ASPECTS AND GEOMETRIC INTERPRETATION IN SOLVING CONICAL SECTIONS by Alina Duta, Ionut - Daniel Geonea, Gordana Djukanovic, Marcela Popescu, Ludmila Sass

“…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. …”
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A Theoretical Method for Calculating the Required Force in Front of a Bulldozer- Blade by Fahim Alhimdani, Munaf Fathi Badr, Abeer Hashim

“…Advantage was taken by Reece’s family of curves from which will be possible to obtain a ready solution to most two – dimensional passive pressure problems. …”
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Optical switching for cognitive photonics by Ong, Junn Yaw

“…The results produced gave a similar family of curves as the electronic transistor. We then included the pinch-off values and the transconductance as well.…”
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The Geometry of the Kiepert Trefoil by Vladimir I. Pulov, Magdalena D. Toda, Vassil M. Vassilev, Ivaïlo M. Mladenov

“…While this curve was classically known and well studied in the literature, some related open problems were recently solved, and the goal of this paper is to present and characterize the general solution of the equation that governs this trefoil’s family of curves by involving elliptic functions and elastica theory in the mechanics.…”
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Co-convexial reflector curves with applications by Abdallah M. Al-Rashed, Neyamat Zaheer

“…The present study not only proves this conjecture and establishes the corresponding results on Stleltjes and Van Vleck polynomials in its full generality as proposed earlier by the authors, but it also furnishes a more general family of curves sharing the properties of confocal ellipses.…”
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A geometric method for eigenvalue problems with low-rank perturbations by Thomas J. Anastasio, Andrea K. Barreiro, Jared C. Bronski

“…We use the fact that the system is a low-rank perturbation of a solved problem, together with a simple idea of classical differential geometry (the envelope of a family of curves) to completely analyse the spectrum. We use these techniques to analyse three problems of this form: a model of the oculomotor integrator due to Anastasio & Gad (2007 J. …”
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A homotopy exact sequence for overconvergent isocrystals by Christopher Lazda, Ambrus Pál

“…In characteristic p, we then proceed by a series of reductions to the case of a liftable family of curves, where we can apply the rigid analytic result. …”
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Design of the Initiative Parameterization Accurate 3D Model of ZA Worm gear and Worm by Liu Guangwu, Hou Hongsheng, Tang Yangyang

“…The tooth surface of worm gear of ZA-type worm gear and worm transmission is spatial conjugate surface of complex worm cylindrical spiral surface,the mathematical equations describing of the worm gear tooth surface is complex,parametric accurate modeling is difficult.According to the principle of worm hob enveloping machining worm tooth surface,collaborative using the PDG,GSD,ASD,DMU SPA,DMU KIN 5functional modules and knowledge tools of CATIAV5 platform,the method of control the affine parameter family of curves to create a leading multi-section composite configuration 3Ddigital modeling used for precise parametric digital modeling of the ZA worm gear is proposed,a controllable parameter modeling processes with the negative feedback control of the contact analysis of the static and dynamic area is constructed,a foundation of accurate parametric 3Ddigital modeling for worm gear and worm transmission CAE advanced analysis is laid.…”
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Generating hydrodynamic surfaces by families of Lame curves for modelling submarine hulls by Valery V. Karnevich

“…The surface is constructed by a family of curves in one of the three mutually perpendicular planes, which permits to obtain three algebraically different, but geometrically identical surfaces. …”
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Stability of Fluctating Baby-Skyrme Brane by Fadhilla Emir S., Gunara Bobby E., Suroso Agus, Atmaja Ardian N.

“…The solutions can be realized as a family of curves on a surface in ℝ3. We found that there exist stable solutions provided that the physical parameters (α, σ, k) satisfy certain conditions that are deduced from the linear stability conditions near the critical points.…”
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Free curves on varieties by Gounelas, F

“…We assume the existence of a covering family of curves which dominates the product of a variety with itself either by allowing the curves in the family to vary in moduli, or by assuming the family is trivial for some fixed curve of genus g. …”

Criteria for assessing the adequacy of image recognition methods and their verification using examples of artificial series of signals by Ramin Rzayev, Azer Kerimov, Uzeyir Gurbanli, Fuad Salmanov

“…In the context of this study, a verification of a previously proposed signal recognition algorithm is carried out based on the artificial family of curves, for which the most accessible and acceptable method of displacement is established: horizontally or simultaneously horizontally and vertically.…”
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Generalized Lie symmetries and almost regular Lagrangians: a link between symmetry and dynamics by Achilles D Speliotopoulos

“…The number of such symmetries gives a lower bound to the dimensionality of the family of curves emanating from any set of allowed initial data in the Lagrangian phase space. …”
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Calibration features of information-measuring systems for diagnosing technical condition based on the analysis of the mark image blurring by Nikita S. Reuta, Nikolay K. Yurkov, Aleksey V. Grigoriev, Igor' I. Kochegarov, Evgeniya A. Danilova

“…A method for estimating measurement errors of calibration vibration displacement has been developed, justified and illustrated with a specific numerical example. A family of curves has been constructed showing the dependence of the reduced error of the calibration system of vibration displacement measuring instruments on the radius of the calibration round mark for different values of the number of pixels per image of the calibration round mark. …”

A Review of Physicochemical Stabilization for Improved Engineering Properties of Clays by Ahmed Bukhary, Shahid Azam

“…The variation of hydraulic conductivity, compression index, and compressive strength are largely within the family of curves identified by typical relationships for compacted clays. …”
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Influence of the Expected Wind Speed Fluctuation on the Number of Batteries of the Balancing System by Yaremenko Mykhailo, Klen Kateryna

“…The technique of considering ambient temperature, depth of discharge, and wind speed forecasting error when deciding the size of energy storage of the balancing system (the number of batteries and their capacity) is provided. A family of curves representing the dependence of the number of batteries constituting the balancing system on the ambient temperature and the wind speed forecasting error are presented. …”
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On the stability of the difference analogue of the boundary value problem for a mixed type equation by G.B. Bakanov, S.K. Meldebekova

“… This paper considers a difference problem for a mixed-type equation, to which a problem of integral geometry for a family of curves satisfying certain regularity conditions is reduced. …”
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EVALUATION OF THE METHODOLOGICAL ERRORS OF MEASURING THE GENERAL VIBRATION LEVEL BASED ON THE IMAGE BLUR ANALYSIS OF A ROUND BAR by A.V. Grigoriev

“…The principle of vibration signal intensity estimation is stated. A family of curves is presented, reflecting the reduced methodological error of measuring the intensity of vibration based on the analysis of the vibrational increment of the area of the image of a round mark. …”

On the stability of the difference analogue of the boundary value problem for a mixed type equation by G.B. Bakanov, S.K. Meldebekova

“… This paper considers a difference problem for a mixed-type equation, to which a problem of integral geometry for a family of curves satisfying certain regularity conditions is reduced. …”
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Flexural fatigue strength prediction of steel fibre reinforced concrete beams by S. P. Singh, Y. Mohammadi, S. K Kaushik

“…It was found that this relationship can be represented reasonably well graphically by a family of curves. The experimental coefficients of the fatigue equation have been obtained from the fatigue test data to represent the curves analytically …”
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