6. Special Functional Forms II: Quadratic Functions

2010 ◽  
pp. 167-205
1988 ◽  
pp. 167-205
Author(s):  
Mordecai Avriel ◽  
Walter E. Diewert ◽  
Siegfried Schaible ◽  
Israel Zang

Author(s):  
Arie Gusman ◽  
Kamid Kamid ◽  
Syamsurizal Syamsurizal

Learning quadratic functions that had been performed by the majority of vocational school and high school mathematics teacher in Kuala Tungkal is still using conventional learning media. The use of conventional learning media is experiencing a lot of obstacles, such as: a fairly long time in describing the graph function, especially when analyzing some quadratic function graphs with various characteristics. APOS is one of the constructivist learning theory which states that students learn through several stages, namely: action – process – object – schema. And to integrate into media APOS writer adapting ADDIE development model. The effectiveness of the use of media-based learning theory APOS seen from the student activity sheet can be concluded more increased activity of students in the learning process. Study of the test results, students were able to meet the completeness criteria stipulated minimum is 75. With an average value of learning outcomes, namely 87.14. It can be seen from the students' responses on a test group of small and large groups where it is concluded that researchers develop learning media can be categorized as good / interesting in the teaching and learning of mathematics.


2021 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Alexander Koch ◽  
Tim Bürchner ◽  
Thomas Herrmann ◽  
Markus Lienkamp

Electrification and automatization may change the environmental impact of vehicles. Current eco-driving approaches for electric vehicles fit the electric power of the motor by quadratic functions and are limited to powertrains with one motor and single-speed transmission or use computationally expensive algorithms. This paper proposes an online nonlinear algorithm, which handles the non-convex power demand of electric motors. Therefore, this algorithm allows the simultaneous optimization of speed profile and powertrain operation for electric vehicles with multiple motors and multiple gears. We compare different powertrain topologies in a free-flow scenario and a car-following scenario. Dynamic Programming validates the proposed algorithm. Optimal speed profiles alter for different powertrain topologies. Powertrains with multiple gears and motors require less energy during eco-driving. Furthermore, the powertrain-dependent correlations between jerk restriction and energy consumption are shown.


Author(s):  
Jorge Arroyo-Esquivel ◽  
Nathan G. Marculis ◽  
Alan Hastings

AbstractOne of the main factors that determines habitat suitability for sessile and territorial organisms is the presence or absence of another competing individual in that habitat. This type of competition arises in populations occupying patches in a metacommunity. Previous studies have looked at this process using a continuous-time modeling framework, where colonizations and extinctions occur simultaneously. However, different colonization processes may be performed by different species, which may affect the metacommunity dynamics. We address this issue by developing a discrete-time framework that describes these kinds of metacommunity interactions, and we consider different colonization dynamics. To understand potential dynamics, we consider specific functional forms that characterize the colonization and extinction processes of metapopulations competing for space as their limiting factor. We then provide a mathematical analysis of the models generated by this framework, and we compare these results to what is seen in nature and in previous models.


Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 465
Author(s):  
Agnieszka Prusińska ◽  
Krzysztof Szkatuła ◽  
Alexey Tret’yakov

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.


Author(s):  
Maria J. Perez-Villadóniga ◽  
Ana Rodriguez-Alvarez ◽  
David Roibas

AbstractResident physicians play a double role in hospital activity. They participate in medical practices and thus, on the one hand, they should be considered as an input. Also, they are medical staff in training and, on the other hand, must be considered as an output. The net effect on hospital activities should therefore be empirically determined. Additionally, when considering their role as active physicians, a natural hypothesis is that resident physicians are not more productive than senior ones. This is a property that standard logarithmic production functions (including Cobb–Douglas and Translog functional forms) cannot verify for the whole technology set. Our main contribution is the development of a Translog modification, which implies the definition of the input “doctors” as a weighted sum of senior and resident physicians, where the weights are estimated from the empirical application. This modification of the standard Translog is able, under suitable parameter restrictions, to verify our main hypothesis across the whole technology set while determining if the net effect of resident physicians in hospitals’ production should be associated to an output or to an input. We estimate the resulting output distance function frontier with a sample of Spanish hospitals. Our findings show that the overall contribution of resident physicians to hospitals’ production allows considering them as an input in most cases. In particular, their average productivity is around 37% of that corresponding to senior physicians.


Author(s):  
Caroline Khan ◽  
Mike G. Tsionas

AbstractIn this paper, we propose the use of stochastic frontier models to impose theoretical regularity constraints (like monotonicity and concavity) on flexible functional forms. These constraints take the form of inequalities involving the data and the parameters of the model. We address a major concern when statistically endogenous variables are present in these inequalities. We present results with and without endogeneity in the inequality constraints. In the system case (e.g., cost-share equations) or more generally, in production function-first-order conditions case, we detect an econometric problem which we solve successfully. We provide an empirical application to US electric power generation plants during 1986–1997, previously used by several authors.


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