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Optical activity is investigated in a chiral medium by employing the four level cascade atomic model, in which the optical responses of the atomic medium are studied with Kerr nonlinearity. Light entering into a chiral medium splits into circular birefringent beams. The angle of divergence between the circular birefringent beams and the polarization states of the two light beams is manipulated with Kerr nonlinearity. In the stationary chiral medium the angle of divergence between the circular birefringent beams is calculated to be 1.3 radian. Furthermore, circular birefringence is optically controlled in a spinning chiral medium, where the maximum rotary photon drag angle for left (right) circularly polarized beam is ±1.1 (±1.5) microradian. The change in the angle of divergence between circular birefringent beams by rotary photon drag is calculated to be 0.4 microradian. The numerical results may help to understand image designing, image coding, discovery of photonic crystals and optical sensing technology.

In the referenced paper, Ian Mills addresses the confusion caused by the treatment of plane angle in the International System of Units (SI). As he points out, what the SI calls an 'angle' is not a dimensional physical quantity but, rather, the dimensionless numerical value of the angle when expressed in radians, thus creating widespread confusion regarding terminology and notation. For example, Mills shows that for the harmonic oscillator, if the conventional argument of the sinusoid represents an angle, it must be divided by a dimensional constant equal to one radian in order to correctly render it dimensionless, thereby greatly clarifying the notation. However, there is a problem with the author's interpretation of frequency. Although, for uniform rotation, Mills correctly defines the revolution frequency as the number of complete revolutions, N, divided by the time interval, he takes the unit for N to be 'cycle' (which he defines as one revolution) rather than the correct unit: the number one. The unit for 'frequency' then appears to be 'cycle per second' (i.e. revolution per second), whereas it should be one per second, correctly called hertz. Thus Mills concludes that 'frequency' is the same physical quantity as angular velocity and calls for the 'hertz' to be redefined as 2π rad s−1, a non-coherent derived unit for angular velocity. This misinterpretation of frequency corrupts the remainder of the author's discussion of the examples considered. In my comment, I explain and correct these and related errors.

The calibration of polarization imaging system is the premise to obtain target polarization information accurately, in this paper, we propose a method of calibration based on the radian of distorted curves in the checkboard to solve the problem of losing polarization information in the underwater distorted polarization images. Firstly, we use the radian of distorted curves in the checkboard to calculate the coordinates of distortion center, and calibrate the region near the distortion center. Then we use the calibrated region to reconstruct the whole image. Finally, we combine the distorted image, the reconstructed image and the distortion model to obtain the calibration parameters. With these parameters we can get the calibrated polarization images. The experiments show that our method can calibrate the polarization image accurately, reduce the coupled error and calculate parameters independently.

This paper is concerned with the names and symbols for quantities used to describe oscillatory motion such as for a harmonic oscillator, and the units to be used for the quantity plane angle and phase angle for an oscillator, and related quantities. I draw attention to the need to carefully distinguish the names and symbols for quantities from the names and symbols for their numerical values in any application, and the significance of including units such as radian and cycle for the quantity plane angle. The familiar equations for a harmonic oscillator such as ω = 2πν, and the relation ħ = h/2π for the Planck constant, are shown to hold only if the symbols are taken to represent the dimensionless numerical values of the quantities concerned in particular units, rather than the actual values which are not dimensionless as generally used in the equations of physics. Alternative ways of handling these quantities and units are discussed.

WOS: 000400660300007, The objective of the study was to carry out an automatic classification of the lithological units of interest using the integration of remote sensing image, in which various objects are spread on, and terrestrial spectral measurement data. Only endmembers of interest are classified using spectral classification methods such as Spectral Angle Mapper. Following the identification of the types of rock and minerals, integration of remote sensing images and spectral measurement data enable spectral classification. In this study, Short Wave Infrared detector images of Advanced Spaceborne Thermal Emission and Reflection Radiometer satellite and spectroradiometer measurements were used. The study area, Golova with its geological diversity is located in the Kelkit Valley section of the North Anatolian Fault Zone in Northeast of Turkey. Seventeen rock samples were collected and their coordinates were recorded. The samples were categorized via spectral measurements on their thin sections through petrographic analyses. Marble and Meta lava with different lithological were selected as endmembers. SAM was used as the classification method that enables the analysis of the endmember with the threshold value of 0.009 radian for marble and 0.010 radian for metalava. SAM analysis was compared by visual analysis to principle component analysis, decorrelation stretch, band ratio (R: 4/7, G: 4/1, B (2/3) x (4/3)) and band combination analysis (R: 9, G: 4 and B: 5). This study demonstrates that the SAM method can be successfully used in both the integration of remote sensing image and terrestrial spectral measurement data in lithological classification. Both the endmembers of metalava and marbles were detected in the SAM results at the GPS coordinates noted down whilst collecting the rock samples for accuracy assessment., CUBAP [M-371, M-523], We extend our gratitude to Assoc. Prof. Dr. Ziyadin Cakir, Assoc. Prof. Dr. Gursel SUNAL and Assoc. Prof. Dr. Gultekin TOPUZ for their efforts in thin sectioning and petrographic analysis of the rock samples used in this study. We also extend our gratitude CUBAP that provided the M-371 and M-523 numbered projects and data.

The radian and steradian are unusual units within the SI, originally belonging to their own category of 'supplementary units', with this status being changed to dimensionless 'derived units' in 1995. Recent papers have suggested that angles could be handled in two different ways within the SI, both differing from the present system. The purpose of this paper is to provide a framework for putting such suggestions into context, outlining the range of options that is available, together with the advantages and disadvantages of these options. Although less rigorously logical than some alternatives, the present SI approach is generally supported, but with some changes to the SI brochure to make the position clearer, in particular with regard to the designation of the radian and steradian as derived units.

In this study, the seismic performance of connections between filled composite beam (CG beams) and forming angle composite (FAC) column was experimentally evaluated. First, the bending tests were conducted on two CG beams and the axial tests were conducted on two FAC columns. Then, based on these preliminary test results, the cyclic loading test were performed on two interior connections between CG beam and FAC column. The main difference of two specimens is the plate shape of the CG beam. The test results showed that both specimens achieved the maximum story drift capacity over 0.04 radian which is required for special moment frame.

Instead of calculating the number π in this article special attention is paid to the method of measuring it. It has been found that there is a direct and indirect measurement of that number. To perform such a measurement, a selection was made of some mathematical and physical quantities which within themselves contain a number π. One such quantity is a straight angle Pi, which may be expressed as Pi = π rad. By measuring the angle, using the direct method, we determine the number π as π = arccos(-1). To implement an indirect measurement of the number π, a system consisting of a container with liquid and equating it with the measuring pot has been conceived. The accuracy of measurement by this method depends on the precision performance of these elements of the system.

The scattering of a plane electromagnetic wave by a metallic trihedral corner reflector is analyzed, in the phasor domain. Two of the metal planes of the reflector intersect the third plane perpendicularly, and form an angle between them that is equal to $\pi $ radian divided by an integer. The exact solution is obtained in closed form, and is shown to consist of the sum of a finite number of plane waves.

This paper presents a mechanical equilibrium equation for coiled tubing (CT) with an initial curvature for use in a constant-curvature wellbore, based on the beam–column method. The critical sinusoidal and helical buckling loads, the rules for the contact between the CT and wellbore, and the transmission of the axial force along the length are determined. The proposed model shows that the initial curvature of the CT has a greater influence on the critical sinusoidal buckling than on the helical buckling. In addition, both critical buckling loads increase with the initial angular radian value, and the buckling loads in constant-curvature wellbores are greater than those in vertical wells. The critical buckling loads decrease exponentially with an increase in the borehole curvature radius, which changes slightly when the curvature radius of the well increases to a certain extent. When the CT is undergoing sinusoidal buckling, the contact force between the CT and well is sensitive to the initial angular radian value, axial force, and curvature radius of the well. However, when the CT experiences helical buckling, the contact force is primarily affected by the axial force. When the CT has a small amount of residual buckling, its buckled shape is similar to that of a straight pipe. Thus, the distribution and magnitude of the contact force are similar. Meanwhile, the transmission of an axial force along the length is affected more significantly by the friction coefficient and outer diameter of the CT than by the initial angular radian value and curvature radius of the well.

A 90°-deflection imaging electron analyzer for measuring wide 2D angular distribution and perpendicular spin texture is proposed. This analyzer, which we call “right-angle-deflection imaging analyzer (RADIAN)”, provides electrostatic 90°-deflection and 2D focusing of an electron beam. Here a large acceptance angle comparable to that of cylindrical mirror analyzer (CMA) is achieved without using a grid, while CMA uses grids at the entrance and the exit of an electrostatic field. The 90° deflection allows measuring spin polarization not only in the in-plane direction, but also in the surface-normal direction. Basic properties of RADIAN, calculated by ray tracing, are shown in comparison with those of the most widely used electron energy analyzer, i.e., concentric hemispherical analyzer (CHA). RADIAN has a much higher 2D focusing capability than CHA and allows a much larger acceptance angle for 2D imaging. Moreover, the high focusing capability of RADIAN allows us to obtain high energy resolution comparable to that obtained in CHA. A simple and effective way to achieve higher energy resolution is to combine two or more RADIANs in tandem. Double-pass and triple-pass analyzers in this combination are taken into account. For a practical application, we consider a combination of RADIAN with the recently proposed ±90° omnidirectional photoelectron acceptance lens. RADIAN can be suitably used to develop a wide-angle 2D imaging analyzer, and can also be used to develop a spin-resolved 2D imaging analyzer that can perform perpendicular-spin-texture imaging.

The traditional phase gradient method can effectively measure the orbital angular momentum (OAM) number of the vortex beam. However, its spatial sampling phase aperture span is strictly restricted within only π radian. In this paper, we presented a more flexible extended aperture sampling reception (EASR) method for the radio frequency (RF) applications, which can break through this restriction condition. It could make the reception and measurement methods about the OAM mode number become more complete and versatile. By converting the higher-order OAM mode to a lower-order OAM mode, the spatial phase aperture span between the adjacent receiving sampling points can realize extensions. We have conducted a comprehensive theoretical analysis and summarized the general guidelines of this EASR method in the main body of the paper. Subsequently, we perform the related numerical simulation calculations to receive and measure the OAM mode number of a high-order mode vortex beam using the EASR method. Simulation results and theoretical analysis are in good agreement.

Giacomo Prando summarizes the troubled history of the radian, a unit with the odd property of appearing and disappearing seemingly at will in dimensional formulas.

The birefringence of rotary photon drags is investigated through induced chiral atomic medium. The birefringence of refractive and group indices, divergent angle and rotary photon drags were controlled and modified with detuning, phases and strength of Rabi frequencies of the driving fields. The value of divergent angle oscillated between ±0.01 radian with phases of control fields 3,4 and is minimum at 3 = π, while maximum at 4 = π. The left and right circularly polarized beams are drag clockwise due clockwise spinning of the medium in the normal dispersive region, while the left and right circularly polarized beams are drag clockwise due anticlockwise spinning of the medium in anomalous dispersive region. The maximum rotary photon drags of birefringent beams of light is calculated to ±5 milli radian. The results show advancement in molecular structure, dual image coding and image designing technology.

There is significant interest in the generation of complex vector beams, where the combined polarisation and phase profile is chosen to have particular properties. These beams have often been implemented in an adaptable manner using liquid crystal spatial light modulators (SLMs). Existing methods have concentrated mainly on the generation of these vector beams from a fixed polarisation state, but there are also applications were conversion between vectorial states is necessary. We discuss the limitations of existing SLM-based modulation systems for conversion between arbitrary vectorial states. Three degrees of freedom are required in principle for transition between two arbitrary states. We show that a three-SLM system can provide conversion between two arbitrary polarisation states, but cannot necessarily provide a full 2 π radian phase modulation. Hence, we propose a design using four SLMs that removes these limitations on the phase modulation.

An improved intersection feedback laser self-mixing sensing system is presented for measuring the micro-radian angle by means of the self-mixing interference effect. The experimental results demonstrate that this angle-measurement system can effectively prevent the low resolution and narrow measurement-angle range existing in traditional angle-measurement techniques. Meanwhile, the theoretical illustration and experimental analysis elucidate that both the different radii of the rotary disk and the different angles between two mirrors significantly affect angle-measurement resolution. Accordingly, over the full-circle ranging from 0 to 2π rad, the practical measurement resolution can reach up to 6.28 μrad, which is in good consistency with the simulated value. Furthermore, the absolute error of the self-mixing angle experimental measurement system is less than ± 0.97 μrad, and the relative error is less than 2.40 × 10 − 6 μrad, both of which indicate better feasibility and system reliability. As a result, it can be further extended to other applications owing to its small space size and high measurement accuracy.

In this study, we show that angular measurement of nuclear tracks produced in heavy ion interactions can be made with high precision using a CR-39 solid-state nuclear track detector. For this purpose, we have increased the position resolution of nuclear track (etch pit) analysis and the precission of thickness measurement of the CR-39 detector. The position resolution of the heavy ion track was verified to be 0.02 μm by the dedicated image analysis software package PitFit. The precision of the thickness measurement of the CR-39 detector was increased to 0.6 μm by our new both sides imaging method of the CR-39 detector using the autofocus system of the microscope. As a consequence, the angular distributions of projectiles and fragments can be realized with a precision of 1.4 × 10−2 degrees (2.5 × 10−4 radian). As a demonstration, we applied the angular measurement technique to the diagnosis of heavy ion beam and the small Coulomb scattering angle measurement of interactions of 12C + Al in energies below 100 MeV/nucleon. By this new imaging technique, event-by-event interaction of the projectiles in the CR-39 detector can be measured rapidly and can be applied to the measurement of the total charge-changing cross section, the decay mode, and the branching ratios of the projectile with higher angular precision.

Pipeline inspection gauge (PIG), as a kind of pipeline robot, Pipeline inspections gauges (PIGs) have been the main equipment during different stages of operation to perform functions such as pigging and inner inspecting. However, due to the failure of the sealing cup, the PIG is often stuck when it runs in the oil and gas pipeline especially in dented pipe. The distribution of stress and strain on the outer edge of the spherical sealing cup is complex but rewarding for understanding the blockage problems. When the PIG is in a straight pipeline section, it can be abstracted as an interference problem between polyurethanes rubber and steel. In this study, the numerical solution and the analytical solution of the polyurethane rubber and steel interference problem was first compared with each other to verify the numerical solution. Then, effects of the interference (δ), thickness (t), and radian (θ) of the spherical sealing cup on the stress and strain distribution on the outer edge of the cup were discussed using MSC Marc 2016 when the PIG was in dented pipe. Results indicate that the interference of the sealing disc has the greatest impact on the stress and strain distribution when PIG runs in the straight pipeline section. However, the thickness of the sealing cup has the greatest impact on the stress and strain distribution when PIG runs through the dent. The conclusions obtained in this study are beneficial for the selection and design of the spherical sealing cups PIG.

This study presents a theoretical approach to investigate the distinguishing features of surface plasmon polaritons (SPPs) at the interface of graphene and a four-level chiral atomic medium. The SPPs show the left and the right circularly polarized (LCP and RCP) propagation modes due to the cross coupling of electric and magnetic fields in the chiral medium. The two propagation modes of the SPPs are controlled with the strengths of control fields and their corresponding phases under the effect of Kerr nonlinearity (KNL). A 0.15 radian angle of divergence is calculated between the LCP and RCP modes of the SPPs under the effect of KNL, which is further modified to 0.5 radian with the strengths of control fields at a propagation length equal to $80 \lambda_{0}$ . The possibility of such hybrid mode SPPs propagation may result into new technological applications in the design of more compact nano-photonic devices.

In this paper, we propose a new method that using power estimation to calculate the angle between the LED transmitter and the multi-PIN receiver. We simulate the system and compare maximum power estimation and minimum power estimation and realize the precise indoor position the angle within 0.03 radian. We experimentally demonstrate that this method is practical and can be used in future indoor positioning.

The article analyzes the arguments that became the basis for declaring in 1995, at the 20th General Conference on Weights and Measures that the plane and solid angles are dimensionless derived quantities in the International System of Units. The inconsistency of these arguments is shown. It is found that a plane angle is not a derived quantity in the SI, and its unit, the radian, is not a derived unit. A solid angle is the derived quantity of a plane angle, but not a length. Its unit, the steradian, is a coherent derived unit of the radian., Correction of error in the calculation of the ratio between the steradian and the radian. 13 pages, 3 figures

Precise measurement of extremely small tilt angles is of immense importance in various scientific and technological applications. Interferometry has always been a tool of great importance in such applications. Most of the conventional interferometric techniques use a Michelson configuration and the problem with this interferometer is that it is extremely sensitive to environmental turbulances and vibrations. In our privious works, we had introduced a cyclic interferometer for the measurement of tilt angles which showed excellent stability against environmental turbulances and vibrations as well as twice the sensitivity. Also, with the introduction of multiple reflections, sensitivity as low as 5 micro radian had been achieved by us. To improve the sensitivity further, we had employed phase shifting techniques. The cyclic configuration being a same path interferometer, we used a polarizing phase shifting technique. For acieving this, we developed a new scheme of polarizing phase shifting techique which is rather simpler compared to those reported in the literature. With this we could precisely measure angles as low as 2 nano radians. However, in these measurements we found that the precise alignment of the quarter wave plate plays an important role in the visibility of the fringes which affects the accuracy of measurement. In this work, we numerically investigate the effect of the misalignment of the quarter wave plate on the visibility of the fringes and consequently on the accurcy of the measurement.

Designer spectacles look great and we want the same for a virtual display. A curved wedge guide will be described that can transfer the virtual image from a projector near the ear round to the pupil of the eye. The eye-box is tiny but the plan is to steer it so as to follow the pupil of the eye and this will be done by shearing the holographic combiner. Ray-tracing predicts a field of view of 115° per eye and a resolution of 2000 pixels per radian at the fovea using pre-distortion in the projector. Guide tolerances are lax, image accommodation is variable and a few milliWatts suffice to steer the pupil.

The stabilization system implemented has allowed one to achieve phase residual instability ~0.17 radian (rms) for the 30 fs-pulse, which is sufficient for nonlinear interaction radiation with optical medium in forthcoming lightwave electronics experiments.

Unmanned Aerial Vehicles cannot work efficiently without a control system. Before any form of control is applied to it, modeling of the system is necessary. This work focuses on the development of a Taxi model of UAV. The reformulated model has been developed and simulated in Simulink and Simscape. Three scenarios have been considered in Simulation: Normal conditions with no wind, head and tail wind of 15 m/s and steering angle of 1 radian. The key objective of this model is to include all the necessary dynamics of UAV when it is in taxi phase. This has been done by modifying the vehicle body model in Simscape to fit to the specifications of the UAV and moreover integrating it with an undercarriage model from previous literature to include the forces.

High resolution Optical imaging instruments based on aperture synthesis have been developed over the last decades with the aim of reaching angular resolution in the nano radian range. These different instruments [1] take avantage of the property of the Zernike van Cittert theorem to recover the intensity distribution of the object from its spatial coherence analysis. With this method, the instrument can never select the light coming only from one of the pixels composing the full object because the measurements are being carried out on the Fourier spectral domain.

Radian is an angle measurement in which the students studied at trigonometry subject. Educational research showed that secondary school students were found lack of radian understanding. The students know how to convert radian to a degree and vice versa. However, they fail to understand what radian is and why there are two measurements of angle in trigonometry. In this study, we propose and describe a lesson design through constructing knowledge for high school students in radian understanding. We also report on the results of a classroom case study in which the lesson design had been implemented. This study used a phenomenological investigation based on interviews and classroom observations. We also discuss the task-related difficulties that students faced in their concept development and we describe their radian understanding in terms of our framework.

A novel tool has been developed to automate the process of locating the isocenter, center of rotation, and sphere of confusion of a proton therapy gantry. The tool uses a Radian laser tracker to estimate how the coordinate frame of the front-end beam-line components changes as the gantry rotates. The coordinate frames serve as an empirical model of gantry flexing. Using this model, the alignment of the front and back-end beam-line components can be chosen to minimize the sphere of confusion, improving the overall beam positioning accuracy of the gantry. This alignment can be performed without the beam active, improving the efficiency of installing new systems at customer sites.

Several projects deploy probes in the Internet. Probes are systems that continuously perform traceroutes and other networking measurements (e.g., ping) towards selected targets. Measurements can be stored and analyzed to gain knowledge on several aspects of the Internet, but making sense of such data requires suitable methods and tools for exploration and visualization. We present Radian, a tool that allows to visualize traceroute paths at different levels of detail and to animate their evolution during a selected time interval. We also describe extensive tests of the tool using traceroutes performed by RIPE Atlas Internet probes.

HSRL measurements of extinction are more difficult than backscatter measurements. This is particularly true for low-power, eye-safe systems. This paper looks at error sources that currently provide an error limit of ~10-5 m-1 for boundary layer extinction measurements made with University of Wisconsin HSRL systems. These eye-safe systems typically use ~300mW transmitters and 40 cm diameter receivers with a 10-4 radian field-of-view.

Unit representation in the Transducer Electronic Data Sheet (TEDS) specified in the IEEE 1451 standards is a binary sequence of 10 octets that encode the physical units as a product of the seven Système International base units, plus radian and steradian, each raised to a rational power in addition to an unsigned integer indicating the structure of the unit. While this representation seems trivial, manual compilation is prone to be erroneous and impractical, especially for complex units used in the hydroclimatology field. Hence, the development of a software application to automatically generate this vector represents a critical step to both reduce work load and automate unit conversion. Existing conversion packages for manipulating units fall short in many ways and also suffer from not integrating with a units controlled vocabulary. We developed HydroUnits (Python-based) to compute the vectorial representation for the Consortium of Universities for the Advancement of Hydrologic Sciences, Inc's Observations Data Model units for use in an IEEE 1451.0-based TEDS generator. In addition, the package has been extended to support dimensional analysis, unit reduction and unit conversion and contains provision to convert time series data between different unit systems.

We developed a novel wood recognition scheme based on wood surface spectral features that aimed to solve three problems. First was elimination of noise in some bands of wood spectral reflection curves. Second was improvement of wood feature selection based on analysis of wood spectral data. The wood spectral band is 350–2500 nm, a 2150D vector with a spectral sampling interval of 1 nm. We developed a feature selection procedure and a filtering procedure by solving the eigenvalues of the dispersion matrix. Third, we optimized the design for the indoor radian’s mounting height. We used a genetic algorithm to solve the optimal radian’s height so that the spectral reflection curves had the best classification information for wood species. Experiments on fivecommon wood species in northeast China showed overall recognition accuracy >95 % at optimal recognition velocity.

The possibility of the analysis and interpretation of the reported experiments with the megajoule National Ignition Facility (NIF) laser on the compression of capsules in indirect-irradiation targets by means of the one-dimensional RADIAN program in the spherical geometry has been studied. The problem of the energy balance in a target and the determination of the laser energy that should be used in the spherical model of the target has been considered. The results of action of pulses differing in energy and time profile (“low-foot” and “high-foot” regimes) have been analyzed. The parameters of the compression of targets with a high-density carbon ablator have been obtained. The results of the simulations are in satisfactory agreement with the measurements and correspond to the range of the observed parameters. The set of compared results can be expanded, in particular, for a more detailed determination of the parameters of a target near the maximum compression of the capsule. The physical foundation of the possibility of using the one-dimensional description is the necessity of the closeness of the last stage of the compression of the capsule to a one-dimensional process. The one-dimensional simulation of the compression of the capsule can be useful in establishing the boundary behind which two-dimensional and three-dimensional simulation should be used.

Considering topography conditions, economic factors and driving safety, in real traffic, a road may be built as curved road. Traffic flow on curved road is different from the one on straight road. And it is worth to investigate the influencing mechanism of traffic flow on curved road. In order to investigate traffic flow on curved road analytically, in this paper, an extended one-dimensional lattice hydrodynamic model for traffic flow on curved road is proposed. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow varies with the radian, friction coefficient and curvature radius of curved road. The Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived to describe the nonlinear density waves in the stable, metastable and unstable regions, respectively. The simulations are given to verify the analytical results. The results, which obtained from the theoretical analysis and numerical simulations, show that traffic flow may be affected by the angle going into curved road, the increment of angle, friction coefficient and curvature radius of curved road. And the maximal theoretical flux and velocity of traffic flow are influenced by the above factors as well.

Digital video is being used widely in a variety of applications such as surveillance and security. Big amount of video in surveillance and security requires systems capable to process video automatically to detect events and track moving objects to alleviate the load on humans and enable preventive actions when events are detected [4]. our paper focuses to develop an intelligent visual surveillance system to replace the traditional passive video surveillance that is proving ineffective as the number of cameras exceeds the capability of human operators to monitor them, and it is able to track objects within a maximum solid angle speed which is measured at about 0.3 to 0.2 radian per second, further it also depends on the complexity of the system and the processor speed as well.

Soft X-ray spectra (30–70 A) of aluminum plasma have been measured in experiments carried out at the Kanal-2 laser facility at laser intensities of (1–7) × 1013 W/cm2. It is shown that the measured spectra satisfactory agree with those calculated using the RADIAN numerical code.

Intensity-modulated proton therapy (IMPT), non-coplanar 4π intensity-modulated radiation therapy (IMRT), and volumetric-modulated arc therapy (VMAT) represent the most advanced treatment methods based on heavy ion and X-rays, respectively. Here we compare their performance for prostate cancer treatment.Ten prostate patients were planned using IMPT with robustness optimization, VMAT, and 4π to an initial dose of 54 Gy to a clinical target volume (CTV) that encompassed the prostate and seminal vesicles, then a boost prescription dose of 25.2 Gy to the prostate for a total dose of 79.2 Gy. The IMPT plans utilized two coplanar, oblique scanning beams 10° posterior of the lateral beam positions. Range uncertainties were taken into consideration in the IMPT plans. VMAT plans used two full, coplanar arcs to ensure sufficient PTV coverage. 4π plans were created by inversely selecting and optimizing 30 beams from 1162 candidate non-coplanar beams using a greedy column generation algorithm. CTV doses, bladder and rectum dose volumes (V40, V45, V60, V65, V70, V75, and V80), R100, R50, R10, and CTV homogeneity index (D95/D5) were evaluated.Compared to IMPT, 4π resulted in lower anterior rectal wall mean dose as well as lower rectum V40, V45, V60, V65, V70, and V75. Due to the opposing beam arrangement, IMPT resulted in significantly (p 0.05) greater femoral head doses. However, IMPT plans had significantly lower bladder, rectum, and anterior rectal wall max dose. IMPT doses were also significantly more homogeneous than 4π and VMAT doses.Compared to the VMAT and 4π plans, IMPT treatment plans are superior in CTV homogeneity and maximum point organ-at-risk (OAR) doses with the exception of femur heads. IMPT is inferior in rectum and bladder volumes receiving intermediate to high doses, particularly to the 4π plans, but significantly reduced low dose spillage and integral dose, which are correlated to secondary cancer for patients with expected long survival. The dosimetric benefits of 4π plans over VMAT are consistent with the previous publication.

Osteoarthritis sufferers commonly have first metatarsophalangeal joint (MTPJ) problems in which articular surfaces are changed permanently due to fatigue. Therefore, medical devices for early diagnosis would increase the opportunity for prevention of disease progression. In previous studies on stiffness of the first MTPJ many details, although functionally of great importance, have not been fully considered including: design and size of the device, tribology consideration, and errors from device. Therefore, the motivation of our research was to enhance the device design by reducing the size of the device, and device design was enhanced by minimizing measurement errors through development of a new ergonomic left and right foot instrument located medial to the first MTPJ (instead of beneath the foot). The first MTPJ stiffness (N mm/kg radian) measurement was taken on 28 subjects with two replicates per subject by the same tester. The first MTPJ stiffness ranged from 3.49 to 14.42 N mm/kg radian with the mean (SD) value of 8.28 (3.15) N mm/kg radian for the left feet and 3.91 to 11.90 N mm/kg radian with the mean (SD) value of 7.65 (2.07) N mm/kg radian for the right feet. Reliability evaluation was measured using intraclass correlation coefficient and described an excellent reliability between two tests. usc Refereed/Peer-reviewed

Millimeter wave communications rely on narrow-beam transmissions to cope with the strong signal attenuation at these frequencies, thus demanding precise beam-alignment between transmitter and receiver. The resulting signaling overhead may become excessive, especially in mobile environments. This paper addresses the energy efficient design of the beam-alignment protocol, with the goal of minimizing power consumption under a transmission rate constraint. The optimality of fractional search is proved, which allocates a given fraction of the interval of uncertainty on the mobile user's angular coordinate during beam-alignment. The fractional value is shown to be a function of the communication-sensing energy ratio: when large, a wider beam is selected and the fractional value approaches 1/2 (bisection); when small, a narrower beam is used to reduce the energy cost of sensing; finally, when smaller than 1/2, sensing is suboptimal. It is proved that the energy consumption under fractional search is smaller than that under bisection by at least a quantity proportional to the product of the minimum energy per radian used during beam-alignment, and the initial uncertainty on the mobile user's angular coordinate. Numerical results demonstrate a 2dB reduction in the average power consumption compared to bisection, for a wide range of rates.

The 2-2 curved piezoelectric composites were prepared with epoxy resin as matrix and curved piezoelectric ceramics as functional phase, and the curved piezoelectric ceramics were prepared by cutting the piezoelectric ceramics ring into different radian along the radial direction uniformly. The effects of the structural parameters on the performances of piezoelectric composites were studied. The height and thickness of piezoelectric ceramic have little influence on the piezoelectric constant and dielectric constant. And with the increase of the piezoelectric ceramic high and thickness, the variation of electromechanical coupling coefficient increases and decreases respectively, and the mechanical quality factor all appears to decrease. With the increase of the composites radian, the d 33 and K t values all firstly increase and then decrease. The dielectric constant increase with the increase of the composites radian, and the mechanical quality factor shows no obvious varying rule.

We evaluate the piston-removed anisoplanatic error for smaller apertures imaging over long horizontal paths. Previous works have shown that the piston and tilt compensated anisoplanatic error saturates to values less than one squared radian. Under these conditions the definition of the isoplanatic angle is unclear. These works focused on nadir pointing telescope systems with aperture sizes between five meters and one half meter. We directly extend this work to horizontal imaging scenarios with aperture sizes smaller than one half meter. We assume turbulence is constant along the imaging path and that the ratio of the aperture size to the atmospheric coherence length is on the order of unity.

The very first Standard for Mathematical Practice asks—requires!—that we educators pay explicit attention to teaching problem-solving: MP1 Make sense of problems and persevere in solving them. And one can argue that several, if not all, of the remaining seven Standards for Mathematical Practice can play prominent roles in supporting this first standard. For example, when solving a problem, students will likely be engaging in the activities of these standards too: MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP7 Look for and make use of structure. These guides on Clever Studying through the MAA AMC align directly with the Standards for Mathematical Practice. And each individual guide directly addresses content standards too! This volume on trigonometry attends to the following standards. (The section numbers refer to the sections of this text in which the standards appear.) 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. (Sections 1 and 14.) 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Section 1.) 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (Section 1.) F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. (Section 4.) F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. (Sections 2, 3, 4, and 11.) F-TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/ 3, π/ 4 and π/ 6, and use the unit circle to express the values of sines, cosines, and tangents for π - x , π + x , and 2 π - x in terms of their values for x , where x is any real number. (Sections 3 and 7.) F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. (Sections 3, 5, 6, and 7.) F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Common Core State Standards More background to … F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Movement towards … F-TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/ 3, π/ 4 and π/ 6, and use the unit circle to express the values of sine, cosine, and tangent for π – x , π + x , and 2 π – x in terms of their values for x , where x is any real number. F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions Let's imagine a point—the Sun, say—moving counterclockwise about a circle centered at the origin, always rising in the east and setting in the west. A problem: What radius circle do we consider? Just to get the mathematics going, let's work with a circle of radius of 1 unit. For the Sun moving about the Earth (from our perspective) this is one very large unit: the number of miles from the Earth to the Sun. But let's call it one unit nonetheless. Comment. Astronomers call the mean distance of the Earth from the Sun one astronomical unit , so we are right in line with the astronomical origins of this subject doing this! If the Sun has risen x degrees from the positive horizontal axis (east), we define sin ( x ) , read “sine of x ,” is the height of the Sun at that angle of elevation. cos ( x ) , read as “cosine of x ,” is the “overness” of the Sun at that angle of elevation. That's it! Comment. Indian scholars did not think to set a convention of using a circle of radius 1. In theirwork the value of sine for a given angle of elevation also depended on the radius of the circle being examined. We'll see later on how to change the radius of the circle in our considerations too.

Common Core State Standards The background to … F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Mankind is on a perpetual scientific and intellectual quest, to answer the fundamental question: What is this universe we find ourselves in? Our need to understand our existence and our place and role in the universe, and the nature of the universe itself, has propelled grand scientific, psychological, theological, social, and creative musings since the dawn of time. The study of astronomy was one of the earliest fields of scientific pursuit. Imagine a human back at the dawn of time, sitting on the ground, observing the universe around her. She notices the Sun, the Moon, and the stars, and their motion. Each body seems to move in arcs across the day or night sky. It is natural to wonder what these objects are, how high or far away they are, what their influence on us might be, and so on. The mathematics to begin understanding the heavenly motions dates back to the ancient Babylonians (ca. 2000 bce), if not earlier. Let's address one particular natural question: How high is the Sun? Each day, the Sun rises in the east, moves across the day sky in a large arc, sets in the west, and then returns to rise in the east again the next day (on average twelve hours later). It seems natural to suspect that the Sun stays in motion during the night, moving perhaps below us on the other side of the ground. Can we determine the height of the Sun at any desired time of day? Unfortunately it is not possible to climb up to the Sun, drop a rope back down to the ground, and measure its length. From our vantage point, here on the ground, there is only one measurement we can make: the measure of the angle of elevation at which we observe the Sun. Can we determine the height of the Sun from one angle measurement? Scholars of ancient times were fully aware that the Sun does not move on a perfectly circular arc across the day sky.

The inverted pendulum on the cart which has one input and two outputs is an unstable object. Unstable object parameters estimation assumes the active method of identification. The initial angular situation of a pendulum is set, in this case 0.7 radian, and the pendulum corner measurement and the cart position definition is performed further. It gives three numbers — three amplitudes values. Thus, it is necessary to establish connection between the object parameters and the transition processes amplitudes values measured at some points in time. The special tables and nomograms are formed on the basis of the measurements executed as the result of the regulation system modeling. It is simple to determine the identified object parameters by these tables and nomograms.

We present the SI and other unit systems, including cgs-em and cgs-es, in a framework whereby a system of fully independent and dimensionally orthogonal base units is modified by conventions designed to simplify the equations that are used within each system. We propose that the radian can be seen as an independent unit whose dimensional status is modified in the SI and other unit systems for this purpose. This framework clarifies how different unit systems are interrelated, and identifies the key pieces of information that are needed to define both a unit system and the equations that are to be used with it. Specifically, these are the size of the base units in the unsimplified system, together with sufficient equations to identify all the conventions adopted by the particular unit system. The appropriate extra information for the revised SI is presented. We do not propose that the treatment of angles as dimensionless within the SI is changed. It is also proposed that the Gaussian unit system is best seen as identical to cgs-es, but with the B and H symbols in equations used to represent relativistic versions of B and H, which should properly be treated as different quantities. These different versions of B and H can similarly be used within the SI, with many of the advantages of the Heaviside-Lorentz system., 10 pages, accepted by Metrologia