Conic Research Articles

Optical wavelength meter with machine learning enhanced precision

A photonic implementation of a wavelength meter typically applies an interferometer to measure the frequency-dependent phase shift provided by an optical delay line. This work shows that the information to be retrieved is encoded by a vector restricted to a circular cone within a 3D Cartesian object space. The measured data belong to the image of the object space under a linear orthogonal map. Component impairments result in broken orthogonal symmetry, but the mapping remains linear. The circular cone is retained as the object space, which suggests that the conventional conic section fitting for the wavelength meter application is a premature reduction of the object space from R3 to R2. The inverse map, constructed by a learning algorithm, compensates impairments such as source intensity fluctuation and errors in delay time, coupler transmission, and photoreceiver sensitivity while being robust to noise. The simple algorithm does not require initial estimates for all parameters except for a broad bracket of the delay; further, weak nonlinearity introduced by uncertain delay can be corrected by a robust golden search algorithm. The phase-retrieval process is invariant to source power and its fluctuation. Simulations demonstrate that, to the extent that the ten parameters of the interferometer model capture all significant impairments, a precision limited only by the level of random noise is attainable. Applied to measured data collected from a fabricated Si3N4 wavelength meter, greater than an order of magnitude improvement in precision compared with the conventional method is achieved.

A Flexible Miniature Antenna for Body-Worn Devices: Design and Transmission Performance

The last few years have seen a rapid increase in body-worn devices because these devices cover a broad spectrum of potential uses. Moreover, body-worn devices still require improvements in their flexibility, size, and weight that necessitate the development of flexible and miniature antennas. In this paper, we present a new flexible miniature antenna for body-worn devices. To ensure flexibility and comfort when the antenna is in contact with the human body, a substrate from natural rubber filled with TiO2 is developed. The miniaturization is achieved using the quadratic Koch curve. The antenna design, optimization, and characterization are performed on a human body model. The performance of the antenna is analyzed in two scenarios: (1) in- to on-body, and (2) on- to off-body wireless communications. The results show that the antenna realized the maximum telemetry range of more than 80 mm for in-body communications and more than 2 m for off-body communications. Moreover, the highest 10 g specific absorption rate value was 0.62 W/kg. These results, in addition to the antenna's compact dimensions (12 mm × 26 mm × 2.5 mm) and the low manufacturing price, make the proposed antenna an ideal candidate for health telemetry applications.

Simplified BEM-based mathematical model for bottom-hinged oscillating wave surge converters under large-amplitude regular waves

The linear relationship between wave amplitude and wave torque based on the boundary element method (BEM) is widely employed for small-amplitude waves. However, linear relationships are unsuitable for bottom-hinged oscillating wave surge converters (OWSCs) under high waves owing to nonlinearities, such as wave overtopping. This paper presents an improved BEM introducing an incident wave amplitude correcting factor to simplify the complex nonlinearities under high regular waves. The correcting factors were calibrated with computational fluid dynamics (CFD) using OpenFOAM. An Oyster 800-like OWSC was adopted as the study model. A quadratic fitting curve of correcting factor vs. wave height is applicable because the calibrated correcting factors significantly correlate with wave heights but are almost irrelevant to wave periods. Though the time–history responses differ in BEM and CFD under high waves, BEM-based time-averaged results show good accuracy and high computational efficiency, such as equivalent pitch amplitude and capture width ratio (CWR). At mid-low periods, simultaneously varying power take-off (PTO) stiffness and damping than solely varying PTO damping, significantly increases CWR, especially under low waves. The capturing power under high waves substantially increases because of pitch motion amplification. At long periods, adjusting PTO inertia produces negligible efficiency improvement even with amplified oscillation.

Ferroelectric nematic liquids with conics

Spontaneous electric polarization of solid ferroelectrics follows aligning directions of crystallographic axes. Domains of differently oriented polarization are separated by domain walls (DWs), which are predominantly flat and run along directions dictated by the bulk translational order and the sample surfaces. Here we explore DWs in a ferroelectric nematic (NF) liquid crystal, which is a fluid with polar long-range orientational order but no crystallographic axes nor facets. We demonstrate that DWs in the absence of bulk and surface aligning axes are shaped as conic sections. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, play a central role as intrinsic features of liquid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.

Number of Limit Cycles for Planar Systems with Invariant Algebraic Curves

AbstractFor planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We present a general approach to prove non-existence of periodic orbits not contained in this given algebraic curve. When the method is applied to parametric families of polynomial systems that have limit cycles for some values of the parameters, our result leads to effective algebraic conditions on the parameters that force non-existence of the periodic orbits. As applications we consider several families of quadratic systems: the ones having some quadratic invariant algebraic curve, the known ones having an algebraic limit cycle, a family having a cubic invariant algebraic curve and other ones. For any quadratic system with two invariant algebraic curves we prove a finiteness result for its number of limit cycles that only depends on the degrees of these curves. We also consider some families of cubic systems having either a quadratic or a cubic invariant algebraic curve and a family of Liénard systems. We also give a new and simple proof of the known fact that quadratic systems with an invariant parabola have at most one limit cycle. In fact, what we show is that this result is a consequence of the similar result for quadratic systems with an invariant straight line.

Evaluation of Deoxyribonucleic Acid Damage Using Neutral Comet Assay for High Radiation Doses: A Feasibility Study.

This study aims to investigate the use of the neutral comet assay to assess deoxyribonucleic acid (DNA) damage in lymphocytes exposed to high doses of radiation. The research was conducted by obtaining informed consent, after which blood samples were taken from seven healthy individuals and this study was approved by the institutional ethics committee. At first, for the determination of dose-effect curves, samples obtained from the first five individuals were irradiated for doses ranging from 0 to 35 Gy after which they were processed under neutral comet assay. In order to verify the determined dose-effect curves, a test dose of 15 Gy was delivered to the samples obtained from the sixth and seventh individuals. The amount of DNA damage from the obtained comet assay images was analyzed using four comet assay parameters namely % tail DNA, tail length, tail moment (TM), and Olive TM (OTM). The most suitable comet assay parameter was evaluated based on the obtained dose-effect curves. Furthermore, the distribution of individual cells for each dose point was evaluated for all the four comet assay parameters to find the optimal parameter. From our results, it was found that from 0 to 25 Gy all the four comet assay parameters fit well into a linear quadratic curve and above 25 Gy saturation was observed. Based on the individual cell distribution data, it was found that % tail DNA could be an optimal choice to evaluate DNA damage while using neutral comet assay for high-dose ionizing radiation. The neutral comet assay could be a potential tool to assess DNA damage from high doses of ionizing radiation greater than 5 Gy.

Multiple sclerosis incidence temporal trend in the Northeast of Iran: Using the Empirical Bayesian method.

In recent years dramatic changes in multiple sclerosis (MS) incidence have been reported in different provinces in Iran. This study was conducted to assess MS incidence temporal trends from March 21, 2005, to March 20, 2020, and provide a forecast until the end of 2025 in Shahroud county. This longitudinal study was carried out based on the data obtained from the MS registration system in Shahroud county. First, the annual incidence rates were calculated based on the year of diagnosis and smoothed using the Empirical Bayesian Method. Then temporal trends and annual percent change (APC) of MS incidence were analyzed using Joinpoint (JP) regression. Finally, the univariate time series model analysis was used to estimate the MS incidence trend until the end of 2025. A total of 234 newly diagnosed cases (60 [25.64%] males and 174 [74.36.4%] females) were examined in this study. The mean age of patients at the time of diagnosis was 31.40±3.78. It was 32.01±6.35 and 30.66±4.27 years for males and females, respectively (P<0.22). The mean annual MS incidence was 5.99±1.46, 3.03±0.21, and 8.98±2.79 per 100,000 in overall, males and females respectively. The MS incidence increased significantly from 5.67 (95% CI: 3.63-7.99) in 2005 to 7.58 (95% CI: 5.17-10.28) in 2020 with an APC of 4.5 (2.8 - 6.1). The MS incidence had a non-linear time trend in the study period and the best time trend fitted to the annual MS incidence trend was the non-linear quadratic curve. Based on this model, the annual MS incidence is expected to increase until the end of 2025. Shahroud county is one of the high-risk areas for MS and the increasing trend of MS incidence in it is similar to regional and global changes. This study, also, showed that MS incidence in Shahroud county will be increasing in the coming years.

Experimental checking and modeling of the influence of operation conditions on the first order kinetic constants in free water surface wetlands

The most commonly used model in constructed wetlands is the first-order removal model, and first order kinetic constants (k) are the key parameters. The presumption is often made that k are constants. However, it is possible that k are functions of operating conditions, but the influence of operation conditions on k is unclear. In this study, response surface methodology was used to explore the variation patterns of ka (area rate constants) and kV (volume rate constants) for the removal of total nitrogen (TN) and total phosphorus (TP) in free water surface (FWS) wetlands. The experimental variables included hydraulic loading rate (HLR), water depth, and inlet concentration (Cin). The results showed that kV was more variable than ka, and the area-based first-order model is more suitable for simulating TN and TP in FWS wetlands. Inlet concentration (Cin) was significant for ka; Cin and water depth were significant for kV; HLR and the interaction between factors were insignificant. The effects of Cin on ka and kV can be described by an upward convex quadratic curve, while the effect of water depth on kV demonstrates a downward convex quadratic curve. The first-order area rate constant for TN removal was given by k = −47.66 + 22.01 Cin - 1.154 Cin2; the first-order area rate constant for TP removal was given by k = −27.75 + 95.88 Cin – 30.73 Cin2. Based on the variation patterns, the traditional k-C model was modified to the kψ-C model. The kψ-C model produced the best results at simulating the outlet concentration and removal efficiency (RE).

The Protective Role of Social-Oriented Digital Media Use in Children’s and Adolescents’ Life Satisfaction During the Covid-19 Pandemic

Covid-19 measures have reduced children’s and adolescents’ life satisfaction (LS), a key indicator of well-being. However, we have limited evidence of the longitudinal associations between changes in LS and different types of digital media use throughout the pandemic. Using data collected in Ticino, Italian-speaking Switzerland from 764 children and adolescents (Mage = 12.51, SDage = 4.00, 52% females) over five months starting from September 2020, the current study investigated temporal variations in LS, and how process-oriented versus social-oriented digital media use predicted LS, controlling for socio-demographic variables. Results of the quadratic latent growth curve model showed a steeper decrease in LS at the beginning of the second wave of the pandemic in Autumn 2020. Process-oriented digital media use predicted lower starting levels (i.e., the intercept) of LS, whereas social-oriented digital media use acted as a protective factor against the initial decrement of LS (i.e., linear slope) and positively influenced the rate of change of LS (i.e., the quadratic slope), pointing towards a faster return to baseline levels. Females, adolescents, participants with low subjective socio-economic status, and non-Swiss participants reported lower levels of LS. Results suggest that when in-person social contacts are compromised, social-oriented use of digital technologies should be promoted in young people to obtain and maintain social contacts that are crucial for LS and their well-being. LS may be conceived as a predisposing condition to accumulate, preserve, and restore mental and social well-being, which, in turn, allow individuals to contribute to their community and society at large.

역동기하를 활용한 이차곡선의 접선 탐구와 문제해결

Objectives The purpose of this study is to explore methods of effective teaching the tangent line of quadratic curves in a dynamic geometric environment.&#x0D; Methods The exploratory software GeoGebra was used as a dynamic geometric environment, and the activity worksheets for exploring the geometric properties of the tangent line to quadratic curves were developed. The changes in students’ perspective of geometry appeared were examined and their influences were analyzed.&#x0D; Results The results show that the dynamic geometric environment is significant as a means for students to think geometrically by intuitive observation and explore the inherent properties of the tangent line to quadratic curves. Teaching from the perspective of geometry made students change their views that they need to memorize formulas and be familiar with the types of problems to learn quadratic curves. There is a positive response about changes in students understanding the problem situations and leading the solving process.&#x0D; Conclusions The result of this study provides some useful implications to geometry education that harmonize perspectives of analytic geometry and synthetic geometry.

An Image-Aided Sparse Point Cloud Registration Strategy for Managing Stockpiles in Dome Storage Facilities

Stockpile volume estimation plays a critical role in several industrial/commercial bulk material management applications. LiDAR systems are commonly used for this task. Thanks to Global Navigation Satellite System (GNSS) signal availability in outdoor environments, Uncrewed Aerial Vehicles (UAV) equipped with LiDAR are frequently adopted for the derivation of dense point clouds, which can be used for stockpile volume estimation. For indoor facilities, static LiDAR scanners are usually used for the acquisition of point clouds from multiple locations. Acquired point clouds are then registered to a common reference frame. Registration of such point clouds can be established through the deployment of registration targets, which is not practical for scalable implementation. For scans in facilities bounded by planar walls/roofs, features can be automatically extracted/matched and used for the registration process. However, monitoring stockpiles stored in dome facilities remains to be a challenging task. This study introduces an image-aided fine registration strategy of acquired sparse point clouds in dome facilities, where roof and roof stringers are extracted, matched, and modeled as quadratic surfaces and curves. These features are then used in a Least Squares Adjustment (LSA) procedure to derive well-aligned LiDAR point clouds. Planar features, if available, can also be used in the registration process. Registered point clouds can then be used for accurate volume estimation of stockpiles. The proposed approach is evaluated using datasets acquired by a recently developed camera-assisted LiDAR mapping platform—Stockpile Monitoring and Reporting Technology (SMART). Experimental results from three datasets indicate the capability of the proposed approach in producing well-aligned point clouds acquired inside dome facilities, with a feature fitting error in the 0.03–0.08 m range.

Development of a non-titration potentiometric method for the determination of acidity in vinegar

The acidity of a solution is associated with the concentration of Brønsted acids. This work proposes a new non-titrimetric potentiometric method using citrate buffer for the determination of vinegar acidity. The difference between the pH values before and after the addition of a diluted vinegar sample to 10 mmol L-1 citrate buffer (pH 5.5) was related to the acetic acid concentration. The dynamic range of the quadratic analytical curve was from 3.5 to 20 mmol L-1 (R2 = 0.998). The repeatability was 0.8% for acetic acid at 0.01 mol L-1. Comparison with the conventional titration method showed an error between 0.7% and 4.64% (n = 9) for analysis of commercial vinegar samples The behaviour of the system could be explained using the buffering function.

Three Diverse Applications of General-Purpose Parameter Optimization Algorithm

Parameters often take key roles in determining the accuracy of algorithms, logics, and models for practical applications. Previously, we have proposed a general-purpose parameter optimization algorithm, and studied its applications in various practical problems. This algorithm optimizes the parameter values by repeating small changes of them based on a local search method with hill-climbing capabilities. In this paper, we present three diverse applications of this algorithm to show the versatility and effectiveness. The first application is the fingerprint-based indoor localization system using IEEE802.15.4 devices called FILS15.4 that can detect the location of a user in an indoor environment. It is shown that the number of fingerprints for each detection point, the fingerprint values, and the detection interval are optimized together, and the average detection accuracy exceeds 99%. The second application is the human face contour approximation model that is described by a combination of half circles, line segments, and a quadratic curve. It is shown that the simple functions can well approximate the face contour of various persons by optimizing the center coordinates, radii, and coefficients. The third application is the computational fluid dynamic (CFD) simulation to estimate temperature changes in a room. It is shown that the thermal conductivity is optimized to make the average temperature difference between the estimated and measured 0.22∘C.

Elementary Treatise on Melted-like Curves Derived from Center Ellipse and Circle

This study deals with a special case in the geometry of 2D special plane curves. The research treaties the development of a method for locating points and drawing curves derived from moving points on two curved paths of conic sections, namely, circle and ellipse. The paper presents geometrical methods to determine points and nodes and to draw these melted-like curves in two cases. Parametric equations are also used to determine the ordinates of the points of each curve of the two cases of the curves. This research is the initial phase for the new type of curves and awaits future studies that will deal on 3D surfaces, such as a sphere, a right cone, or a right cylinder.

Poncelet's discovery of homology

Homology was among the concepts introduced in Jean Victor Poncelet's 1822 Traité des Propriétés Projectives des Figures. Homology is a projective transformation which has an axis, a line of fixed points. The Traité develops a straightedge construction of points under homology, essentially that found in work on perspective drawing and by Phillipe de la Hire, 1673. However, Poncelet's very distinct path to homology was through similitude, where the radical axis of a pair of circles became the axis of homology. We end with Poncelet's application of homology involving the focus of a conic section.

Method of spatial cross-coupling elimination of control system channels for object guidance using two TDoA measurements

The problem of object guidance to the target point using two time difference of arrival (TDoA) measurements obtained from three navigation positions is considered. A general equation that describes a kinematic trajectory of the object along the line of intersection of two object position hyperboloids corresponding to the two TDoA measurements is obtained. It has been found out that the kinematic trajectory of the object lies in a plane perpendicular to the plane of three navigation positions. This kinematic trajectory can be described by the conic equation in the general case, and in the range of position parameters used in practice this equation yields a hyperbola. A method of elimination of object spatial cross-coupled link between control system channels, consisting in a special projection of accelerations of the object during their transformation from the measuring coordinate system to the wind coordinate system is described. This made it possible to implement object control in TDoA navigation system with three navigation positions only using two identical expressions of the kinematic link obtained for a planar case without full spatial equation for kinematic link of the object’s motion and TDoA information. A computer simulation of the object guidance to a target point in space using two TDoA measurements was performed to check the accordance of the acceleration design expressions, which produced a positive results of viewed method. The approach described in the article makes it possible to implement object guidance using TDoA navigation system if available only three of four required navigation positions.

Side-side-angle triangle congruence axiom and the complete quadrilaterals

&lt;abstract&gt;&lt;p&gt;Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.&lt;/p&gt;&lt;/abstract&gt;

Flipped learning and affect in mathematics: Results of an initial narrative analysis

Flipped learning is a constructivist methodology that uses various active learning strategies, drawing on the potential of digital technologies whenever possible. Several research studies have shown the many benefits that flipped learning can bring to students’ learning process and their affective sphere, but studies in the specific area of mathematics are still limited. The present article aims to examine the possible impact of this methodology on affective factors in mathematics. To achieve this goal, it was designed a 20-hour experiment involving about 300 secondary school students, during which conic sections were studied using a flipped approach. At the end of the experiment, textual material was collected on which a narrative analysis was conducted. The analysis took a content-categorical approach, and the reference theory for interpreting the data was the three-dimensional model for attitude toward mathematics by Di Martino and Zan (2010, 2011). The results show that a positive, rather than a negative, emotional disposition prevails, as does a view of mathematics as useful, rather than useless. Students’ perceptions of their own competence are equally distributed between low and high. Initial findings suggest that flipped learning is a methodology that can create a learning environment that has a positive influence on affective factors.

Application Of Peter Chew Theorem For Conic Section (Classification Type Of Conic Section Basis Coefficient Equation)

Application Of Peter Chew Theorem For Conic Section (Classification Type Of Conic Section Basis Coefficient Equation)

Robust Bayesian growth curve modeling: A tutorial using JAGS

Latent growth curve models (LGCM) are widely used in longitudinal data analysis, and robust methods can be used to model error distributions for non-normal data. This tutorial introduces how to modellinear, non-linear, and quadratic growth curve models under the Bayesian framework and uses examples to illustrate how to model errors using t, exponential power, and skew-normal distributions. The code of JAGS models is provided and implemented by the R package runjags. Model diagnostics and comparisons are briefly discussed.