Auxiliary Lines Research Articles

Did assessors select attributes by chance alone in your TDS study, and how relevant is it to know?

Dominance rates arising from Temporal Dominance of Sensations (TDS) data are almost always plotted and understood with reference to chance and significance lines, which are based on the assumption of random attribute selection. These lines are auxiliary to the chart, and used to interpret the dominance rates; when the dominance rate for some attribute exceeds the significance line, the conventional interpretation is that this attribute is being noticed significantly. Thus, these auxiliary lines are used to provide a convenient, qualitative interpretation of TDS data. However, the concept of the significance lines has some deficiencies that we explore in this paper.We were interested in what real TDS data look like under a true null hypothesis of random attribute selection. To obtain such data, we sampled from real TDS data (keeping products and assessors' selection patterns intact) to create dominance rates based on random attribute selections. Dominance rates exceed the significance line about 5% of the time (across attributes and time points), as expected. These curves differed from any real TDS curves that we have ever observed previously insofar as that they were unusually flattened.Next, we sampled again from real TDS data (keeping attributes and assessors' selection patterns intact) to create dominance rates based on attribute selections for random (hybrid) products. Derived TDS curves much more closely resemble curves from real TDS studies and show a lot of “significances”, even though products are artificially created by the permutations. This is due to properties of the products that are inherent to the product category: e.g., hard will occur early during the evaluation of a chocolate (if at all), but not towards the end.From these simulations, we reach two conclusions. First, we recognize that the hypothesis that assessors select the dominant attribute completely at random is almost always false. Second, the reason that it is false is that, regardless of the product, there is a time-dependent category signature present, as well as competition between attributes, such that significances for one attribute depend on which other attributes are on the list. These properties limit the informative value of the conventional TDS significance lines that are widely used.As an alternative, we explore the possibility of context-dependent significance thresholds which are customized for and aligned with research objectives. These reference lines are recommended for improved interpretation of data arising from TDS studies.

ANALISIS TAHAP PEMBUKTIKAN TEOREMA STEWART PADA MAHASISWA PROGRAM STUDI PENDIDIKAN MATEMATIKA UNIVERISTAS KATOLIK WIDYA MANDALA MADIUN

The purpose of this research was to find out how the stage of proofing the Stewart theorem was conducted by students of the Mathematics Education Department at Catholic Widya Mandala University of Madiun. This type of research is qualitative research with descriptive data analysis. The number of research subjects consisted of three students. This study describes the stage of proofing Stewart's theorem by students. The data collection process begins with the subject being asked to prove Stewart's theorem and write down the process of proving Stewart's theorem on the answer sheet provided. From the results of data collection, it was found that the verification process carried out by the three students used the direct verification method, there were some similarities between the three students in initiating the verification process, namely: drawing a high line on a triangle and using the pythagoras theorem to add information used in the verification process, to proving that Stewart's theorem required precision when describing an algebraic form and understanding of algebraic concepts from numbers, to prove Stewart's theorem needed time according to the speed of thinking that proves, to prove the Stewart theorem required problem solving skills, logical thinking, critical, analytical and systematic. Thus it can be concluded that, in general the steps of proving Stewart's theorem carried out by students of the Mathematics Education Department, starting with drawing ABC triangles and also describing auxiliary lines (high of CE), collecting information used in the verification process, then use the information obtained to describe the shape of the right side of the equation becomes the left hand side, so that the equation applies.

A universal modification of the linear coupling method

ABSTRACTIn the late sixties, N. Shor and B. Polyak independently proposed optimal first-order methods for solving non-smooth convex optimization problems. In 1982 A. Nemirovski proposed optimal first-order methods for solving smooth convex optimization problems, which utilized auxiliary line search. In 1985 A. Nemirovski and Yu. Nesterov proposed a parametric family of optimal first-order methods for solving convex optimization problems with intermediate smoothness. In 2013 Yu. Nesterov proposed a universal gradient method which combined all good properties of the previous methods, except the possibility of using auxiliary line search. One can typically observe that in practice auxiliary line search improves performance for many tasks. In this paper, we propose the apparently first such method of non-smooth convex optimization allowing the use of the line search procedure. Moreover, it is based on the universal gradient method, which does not require any a priori information about the actual degree of smoothness of the problem. Numerical experiments demonstrate that the proposed method is, in some cases, considerably faster than Nesterov's universal gradient method.

Energy and environmental analysis of a natural gas pressure reduction station equipped with turboexpander, solar collector, and storage tank

The pressure of natural gas in the transmission pipelines is high, and it is not suitable for urban consumptions. Therefore, it should be decreased to a certain lower amount in the pressure reduction stations near the urban area by the pressure reducing valves. Recently, for recovering the energy losses in these valves and generating electricity, turboexpanders are utilized. However, the pressure decrease in the turboexpander results in a sudden decrease in temperature, which leads to the formation of hydrates. To prevent the hydrate formation, preheating is required, which is conventionally done by a line heater. In this study, the required energy for preheating the natural gas entering the station is supplied from the solar energy and an auxiliary line heater for a case study of Mashhad city (Iran). Parabolic trough thermal collectors are used for the absorption of the solar radiant energy. The collector was modeled through one-dimensional implicit finite-difference method and using discretization of energy balance equation between the working fluid, the absorbent pipe, and the glass envelope. The reduction in natural gas consumption and the produced CO2 emission are computed for the pressure reduction station with a thermal collector and a storage tank. The results reveal that the presence of the thermal collector and the storage tank reduces the consumption of fuel and consequently the generation of pollutant about 90%.

Method for Measuring Clearance of Automobile Body Panel with Double Structured Light System

According to the changes of the autobody measuring clearance often face the shooting angle problem caused by internal decline caused by the lack of data acquisition accuracy, a high precision and robust measurement of binocular gap line structured light and the system parameter calibration method of system integration. First the mathematical measurement model of the system is established according to the Zhang Zhengyou camera calibration model to calculate the camera parameters, the extrinsic parameters of the camera calibration of the light plane, while the introduction of auxiliary line structured light laser by solving the intersection of two camera coordinate system, finally gives the calculation model of the door gap and combined with the calibration data for the gap size. Compared with a three-dimensional scanning measuring device, the system can measure only two images at the same time. The experimental results show that when the shooting angle is less than 45 degrees at the working distance of 400mm and 50*50 field of view, the accuracy reaches 0.08mm, which meets the needs of fast and real-time measurement gap.

Focusing attention on auxiliary lines when introduced into geometric problems

ABSTRACTThe introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students’ attention. We present and compare various examples of how auxiliary elements can be introduced in various problems and proofs and characterize their auxiliary quality. Some auxiliary elements unite previously unrelated components of the original diagram; others divide a given complex entity into manageable ones. Implications for further educational research and mathematics instruction are proposed.

Finite Element Analysis and Optimization of Helical Gear-pairs with Web based on SolidWorks

In this paper, Finite element analysis is implemented for helical gear-pairs by SolidWorks simulation. Firstly, GearTrax that is seamlessly integrated with SolidWorks is used to input the relevant parameters of helical gears. Then the gear entity is established in SolidWorks. Finally 3D models of gear-pairs are built up. Through the creation of auxiliary lines and auxiliary surfaces, the correct assembly of gear-pairs is completed, which guarantees the accuracy of subsequent finite element analysis. According to the results of finite element analysis, both the web thickness and the web hole diameter of the large gear are optimized to meet the maximum requirements. This work is able to provide reference for parameter design of helical gear-pairs with web.

A computational study on system dynamics of an ocean current turbine

In this paper, we present the study of system dynamics of the floating kuroshio turbine (FKT) system which is designed to harness ocean current energy. We focus on the mooring line system design and its interaction with the FKT system. The effects of line diameter and two different auxiliary line systems were studied. Their responses in waves were also investigated. We integrated several commercial and in-house packages. The system buoyancy and weight and their centers were estimated using the Rhino software. The system hydrodynamic coefficients were obtained through WAMIT, system drag coefficient through FLUENT, turbine propulsive force through lifting surface code, and system dynamics through OrcaFlex. The results show that the mooring line system can create strong influence on the FKT system operations in the ocean current environments.

Development and numerical modelling of a supercharging technique for positive displacement expanders

This study presents a novel strategy to enhance the recovery performance of any positive displacement expander technology which aims at the maximization of the power output rather than solely its efficiency. The approach is based on an auxiliary injection of fluid under the same suction conditions as the main intake but during the closed volume expansion phase. The operating principle of the supercharging technology is firstly outlined in theoretical terms, while the benefits over a conventional configuration are numerically assessed with reference to a sliding vane expander for applications based on Organic Rankine Cycles (ORC). The holistic modelling platform used for the benchmarking is preliminarily validated over an experimental campaign in which the vane expander was installed in a heavy-duty automotive ORC system and generated up to 1.9 kW (3% of the engine mechanical power) with an overall efficiency of 51.2%. After the simulation platform is validated, the auxiliary intake line is parameterized in terms of four geometrical quantities and the effects of the supercharging with respect to baseline angular pressure trace are shown. An optimization based on a genetic algorithm is eventually performed and the resulting optimized design led to an average mechanical power increase of 50.6%.

Top-forms of leading singularities in nonplanar multi-loop amplitudes

The on-shell diagram is a very important tool in studying scattering amplitudes. In this paper we discuss the on-shell diagrams without external BCFW bridges. We introduce an extra step of adding an auxiliary external momentum line. Then we can decompose the on-shell diagrams by removing external BCFW bridges to a planar diagram whose top-form is well known now. The top-form of the on-shell diagram with the auxiliary line can be obtained by adding the BCFW bridges in an inverse order as discussed in our former paper (Chen et al. in Eur Phys J C 77(2):80 2017). To get the top-form of the original diagram, the soft limit of the auxiliary line is needed. We obtain the evolution rule for the Grassmannian integral and the geometry constraint in the soft limit. This completes the top-form description of leading singularities in nonplanar scattering amplitudes of mathcal {N}=4 Super Yang–Mills (SYM), which is valid for arbitrary higher-loops and beyond the Maximally-Helicity-Violation (MHV) amplitudes.

GAN-Assisted Two-Stream Neural Network for High-Resolution Remote Sensing Image Classification

Using deep learning to improve the capabilities of high-resolution satellite images has emerged recently as an important topic in automatic classification. Deep networks track hierarchical high-level features to identify objects; however, enhancing the classification accuracy from low-level features is often disregarded. We therefore proposed a two-stream deep-learning neural network strategy, with a main stream utilizing fine spatial-resolution panchromatic images to retain low-level information under a supervised residual network structure. An auxiliary line employed an unsupervised net to extract high-level abstract and discriminative features from multispectral images to supplement the spectral information in the main stream. Various feature extraction types from the neural network were selected and jointed in the novel net, as the combined high- and low-level features could provide a superior solution to image classification. In traditional convolutional neural networks, increased network depth might not influence the network performance perceptibly; however, we introduced a residual neural network to develop the expressive ability of the deeper net, increasing the role of net depth in feature extraction. To enhance feature robustness, we proposed a novel consolidation part in feature extraction. An adversarial net improved the feature extraction capabilities and aided digging the inherent and discriminative features from data, with increased extraction efficacy. Tests on satellite images indicated the high overall accuracy of our novel net, verifying that net depth or number of convolution kernels affected the classification capability. Various comparative tests proved the structural rationality for our two-stream structure.

Design of large-scale streamlined head cars of high-speed trains and aerodynamic drag calculation

Aerodynamic drag plays an important role in high-speed trains, and how to reduce the aerodynamic drag is one of the most important research subjects related to modern railway systems. This paper investigates a design method for large-scale streamlined head cars of high-speed trains by adopting NURBS theory according to the outer surface characteristics of trains. This method first created the main control lines of the driver cab by inputting control point coordinates; then, auxiliary control lines were added to the main ones. Finally, the reticular region formed by the main control lines and auxiliary ones were filled. The head car was assembled with the driver cab and sightseeing car in a virtual environment. The numerical simulation of train flow field was completed through definition of geometric models, boundary conditions, and space discretization. The calculation results show that the aerodynamic drag of the high-speed train with large-scale streamlined head car decreases by approximately 49.3% within the 50-300 km/h speed range compared with that of the quasi-streamlined high-speed train. This study reveals that the high-speed train with large-scale streamlined head car could achieve the purpose of reducing running aerodynamic drag and saving energy, and aims to provide technical support for the subsequent process design and production control of high-speed train head cars.

Upgraded Graphical Method for the Synthesis of Direct Work Exchanger Networks

Numerous studies on heat integration have made significant progress in reducing external thermal energy in chemical plants. However, the notion of work exchange between high- and low-pressure streams to reduce the costly mechanical energy has not been fully explored. In this paper, an upgraded graphical method is proposed for the synthesis of direct work exchanger networks (WEN) using direct work exchangers under any operating conditions, such as isothermal, isentropic, and polytropic. In this method, the improved composite curves of work sources and work sinks are plotted in the pressure index (μ) versus work (W) diagram. On the basis of thermodynamic and numerical analysis, two improved linear-approximation auxiliary lines for every work sink are presented to assist identifying the feasible match. Several matching rules are proposed to accurately identify the feasible matches between work sinks and work sources. From the proposed method, the maximum amount of mechanical energy recovery, the minimum amou...

Frequency estimator of sinusoid based on interpolation of three DFT spectral lines

A frequency estimator of sinusoid based on interpolation of three discrete Fourier transform (DFT) spectral lines is proposed. The FFT is performed first on the sampled sinusoid signal and the coarse frequency estimation is made by searching the location of the discrete spectral line with maximum amplitude (the primary spectral line). Fine frequency estimation is made by the interpolation using the primary spectral line and two auxiliary spectral lines located at arbitrary position within the main lobe or the first sidelobe of the frequency spectrum. The formula for calculating the MSE of the proposed estimator in additive white noise is derived. The influence of the interval between the primary spectral line and the auxiliary spectral lines on the MSE is analyzed through theoretical analysis and simulation experiments. To further improve the estimation performance, iterative procedures are used. Simulation results show that the RMSE of the proposed estimator is closer to CRLB than the competing estimators especially at high SNR.

Leveraging Spatial Context Disparity for Power Line Detection

For the safety of low flying aircraft, it will become increasingly important that an aircraft should have the ability to detect and avoid small obstacles in the low flying environment. In recent years, using context information to assist in detecting power lines has shown great potential to better detect power lines at a remote distance. Therefore, how to adequately use the context information for a better detection is a hot issue of concern. This paper proposes a novel auxiliary assisted power line detection method, in which the spatial context disparity of auxiliaries is quantitatively and uniformly evaluated for the first time. As a cognitive strategy, the spatial context disparity depends on two factors, the spatial context peakedness and the spatial context difference. With this cognitive method, objects that achieve high spatial context disparity scores are more suitable for being the auxiliaries of the power lines. Experimental results show that, owing to the spatial context disparity, the proposed method can acquire proper auxiliaries with abundant context information to support the detection, so that better power line detections are achieved comparing to traditional power line detection methods. The proposed power line detection method, which can automatically choose the optimal auxiliaries, is effective and has the potential for practical use in ensuring the flight safety of unmanned air vehicles (UAVs) in the low flying environment.

Euclid 원론에서 작도의 의미에 대한 고찰

The construction in the ancient Greek era had more meanings than a construction in the present education. Based on this fact, this study examines the meaning of the current textbook. In contrast, we have extracted the meaning of the constructions in Euclid Elements. In addition, we have been thinking about what benefits can come up if the meaning of the construction in Euclid Elements was reflected in current education, and suggested a way to exploit that advantage. As results, it was confirmed that the construction in the current textbook was merely a means for introducing and understanding the congruent conditions of the triangle. On the other hand, the construction had four meanings in Euclid Elements; Abstract activities that have been validated by the postulates, a mean of demonstrating the existence of figures and obtaining validity for the introduction of auxiliary lines, refraining from intervening in the argument except for the introduction of auxiliary lines, a mean of dealing with numbers and algebra. Finally we discussed the advantages of using the constructions as a means of ensuring the validity of the introduction of the auxiliary line to the argument. And we proposed a viewpoint of construction by intervention of virtual tools for auxiliary lines which can not be constructed with Euclid tool.

Does a transformation approach improve students’ ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students’ ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were 130 eighth-grade students in two classes with a comparable background that were taught by the same teacher. A two-week intervention was implemented in the experimental class aiming to help students learn how to use geometric transformations to draw auxiliary lines in solving geometric problems. The data were collected from a teacher interview, video-recordings of the intervention, and pre- and post-tests. The results revealed that there was a positive impact of using geometric transformations on the experimental students’ ability in solving high-level cognitive problems by adding auxiliary lines, though the impact on the students’ ability in solving general geometric problems as measured using the overall average scores was not statistically significant. Recommendations for future research are provided at the end of the article.

Management of lung nodules newly found by virtual-assisted lung mapping: a case report

BackgroundVirtual-assisted lung mapping is a novel bronchoscopic lung marking technique that uses virtual images to perform multiple concurrent dye marking of barely palpable pulmonary tumors. Subsequent chest computed tomography is required to confirm the locations marked. We here report a patient in whom computed tomography after virtual-assisted lung mapping unexpectedly revealed additional tiny pulmonary nodules.Case presentationA 64-year-old woman with a history of renal cell carcinoma presented with two pulmonary nodules suspicious of metastases from renal cell carcinoma. Because we anticipated that the nodules would be difficult to palpate intraoperatively, we performed virtual-assisted lung mapping prior to attempting to resect them. Computed tomography after mapping unexpectedly detected two additional nodules. Although the existing markings did not relate to the newly found nodules, we used imaginary auxiliary lines and anatomical landmarks to extend the lung map to incorporate the unexpected nodules. The additional nodules were successfully resected by thoracoscopic wedge resection. Pathologic examination identified all nodules as metastases from renal cell carcinoma, and the surgical margins were negative.ConclusionsImaginary auxiliary lines and anatomical landmarks extended the existing lung map of virtual-assisted lung mapping, enabling resection of unexpected pulmonary nodules found in post-mapping computed tomography images.

Setting services in public transit lines in short time periods under time-varying demand

Abstract: This paper focuses on a mathematical programming based model for setting the schedule of a given number of services on a public transportation network. The structure of the model is that of a time-expanded or diachronic network, where origin to destination flows vary dynamically over a short time horizon (several hours) and are assumed to be known deterministically. The model basically aims to minimize the total travel time of passengers during the time horizon by properly setting the lag times between services on the lines and thereby accommodating conveniently the schedules of the services on different lines in order to enhance transfers. Two different types of diachronic networks are considered, in which three basic algorithmic alternatives have been tested: a heuristic method based on the classical projected gradient, Benders decomposition, and a combination of both. Among other applications, the model can potentially be applied in operational aspects for disruption recovery in Rail-Rapid Transit and Suburban Railway systems by using bus shuttles or auxiliary bus lines. The computational viability of the model, in terms of adequate response time, is shown using test networks of auxiliary bus lines. Its computational performance in readjusting schedules for larger suburban rail systems is also evaluated.

Otimization of auxiliary lines for proximal femoral intramedullary nail in the treatment of simple femoral intertrochanteric fractures

To investigate the clinical outcomes of C-arm X-ray fluoroscopy before incision to make assistant lines and insert the guide wire of PFNA and PFNA blade. From January 1st 2012 to January 1st 2015, 132 intertrochanteric fracture patients of type 31A1 and 31A2 according to AO-classification, were retrospectively analyzed. Among them, 62 patients(14 males and 48 females) aged from 52 to 95 years with a mean age of(69.58±8.55) years in traditional group were operated by traditional procedure, while 70 patients in the skin marking group included 15 males and 55 females aged from 61 to 88 years with a mean age of(71.94±7.64) years, on the basis of the traditional operation method, the assistant line of the body surface and the C-arm X-ray was increased, and the guide pin positioning of the proximal femoral nail and the spiral blade was guided by the auxiliary line in the operation. Operative time, frequency of C-arm fluoroscopy, Harris hip score of the third months after surgery and the complications in both groups were queried for statistical analysis. In addition to skin making group 1 patients had superficial wound infection complications, all patients were stage I wound healing. All patients were followed up for 3 to 18 months with an average of (6.81±3.07) months. The operative time was significantly reduced in skin marking group (56.16±6.36) minutes compared to traditional group (59.06±9.19) minutes (P>=0.035). And the frequency of C-arm fluoroscopy of skin marking group was(25.89±5.81) times which was also significantly reduced compared to traditional group(31.32±9.81) times (P<0.001). There was no statistical difference in Harris hip score at 3 months after operation and the complication rate between the two groups(P>0.05). In this study, a simple and easy method of assistant line marking can shorten the operation time and reduce the number of times of operation.