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The purpose of this paper is to investigate what might be relevant to younger children’s understanding of a number line and how teaching can be designed according to variation theory to give pupils the opportunity to develop an understanding of the number line as a tool for mathematical thinking.

A Learning Study was conducted by mathematics teachers at Sjöstadsskolan in Stockholm. Variation theory was used as a theory of learning. In order to use the number line as a tool in mathematical thinking, pupils have to discern what is important for this form of representation of the numeral system. Critical aspects from other studies with similar learning objects have been taken into consideration for pre-test design. These aspects supplemented and enhanced the analysis of the results and the results were consistent with earlier learning studies’.

Four critical features, for younger pupils’ understanding of how the number line can be constructed, have been established in the study: the number line can have a different range (e.g. 0-20 or 30-60), correlation between the distance and value, two reference points are needed to place a third number and determine the scale, and the correlation between a part and whole.

Learning Study is emphasized as a powerful and structured model for teacher driven research aiming to develop the praxis. The use of experiences and results from other studies is recommended.

The purpose of the present study is to investigate the flow and turbulence characteristics of a turbulent wall jet flowing over a surface inclined with the horizontal and to investigate the effect of variation of the angle of inclination of the wall on the flow structure of the wall jet.

The high Reynolds number two-equation κ− model with standard wall function is used as the turbulence model. The Reynolds number considered for the present study is 10,000. The Reynolds averaged Navier-Stokes (RANS) equations are used for predicting the turbulent flow. A staggered differencing technique employing both contravariant and Cartesian components of velocity has been applied. Results for distribution of wall static pressure and skin friction, decay of maximum streamwise velocity, streamwise variation of integral momentum and energy flux have been compared for the cases of α=0°, 5°, and 10°.

Flow field has been represented in terms of streamwise and lateral velocity contours, static pressure contour, vorticity contour and streamwise velocity and static pressure profiles at different locations along the oblique offset plate. Distribution of Reynolds stresses in terms of spanwise, lateral and turbulent shear stresses, and turbulent kinetic energy and its dissipation rate have been presented to describe the turbulent characteristics. Similarity of streamwise velocity and the velocity parallel to the oblique wall has been observed in the developed region of the wall jet flow. A decaying trend is observed in the variation of total integral momentum flux in the developed region of the wall jet which becomes more evident with increase in oblique angle. Developed flow region has indicated trend of similarity in profiles of streamwise velocity as well as velocity component parallel to the oblique wall. A depression in wall static pressure has been observed near the nozzle exit when the wall is inclined and the depression increases with increase in inclination. Effect of variation of oblique angles on skin friction coefficient has indicated that it decreases with increase in oblique angle. Growth of the outer and inner shear layers and spread of the jet shows linear variation with distance along the oblique wall. Decay of maximum streamwise velocity is found to be unaffected by variation in oblique angle except in the far downstream region. The streamwise variation of spanwise integral energy shows increase in oblique angle and decreases the magnitude of energy flux through the domain. In the developed flow region, streamwise variation of centreline turbulent intensities shows increased values with increase in oblique angle, while turbulence intensities along the jet centreline in the region X<12 remain unaffected by change in oblique angles. Normalized turbulent kinetic energy distribution highlights the difference in turbulence characteristics between the wall jet and reattached offset jet flow. Near wall velocity distribution shows that the inner region of boundary layer of the developed oblique wall jet follows a logarithmic profile, but it shows some difference from the standard logarithmic curve of turbulent boundary layers which can be attributed to an increase in skin friction coefficient and a decrease in thickness of the wall attached layer.

The study presents an in-depth investigation of the interaction between the jet and the inclined wall. It is shown that due to the Coanda effect, the jet follows the nearby wall. The findings will be useful in the study of combined flow of wall jet and offset jet and dual offset jet on oblique surfaces leading to a better design of some mechanical jet flow devices.

This paper aims to propose methods for on-line monitoring and process quality assurance of Selective Laser Melting (SLM) technology as a competitive advantage to enhance its implementation into modern manufacturing industry.

Monitoring of thermal emission from the laser impact zone was carried out by an originally developed pyrometer and a charge-coupled device (CCD) camera which were integrated with the optical system of the PHENIX PM-100 machine. Experiments are performed with variation of the basic process parameters such as powder layer thickness (0-120 μm), hatch distance (60-1,000 μm) and fabrication strategy (the so-called “one-zone” and “two-zone”).

The pyrometer signal from the laser impact zone and the 2D temperature mapping from HAZ are rather sensible to variation of high-temperature phenomena during powder consolidation imposed by variation of the operational parameters.

Pyrometer measurements are in arbitrary units. This limitation is due to the difficulty to integrate diagnostic tools into the optical system of a commercial SLM machine.

Enhancement of SLM process stability and efficiency through comprehensive optical diagnostics and on-line control.

High-temperature phenomena in SLM were monitored coaxially with the laser beam for variation of several operational parameters.

The purpose of this chapter is to make sense of the cultural distance paradox through a basic assessment of the cross-cultural comparability of cultural distance measures. Cultural distance between a base country and partner countries is a key construct in international business (IB). However, we propose that what exactly is measured by cultural distance is unique for each country that is chosen as the base country to/from which cultural distance to a set of partner countries is calculated.

We use a mathematical argument to establish that cultural distance may correlate rather differently with the culture of partner countries depending on which base country one considers, for example, the United States or China. We then use empirical analysis to show the relevance of this argument, using Hofstede’s data on national culture for 69 countries.

Results show that cultural distance indeed has very different correlations with partner country culture, depending on which country one selects as the base country in one’s distance calculations.

Implication of our findings is that measured cultural distance is not equivalent across different base countries. The effect of cultural distance on such issues as foreign market entry mode or market selection, therefore, lacks international generalizability.

This chapter presents the first assessment of the cross-cultural comparability of cultural distance. Paradoxical findings that plague extant cultural distance research may be understood from the found lack of measurement equivalence.

In studies of engines and engine lubricants, it is often desirable to measure clearances between shafts and sleeve—or journal‐type bearings during operation. However, it is usually rather difficult to obtain such measurements without affecting the operation, particularly at high speeds. A method recently developed by M. L. Greenough and associates of the National Bureau of Standards for the Navy Bureau of Ships appears to offer a satisfactory solution of the problem. The heart of the new system is a mutual‐inductance type of electrical distance‐measuring element; variation of the distance of the rotating shaft from two small fixed coils results in a readily measurable variation in the coupling between the coils.

The introduction of automation for the assembly of aircraft wing box structures will require individual components to conform closely to the CAD design specification with regard to shape geometry and dimensional tolerances. Often, due to a variety of previous manufacturing processes, the 3D shape of these large components lose the accuracy of their designed dimensional specifications. Under these circumstances part‐to‐part assembly becomes tedious and it would be impossible to rely on robots to achieve precise assembly in an automated system. For this reason, variations need to be accurately quantified in order to provide a reliable prediction model in aid of any future automated assembly. This paper describes the measurement method used to record the possible variations occurring during the assembly process. The measurements were made using a laser tracker where the results are expected to offer some explanations as to the causes of the variation. The suitability of a laser tracker in a large assembly jig environment is then assessed. This study is based on the work that was carried out at BAE Systems UK, where the Airbus commercial aircraft wings are manufactured.

This paper aims at studying numerically the entropy generation of nanofluid flowing over an inclined sheet in the presence of external magnetic field, heat source/sink, chemical reaction along with slip boundary conditions imposed on an impermeable wall.

A suitable similarity transformation technique has been used to convert the coupled nonlinear partial differential equations to ordinary differential equations (ODEs). The ODEs are then solved simultaneously using the finite difference method implemented through an in-house computer program. The effects of different controlling parameters such as magnetic parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, chemical reaction parameter, Reynolds number, Brinkmann number, Prandtl number, velocity slip parameter, temperature slip parameter and the concentration slip parameter on the entropy generation and Bejan number have been discussed comprehensively through the relevant physical insights for the first time.

The relative strengths of the irreversibilities due to heat transfer, fluid friction and the mass diffusion arising due to the change in each of the controlling variables have been delineated both in the near-wall and far-away-wall regions, which may be helpful for a better understanding of the thermo-fluid dynamics of nanofluid in boundary layer flows. The numerical results obtained from the present study have also been validated with results published in open literature.

The effects of different controlling parameters such as magnetic parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, chemical reaction parameter, Reynolds number, Brinkmann number, Prandtl number, velocity slip parameter, temperature slip parameter and the concentration slip parameter on the entropy generation and Bejan number have been discussed comprehensively through the relevant physical insights for the first time.

The purpose of this paper is to focus on the adjustment of the GM(1, 2) errors for financial data series that measures changes in the public sector financial indicators, taking into account that the errors in grey models remain a key problem in reconstructing the original data series.

Adjusting the errors in grey models must follow some rules that most often cannot be determined based on the chaotic trends they register in reconstructing data series. In order to ensure the adjustment of these errors, for improving the robustness of GM(1, 2), was constructed an adaptive fuzzy controller which is based on two input variables and one output variable. The input variables in the adaptive fuzzy controller are: the absolute error ε i 0 ( k ) [ % ] of GM(1, 2), and the distance between two values x i 0 ( k ) [ % ] , while the output variable is the error adjustment A ε i 0 ( k ) [ % ] determined with the help of the above-mentioned input variables.

The adaptive fuzzy controller has the advantage that sets the values for error adjustments by the intensity (size) of the errors, in this way being possible to determine the value adjustments for each element of the reconstructed financial data series.

To ensure a robust process of planning the financial resources, the available financial data are used for long periods of time, in order to notice the trend of the financial indicators that need to be planned. In this context, the financial data series could be reconstituted using grey models that are based on sequences of financial data that best describe the status of the analyzed indicators and the status of the relevant factors of influence. In this context, the present study proposes the construction of a fuzzy adaptive controller that with the help of the output variable will ensure the error’s adjustment in the reconstituted data series with GM(1, 2).

The mixing of fuel and air plays a pivotal role in enhancing combustion in supersonic regime. Proper mixing stabilizes the flame and prevents blow-off. Blow-off is due to the shorter residence time of fuel and air in the combustor, as the flow is in supersonic regime. The flame is initiated in the local subsonic region created using a flameholder within the supersonic combustor. This study aims to design an effective flameholder which increases the residence time of fuel in the combustor allowing proper combustion preventing blow-off and other instabilities.

The geometry of the strut-based flameholder is altered in the present study to induce a streamwise motion of the fluid downstream of the strut. The streamwise motion of the fluid is initiated by the ramps and grooves of the strut geometry. The numerical simulations were carried out using ANSYS Fluent and are validated against the available experimental and numerical results of cold flow with hydrogen injection using plain strut as the flameholder. In the present study, numerical investigations are performed to analyse the effect on hydrogen injection in strut-based flameholders with ramps and converging grooves using Reynolds-averaged Navier–Stokes equation coupled with Menter’s shear stress transport k-ω turbulence model. The analysis is done to determine the effect of geometrical parameters and flow parameter on the flow structures near the base of the strut where thorough mixing takes place. The geometrical parameters under consideration include the ramp length, groove convergence angle, depth of the groove, groove compression angle and the Mach number. Two different strut configurations, namely, symmetric and asymmetric struts were also studied.

Higher turbulence and complex flow structures are visible in asymmetric strut configuration which develops better mixing of hydrogen and air compared to symmetric strut configuration. The variation in the geometric parameters develop changes in the fluid motion downstream of the strut. The fluid passing through the converging grooves gets decelerated thereby reducing the Mach number by 20% near the base of the strut compared to the straight grooved strut. The shorter ramps are found to be more effective, as the pressure variation in lateral direction is carried along the strut walls downstream of the strut increasing the streamwise motion of the fluid. The decrease in the depth of the groove increases the recirculation zone downstream of the strut. Moreover, the increase in the groove compression angle also increases the turbulence near the base of the strut where the fuel is injected. Variation in the injection port location increases the mixing performance of the combustor by 25%. The turbulence of the fuel jet stream is considerably changed by the increase in the injection velocity. However, the change in the flow field properties within the flow domain is marginal. The increase in fuel mass flow rate brings about considerable change in the flow field inducing stronger shock structures.

The present study identifies the optimum geometry of the strut-based flameholder with ramps and converging grooves. The reaction flow modelling may be performed on the strut geometry incorporating the design features obtained in the present study.

Autonomous mobile cleaning robots are widely used to clean solar panels because of their flexibility and high efficiency. However, gravity is a challenge for cleaning robots on inclined solar panels, and robots have problems such as high working power and short battery life. This paper aims to develop a following robot to improve the working time and efficiency of the cleaning robot.

The mechanical structure of the robot is designed so that it can carry a large-capacity battery and continuously power the cleaning robot. The robot determines its position and orientation relative to the edge of solar panel by using optoelectronic sensors. Based on the following distance, the robot changes its state between moving and waiting to ensure that supply cable will not drag.

Prototype following robot test results show that the following robot can stably follow the cleaning robot and supply continuous power to cleaning robot. The linear error of the following robot moving along the solar panel is less than 0.3 m, and the following distance between the robot and the cleaning robot is in 0.5–1.5 m.

The working time of cleaning robots and working efficiency is improved by using following robot, thereby reducing the labor intensity of workers and saving the labor costs of cleaning.

The design of the following robot is innovative. Following robot works with the existing cleaning robots to make up for shortcomings of the existing cleaning system. It provides a more feasible and practical solution for using robots to clean solar panels.