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This study aims to examine the radian definition and figure representations in mathematics textbooks in Turkey. The data of this qualitative research consist of five 11th grade upper secondary mathematics textbooks used during the 2019-2020 academic year. Definitions and figures of radian angle measurement were analyzed descriptively using Alyami’s (2020) framework based on qualitative and quantitative views of angle. According to the findings, the definitions and representations of radian focus on one radian rather than the proportional relationships except the case of equality of arc length and radius. Considering the findings, we propose that the textbooks definitions and figures should highlight the quantitative relationships in addition to the case of equality of arc length and radius., Bu çalışmanın amacı Türkiye’deki matematik ders kitaplarında yer alan radyan tanım ve şekil temsillerinin incelenmesidir. Bu nitel araştırmanın verileri 2019-2020 eğitim-öğretim yılında 11. sınıf ortaöğretim matematik derslerinde okutulması kararlaştırılan beş ders kitabından toplanmıştır. Bu belgelerden elde edilen veriler Alyami’nin (2020) radyan açı ölçüsünün tanım ve şekilleri için nitel ve nicel açı görüşü ayrımına dayanan analiz çerçevesi kullanılarak betimleme çözümlemesine tabi tutulmuştur. Araştırmanın sonuçlarına göre ders kitaplarındaki radyan tanımları ve tanımı açıklayan radyan şekil temsilleri bir radyana odaklanmaktadır. Bu tanım ve şekillerde yay uzunluğu ile yarıçapın eşitlik dışındaki orantısal ilişkiye yeterince vurgu yapılmamıştır. Araştırmanın sonuçları doğrultusunda ders kitaplarındaki radyan tanımı ve radyan temsili şekillerde yay uzunluğu ile yarıçap uzunluğunun eşitlik dışındaki nicel ilişkisinin ön plana çıkarılması önerilebilir.

Layup temperature is a vital factor that affects the production quality of automated fiber placement for thermoset composites. For high quality production, this paper proposes a new prediction model of layup temperature by considering the structure of infrared heater of automatic fiber placement equipment. The model was first verified by comparing with the temperature results of layup experiments. Then a prediction on the effects of heater structure arrangement on layup temperature was conducted in the model. The research shows that the length of infrared tube and the radian of reflective-film have significant influences, rather than other parameters. According to this investigation, a heater structure-based heating strategy was presented in the paper to efficiently achieve constant temperature control in variable speed layup process.

Background The number of soft-tissue filler injections performed in the United States is constantly increasing and reflects the high demand for enhanced facial and body attractiveness. The objective of the present study was to measure the viscoelastic properties of soft-tissue fillers when subjected to different testing frequencies. The range of tested frequencies represents clinically different facial areas with more [lips (high frequency)] or less [zygomatic arch (low frequency)] soft-tissue movement. Methods A total of 35 randomly selected hyaluronic acid-based dermal filler products were tested in an independent laboratory for their values of G', G″, tan δ, and G* at angular frequencies between 0.1 and 100 radian/second. Results The results of the objective analyses revealed that the viscoelastic properties of all tested products changed between 0.1 and 100 radian/second angular frequency. Changes in G' ranged from 48.5 to 3116 percent, representing an increase in their initial elastic modulus, whereas changes in G″ ranged from -53.3 percent (i.e., decrease in G″) to 7741 percent (i.e., increase in G″), indicating both an increase and a decrease in their fluidity, respectively. Conclusions The increase in G' would indicate the transition from a "softer" to a "harder" filler, and the observed decrease in G″ would indicate an increase in the filler's "fluidity." Changes in the frequency of applied shear forces such as those occurring in the medial versus the lateral face will influence the aesthetic outcome of soft-tissue filler injections.

Sloshing is associated with the structural safety of liquid storage vessel. Installing the baffles inside the containers would be beneficial for the mitigating the damage due to the severe sloshing. In this study, an innovative type of double-side curved baffle was proposed to evaluate its effect on reducing sloshing in a rectangular tank under surge and pitch excitation. For comparison with conventional baffles, effects of the vertical baffle and the T-type baffle on mitigating sloshing were also studied experimentally and numerically by analyzing the free surface wave elevation as well as the hydrodynamic pressure on the tank wall. The effective stress at the double-side curved baffle along the height direction of the baffle is much smaller than that at the T-type baffle although they have the same mitigation effect on sloshing wave heights. The sloshing-induced effective stress on the double-side curved baffles was analyzed by varying their radian. Findings show that the effective stress on the baffle tends to decrease with the increase in the radian. The velocity field was presented to observe effect of the baffles on sloshing with the aid of ADINA and laboratory experiments conducted on a hexapod motion platform.

Based on the common existence of the mixed road, a switched controller with consideration of the difference between estimation optimal and current flux (EOCFD) is presented in the lattice hydrodynamic model of traffic flow. Based on the Hurwitz criteria and the $H_{\infty }$ -norm, stability conditions for the curved road and straight road scenarios are obtained with the transfer functions $G_{0}$ and $G_{1}$ respectively. By analyzing the Bode-plot of transfer functions $G_{0}$ and $G_{1}$ , stability analysis is performed with the feedback gain $k$ , the radian $\theta _{j}$ and the curvature radius $R$ . These theoretical results indicate that the switched control scheme prompts the traffic flow to be more stable in both curved and straight roads. Compared with Cheng’s model, numerical simulations with multiple perturbations confirm that the switched control scheme can further suppress the traffic congestion with a lower feedback gain on mixed road.

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

In this article, two kinds of dual-layer segmented Halbach arrays have been proposed for permanent-magnet (PM) brushless machines. The analytical expressions of magnetic fields due to the inner-/outer-layer Halbach magnets have been separately obtained. For the maximal flux density in the air gap, the optimal magnet segment radian ratios or magnetization angles for each dual-layer Halbach array have been analytically determined separately. The induced back electromotive force and electromagnetic torque have been analytically obtained. The prediction results show that the optimized electromagnetic performances for each double-layer segmented Halbach array with different slot and pole combinations are better than those for the corresponding single-layer one. The proposed analytical model can also be applied for optimizing the multi-layer segmented Halbach array. The analytical prediction results of a PM machine with the double-layer segmented Halbach array have been compared with those obtained by a finite-element method.

The emergence of the Global Positioning System (GPS) receiver over the years has afforded the avenue to acquire data from various geospatial locations. This paper analyses and compares the accuracy of point positions collected using three Global Positioning System (GPS) receivers— South H66/H88, Sokkia radian IS, and ProMark 3. A field study was conducted on 5 control points within the Federal University of Technology Akure (FUTA) Campus. The One-way ANOVA test performed for the coordinates obtained from the three GPS receivers at an alpha level of 0.05 using SPSS version 16 reveals no statistically significant difference between the coordinates. Analysis of the result shows that South GPS, Sokkia GPS, and ProMark GPS receivers had horizontal misclosure values of 0.1337, 0.1625 and 0.2425 respectively, making South GPS best in obtaining accurate information onhorizontal positions. For the vertical position, misclosure values of 0.0902, 0.2336, and 0.2771 respectively were obtained for the Three GPS receivers, thereby revealing that Sokkia GPS performed optimally in obtaining heights above the ellipsoid. However, as a combination of horizontal and vertical positions (3-Dimension), Sokkia GPS performed best while ProMark GPS performed averagely and South GPS performed least. This study shows that any of the three GPS receivers can provide reasonable accurate geographic data. However, a definite conclusion remains that the selection of an optimal GPS receiver in this study for any project will largely depend upon the user’s needs and project requirements as the significant variation observed in the height coordinates should be further investigated. Keywords: GPS Receivers, Accuracy, Position Determination, GPS Coordinates

Land subsidence is a phenomenon present in several cities in central Mexico, and results from a combination of groundwater resources' overexploitation and the local stratigraphic nature. Furthermore, subsidence occurs inhomogeneously in space, producing differential vertical displacements, which affect both the natural media, as well as human-built structures. Subsidence associated structural-vulnerability assessments usually rely on direct field measurements to determine parameters such as angular distortion. However, the large areas in which land subsidence occurs (city-scale) in Mexico City hinders a direct quantification of differential displacements for all buildings and structures present in it. A Sentinel-1 based subsidence analysis shows that the highest velocities are located on the eastern sector of the city. This velocity map was used as the basis for a population density weighted land subsidence correlation analysis. Our Land Subsidence Risk assessment indicates that 15.43 % of the population of Mexico City live in intermediate, high and very-high risk zones which corresponds to 1 358 873 inhabitants. Therefore, a significant percentage of Mexico City's population is vulnerable to suffering damage in their housing structures due to land subsidence. Furthermore, the lower income inhabitants share a proportionally greater economic cost due to land subsidence and associated shallow faulting. The structural vulnerability analysis of the civil structures in the city was performed using angular distortion maps derived from the subsidence velocity gradient between October 2014–October 2017 period. These maps indicate that within this time window, ∼12 % of the total urbanized area in Mexico City had already exceeded a 0.002 radian angular distortion threshold; above which damage in civil structures is more likely to occur. In fact, more than 1 million people have already suffered damages in their houses due to the differential ground subsidence and the resulting structural angular distortion. With these results, we can evaluate correspondence between angular distortion map and critical infrastructure of the city, as a result, we found that between 0 % and 12.84 % of these buildings have undergone over 0.002 radian angular distortion.

The indirect compression dynamics of targets containing capsules with ablators of a plastic, high-density carbon and beryllium is simulated in the framework of a one-dimensional model based on the 1D RADIAN code. Experiments with such targets are performed on the NIF facility in the Livermore Laboratory (USA) in 2014 – 2018. The 1D simulation data are consistent with the results of experiments and calculations made at this Laboratory. The effect of the hard part of hohlraum radiation on capsule compression parameters is confirmed. We demonstrate the feasibility of eliminating this influence not only by selecting the hohlraum material but also by introducing admixtures into the capsule that absorb this radiation. It is shown how varying the amount of admixture in the capsule ablator varies the spectrum of the radiation that heats the DT fuel.

Aiming at the shortcomings of traditional elliptic contour grinding methods, such as large grinding roughness and poor contour accuracy, a multi-axis mechanical grinding method based on algebraic geometry is proposed. This method studies the first attempt of elliptic contour. The process includes selecting suitable multi-axis grinding tools and selecting appropriate grinding methods according to grinding process. Using specific workpieces, grinding path planning, motion attitude determination and error compensation based on algebraic geometry for multi-axis mechanical grinding are carried out. The results show that compared with the traditional grinding method, the device has the smallest surface roughness, the contour radian is closer to the expected results, and has higher performance, which solves the grinding defects.

The physical behavior of the combined effect of temperature dependent viscosity and thermophoretic motion on mixed convection flow around the surface of a sphere is investigated. The set of non-linear coupled PDE is formulated and then non-dimensionalized by using an appropriate set of dimensionless variables. The dimensionless model is then transformed to convenient form for integration by employing a suitable set of primitive variables formulation and then discretized by using an efficient implicate finite difference scheme for numerical simulation. The effect of controlling parameters on velocity profile, temperature profile, and mass concentration as well as skin friction, rate of heat transfer, and mass transfer rate are analyzed. The obtained numerical results for different values of controlling parameters indicate that, velocity profile gains its largest magnitude at position X = 1.5 radian and slows down at postion X = ? radian. It is also predicted that the temperature distribution and mass concentration are diluted at position X = 1.5 radian due to rapid motion of fluid. The numerical results are highlighted in graphical as well as in tabular form.

The Gain assisted medium is being investigated to modify the rotary photon drag with the phase and angular momentum of the photon. Significant gain doublets and normal/anomalous dispersion with high subliminal/superluminal are controlled and modified by the angular quantum number and phase of angular momentum of the probe beam. Parameters of pump and control and angular momentum of probe fields enhanced photon drag from micro radian to milli radian. A $$\pm\,5$$ micro radian drag is tune to $$\pm\, 100$$ milli radian with these parameters. The rotary photon drag show large fluctuation with phase and quantum number of angular momentum of probe beam. The rotary photon drag is greatly improved as compared to the previously studied cases. The work is useful for advancing the technologies of position control, phase matching conditions and special modes of imaging coding.

The purpose of the present study was to assess the agreement at the categorical level between the Vitek 2 system and the Colibri coupled to the Radian under real routine laboratory conditions. The 675 nonduplicate clinical strains included in this study (249 Enterobacterales isolates, 198 Pseudomonas aeruginosa, 107 Staphylococcus aureus, 78 coagulase-negative staphylococci, 38 Enterococcus faecalis, and 5 Enterococcus faecium) were isolated from nonconsecutive clinical samples referred to our laboratory between June and November 2020. In addition, 43 carbapenemase-producing Enterobacterales (CPE) formerly identified and stored in our laboratory were added to the panel, for a total of 718 strains. The overall categorical agreements between the two compared methods were 99.3% (4,350/4,380; 95% CI 99% to 99.5%); 98.6% (2,147/2,178; 95% CI 98.0% to 99.0%); 99.4% (1,839/1,850; 95% CI 98.9% to 99.7%); and 99.4% (342/344; 95% CI 97.9% to 99.8%) for Enterobacterales, P. aeruginosa, Staphylococcus spp., and Enterococcus spp., respectively. The most important cause of the very major errors encountered on the Vitek 2 for P. aeruginosa (62%, 13/21) was related to the presence of heteroresistant populations. Among the 43 CPE included in this study, one OXA-48-like, and one OXA-181-like were missed by the Vitek 2, even by rigorously applying the CPE screening cutoffs defined by EUCAST. The Colibri coupled to the Radian provide a fully automated solution for antimicrobial disk diffusion susceptibility testing with an accuracy that is equal to or better than that of the Vitek 2 system.

Generally, the beam width of planar hydrophone is limited by its wavelength size, that is, when the receiving aperture is fixed, the beam width at a certain frequency is also fixed. When the working frequency is increased, in order to meet the beam width index, the receiving area of the hydrophone must be reduced accordingly, which reduces the capacitance value of the hydrophone and the ability of anti-interference and anti-current noise of the hydrophone. Large area receiving is one of the biggest advantages of PVDF hydrophone, so how to improve the beam width without reducing the receiving area is an important problem to be solved. Therefore, a circular arc backed PVDF hydrophone is proposed in this paper, which can improve the directivity of the hydrophone and make the beam width no longer limited by its wavelength size. The beam width can be adjusted by changing the shape and radian of the arc backing, so that it can be applied to different frequencies.

In this study, control research of chip morphology and removal is conducted theoretically and experimentally on the basis of the low-frequency vibration-assisted drilling process of titanium alloy. The chip morphology prediction model is established on the basis of the modified kinematic model, in which the shear angle variation, critical cutting thickness, and stiffness of a vibration generator system are considered. In terms of chip removal monitoring, a new monitoring method based on high speed camera is proposed in this paper. And the reliability of the new method is verified by comparing the signals obtained by the power sensor and the force sensor. An empirical prediction model for chip removal is also established on the basis of the modified kinematical model, the chip morphology prediction model, and the force balance analysis of fragmental chips. Validation experiments show that the mean error of chip radian, which can reflect the difference between the predicted chip morphology and the experimental one, is 6%. The mean error of the predicted chip removal index compared with the experimental one is 10.4%. The results obtained show that chip removal can be controlled effectively by low rotation speed, small chip radian, light chip weight, high minimum quantity lubrication cooling pressure, and high oscillation frequency. On the basis of the prediction model of chip removal, the effects of drilling parameters on chip removal behavior are analyzed, and the optimal drilling parameter combination with highest processing efficiency is given.

In the fields of earth observation, deep space detection, laser communication, and directional energy weapon, the target needs to be observed and pointed at accurately. Acquisition, tracking, and pointing (ATP) systems are usually designed to stabilize the line of sight (LOS) within sub-micro radian levels. In the case of an ATP system mounted on a mobile platform, angular disturbances experienced by the mobile platform will seriously affect the LOS. To overcome the problem that the sampling frequency of detectors is usually limited and achieving several hundreds of hertz is difficult, the wide-bandwidth inertial reference system (WBIRS) and fast steering mirror are usually integrated into ATP systems to mitigate these angular disturbances. To reduce the structural stress, a flexible support providing two rotational degrees of freedom is usually adopted for the system. However, the occurrence of resonant points within the bandwidth will be inevitable. Measurements have to be taken to compensate these low-frequency resonant points to realize a wide bandwidth and high precision. In this paper, the low-frequency resonant points of a system were simulated using finite element analysis and tested by a system identification method. The results show that the first-order resonance happened at 34.5 Hz with a gain of 28 dB. An improved double-T notch filter was designed and applied in a real-time system to suppress the resonance at 34.5 Hz. The experimental results show that the resonance was significantly suppressed. In particular, the resonance peak was reduced by 79.37%. In addition, the closed-loop system settling time was reduced by 36.2%. Keywords: Resonance suppression, Notch filter, System identification, Inertial reference

The shear behavior of the discontinuities has a significant influence on the stability of rock engineering. In this paper, the numerical and experimental direct shear tests were performed to investigate the shear behavior of non-persistent jointed rocks. Through a comprehensive calibration of shear stress-displacement curves and failure mode, good agreement was successfully achieved. Further numerical analysis was conducted to study the macro–micro failure mechanism. The results indicate that the shear failure of fractured rock mass begins at the end of crack in the rock mass where the crack initiation appears and as the crack expands inward of rock a macroscopic shear fracture zone is formed along the fracture plane finally. The rotation radian of particles appears obvious zoned phenomenon. The particles with larger rotation radian are mainly distributed at the location where the cracks occurred. The process of specimen failure is the process of unceasing redistribution of the rotation radians of particles inside the specimen. The distribution of contact force is obviously regional and directional and the distribution area of crack is always consistent with that of compressive stress concentration. The failure process of rock is the process of energy dissipation within the specimen, and the failure of the specimen is a kind of instability phenomenon driven by energy.

Trigonometry is among the mathematics subjects that students have difficulty in understanding due to the lack of proper understanding of the basic concepts. Research on radian, a concept that is among the fundamental concepts of trigonometry, has revealed that teachers, pre-service teachers and students lack, in some regards, proper conceptual knowledge about the subject term. Accordingly, studies on the issue bear particular importance. In the relevant literature, studies on the concept of radian focus mainly on students and pre-service teachers. However, there are not any national and contemporary studies that are conducted with teachers. In view of these, the current study aims to analyze mathematics teachers’ ways of understanding of the concept of radian. In this regard, the study attempts to explore the reasons behind teachers’ lack of conceptual knowledge regarding the concept of radian and to propose solutions that would help eliminate these reasons. The study employs case study method. The sample group consists of 41 in-service mathematics teachers who work in different types of schools. General Information Form and Concept Test developed by the researchers of the study as well as unstructured face-to-face interviews were utilized as data collection tools. As a consequence, majority of the participant teachers were found to lack an accurate and complete understanding of the concept of radian and to have some conceptual misunderstandings regarding the subject. In the conclusion section, findings of the study are discussed in relation to the relevant literature and some recommendations are made for teaching the concept of radian more efficiently.

Although much work has been done on the optimization of the recuperative heat exchangers, little attention has been paid to the optimization of rotary regenerative air preheater (RAPH) in coal-fired power plants. It is known that the ammonium bisulfate deposition (ABS) can adversely affect the safe operation of RAPH, so an improved Radian number was proposed to estimate the impact of ABS in the optimization of RAPH. The thermal hydraulic calculation program integrated with genetic algorithms was developed to conduct optimizations of RAPH. The design parameters included rotor radius, each fluid sector angle and each matrix layer height. The multi-objective optimization was carried out to maximize the effectiveness and to minimize the pressure drop from the perspective of users, while the single-objective optimization was performed to minimize the weight of the heat transfer elements from the perspective of manufacturers. The improved Radian number is more reasonable to reflect the ABS deposition compared with the original Radian number. The designer can estimate the ABS deposition status using the improved Radian number not only in the operating process but also in the design process of RAPH. The range of optimal solution becomes smaller but the rank of the Pareto solution stays unchanged with the decrease in the restriction of improved Radian number. The optimization with larger rotor radius restriction could obtain better Pareto results. The total weight of heat transfer elements could be reduced by at least 26.5% compared with that of the original design by using genetic algorithm.

This paper investigates the dispersion characteristics of guided waves in a multilayered magneto-electro-elastic curved panel. Based on the Hamilton principle, the Chebyshev spectral element method is applied along the radial and circumferential directions to obtain the dispersion equation of the waves. The advantage of the spectral element method over a high degree piecewise polynomial basis function is the high order of accuracy. The influences on the dispersion characteristics is analyzed in terms of four factors: structural radian, magneto-electro effect, thickness-diameter ratio, and stacking sequence. In addition, the dispersion curves in the curved panel display a phenomenon which different from plate and hollow cylinders: mode conversion. We explain this from the perspective of physics and mathematics, separately. The structural radian and thickness-diameter ratio show the most significant effect on the mode conversion.

Purpose: The concept of 4πc radiotherapy is a radiotherapy planning technique receiving much attention in recent times. The aim of this article is to disprove the feasibility of the 4π radiotherapy using a cantilever-type linear accelerator or any other external-beam delivery machines. Materials and Methods: A surface integral-based mathematical derivation for the maximum achievable solid angle for a linear accelerator was carried out respecting the rotational boundary conditions for gantry and couch in three-dimensional Euclidean space. The allowed movements include a gantry rotation of 0–2πc and a table rotation of πc/2 - 0 - 3πc/2) . Results: Total achievable solid angle by cantilever-type linear accelerator (or any teletherapy machine employing a cantilever design) is 1/r2 π ∫ - θ=0 π ∫ φ=0 (rSinθdφ). (rdθ) = 2πc, which is applicable only for the foot and brain radiotherapy where the allowed table rotation is 90°–0°–270°. For other sites such as pelvis, thorax, or abdomen, achievable solid angle as the couch rotation comes down significantly. Practically, only suitable couch angle is 0° by avoiding gantry–couch–patient collision. Conclusions: Present cantilever design of linear accelerator prevents achieving a 4π radian solid angle at any point in the patient. Even the most modern therapy machines like CyberKnife which has a robotic arm also cannot achieve 4π geometry. Maximum achievable solid angle under the highest allowable boundary condition(s) cannot exceed 2πc, which is restricted for only extremities such as foot and brain radiotherapy. For other parts of the body such as pelvis, thorax, and abdomen, the solid angle is reduced to 1/5th (maximum value) of the 4πc. To obtain a 4πc solid angle in a three-dimensional Euclidean space, the patient has to be a zero-dimensional point and X-ray head of the linear accelerator has a freedom to rotate in every point of a hypothetical sphere of radius 1 m. This article establishes geometrically why it is not possible to achieve a 4πc solid angle.

This chapter presents a description of a guidance and control system on robust pathfollowing flight for Unmanned Aerial Vehicle (UAV). Guidance and control systems on path-following flight for UAV, most based on a tracking-error-correction approach, have been studied for several years (Blajer, 1990; Baba et al., 1996, 2002; Kaminer et al., 1998; Boyle & Chamitoff, 1999; Ochi et al., 2002; Park et al., 2004; Rysdyk, 2006). However, these systems present the difficulty of following in large tracking-error situations, e.g. steep curved path-following or tracking under wind turbulence, which might cause control saturation or divergence because the control command tends to increase as the trackingerror becomes large. One coauthor proposed a variable gain method using fuzzy logic (Baba & Takano, 1998), which gathers and weighs on control laws according to tracking-error quantities. It performed well, but it was necessary to set some design points and to conduct several gain tunings before applying fuzzy logic. This chapter presents a novel, simple, yet robust guidance method for path-following UAV (Sato et al., 2006; Yamasaki et al., 2007). The methodology uses pure pursuit guidance instead of traditional tracking-error correction-based methods. Pure pursuit guidance (e.g. Machol et al., 1965) demands only one gain-tuning. It produces guidance commands that are not large, with no relation to tracking error quantities. It can avoid control divergence because the pure pursuit guidance system generates guidance commands in relation to the line-of-sight angle (the angle formed by the UAV velocity vector and the line-of-sight to the target point), which is, at most, π radian. That angle might be much less than the tracking error, e.g. 10 m. For that reason, a robust path-following UAV can be realized assisted by pure pursuit guidance (Park et al., 2007). A target point for the UAV to orient is necessary for applying pure pursuit guidance for path-following. We introduced a receding virtual waypoint, which is placed at a proper point along a desired trajectory. This is the point of difference from the error-based reference point described in the literature (Park et al., 2007). The desired path can be provided easily in a form of a function of the trajectory arc length using cubic-spline interpolation based on some waypoints through which the UAV is presumed to fly. Once the path is generated in the form of the function of the arc length, the receding virtual waypoint, which is the target point for pure pursuit guidance, is calculable using the cubic-spline function based on the UAV flight arc length added a few seconds ahead of the future flight path length, as inferred from the UAV dynamics. This added term

In this paper, a tunable aperture driven by a single-phase piezoelectric motor is presented. The piezoelectric motor is composed of piezoelectric ceramic and carbon fiber layer. The influence of fiber orientation on the mechanical characteristics of the motor is analyzed by finite element method. The prototype of the aperture is manufactured and tested. The results show that the opening and closing durations of the aperture are 89 ms and 92.4 ms, respectively, for a rotation range of 90°, under a driving voltage of 150V. The minimum angular resolution can reach $4^{*}$10-5 radian.

We present a spectral phase measurement and correction method utilizing a pulse shaper. Positive and negative π/2 spectral phase steps are scanned across the spectrum of the pulse while collecting second harmonic spectra. Second and third order phase distortions show characteristic features in the difference between the spectra. Computer simulations show the amplitude and sign of these features quantitatively determine the magnitude and sign of the second and third order dispersion with milliradian accuracy. Experimental dispersion measurements are benchmarked by measuring the group velocity dispersion of air as well as fused silica windows.

A Wheeler method for the evaluation of the radiation efficiency of submerged antennas within lossy media is presented and demonstrated for the first time in the literature. Extensive investigations have been devised by empirical and simulation methods. Normal-mode helical antenna (NMHA) was first designed and fabricated to exemplify a real-life application at the UHF band (0.3 to 3 GHz). The antenna under test (AUT) was evaluated within an artificial lossy material using a series of Wheeler caps featuring different radii to study the validity of this method. The error between the experimental and simulation radiation efficiency is below 3% near the theoretical radian length. The presented measurement method of radiation efficiency without any essential measurement facilities or accessories could be a promising candidate for fast and accurate evaluation for any wire-type antenna submerged within lossy media.

The Fizeau’s light birefringence dragging effect is investigated in a moving chiral medium. The effect significantly influences the subluminality, superluminality, phase shift and divergence angle between the circularly polarized birefringent modes. The maximum superluminal group velocity is measured in the range $$-4\times 10^8$$ – $$1\times 10^{10}$$ m/s. The group index and group velocity measured with phase of the control field and phase of the superposition states are in the range $$0.4\le n^{(\pm )}_g\le 0.8$$ and $$4\times 10^8$$ m/s $$\le v^{(\pm )}_g\le 8\times 10^8$$ m/s, respectively. The maximum Fizeau’s birefringence dragging coefficient is noted in the range $$-20\le F_D\le 20$$ and varies with phases of the applied fields in the range $$\pm 1$$ . The birefringent phase uncertainty between the phase shift under dragging and in the absence of the dragging effect is in the range $$0.005\le \Delta \Phi ^{(\pm )}\le 0.015$$ radian. The divergence angle between the two modes is in the range $$0.000\le \theta _d\le 0.004$$ radian. The controlled birefringence phase uncertainty may show significant applications in interferometry, velocimetry and sensitivity.

As one of the important storage facilities for petroleum and petrochemical products, storage tanks are widely used by enterprises. With the increase of tank service time, tank deformation becomes one of the safety hazards of tank. The traditional Radian ruler, whole station instrument and other methods are slow to check the speed, it is difficult to meet the needs of the scene. In this paper, three-dimensional laser scanning technique is applied to tank deformation detection, the characteristics of cloud distribution of tank deformation point are analyzed, and the deformation of tank is evaluated by using point cloud data. The results show that 3D laser scanning technology can effectively detect tank deformation and provide technical support for improving tank risk control ability.

Influenced by radian of the Earth and the waves, also the shelter of ships and sea waves, wireless channels above the sea have the effects of deep fading and multipath. Microwaves of very high frequency and ultrahigh frequency are analyzed in oceanic environments. We considered the direct path, paths of mirror reflection, and diffuse scattering, and we calculated the power of mirror reflection and diffuse scattering theoretically. Area of effective diffuse scattering and partitioning was introduced to calculate the power of multipath. We built a generalized channel model with different frequency band and communication range.

To explore the rectification parameters of the diversion piers optimized for the forebay of the pump station with a lateral angle of 45°, the orthogonal experiment and computational fluid dynamics methods are used to analyze the flow characteristics of the diversion piers under different parameter combinations. The flow pattern in the forebay of the side water inlet is improved. The rectification effect of the diversion piers under 16 schemes is analyzed, considering the length, width, radian, and relative height of the diversion piers. Combined with numerical simulation, a better rectification scheme is provided, and finally, a reasonable range of values for the rectification parameters of the forebay diversion pier of the side 45° bend angle pump station is obtained.

With the improvement of living standards around the world, people's love for sports has also increased; basketball is especially loved by people. It is of great importance to provide sound motor instruction for basketball. To this end, this paper comprehensively investigates the dependence between the optimal release conditions and the corresponding shooting arm movements in basketball players. We carry out kinematic feature analysis of basketball sports videos, propose a hybrid CNN-LSTM model that can predict the arc of the shooting parry, and identify the key movements of the arm joint that produce optimal release velocity, angle, and backspin in short-, mid-, and long-range shots. The experiment demonstrates that the model has three rigid planar links with rotational joints that mimic the shoulder, elbow, and wrist joints of the upper arm, forearm, and hand, which are better at guiding the optimal ball release speed, angle, and backspin for different players with the fastest ball speed being about 4.6 m/s and the slowest being about 1.7 m/s.

The Gaia satellite was launched at the end of 2013 to collect data that will allow the determination of highly accurate positions, parallaxes, and proper motions for over one billion sources brighter than magnitude 20.7, from the solar system to our Milky Way and beyond. I will discuss the astrometric measurement concept and the design considerations and engineering challenges that follow. I will also review the problems faced in practice during the mission which however did not prevent its phenomenal success, as will be demonstrated with a few scientific highlights.

We present a novel nested-shell Wolter x-ray telescope design that can achieve diffraction-limited performance over the entire telescope aperture. The new design features a compact single-spacecraft mirror assembly, similar in form to that proposed for Lynx, and a separate detector spacecraft. A wide range of design parameter space was considered. We present a specific example which features 10 micro-arcsec resolution, a wide band (0.1-10 keV) with > 2 m2 effective area out to 10 keV, a large flat field (>1010 pixels), achieving diffraction-limited performance (Strehl ratio > 0.8). We will also briefly discuss a potential science case for this telescope.

Contactless actuation powered using light is shown to generate torque densities approaching 10 N m kg−1 at angular velocities ∼102 rad s−1: metrics that compare favorably against tethered electromechanical systems. This is possible even though the extinction of actinic light limits the characteristic thickness of photoresponse in polymers to tens of μm. Confinement of molecularly patterned developable shells fabricated from azobenzene-functionalized liquid crystalline polymers encodes torque-dense photoactuation. Photostrain gradients from unstructured irradiation segment this geometry into two oppositely curved regions connected by a curved crease. A monolithic curved shell spontaneously bifurcates into a jointed, arm-like mechanism that generates flexure over sweep angles exceeding a radian. Strain focusing at the crease is hierarchical: an integral crease nucleates at smaller magnitudes of the prebiased curvature, while a crease decorated with point-like defects emerges at larger curvatures. The phase-space of morphogenesis is traceable to the competition between stretch and bending energies and is parameterizable as a function of the geometry. The framework for generating repetitive torque-dense actuation from slender light-powered actuators holds broader implications for the design of soft, remotely operated machines. Here, it is harnessed in illustrative mechanisms including levers, lifters and grabbers that are powered and regulated exclusively using light.

Hyperlensing devices have drawn great attention in recent years due to their ability to amplify the subwavelength image of objects with more detail and information. In this work, a hyperlens with a radian inner surface is designed and demonstrated. The proposed hyperlens is capable of imaging different types of sub-wavelength objects efficiently. Plasmonic resonant cavity is also employed in order to achieve a super-resolution imaging effect. Different objects are investigated to test the performance of the proposed hyperlens. As expected, our hyperlens shows better tolerance than the conventional hyperlensing designs and can achieve imaging resolution down to 60 nm for different types of objects.

This paper proposes a calculation method to determine the frequency deviation of microgrid (MG) system in transferring mode, using the mathematical model of distribution slack bus load flow (DSLF). In the proposed method, the modified incorporating Newton-Raphson load flow incorporating generation control equations are used to find the primary frequency deviation. The IEEE radian distribution 33-bus was modified as an microgrid model and used to test the proposed method.