

Lake Erie is part of the Great Lakes systems in North America, which represent the largest continental lake systems in the world. Anthropogenic eutrophication in the Western Basin of Lake Erie, a Case II environment, has an adverse impact on the surrounding ecosystems and the regional economy. The optical complexity found in Lake Erie is a feature of many aquatic environments making it a challenging setting for remote-sensing applications. To assess the controls on these optical properties, we sampled 20 locations, encompassing a variety of optical environments in the Western Basin and Sandusky Bay during four research cruises. Strong correlations between light extinction and phycocyanin (correlation coefficient, r ≥ 0.95), suspended sediment (r = 0.90), and chlorophyll-a (r ≥ 0.86) indicate that surface conditions are representative down to at least the first optical depth. Application of varimax-rotated principal component analysis to lab-based, hyperspectral reflectance data identified three components related to a diatom/green algae community, and two blue-green algae communities, one of which was associated with suspended sediment. Phycocyanin and chlorophyll-a content inferred using a semi-analytic red/near-infrared algorithm correlated well with concentrations measured in situ using a multiparameter sonde. Chlorophyll-a retrievals from a regional, blue : green algorithm developed for the Western Basin of Lake Erie compared well with retrievals from the semi-analytic algorithm for all samples from the Western Basin and 25% of samples from Sandusky Bay. Chlorophyll-a retrieval errors using the blue : green algorithm occurred when high ratios of suspended sediment to phycocyanin biased samples from the extremely turbid waters of Sandusky Bay. The bias likely resulted when suspended sediment altered the blue : green ratio or when phycocyanin interfered with the chlorophyll-a absorption peaks. This approach can be applied to other Case II environments to provide insights during the design of experimental field studies and for spectral band selection with the next generation of visible near-infrared remote-sensing instruments.     

Statistical model development and estimation of suspended particulate matter concentrations with Landsat 8 OLI images of Dongting Lake,China

Suspended particulate matter (SPM) is a dominant water constituent of case-II waters, and SPM concentration (C_SPM) is a key parameter describing water quality. This study, using Landsat 8 Operational Land Imager (OLI) images, aimed to develop the C_SPM retrieval models and further to estimate the C_SPM values of Dongting Lake. One Landsat 8 OLI image and 53 C_SPM measurements were employed to calibrate Landsat 8-based C_SPM retrieval models. The C_SPM values derived from coincident Landsat 8 OLI and Moderate Resolution Imaging Spectroradiometer (MODIS) images were compared to validate calibrated Landsat 8-based C_SPM models. After the best stable Landsat 8-based C_SPM retrieval model was further validated using an independent Landsat 8 OLI image and its coincident C_SPM measurements, it was applied to four Landsat 8 OLI images to retrieve the C_SPM values in the South and East Dongting Lake. Model calibration results showed that two exponential models of the red band explained 61% (estimated standard error (SE) = 7.96 mg l^–1) and 67% (SE = 6.79 mg l^–1) of the variation of C_SPM; two exponential models of the red:panchromatic band ratio obtained 81% (SE = 5.48 mg l^–1) and 77% (SE = 4.96 mg l^–1) fitting accuracy; and four exponential and quadratic models of the infrared band explained 72–83% of the variation of C_SPM (SE = 5.18–5.52 mg l^–1). By comparing the MODIS- and Landsat 8-based C_SPM values, an exponential model of the Landsat 8 OLI red band (C_SPM = 1.1034 × exp(23.61 × R)) obtained the best consistent C_SPM estimations with the MODIS-based model (r = 0.98, p < 0.01), and its further validation result using an independent Landsat 8 OLI image showed a significantly strong correlation between the measured and estimated C_SPM values at a significance level of 0.05 (r = 0.91, p < 0.05). The C_SPM spatiotemporal distribution derived from four Landsat 8 images revealed a clear spatial distribution pattern of C_SPM in the South and East Dongting Lake, which was caused by natural and anthropogenic factors together. This study confirmed the potential of Landsat 8 OLI images in retrieving C_SPM and provided a foundation for retrieving the spatial distribution of C_SPM accurately from this new data source in Dongting Lake.     

Relationship between trapezius muscle activity and typing speed: taping effect

Clinically, over-activation of upper trapezius (UT) muscular activity is a common cause of symptoms in computer users. The purpose of this study was to investigate the correlation between trapezius muscular activity and typing speed with and without taping. Twelve participants performed a typing task for 15 min with and without taping on the UT muscle. Electromyography (EMG) of the muscular activity of UT and lower trapezius (LT) was recorded. With or without taping, there was a significantly positive correlation (r = 0.40, p = 0.04) between typing speed and UT/LT. Additionally, UT and UT/LT ratios were lower with taping than without taping (difference = 5.2% and 26.9%). The LT ratio was higher with taping than without taping (difference = 5.8%). Taping can alter the muscular activity of the trapezius during typing and may have the potential to be applied in computer users to prevent over-activation of UT muscular activity.

Practitioner Summary: The effect of taping was tested on typing speed and trapezius muscular activity. With or without taping, typing speed was correlated with trapezius activity. The muscle activity of the trapezius, however, was lower with taping than without taping. Thus, taping has the potential to prevent over-activation of UT muscular activity during typing.     

Associations between cycling skill,general motor competence and body mass index in 9-year-old children

Learning to ride a bicycle is an important milestone in a child's life. Unfortunately, young traffic casualties remain overrepresented in traffic reports, with single-bicycle crashes as principal cause in children. This correlational, cross-sectional study focuses on the association between cycling skills and two intrinsic characteristics: general motor competence and body mass index (BMI). Therefore, general motor competence, BMI and practical cycling competence were measured in 9-year-old children (n = 40). Significant correlations were found between cycling skills and general motor competence (r = 0.434, p ≤ 0.01), and between cycling skills and BMI (r = ? 0.400, p ≤ 0.05). A multiple regression analysis revealed that children's general motor quotient and BMI together predicted 19% of cycling skill score. These findings indicate that general motor competence and bicycle skills are not independent of each other stressing the importance of young children's characteristics when actively participating in traffic. In addition, BMI might be negatively associated with the development of cycling skills in children.     

Interpersonal violations,speeding violations and their relation to accident involvement in Finland

The aim of the present study was to replicate the distinction between errors, lapses and violations, and to identify aggressive violations from normal or highway code violations. Furthermore, the relationship of these behaviours with road traffic accidents was examined. A total number of 1126 Finnish drivers completed a questionnaire containing the Driver Behaviour Questionnaire (DBQ) with extended violations scale, and questions regarding background information, such as age, gender and mileage. Also, questions about previous accidents and fines were asked. Factor analysis showed that a four-factor structure seemed more appropriate than the earlier established three-factor structure. The four factors were errors, lapses, speeding violations and interpersonal violations. The two types of violations result from different motives, and seem to be associated with different kinds of affect. Both interpersonal and speeding violations were reported most by young males, which was consistent with earlier findings. Logistic regression analyses indicated that errors predicted active accident involvement after partialling out the effects of demographic variables, whereas interpersonal violations were positively related to involvement in passive accidents. This was presumably due to different reporting tendencies of respondents. Speeding tickets were predicted by speeding and interpersonal violations and lapses and penalties for speeding by both kinds of violations and errors. Penalties for speeding, parking and other offences were predicted by interpersonal violations. The implications of these results are discussed.     

Interpersonal violations,speeding violations and their relation to accident involvement in Finland

The aim of the present study was to replicate the distinction between errors, lapses and violations, and to identify aggressive violations from normal or highway code violations. Furthermore, the relationship of these behaviours with road traffic accidents was examined. A total number of 1126 Finnish drivers completed a questionnaire containing the Driver Behaviour Questionnaire (DBQ) with extended violations scale, and questions regarding background information, such as age, gender and mileage. Also, questions about previous accidents and fines were asked. Factor analysis showed that a four-factor structure seemed more appropriate than the earlier established three-factor structure. The four factors were errors, lapses, speeding violations and interpersonal violations. The two types of violations result from different motives, and seem to be associated with different kinds of affect. Both interpersonal and speeding violations were reported most by young males, which was consistent with earlier findings. Logistic regression analyses indicated that errors predicted active accident involvement after partialling out the effects of demographic variables, whereas interpersonal violations were positively related to involvement in passive accidents. This was presumably due to different reporting tendencies of respondents. Speeding tickets were predicted by speeding and interpersonal violations and lapses and penalties for speeding by both kinds of violations and errors. Penalties for speeding, parking and other offences were predicted by interpersonal violations. The implications of these results are discussed.     

Estimating fractional cover of plant functional types in African savannah from harmonic analysis of MODIS time-series data

Assessments of tree/grass fractional cover in savannahs using remote sensing are challenging due to the heterogeneous mixture of the two plant functional types. Time-series decomposition models can be used to characterize vegetation phenology from satellite data, but have rarely been used for attributing phenological signal components to different plant functional types. Here, tree/grass dynamics are assessed in savannah ecosystems using time-series decomposition of 14 years of Moderate Resolution Imaging Spectroradiometer (MODIS) normalized difference vegetation index data acquired from 2002 to 2015. The decomposition method uses harmonic analysis and tests the individual harmonic terms for statistical significance. Field data of fractional cover of trees and grasses were collected for 28 plots in Kruger National Park, South Africa. Matching MODIS pixels were analysed for their tree/grass phenological signals. Tree/grass annual and interannual variability were then assessed based on the harmonic models. In most harmonic cycles, grass-dominated sites had higher amplitudes than tree-dominated sites, while the tree green-up started earlier than grasses, before the start of the wet season. While changes in tree phenology are gradual, grasses present higher variability over time. Tree cover showed a significant correlation with the amplitude (r (correlation coefficient) = ?0.59, p = 0.001) and phase of the first harmonic term (r = ?0.73, p = 0.0001) and the number of cycles of the second harmonic term (r = 0. 56, p = 0.002). Grass cover was also significantly correlated with the amplitude (r = 0. 51, p = 0.005) and phase of the first harmonic term (r = 0.55, p = 0.002) and the number of cycles of the second harmonic term (r = ?0.52, p = 0.005). The positive correlation of grass cover with phase and negative correlation with number of cycles is indicating a late greening period and higher variability, respectively. Tree cover estimated from the phase of the strongest harmonic term showed a positive correlation with field-measured tree cover (R² (coefficient of determination) = 0.55, p < 0.01, slope = 0.93, root mean square error = 13.26%). The estimated tree cover also had a strong correlation with the woody cover map (r = 0.78, p < 0.01) produced by Bucini. The results show that MODIS time-series data can be used to estimate the fractional tree cover in heterogeneous savannahs from the phase of the plant functional type’s phenological behaviour. This study shows that harmonic analysis is able to discriminate between fractional cover by trees and grasses in savannahs. The quantitative analysis of tree/grass phenology from satellite time-series data enables a better understanding of the dynamics of the tree/grass competition and coexistence.     

Investigating the effect of real-time spinal postural biofeedback on seated discomfort in people with non-specific chronic low back pain

A total of 24 participants with non-specific chronic low back pain (NSCLBP) sat for 2 h while their seated posture and low back discomfort (LBD) were analysed. A total of 16 pain developers (PDs), whose LBD increased by at least two points on the numeric rating scale, repeated the procedure 1 week later, while receiving postural biofeedback. PDs were older (p = 0.018), more disabled (p = 0.021) and demonstrated greater postural variability (p < 0.001). The ramping up of LBD was reduced (p = 0.002) on retesting, when sitting posture was less end-range (p < 0.001), and less variable (p = 0.032). Seated LBD appears to be related with modifiable characteristics such as sitting behaviour. Among people with sitting-related NSCLBP, the ramping up of LBD was reduced by modifying their sitting behaviour according to their individual clinical presentation. The magnitude of change, while statistically significant, was small and no follow-up of participants was completed. Further research should examine integrating biofeedback into comprehensive biopsychosocial management strategies for NSCLBP.

Practitioner Summary: The effect of real-time postural biofeedback on LBD was examined among people with LBP. Postural biofeedback matched to the individual clinical presentation significantly reduced LBD within a single session. Further research should examine the long-term effectiveness of postural biofeedback as an intervention for LBP.     

Rapid determination of soil organic matter content based on soil colour obtained by a digital camera

ABSTRACT

Soil organic matter (SOM) is an important component of soil and a significant criterion in determining the dynamics of soil quality. A rapid, low-cost method to measure SOM content is needed to support the development of precision agriculture. This article studied the quantitative relationship between SOM and soil colour using a digital camera, which is relatively inexpensive and easy to operate, as a portable tool for obtaining colour information of the soil surface. The results show that mixed samples with different soil particle sizes reduce the noise of the image and are more suitable than uniform soil samples for predicting the SOM. Among the three bands of red, green, and blue (RGB), the red band had the best correlation with SOM, and its reciprocal correlation coefficient (r) reached 0.75. The reciprocal regression model of the RGB colour model provided good prediction results for mixed soil samples, with a coefficient of determination (R²) of 0.76 and a root mean square error (RMSE) of 0.55, and the validation result had an excellent predictive ability (R²_val = 0.85 and RMSE_val = 0.53). The single-variation predictive model of CIELa*b* colour space model through transformation of the RGB colour space model performed well. The model built by colour intensity values had a strong stability and forecasting capacity. Thus, a digital camera can be used as an alternative tool to rapidly measure SOM.     

Evaluation of linear spectral unmixing and ΔNBR for predicting post‐fire recovery in a North American ponderosa pine forest

The Differenced Normalized Burn Ratio (ΔNBR) is widely used to map post‐fire effects in North America from multispectral satellite imagery, but has not been rigorously validated across the great diversity in vegetation types. The importance of these maps to fire rehabilitation crews highlights the need for continued assessment of alternative remote sensing approaches. To meet this need, this study presents a first preliminary comparison of immediate post‐fire char (black ash) fraction, as measured by linear spectral unmixing, and ΔNBR, with two quantitative one‐year post‐fire field measures indicative of canopy and sub‐canopy conditions: % live tree and dry organic litter weight (gm^?2). Image analysis was applied to Landsat 7 Enhanced Thematic Mapper (ETM+) imagery acquired both before and immediately following the 2000 Jasper Fire, South Dakota. Post‐fire field analysis was conducted one‐year post‐fire. Although the immediate post‐fire char fraction (r ² = 0.56, SE = 28.03) and ΔNBR (r ² = 0.55, SE = 29.69) measures produced similarly good predictions of the % live tree, the standard error in the prediction of litter weight with the char fraction method (r ² = 0.55, SE = 4.78) was considerably lower than with ΔNBR (r ² = 0.52, SE = 8.01). Although further research is clearly warranted to evaluate more field measures, in more fires, and across more fire regimes, the char fraction may be a viable approach to predict longer‐term indicators of ecosystem recovery and may potentially act as a surrogate retrospective measure of the fire intensity.     

Optimum Control of a Certain Class of Servomechanism†

Linear control systems governed by the vector matrix differential equation x = A x + B u have been considered. It has been shown how to find the optimum control u so that the system, starting from an initial position x(0), is steered to a state specifying the first p coordinates of the system in time t _o fixed in advance, the values attained by the (n—p) coordinates being immaterial, where n is the dimension of the system. The optimization considered here is with regard to the norm of u supposed to belong to L _m E _r space.