In mathematics, a conic is the curve that is obtained by intersecting a plane with a cone. Is well known that the shape of this curve may differ quite a bit depending on the position of the ...intersection plane relative to the cone axis, as it is actually a family of curves, commonly called "conical". In the first part, we determine the relation between the shape of the section curve and the angle of the plane of the section plane. The paper also proposes a reassembly of the cone from the fragments resulting from the sectioning with different planes. These recommences can be found as technical solutions for joining two pipes with different diameters and whose axes are not coaxial.
Locating peaks of transformed anomalies provides an effective perspective to detect lateral changes in potential field data. Recently, a number of peak detection methods based on the curvature and ...parabola-based approaches have been introduced to interpret potential field data. As a result of differences in their calculations, the various methods produce slightly different results for any given source geometry, depth and contrast or magnetization. The purpose of this study is to compare the performance of these methods in locating peaks of transformed anomalies. To obtain optimum results, these methods have been tested on synthetic datasets and also real gravity data from the Red River Trough, Vietnam. The results show that the parabola-based method and its modified version are less effective for detecting peaks in the intersection regions of sources. In addition, although the curvature-based method does not have such a problem, it can bring the secondary maximum locations.
Theoretical spectroscopic studies of beryllium oxide has been carried out, potential energy curves for ground states X1Σ+ and exited states A1Π , B1Σ+ by using two functions Morse and and ...Varshni compared with experimental results. The potentials of this molecule are agreement with experimental results. The Fortrat Parabola corrcponding to and branches were determind in the range 1<J<20 for the (0-0) band. It was found that for electronic transition A1Π- X1Σ+ the bands head lies in branche of Fortrat parabola and the bands degraded towards red region. For electronic transition B1Σ+ - A1Π Fortart parabola appeared the bands head lies in branche and the bands degraded toward violet region.
We prove (under some technical assumptions) that each surface in R3 containing two arcs of parabolas with axes parallel to Oz through each point has a parametrization ...(P(u,v)R(u,v),Q(u,v)R(u,v),Z(u,v)R2(u,v)) for some P,Q,R,Z∈Ru,v such that P,Q,R have degree at most 1 in u and v, and Z has degree at most 2 in u and v. The proof is based on the observation that one can consider a parabola with vertical axis as an isotropic circle; this allows us to use methods of the recent work by M. Skopenkov and R. Krasauskas in which all surfaces containing two Euclidean circles through each point are classified. Such approach also allows us to find a similar parametrization for surfaces in R3 containing two arbitrary isotropic circles through each point (under the same technical assumptions). Finally, we get some results concerning the top view (the projection along the Oz axis) of the surfaces in question.
•We find explicit parametrizations of the surfaces containing two arcs of parabolas with vertical axes through each point.•The idea is that a parabola with vertical axis can be considered as a circle in isotropic geometry.•We also parametrize surfaces containing two isotropic circular arcs through each point.•For the surfaces in question we describe the top views of parabolas and isotropic circles through each point.
The size and shape of the glue droplets along the spiral threads of orb webs play an important role in web function. Despite this, methods for estimating droplet volume are not well defined, with ...contradicting formulas published. Here we address the discrepancies in the published formulas with a mathematical derivation that assumes that a glue droplet conforms to a parabola along one side of the axial line. We confirmed the validity of our derived formula by comparing it with the results of numerical integration. We also document that a droplet continues to conform to a parabola as its volume changes with environmental humidity. Our formula can be applied simply by collecting the spiral threads, examining the droplets under a light microscope and measuring their length and width, making it easy to compare the droplets of different species collected at different relative humidities.
Background:
Metatarsal length is believed to play a role in plantar plate dysfunction, although the mechanism through which progressive injury occurs is still uncertain. We aimed to clarify whether ...length of the second metatarsal was associated with increased plantar pressure measurements in the forefoot while walking.
Methods:
Weightbearing radiographs and corresponding pedobarographic data from 100 patients in our practice walking without a limp were retrospectively reviewed. Radiographs were assessed for several anatomic relationships, including metatarsal length, by a single rater. Pearson correlation analyses and multiple linear regression models were used to determine whether metatarsal length was associated with forefoot loading parameters.
Results:
The relative length of the second to first metatarsal was positively associated with the ratio of peak pressure beneath the respective metatarsophalangeal joints (r = 0.243, P = .015). The relative length of the second to third metatarsal was positively associated with the ratios of peak pressure (r = 0.292, P = .003), pressure-time integral (r = 0.249, P = .013), and force-time integral (r = 0.221, P = .028) beneath the respective metatarsophalangeal joints. Although the variability in loading predicted by the various regression analyses was not large (4%-14%), the relative length of the second metatarsal (to the first and to the third) was maintained in each of the multiple regression models and remained the strongest predictor (highest standardized β-coefficient) in each of the models.
Conclusions:
Patients with longer second metatarsals exhibited relatively higher loads beneath the second metatarsophalangeal joint during barefoot walking. These findings provide a mechanism through which elongated second metatarsals may contribute to plantar plate injuries.
Level of Evidence:
Level III, comparative study.
The geomorphic literature contains many analytic solutions for the topographic evolution of gently sloping soil‐mantled hillslopes responding to base level changes. Most of these solutions are ...limited to vertical base level changes and/or to simplified geometries, however. In this paper we present an analytic solution for the morphology of a valley and its adjacent hillslopes undergoing steady headward growth. The mathematics of this problem were first solved by Ivantsov (1947) in the context of heat flow near a parabolic solidification boundary. Here we test whether the Ivantsov solution provides an accurate first‐order prediction of the morphology of valley heads and their adjacent hillslopes by comparing the model predictions to survey data from two study sites in southeastern Arizona. The model predicts that elevation contours of valley heads are parabolas and that topographic transects normal to contour lines are error functions. High‐resolution Digital Elevation Models (DEMs) were constructed for the two study sites using Real‐Time Kinematic Global Positioning System (RTK‐GPS) measurements and a Terrestrial Laser Scanner (TLS). Our analyses show that the model reproduces the first‐order morphology of headward‐growing valleys and their adjacent hillslopes. We also show that by analyzing hillslope profiles at different distances from the valley head, the model framework can be used to infer likely changes in the valley head migration rate through time.
Key Points
Topographic contours of growing valley heads are parabolas
Topographic transects of growing valley heads are error functions
Deviations from the anaytic solution indicate deviations from steady state
Purpose
Most opponents of assistive technologies in orthopedic surgery consider them as a marketing ruse or fashion. Our hypothesis was that many innovations in modern knee arthroplasty are not ...following the Scott Parabola. This parabola represents the visual curve of a procedure or therapy showing great promise at the beginning, becoming the standard treatment after reports of encouraging results, only to fall into disuse due to adverse outcome reports. This study aimed to assess the interest in these assistive technologies by (1) their number of publications/year and (2) their actual surgical use reported in the National Joint Registries.
Methods
The search was performed through PubMed, EMBASE, and MEDLINE databases from 1997 to 2021 inclusive to identify all available literature that described the use and results of assistive technologies or new surgical techniques in knee arthroplasty. In the Australian and Norwegian registries, the number of cases performed with these techniques in knee arthroplasty has been quantified year by year.
Results
Following the initial online search, a total of 4085 articles was found. After the assessment mentioned above, 2106 articles were included in the study. The orthopedic techniques assessed in this study are not following the “Scott’s parabola” in the literature. Computer-assisted knee arthroplasty and patient-specific instrumentation have increased quickly to have reached a plateau, with a stable number of publications over the last 6 years. The number of publications concerning robotic surgery, accelerometers and sensors continue to rise. In the Australian registry, the proportion of primary TKA performed by computer-assisted systems increased from 2.4% in 2003 to 32% in 2019. In the Norwegian registry, the proportion of computer-assisted TKA remained between 8 and 12% of primary TKA since 2007.
Conclusion
Most of the innovations in modern knee arthroplasty are not following the Scott Parabola. After a fast rise, these techniques do not disappear but continue to evolve. Their evolution is synergistic, and techniques appeared to be linked to each other’s. Despite persisting concerns about the cost-efficiency of assisting technologies in knee arthroplasties, the interest and use do not decrease and seems to be directly linked to an exponential increase in interest for a better understanding of alignment targets and improved functional recovery.
An optical film with aspherical microlens array (A-MLA) by using multi-step lithography process for an OLED (Organic Light-Emitting Diode) package is fabricated, by which method the luminance of ...OLEDs can be enhanced. The method of design and fabrication of an A-MLA is explored in this study. In the design process, various parameters of an A-MLA such as curved profiles, layout template and dimensions of microlens are analyzed and characterized. Curved profiles include hyperbola, parabola, ellipse and sphere; and layout templates include square, hexagon, triangle and tangential circle. The profile of the A-MLA was determined by using a commercial optical simulation software, FRED. Based on the simulated result, a film with an A-MLA was fabricated using the LIGA-like (Lithographie Galvanoformung Abformung, LIGA) process, including lithography, sputtering, micro-molding with PDMS (Polydimethylsiloxane) and UV (Ultraviolet)-cured technology. The major challenge to this process is to use JSR-126N negative thick photoresist to manufacture an approximate A-MLA optical film with multi-step lithography method. Finally, the films with A-MLAs are attached to an OLED to measure their optical-electric properties. The effectsof A-MLA optical films on OLED luminance are analyzed. In addition, the measured results are compared with simulated ones. They show good agreement with each other.
► The aspherical curved profile of the microlens array can improve the luminance of the OLED. ► An A-MLA with various profiles can substantially enhance intensity up to about 36%. ► The performance of a multi-level A-MLA has good agreement with simulation result. ► The view angles of an OLED can be increased through an A-MLA.
In this paper we prove the existence of weak solutions for a class of quasilinear parabolic systems, which correspond to diffusion problems, in the form where Ω is a bounded open domain of be given ...and The function v belongs to is in a moving and dissolving substance, the dissolution is described by f and the motion by g. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.
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