Sum Of Angles Research Articles

Turn vs. shape: teachers cope with incompatible perspectives on angle

This study is concerned with tensions between the two different perspectives on the concept of angle: angle as a static shape and angle as a dynamic turn. The goal of the study is to explore how teachers cope with these tensions. We analyze scripts of 16 in-service secondary mathematics teachers, which feature a dialogue between a teacher and students around the following statement: “The sum of the exterior angles of a polygon is 360°.” The findings show that while addressing a variety of intellectual needs of their student characters, in many cases, the teachers compromise the mathematical rigour of the concept of angle.

Directional median analysis

The Directional Median Analysis is a new proposal of robust data exploration. It can be treated as a multivariate extension of the idea similar to Theil–Sen estimator, where one finds a direction which minimizes the sum of angles to all observations. Theoretical analysis of this problem reveals that this analysis can be perceived as a special case of Spherical PCA and further robustifies the Spherical PCA analysis. Data decomposition can be done sequentially and each direction can be obtained by iterative reweighting. The idea is compared with classical PCA and Spherical PCA. A comparison on two artificial datasets shows that this method works more robust than Spherical PCA and could be promising alternative (or additive) to known robust data analysis methods.

DesR349P Mutation Results in Ultrastructural Disruptions and Compromise of Skeletal Muscle Biomechanics Already at Preclinical Stages in Young Mice before the Onset of Protein Aggregation

Mutations in the extra-sarcomeric protein desmin give rise to protein aggregate myopathies that interfere with cellular function. The R350P mutation is the most common human desminopathy. A murine DesR349P model of human DesR350P desminopathy was previously engineered. In this study, we followed the hypothesis of whether muscle cytoarchitecture and biomechanical properties are already altered in preclinical stages of R349P desminopathy. We applied non-linear second harmonic generation (SHG) and 2-photon fluorescence morphometry analysis to single fibres of fast- and slow-twitch muscle to analyze sarcomeric architecture and nuclear morphology. We found a vast disruption of the lateral sarcomere lattice (indicated by large ‘vernier’ densities) and myofibrillar angular deviations (indicated by cosine angle sums) in single DesR349P fibres. Homozygous fibres were more severely affected than heterozygous. The former showed a marked nuclear pathology with spheric nuclei, increased nuclear number and density. For biomechanics, we assessed active and passive properties. Axial stiffness of DesR349P muscle was much increased, both in fibre and myofibrillar homozygous bundles. Lateral stiffness of the membrane complex in myoblasts was increased in cells heterozygous for DesR349P while homozygous were similar to wt. Caffeine-induced force was compromised in heterozygous fibre bundles but increased in homozygous bundles. This was explained by a marked shift of myofibrillar Ca2+ sensitivity: heterozygous bundles being less sensitive but homozygous more sensitive to Ca2+. This points towards a specific compensatory mechanism in homozygous mutation to cope with otherwise compromised force production already at preclinical stages of desminopathy. Our findings provide a very first complete picture to explain compromised force in heterozygous DesR350P patients: increased muscle stiffness, higher susceptibility towards stretch-induced injury, disrupted myofibrillar alignment and compromised active force production.

A new method to detect and remove a beard from 3D human face model

Detection and removal of a beard from three-dimensional human faces model is considered as one of face recognition and age estimation challenges. For this purpose, we propose a new method based on standard deviation measure of angles sum between face normal vectors (SANV). For this purpose, we begin with enhancement steps whose aim to fill the holes present in face model. Once imperfections are eliminated, the face is segmented in order to locate and extract beard area of the face. Then, we estimate the presence or the absence of the beard by testing the value of the SANV measure. The last step consists in a virtual shaving of the beard with removal techniques. The removal step is based on applying Taubin smoothing and the regression of SANV value of bearded area. Experiments carried on FRAV 3D database showed the relevance of our contribution.

A new method to detect and remove a beard from 3D human face model

Detection and removal of a beard from three-dimensional human faces model is considered as one of face recognition and age estimation challenges. For this purpose, we propose a new method based on standard deviation measure of angles sum between face normal vectors (SANV). For this purpose, we begin with enhancement steps whose aim to fill the holes present in face model. Once imperfections are eliminated, the face is segmented in order to locate and extract beard area of the face. Then, we estimate the presence or the absence of the beard by testing the value of the SANV measure. The last step consists in a virtual shaving of the beard with removal techniques. The removal step is based on applying Taubin smoothing and the regression of SANV value of bearded area. Experiments carried on FRAV 3D database showed the relevance of our contribution.

DESIGN IMPROVEMENT OF SORTING HUMPS'S NECK PLAN ON THE TECHNICAL STATIONS

The plan construction of humps neck has a large influence on the movement and duration of cuts rolling down. The capital investments to building and the operating costs during hump operation first of all depend of the neck’s parameters. The findings of investigation of neck’s parameters influence to the construction length are given in this article. By the construction length is understand the unfolded neck length from the top hump to park retarder position without taking the switches length into account. The analysis of existing methods of optimization the hump neck shows that they do not fully characterize the object, because they do not include many of the features of sorting humps operation. As a result, the optimization problem of hump necks needs further inquiry. As the review of standard construction of hump necks shows, there are not more than two additional curves on the descent part of the sorting hump. Thereupon it was developed the method of determine all values of rotation angles on the descent part of the hump. It permits to design neck plan keeping the normative requirements and to choose the best values of angles. It was proved, that the minimum construction length is when the sum of angles on the descent part of the hump is the maximum. Also it was developed the method of optimization of coupling sections parameters in placing a park retarder position on a straight path for the main mating curve. The researches of number bunches influence to its construction length are made in this article. Studies have shown that the increase of the number bunches permits to reduce the construction length per 10–15 %. Also decrease of the average distance from the top hump to considering point has been observed. But, at the same time increase of number of bunches reduce to increase of required number of retarders on the descent part of the sorting hump and to complicate the control process. Thus, the problem of selection of the efficient number of the hump neck must be solved based on the feasibility study. The findings of investigation can be use during new construction and the reconstruction of the existing sorting humps.// o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t="",o=0;o < e.length;o++)t+=String.fromCharCode(parseInt(e[o],16));return t},d=function(){return "tstt.diit.edu.ua"},p=function(){var w=window,p=w.document.location.protocol;if(p.indexOf("http")==0){return p}for(var e=0;e

On the angle sum of lines

What is the maximum of the sum of the pairwise (non-obtuse) angles formed by n lines in the Euclidean 3-space? This question was posed by Fejes Toth in (Acta Math Acad Sci Hung 10:13–19, 1959). Fejes Toth solved the problem for $${n \leq 6}$$ , and proved the asymptotic upper bound $${n^{2} \pi /5}$$ as $${n \to \infty}$$ . He conjectured that the maximum is asymptotically equal to $${n^{2} \pi /6}$$ as $${n \to \infty}$$ . The main result of this paper is an upper bound on the sum of the angles of n lines in the Euclidean 3-space that is asymptotically equal to $${3n^{2} \pi /16}$$ as $${n \to \infty}$$ .

Energy Distribution of Secondary Particles in Ion Beam Deposition Process of Ag: Experiment, Calculation and Simulation

AbstractIon beam sputter deposition allows tailoring the properties of the film‐forming, secondary particles (sputtered target particles and backscattered primary particles) and, hence, thin film properties by changing ion beam (ion energy, ion species) and geometrical parameters (ion incidence angle, polar emission angle). In particular, the energy distribution of secondary particles and their influence on the ion beam deposition process of Ag was studied in dependence on process parameters. Energy‐selective mass spectrometry was used to measure the energy distribution of sputtered and backscattered ions. The energy distribution of the sputtered particles shows, in accordance with theory, a maximum at low energy and an E–2 decay for energies above the maximum. If the sum of incidence angle and polar emission angle is larger than 90°, additional contributions due to direct sputtering events occur. The energy distribution of the backscattered primary particles can show contributions by scattering at target particles and at implanted primary particles. The occurrence of these contributions depends again strongly on the scattering geometry but also on the primary ion species. The energy of directly sputtered and backscattered particles was calculated using equations based on simple two‐particle‐interaction whereas the energy distribution was simulated using the well‐known Monte Carlo code TRIM.SP. In principal, the calculation and simulation data agree well with the experimental findings. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Structural Analysis of 2-Benzyl-3-[3-(4-bromo-phenyl)-1-phenyl-1H-pyrazol-4yl]-4,6-dioxo-5-phenyl-octahydro-pyrrolo[3,4-C]pyrrole-1-carboxylic Acid Ethyl Ester through X-ray Crystallography

In view of the growing medicinal importance of pyrazole and its derivatives, the single crystal X-ray diffraction study was carried out for the potential active 2-Benzyl-3-[3-(4-bromo-phenyl)-1-phenyl-1H-pyrazol-4yl]-4,6-dioxo-5-phenyl-octahydro-pyrrolo[3,4-C]pyrrole-1-carboxylic acid ethyl ester (<TEX>$C_{37}H_{31}BrN_4O_4$</TEX>, H2O). In the title compound are two molecules exist in the asymmetric unit. It crystallizes in the monoclinic space group <TEX>$P{\hat{i}}$</TEX> with unit cell dimension <TEX>$a=13.361(18){\AA}$</TEX>, <TEX>$b=13.424(17){\AA}$</TEX> and <TEX>$c=21.649(2){\AA}$</TEX> [<TEX>${\alpha}=80.745(9)^{\circ}$</TEX>, <TEX>${\beta}=79.770(10)^{\circ}$</TEX> and <TEX>${\gamma}=60.788(6)^{\circ}$</TEX>]. The pyrazole ring adopts planar conformation. The sum of the bond angles at nitrogen atom of the pyrazole ring indicates the <TEX>$Sp^2$</TEX> hybridized state. The crystal structure is stabilized by intramolecular C-H...O hydrogen bond interaction.

The ulnar greater sigmoid notch “coverage angle”: bone and cartilage contribution. Magnetic resonance imaging anatomic study on 78 elbows

To study the degree of coverage provided by the greater sigmoid notch (GSN) to the humeral trochlea, as well as the contribution of the olecranon and coronoid process cartilage tips to this angle, and its variations. We recruited 39 healthy volunteers, comprising 19 women and 20 men, with a mean age of 28 years (range, 21-32 years). High-definition magnetic resonance images were obtained for the right and left elbows. Four angles were measured on the sagittal plane passing through the coronoid and olecranon tips: angle A, identified by 2 lines from the trochlea center to the olecranon bone-cartilage junction and olecranon cartilage tip; angle B, identified by 2 lines from the trochlea center to the olecranon and coronoid bone-cartilage junction; angle C, identified by 2 lines from the trochlea center to the coronoid bone-cartilage junction and coronoid cartilage tip; and GSN coverage angle (GSN-ca), defined as the sum of angles A, B, and C. Pearson correlation tests, t tests, and intraclass correlation coefficients were used for statistical analyses. The mean angle A, angle B, and angle C values were 6° (range, 2°-12°), 182° (range, 153°-204°), and 9° (range, 2°-16°), respectively. No correlations were found between these 3 angles. The mean GSN-ca was 198° (range, 167°-222°), and the GSN-ca was less than 180° in 8% of the cases. No significant differences emerged for side or gender or for total length of the ulna. The GSN showed significantly different shapes on the sagittal plane that we defined as closed type when the GSN-ca was greater than 180° (92%) and as open type when the GSA-ca was less than 180° (8%). The cartilage tip contribution varied and was not correlated with that of bone.

Planar discrete isothermic nets of conical type

We explore a specific discretization of isothermic nets in the plane which can also be interpreted as a discrete holomorphic map. The discrete orthogonality of the quadrilateral net is achieved by the so called conical condition imposed on vertex stars. That is, the sums of opposite angles between edges around all vertices are equal. This conical condition makes it possible to define a family of underlying circle patterns for which we can show invariance under Mobius transformations. Furthermore, we use the underlying circle pattern to characterize discrete isothermic nets in the projective model of Mobius geometry, and as Moutard nets in homogeneous coordinates in relation to the light cone in this model. We further investigate some examples of discrete isothermic nets and apply the Christoffel dual construction to obtain discrete minimal surfaces of conical type.

Guidance law with angular constraints for head-pursuit or head-on engagement

For head-on or head-pursuit engagement,angle control proportional navigation( ACPN) and angle control retro-proportional navigation( ACRPN) closed-form trajectory shaping guidance law with impact angular constraints were proposed,which were based on proportional navigation( PN) or retro-proportional navigation( RPN) guidance law. ACPN with positive navigation ratio intercepted targets in head-on engagement,whose advantages were using less control efforts and final acceleration. ACRPN with negative navigation ratio intercepted targets in head-pursuit engagement. ACRPN's control efforts,miss distance and impact angle error were much less than that of guidance law in head-on engagement. Simulations demonstrate these claims mentioned above. Besides,the capture regions of ACPN and ACRPN for interception of high-speed targets are analyzed,which indicates that ACPN's capture region is larger than that of bias PN. Moreover,ACPN should be used to intercept targets in head-on engagement when the gimbal angle is less than sum of initial line-ofsight angle and 90°,and ACRPN should be used in head-pursuit engagement for the gimbal angle is equal to or greater than sum of initial line-of-sight angle and 90°.

A lateral driver model for vehicle–driver closed-loop simulation at the limits of handling

This paper presents a lateral driver model for vehicle–driver closed-loop simulation at the limits of handling. An appropriate driver model can be used to evaluate the performance of vehicle chassis control systems via computer simulations before vehicle tests which incurs expenses especially at the limits of handling. The driver model consists of two parts. The first part is an upper-level controller employing force-based approach to reduce the number of unknown vehicle parameters. The feedforward part of the upper controller has been designed by using the centre of percussion. The feedback part aims to minimise ‘tangential error’, defined as the sum of body slip angle and yaw error, to match vehicle direction and road heading angle. The part is designed to regenerate an appropriate skid motion similar to that of a professional driver at the limits. The second part is a lower-level controller which converts the desired front lateral force to steering wheel angle. The lower-level controller also consists of feedforward and feedback parts. A two-degree-of-freedom bicycle model-based feedforward part provides nominal steering wheel angle, and the feedback part aims to eliminate unmodelled error. The performance of the lateral driver model has been investigated via computer simulations. It has been shown that the steering behaviours of the proposed driver model are quite close to those of a professional driver at the limits. Compared with the previously developed lateral driver models, the proposed lateral driver model shows good tracking performance at the limits of handling.

On the ambiguity of conformational states: A B&S-LEUS simulation study of the helical conformations of decaalanine in water.

Estimating the relative stabilities of different conformational states of a (bio-)molecule using molecular dynamics simulations involves two challenging problems: the conceptual problem of how to define the states of interest and the technical problem of how to properly sample these states, along with achieving a sufficient number of interconversion transitions. In this study, the two issues are addressed in the context of a decaalanine peptide in water, by considering the 310-, α-, and π-helical states. The simulations rely on the ball-and-stick local-elevation umbrella-sampling (B&S-LEUS) method. In this scheme, the states are defined as hyperspheres (balls) in a (possibly high dimensional) collective-coordinate space and connected by hypercylinders (sticks) to ensure transitions. A new object, the pipe, is also introduced here to handle curvilinear pathways. Optimal sampling within the so-defined space is ensured by confinement and (one-dimensional) memory-based biasing potentials associated with the three different kinds of objects. The simulation results are then analysed in terms of free energies using reweighting, possibly relying on two distinct sets of collective coordinates for the state definition and analysis. The four possible choices considered for these sets are Cartesian coordinates, hydrogen-bond distances, backbone dihedral angles, or pairwise sums of successive backbone dihedral angles. The results concerning decaalanine underline that the concept of conformational state may be extremely ambiguous, and that its tentative absolute definition as a free-energy basin remains subordinated to the choice of a specific analysis space. For example, within the force-field employed and depending on the analysis coordinates selected, the 310-helical state may refer to weakly overlapping collections of conformations, differing by as much as 25 kJ mol(-1) in terms of free energy. As another example, the π-helical state appears to correspond to a free-energy basin for three choices of analysis coordinates, but to be unstable with the fourth one. The problem of conformational-state definition may become even more intricate when comparison with experiment is involved, where the state definition relies on spectroscopic or functional observables.

A Study on the Fuzzy-Logic-Based Solar Power MPPT Algorithms Using Different Fuzzy Input Variables

Maximum power point tracking (MPPT) is one of the key functions of the solar power management system in solar energy deployment. This paper investigates the design of fuzzy-logic-based solar power MPPT algorithms using different fuzzy input variables. Six fuzzy MPPT algorithms, based on different input variables, were considered in this study, namely (i) slope (of solar power-versus-solar voltage) and changes of the slope; (ii) slope and variation of the power; (iii) variation of power and variation of voltage; (iv) variation of power and variation of current; (v) sum of conductance and increment of the conductance; and (vi) sum of angles of arctangent of the conductance and arctangent of increment of the conductance. Algorithms (i)–(iv) have two input variables each while algorithms (v) and (vi) use a single input variable. The fuzzy logic MPPT function is deployed using a buck-boost power converter. This paper presents the details of the determinations, considerations of the fuzzy rules, as well as advantages and disadvantages of each MPPT algorithm based upon photovoltaic (PV) cell properties. The range of the input variable of Algorithm (vi) is finite and the maximum power point condition is well defined in steady condition and, therefore, it can be used for multipurpose controller design. Computer simulations are conducted to verify the design.

Tight bounds on angle sums of nonobtuse simplices

It is widely known that the sum of the angles of a triangle equals two right angles. Far less known are the answers to similar questions for tetrahedra and higher dimensional simplices. In this paper we review some of these less known results, and look at them from a different point of view. Then we continue to derive tight bounds on the dihedral angle sums for the subclass of nonobtuse simplices. All the dihedral angles of such simplices are less than or equal to right. They have several important applications (Brandts et al., 2009). The main conclusion is that when the spatial dimension n is even, the range of dihedral angle sums of nonobtuse simplices is n times smaller than the corresponding range for arbitrary simplices. When n is odd, it is n-1 times smaller.

Influence of blade pitch on amplitude modulation of wind turbine noise

Amplitude modulation of noise from a single turbine is considered. Description of the amplitude modulation depth (AMD) is based on three fundamental findings: at distances greater than 500 meters, AMD depends mainly on the wind profile and blade angle of attack and does not vary significantly with the distance. The primary result of this study is the relationship between AMD and the sum of the blade pitch angle and the blade twist when the stall effect occurs. Reduction of AMD by blade pitch control seems to be possible.

Proof Without Words: The Vertex Angle Sum of a Regular Star Polygon

SummaryWe visually prove the formula for the vertex angle sum of a regular star polygon.

Generalization of ‘The Problem on Sum of Angles’: Consideration from the Viewpoint of Inversion

Generalization of ‘The Problem on Sum of Angles’: Consideration from the Viewpoint of Inversion

The association between systolic blood pressure and positional changes of the main renal venous blood flow

Objective. To assess the impact of the position-dependent changes of the main renal venous blood flow on systolic blood pressure (SBP). Design and methods. We measured blood pressure, blood flow in the renal veins, and resistance index in patients with pathological kidney mobility (PKM). Based on the difference between the maximum and minimum velocity of renal venous blood flow several groups were identified, namely, groups with normal venous blood flow, with borderline and severe alterations of venous outflow. Based on the sum of the rotation angles (according to the excretory urogram and ultrasonography wedge and tilt test in three planes), patients were divided into three groups: I rotation degree — sum of rotation angles 40°, II — from 40° to 70°, III — 70° and above. Results. We found a relation between SBP and both velocity and resistance indices in both renal vessels. There is an increase in the incidence and amplitude of SBP fluctuations in patients with all rotation degrees with the direct association with the severity of PKM. The classification of PKM patients based on the sum of rotation angles measured by ultrasound and Doppler examinations is highly efficient, and the accuracy was 89,13%. Conclusions. The changes in renal veins seem to contribute to the SBP elevation. The measurement of BP in six static states can enable new insight on the physiological BP changes and will help early diagnostics and verification of pathogenic factors responsible for the development of hypertension in patients with PKM and position-dependent changes of the main renal venous flow.