1. Agricultural-Induced Environmental Kuznets Curve for South Africa : A Threshold Regression and ARIMA Forecasting ApproachAndrew Phiri, Rasaq Raimi, 2025, izvirni znanstveni članek Opis: The purpose of the paper is to examine the impact of the agricultural sector on agricultural emissions in South Africa. To this end, we estimate an agricultural-induced environmental Kuznets curve (EKC) for South Africa between 1990 and 2022 using conventional and threshold regression frameworks. Our regression estimates reveal a ‘humped-shaped’ relationship between agricultural production and agricultural emissions, whereby agricultural production produces lower agricultural emissions above threshold estimates of 4,876 and 6,100 metric tons of CO2 emissions. Further investigations show that the South African economy has consistently remained above these thresholds since 2010. Moreover, a forecast analysis of the time series using ARIMA models shows that agricultural productionis (emissions are) on an upward (a downward) trajectory. However, the forecasting analysis also shows that the South African agricultural sector is not scheduled to reach the net-zero emissions target by 2050. Altogether, these findings imply that whilst South Africa had followed a trajectory of sustainable development prior to the COVID-19 pandemic, the current trajectory may not be sufficient to attain the 2050 Sustainable Development Goals.
Ključne besede: agricultural sector, agricultural emissions, environmental Kuznets curve (EKC), threshold regression model, ARIMA forecasting, South Africa
Objavljeno v RUP: 16.01.2026; Ogledov: 193; Prenosov: 0
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2. On ▫$L^2$▫ approximation by planar Pythagorean-hodograph curvesRida T. Farouki, Marjetka Knez, Vito Vitrih, Emil Žagar, 2025, izvirni znanstveni članek Opis: The ▫$L^2$▫ approximation of planar curves by Pythagorean-hodograph (PH) polynomial curves is addressed, based on the distance defined by a metric for planar curves represented as complex valued functions of a real parameter. Because of the nonlinear nature of polynomial PH curves, constructing ▫$L^2$▫ approximants involves solving a nonlinear optimization problem. However, a simplified method that requires only the solution of a linear system may be developed by formulating the ▫$L^2$▫ approximation in the preimage space. The extension of the methodology to approximation by PH B-spline curves is also addressed, and several examples are provided to illustrate its implementation and potential.
Ključne besede: ▫$L^2$▫ approximation, complex polynomial, Pythagorean-hodograph curve, Pythagorean-hodograph spline, preimage
Objavljeno v RUP: 30.05.2025; Ogledov: 2317; Prenosov: 16
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5. Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curvesGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2008, izvirni znanstveni članek Opis: In this paper, the geometric Lagrange interpolation of four points by planar cubic Pythagorean-hodograph (PH) curves is studied. It is shown that such an interpolatory curve exists provided that the data polygon, formed by the interpolation points, is convex, and satisfies an additional restriction on its angles. The approximation order is $4$. This gives rise to a conjecture that a PH curve of degree ▫$n$▫ can, under some natural restrictions on data points, interpolate up to ▫$n+1$▫ points.
Ključne besede: numerical analysis, planar curve, PH curve, geometric interpolation, Lagrange interpolation
Objavljeno v RUP: 03.04.2017; Ogledov: 3611; Prenosov: 140
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6. An approach to geometric interpolation by Pythagorean-hodograph curvesGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2012, izvirni znanstveni članek Opis: The problem of geometric interpolation by Pythagorean-hodograph (PH) curves of general degree ▫$n$▫ is studied independently of the dimension ▫$d \ge 2$▫. In contrast to classical approaches, where special structures that depend on the dimension are considered (complex numbers, quaternions, etc.), the basic algebraic definition of a PH property together with geometric interpolation conditions is used. The analysis of the resulting system of nonlinear equations exploits techniques such as the cylindrical algebraic decomposition and relies heavily on a computer algebra system. The nonlinear equations are written entirely in terms of geometric data parameters and are independent of the dimension. The analysis of the boundary regions, construction of solutions for particular data and homotopy theory are used to establish the existence and (in some cases) the number of admissible solutions. The general approach is applied to the cubic Hermite and Lagrange type of interpolation. Some known results are extended and numerical examples provided.
Ključne besede: mathematics, parametric curve, PH curve, geometric interpolation, Lagrange interpolation, Hermite interpolation, cubic curves, homotopy
Objavljeno v RUP: 03.04.2017; Ogledov: 3727; Prenosov: 86
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7. Lagrange geometric interpolation by rational spatial cubic Bézier curvesGašper Jaklič, Jernej Kozak, Vito Vitrih, Emil Žagar, 2012, izvirni znanstveni članek Opis: V članku obravnavamo Lagrangeovo geometrijsko interpolacijo s prostorskimi racionalnimi kubičnimi Bézierovimi krivuljami. Pokažemo, da pod določenimi naravnimi omejitvami obstaja enolična rešitev problema. še več, rešitev je podana v preprosti zaključeni obliki in je zato zanimiva za praktične aplikacije. Asimptotična analiza potrdi pričakovani red aproksimacije, namreč 6. Numerični primeri nakažejo možnost uporabe te metode pri obetavni geometrijski nelinearni subdivizijski shemi.
Ključne besede: numerična analiza, geometrijska Lagrageova interpolacija, racionalna Bézierova krivulja, prostorska krivulja, asimptotična analiza, subdivizija, numerical analysis, geometric Lagrange interpolation, rational Bézier curve, spatial curve, asymptotic analysis, subdivision
Objavljeno v RUP: 03.04.2017; Ogledov: 3991; Prenosov: 93
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8. High order parametric polynomial approximation of conic sectionsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2013, izvirni znanstveni članek Opis: V članku je obravnavana parametrična polinomska aproksimacija stožnic, ki ohranja obliko. Pristop je osnovan na parametrični aproksimaciji implicitno definiranih ravninskih krivulj. Polinomski aproksimanti so zapisani v zaključeni obliki in ponujajo najvišji možen red aproksimacije.
Ključne besede: matematika, stožnica, parametrična krivulja, implicitna krivulja, aproksimacija, mathematics, conic section, parametric curve, implicit curve, approximation
Objavljeno v RUP: 03.04.2017; Ogledov: 4198; Prenosov: 90
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9. C [sup] 1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcsBohumír Bastl, Michal Bizzarri, Marjetka Knez, Miroslav Lávička, Kristýna Michálkova, Zbiněk Šír, Vito Vitrih, Emil Žagar, 2014, izvirni znanstveni članek Opis: In this paper the ▫$C^1$▫ Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates ▫$C^1$▫ data at one point and they are then joined together with a ▫$C^1$▫ continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with three shape parameters. Two of them are selected based on asymptotic approximation order, while the remaining one can be computed by minimizing the length of the biarc or by minimizing the elastic bending energy. The final interpolating spline curve is globally ▫$C^1$▫ continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations.
Ključne besede: mathematics, parametric curve, PH curve, Pythagorean-hodograph, Hermite interpolation, biarc, cubic curve
Objavljeno v RUP: 03.04.2017; Ogledov: 3418; Prenosov: 51
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