Curves of genus 2 with real multiplication by a square root of 5 by Wilson, J

“…To this end, we review previous work in this area, and are able to use a criterion due to Humbert in the last century to produce a family of curves of genus 2 with RM by $\mathbb{Q}(\sqrt{5})$ which parametrizes such curves which have a rational Weierstrass point. …”

Design of a maximum power point tracking-based PID controller for DC converter of stand-alone PV system by Fatema A. Mohammed, Mohiy E. Bahgat, Saied S. Elmasry, Soliman M. Sharaf

“…The system performance is displayed using a family of curves under different operating conditions and disturbances.…”
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The USLE soil erodibility nomograph revisited by Eva Corral-Pazos-de-Provens, Ígor Rapp-Arrarás, Juan M. Domingo-Santos

“…All models are shown to have areas where the fit is deficient or even unacceptable. Besides, the family of curves on the nomograph for the various values taken by the organic matter are not coincident with the mathematical function from which they presumably derive. …”
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Contact fracture behavior of ice by V. P. Epifanov

“…It is established that under conditions of the experiment (smooth convex indenter surface and icy half-space) a thin intermediate layer is formed, the properties of which determine the physical similarity in the family of curves «instantaneous force-instantaneous velocity». …”
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DETERMINATION OF THE SOIL SOUNDING DEPTH FOR THE EARTHING RESISTANCE CALCULATION OF SUBSTATIONS 35 KV by D. G. Koliushko, S. S. Rudenko, L. V. Asmolova, T. I. Tkachova

“…In the experiments carried out, a family of curves was obtained that describes the effect of separation depth of soil layers for various combinations of soil electrical resistivities and geometric dimensions of the earthing arrangement. …”
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Hyperbolastic type-III diffusion process: Obtaining from the generalized Weibull diffusion process by Antonio Barrera, Patricia Román-Roán, Francisco Torres-Ruiz

“…The present paper introduces a diffusion process whose main characteristic is that its mean function belongs to a wide family of curves derived from the classic Weibull curve. …”
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Growth of Caiman crocodilus yacare in the Brazilian Pantanal. by Zilca Campos, Guilherme Mourão, Marcos Coutinho, William E Magnusson

“…Age-size relationships were estimated using growth models from the Richards family of curves (full model, von Bertalanffy and monomolecular). …”
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Method for Approximating Field-Line Curves Using Ionospheric Observations of Energy-Variable Electron Beams Launched From Satellites by Jake M. Willard, Jay R. Johnson, Jesse M. Snelling, Andrew T. Powis, Igor D. Kaganovich, Ennio R. Sanchez

“…The first step in the procedure would be to use prior information to obtain an initial forecast of the inner magnetosphere. Then, a family of curves would be defined that satisfies the observed geometric attributes measured by the experiments, and the prior forecast would then be used to optimize the curve with respect to the allowed degrees of freedom. …”
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The continuous method of solution continuation with respect to the best parameter in the calculation of shell structures by A.A. Semenov, S.S. Leonov

“…For the system of algebraic or transcendental equations, the solution of which is a one-parameter family of curves, the method of solution continuation is as follows. …”
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Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth by A. Latifi, M. A. Manna, P. Montalvo, M. Ruivo

“…A dimensionless water depth parameter depending to depth and a characteristic wind speed, induces a family of curves representing the wave growth as a function of the wave phase velocity and the wind speed. …”
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Local indicators of geocoding accuracy (LIGA): theory and application by Jacquez Geoffrey M, Rommel Robert

“…</p> <p>Results</p> <p>We find that a family of curves describes the relationship between perturbability and positional error, and use these curves to evaluate sensitivity of alternative spatial weight specifications to positional error both globally (when all locations are considered simultaneously) and locally (to identify those locations that would benefit most from increased geocoding accuracy). …”
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Imaginary geometry I: interacting SLEs by Miller, Jason P., Sheffield, Scott Roger

“…Letting θ vary, one obtains a family of curves that look locally like SLE[subscript κ] processes with κ∈(0,4) (where χ=2[sqrt]κ−[sqrt]κ2), which we interpret as the rays of a random geometry with purely imaginary curvature. …”
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Robust hybrid control for autonomous vehicle motion planning by Frazzoli, Emilio, 1970-

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Influência do período de centrifugação na curva de retenção de água em solos de Cerrado Influence of the centrifugation time in the soil-water retention curve in Cerrado soils... by Euzebio Medrado da Silva, Juscelino Antonio de Azevedo

“…For each soil type, the obtained retention curves were presented as a family of curves to facilitate the visualization of differences among them. …”
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On the phase between pressure and heat release fluctuations for propane/hydrogen flames and its role in mode transitions by Speth, Raymond L., Ghoniem, Ahmed F., Hong, Seung hyuck, Shanbhogue, Santosh

“…This index, plotted against a density-weighted strained consumption speed, indicates that the impact of the operating parameters on the dynamic mode selection of the combustor collapses onto a family of curves, which quantify the state of the combustor within a dynamic mode. …”
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The design of coupled microstrip lines / by 265507 Akhtarzad, Sina, Rowbotham, Thomas R., Johns, Peter B.

“…The results are presented in graphical form using only two universal families of curves. Results are also presented in the form of simple formulas for designprograms and also comparisons with practical results are made.…”

On the relative minimal model program for fourfolds in positive and mixed characteristic by Christopher Hacon, Jakub Witaszek

“…We show the validity of two special cases of the four-dimensional minimal model program (MMP) in characteristic $p>5$ : for contractions to ${\mathbb {Q}}$ -factorial fourfolds and in families over curves (‘semistable MMP’). We also provide their mixed characteristic analogues. …”
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The Brauer-Manin Obstruction and Sha[2]. by Bright, M, Bruin, N, Flynn, E, Logan, A

“…We exploit the relationship with the Tate-Shafarevich group to give new types of examples of Sha[2], for families of curves of genus 2 of the form y^2 = f(x), where f(x) is a quintic containing an irreducible cubic factor.…”

Combinatorial aspects of nodal curves by Simone Busonero, Margarida Melo, Lidia Stoppino

“…To any nodal curve <em>C</em> one associates its degree class group, a combinatorial invariant which plays an important role in the compactification of the generalized Jacobian of <em>C</em> and in the construction of the Néron model of the Picard variety of families of curves having <em>C</em> as special fibre. In this paper we study this invariant.…”
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Reduction of sampling effort assessing macroinvertebrate assemblages for biomonitoring of rivers by Gartzia De Bikuña B., López E., Leonardo J.M., Arrate J., Martínez A., Agirre A., Manzanos A.

“…The macroinvertebrates were identified to family level and a smoothed family accumulation curve fitting the Clench function to the data was calculated for each stream. …”
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