Width Rule Research Articles

Electroweak symmetry breaking by gravity

We consider a simple scale-invariant action coupling the Higgs field to the metric scalar curvature R and containing an R2 term that exhibits spontaneous breaking of scale invariance and electroweak symmetry. The coefficient of the R2 term in this case determines the self-coupling of the Higgs boson in the Einstein frame, and the scalaron becomes a dilaton weakly coupled to the Higgs boson. Majorana mass terms for right-handed neutrinos can be generated in a scale-invariant manner by using the Higgs-field invariant; in this case, the existing experimental limits on the Higgs-boson total width rule out Majorana mass values in a certain range. The model inherits the naturalness issues of general relativity connected with the smallness of the gravitational and cosmological constants.

The Application of Hyperspectral Imaging to the Measurement of Pressure Injury Area.

Wound size measurement is an important indicator of wound healing. Nurses measure wound size in terms of length × width in wound healing assessment, but it is easy to overestimate the extent of the wound due to irregularities around it. Using hyperspectral imaging (HIS) to measure the area of a pressure injury could provide more accurate data than manual measurement, ensure that the same tool is used for standardized assessment of wounds, and reduce the measurement time. This study was a pilot cross-sectional study, and a total of 30 patients with coccyx sacral pressure injuries were recruited to the rehabilitation ward after approval by the human subjects research committee. We used hyperspectral images to collect pressure injury images and machine learning (k-means) to automatically classify wound areas in combination with the length × width rule (LW rule) and image morphology algorithm for wound judgment and area calculation. The results calculated from the data were compared with the calculations made by the nursing staff using the length × width rule. The use of hyperspectral images, machine learning, the length × width rule (LW rule), and an image morphology algorithm to calculate the wound area yielded more accurate measurements than did nurses, effectively reduced the chance of human error, reduced the measurement time, and produced real-time data. HIS can be used by nursing staff to assess wounds with a standardized approach so as to ensure that proper wound care can be provided.

Magnetic Susceptibility Mapping of Rocks and Depth Estimation of Anomalies: A Case Study of Igarra and Its Environs

Magnetic Susceptibility Mapping and Depth Estimation of Anomalies were carried out on Igarra and its environs, Southwest Nigeria. This was to assist in mineral exploration in the area. The study area is located within the Igarra schist belt which is underlain by rocks of Precambrian basement complex. The Total Magnetic Field over the study area was obtained by digitizing the aeromagnetic map of Auchi (Sheet 226) acquired from the Nigerian Geologic Survey Agency (NGSA). A total of 19 (nineteen) magnetic anomalies were identified on the map; 5 magnetic highs and 14 lows. 8 anomalies have a NW-SE strike direction, 4 in the NE-SW and 7 in the E-W direction. The amplitude of the anomalies and strength of the total field were used to determine the susceptibility values for each of the anomalies. The Susceptibility values were used to generate a Magnetic Susceptibility map of the study area on SURFER 13 software. TMI plots on the anomalies were carried out on MICROSOFT EXCEL 2010. Depth estimates of the anomalies were got using three methods: The Half Width rule, Hannel rule and Tirburg rule. The Susceptibility map shows a noticeable pattern of increase in magnetic minerals from the Southwestern to the Northeastern part of the map. The Depth of the basement anomalies were relatively shallow ranging from 0.8 km to 2.6 km. The results of this work provide a preliminary guide to those that engage in mineral exploration / exploitation in the area.

Effective Width Rule in the Analysis of Footing on Reinforced Sand Slope

Abstract This paper presents the results obtained from an experimental programme and numerical investigations conducted on model tests of strip footing resting on reinforced and unreinforced sand slopes. The study focused on the determination of ultimate bearing capacity of strip footing subjected to eccentric load located either towards or opposite to the slope facing. Strip footing models were tested under different eccentricities of vertical load. The obtained results from tests conducted on unreinforced sand slope showed that the increase in eccentricity of applied load towards the slope facing decreases the ultimate bearing capacity of footing. Predictions of the ultimate bearing capacity obtained by the effective width rule are in good agreement with those proposed from the consideration of total width of footing subjected to eccentric load. The ultimate bearing capacity of an eccentrically loaded footing on a reinforced sand slope can be derived from that of axially loaded footing resting on horizontal sand ground when adopting the effective width rule and the coefficient of reduction due to the slope. When increasing the distance between the footing border to the slope crest, for unreinforced and reinforced ground slope by geogrids, the ultimate bearing capacity of footing is no more affected by the slope ground.

Effect of Load Eccentricity on the Bearing Capacity of Strip Footings on Non-homogenous Clay Overlying Bedrock

In underwater infrastructure design, foundations are embedded in soft clay seabeds that exhibited non-homogeneity of cohesion, and subjected to combined actions of vertical, inclined or eccentric loads due to the environmental conditions such as self-weight, wind and wave forces acting on substructure. This paper investigates the undrained bearing capacity for surface and embedded strip footings on non-homogenous clay overlying bedrock. Elasto-plastic finite element analyses are carried out for perfectly rough strip footings on Tresca soil under vertical eccentric loads. Meyerhof’s effective width rule is examined for the cases of surface and embedded footings in non-homogeneous clay. The effect of load eccentricity on the distribution of the normal stresses under strip footings is also investigated in this study. It is found that the effective width rule provides a conservative estimate of the bearing capacity. The elasto-plastic calculations predict that tensile stresses occur for surface footings because of the full bonding at the soil-footing interfaces, while for embedded footings, there is no tensile stresses.

Axial-vector dominance predictions in quasielastic neutrino-nucleus scattering

The axial form factor plays a crucial role in quasielastic neutrino-nucleus scattering, but the error of the theoretical cross section due to uncertainties of $G_A$ remains to be established. Reversely, the extraction of $G_A$ from the neutrino nucleus cross section suffers from large systematic errors due to nuclear model dependencies, while the use of single parameter dipole fits underestimates the errors and prevents an identification of the relevant kinematics for this determination. We propose to use a generalized axial-vector-meson-dominance (AVMD) in conjunction with large-$N_c$ and high energy QCD constrains to model the nucleon axial form factor, as well as the half width rule as an a priori uncertainty estimate. The minimal hadronic ansatz comprises the sum of two monopoles corresponding to the lightest axial-vector mesons being coupled to the axial current. The parameters of the resulting axial form factor are the masses and widths of the two axial mesons as obtained from the averaged PDG values. By applying the half width rule in a Monte Carlo simulation, a distribution of theoretical predictions can then be generated for the neutrino-nucleus quasielastic cross section. We test the model by applying it to the $(\nu_\mu,\mu)$ quasielastic cross section from $^{12}$C for the kinematics of the MiniBooNE experiment. The resulting predictions have no free parameters. We find that the relativistic Fermi gas model globally reproduces the experimental data, giving $\chi^2/ \# bins = 0.81$. A $Q^2$-dependent error analysis of the neutrino data shows that the uncertainties in the axial form factor $G_A(Q^2)$ are comparable to the ones induced by the a priori half width rule. We identify the most sensitive region to be in the range $0.2 \lesssim Q^2 \lesssim 0.6 \,{\rm GeV}^2$.

Hadron form factors and large-Ncphenomenology

The half width rule provides a way to consider 1/Nc corrections to hadronic models containing resonances. Consequences of such ideas for hadron form factors and Regge trajectories are explored, with special emphasis on the possibility to describe the spectrum of light and heavy unflavored vector mesons in a universal way.

Ground Magnetic Survey for The Investigation of Mineral Deposit at Itesi Village in Orile Ilugun, Odeda , South West Nigeria

Advances in technique development and data interpretation have greatly improved our ability to visualize the subsurface. A Magnetic survey was carried out at a site in Itesi village, Ilugun, Odeda Local Government Area of Ogun State, Nigeria using a portable proton precession magnetometer (G-856 AX). A total of ten profiles were established in an E-W direction in the study area. The acquired magnetic field data were corrected for drift. Qualitative and quantitative interpretations were adopted to obtain negative peak value and the maximum positive peak value. The depth to top of basement rock was estimated using Peter’s Half slope. Likewise the depth to centre of basement rock was estimated using the Half width rule. The contour maps, 3-D surface map and the 1-grid vector map present the subsurface image.
 The whole survey area has a total length of 100 m at a line spacing of 10 m and a breadth of 45 m at 5 m spacing. The whole area was characterized by complete varying negative amplitudes from a very low peak value of about -9.9 nT and a maximum positive peak value of about 17.4 nT respectively. The closely spaced, linear sub-parallel orientations of contours from the South western part of the map suggest the possibility of faults or local fractured zones.

Bearing Capacity Factors for Eccentrically Loaded Strip Footings Using Variational Analysis

Bearing capacity factors for eccentrically loaded strip smooth footings on homogenous cohesive frictional material are deduced by the variational limit equilibrium method and by assuming general shear failure along continuous curved slip surface. From the calculated results, the effective width rule suggested by Meyerhof for bearing capacity factors due to cohesion of soil is justified, and the superposition principle of bearing capacity for eccentrically loaded strip smooth footings is derived together with the bearing capacity factors for cohesion and unit weight of soil. The two factors are represented by soil strength parameters and eccentricity of load. The bearing capacity factor related to unit weight for cohesionless soil is less than that for cohesive frictional soil. The reason for this discrepancy lies in the existence of the soil cohesion, for the shape of the critical rupture surface of footing soil depends on both soil strength parameters rather than on friction angle alone in the previous limit equilibrium solutions. The contact between footing and soil is decided by both the load and the mechanical properties of soil. Under conditions of higher eccentricity and less strength properties of soil, part of the footing will separate from the underlying soil.

Design of Suppressing Crosstalk by Vias of Serpentine Guard Trace

The design of the serpentine guard trace (SGT) in the literal is to add two termi- nally matching resistances on the serpentine guard trace. Although this approach can get more layout space and suppress far-end crosstalk, it neglects the interference of near-end crosstalk. Therefore, we propose an approach, namely \vias of serpentine guard trace (VSGT), which the grounded-vias are added on the guard trace by a proper location and the ratio between the length of the horizontal and vertical on the guard trace can be adjusted in a better state such that the near-end crosstalk (NEXT) and far-end crosstalk (FEXT) coe-cient will be minimum and get the better performance. Hence, our proposed approach can simultaneously suppress NEXT and FEXT. Verifled in the frequency-domain simulation results, our approach, VSGT, can improve not only NEXT by 3.7 and 0.83dB but also FEXT by 5.11 and 0.1dB compared to the three- width rule and SGT, respectively. Moreover, verifled in the time-domain, VSGT can reduce not only NEXT by 34.67 and 27.5% but also FEXT by 46.78 and 6.91% than that of the three-width rule and SGT, respectively.

Effective width rule in calculations of bearing capacity of shallow footings

The classical solution to the bearing capacity problem predicts the limit load on symmetrically loaded shallow strip footings. A useful hypothesis was suggested by Meyerhof to account for eccentricity of loading, in which the footing width is reduced by twice-the-eccentricity to its ‘effective’ size. This hypothesis sometimes has been criticized as being overconservative. This paper examines Meyerhof’s suggestion and presents the bearing capacity of eccentrically loaded footings calculated using the kinematic approach of limit analysis. It is found that the effective width rule yields a bearing capacity equivalent to that calculated based on the assumption that the footing is smooth. For more realistic footing models and for cohesive soils the effective width rule is a reasonable account of eccentricity in bearing capacity calculations. Only for significant bonding at the soil-footing interface and for large eccentricities does the effective width rule become overly conservative. For cohesionless soils, however, the effective width rule may overestimate the best upper bound. This overestimation increases with an increase in eccentricity. ©

Control, coordination and conflict on international commodity markets

The effects of price stabilization policies have been investigated for both theoretical and empirical models. The institutional construct for international commodity markets is that a buffer stock manager employs a band width rule or a price adjustment rule to stabilize the world market price. In those investigations it is assumed that the other market participants do not react to the stabilization activities of the buffer stock manager. This paper describes an international commodity market as a difference game between buffer stock manager, producing countries and consuming countries and uses an empirical model for the world cocoa market to analyse the effects. The feedback Nash behavioural equilibrium for this game is compared with the optimal control outcome which ignores the strategic behaviour in producing countries and consuming countries. It is found that producers and consumers engage in storage activities which have a negative effect on the stabilization efforts of the buffer stock manager but which decrease the operating costs of the buffer stock, decrease the revenues of the producers and decrease the costs of consumers.

Context effects and their interaction with development: Area judgments

The perceptual constancy view posits that children perceive rectangular areas dependent on shape, whereas adults do not. Following Brunswik (1934a), we call this dependency the “limited perceptual constancy of area under variation of shape.” A series of four experiments (with 150 children and 80 adults) using ordinal paired comparisons rejected the general equation a i = ( A i, S i) as a model of limited area constancy ( a i is the perceived area, A i and S i the physical area and shape of rectangle i). Children judged area dependent on shape, but dependent on the covariation C set of area and shape in the experimental set of rectangles, rather than on the particular shape of the rectangle judged. A quantitative version of this covariation mechanism that seems to generate limited area constancy is proposed, and its relation to Parducci's range-frequency theory is discussed. Not one child's judgments could be predicted from a height + width rule (assuming identical linear psychophysical functions). We demonstrate and correct serious errors in Anderson and Cuneo's (1978a, 1978b) claims for a height + width rule in children. Our results support a three-step developmental model for paired comparisons of area: (1) centering on one side of the rectangle, (2) limited area constancy, that is, a i = f( A i, C set), and (3) area constancy.

Information integration in an area judgment task: effect of aids on children's perceptual judgments.

This study was designed to examine the cognitive processes involved in perceptual judgments of area with the methodology and concepts of Anderson's (1981) information integration theory. The Area = Height + Width rule, which Anderson and Cuneo (1978) showed to be operant in children's judgments, can in fact cover two different processes. Children may make a height judgment and then a length judgment and apply an additive integration operation to both. Alternatively, children may base themselves on the figure outline and estimate total length directly as a function of the distance scanned. Similarly, the multiplicatory integration pattern can result either from applying a multiplicatory operation to separate estimates or from visual exploration of the area bounded by the figure. In the present experiment, the characteristics of the areas of the test figures were modified (perimeter marking, rows of Xs covering the area, etc.) to elicit additive or multiplicatory integration patterns as a function of condition. The findings demonstrate that the second interpretation of both rules is more likely.

Judgments of quantity and conservation of quantity: The area of a rectangle

This study examines the relationships between perceptive judgment of quantity and conservation judgment of quantity with regard to the concept of area. Twenty children who passed an area conservation task (mean age = 8) and 20 children who failed it (mean age = 6.7) were administered an area judgment task. This task was a replication of Anderson and Cuneo's study (1978, Journal of Experimental Psychology: General, 107, 335–378). The conserving children generally appeared to apply an additive rule (the height and width rule) observed by Anderson and Cuneo in 5 year olds. The nonconserving children in contrast generally presented patterns suggesting centration on one of the two dimensions. The implications for Anderson's and Piaget's conceptions of conservation development are discussed.

Developmental and individual differences in children's area judgment rules

Children at three grade levels (kindergarten, second, and fourth) rated the areas of three types of stimuli (rectangles, triangles, and ellipses). Functional measurement methodology was applied to each subject's ratings in order to assess several one- and two-dimentional rules. At each grade level a large majority of subjects produced judgments that were consistent with one of the rules. Among the kindergartners no single rule predominated: the height + width rule, together with various one-dimensional rules, accounted for most of the classifiable response patterns. Among the second graders the height + width rule predominated. Among the fourth graders the height + width rule and the height × width rule, in almost equal proportions, accounted for most of the classifiable response patterns. These results contradict Piaget's claim that young children are limited to one-dimensional judgments, as well as N. H. Anderson and D. O. Cuneo's (1978, Journal of Experimental Psychology: General, 107, 335–378) hypothesis that young children judge quantity according to a general-purpose additive integration rule.

Shear Lag Analysis and Effective Width of Curved Girder Bridges

The effective width of curved girder bridges is formulated by substituting the flange stress derived from present theory into the equation of effective width definition for the curved girders. The required information in formulating the effective width rule for design of curved girder bridges are provided. The actual longitudinal stress distributions for the curved girders are evolved from the present theory for shear lag in order to determine the effective width. The thin-walled curved girders used in this investigation are based on box and channel cross sections, and are analyzed for a uniform lateral load and for a concentrated load. Numerical examples are shown for several problems to investigate the effect on the effective width of curved girder bridges. The values of the effective width obtained by the present theory are compared with those of the straight girder bridges. According to the results, the values of the effective width of curved girder bridges can be regarded as the values of the straight girder bridges approximately.

Extent, multiplying, and proportionality rules in children's judgments of area

The study examined children's use of multiplying and proportionality rules in judgments of area. In two experiments children judged the area of rectangles. Seven-year-olds used linear extent as an index of area. Eight- and nine-year-olds replaced the extent rule with the height × width rule. In a third experiment 8-through 11-year-olds were presented with a rectangle and a horizontal line representing the width of a second rectangle. Children were asked to indicate the height that would make the second rectangle equal in area to the first. The correct response was proportional to the product of the ratio of the widths of the two rectangles and the height of the first rectangle. Graphical and statistical analyses indicated that children applied the ratio rule to these judgments. The implications for Piaget's theory of cognitive development were discussed.

A General Strategy for Quantity Judgments: The Height + Width Rule

Previous work has found that 5-year-olds judge the area of rectangles by a height width rule. Present results indicated that 3- and 4-year-olds also judge area by a height width rule. This adding rule was interpreted in terms of a general-purpose judgmental strategy that young children employ to make quantitative judgments. Both the use of a rating scale and the use of an adding rule in judgment indicate an impressive level of quantitative ability at a very early age.

A General Strategy for Quantity Judgments: The Height + Width Rule

A General Strategy for Quantity Judgments: The Height + Width Rule