It has become somewhat fashionable to have students derive theQuadratic Formulathemselves; this is done by completing the square for the generic quadratic equationax2+bx+c= 0. While I can understand the impulse (showing students how the Formula was invented, and thereby providing a concrete exampl...
To derive the equation of an ellipse centered at the origin, we begin with the foci (−c,0)(−c,0) and (c,0)(c,0). The ellipse is the set of all points (x,y)(x,y) such that the sum of the distances from (x,y)(x,y) to the foci is constant, as show...
Quadratic functionAdditive functionQuasi-Banach spacep-Banach spaceIn this paper we establish the general solution of the functional equation f ( 2 x + y ) + f ( 2 x y ) = f ( x + y ) + f ( x y ) + 2 f ( 2 x ) 2 f ( x ) and investigate the Hyers–Ulam–Rassias ...
1.) Before we begin deriving the first kinematic equation, we must first define acceleration. a=ΔvΔt 2.) We know Δv=vf−vi and when we plug that in, we get a=vf−viΔt 3.) If we solve for vf then the equation becomes a vf=vi+aΔt 4.) We can denote the time interv...
On the other hand, the Root Mean Square Error (RMSE, [121]) is a quadratic score, in the same units of the dependent variable, in which the average error in the model predictions is computed by averaging the squared individual errors. Our regression model achieves an RMSE equal to 7.76,...
(SAGA) based on the 'Genetic Algorithm for Isotopologues in Metabolic Systems' Table 1 Different forms of objective function Loss function Equation Absolute difference Σ|Ix,obs – Ix,calc| Log difference Square difference Σ|log (Ix,obs) – log (Ix,calc)| Σ (Ix,obs – Ix,calc)2 The ...
In the reservoir computing literature, the information processing capacity is frequently used to characterize the computing capabilities of a reservoir. However, it remains unclear how the information processing capacity connects to the performance on specific tasks. We demonstrate on a set of standard ...
Lee, "Fuzzy stability of a functional equation deriving from quadratic and additive mappings," Abstract and Applied Analysis, vol. 2011, Article ID 534120, 15 pages, 2011.S. S. Jin and Y. H. Lee, Fuzzy stability of a functional equation deriving from quadratic and additive mappings, Abstr....
quadratic functional equationHyers-Ulam stabilityfixed point theoryrandom normed spacesThe authors introduce a finite variable quadratic functional equation and derive its solution. Also, authors examine its Hyers-Ulam stability in Random Normed space(RN-space) by means of two different methods....
based on three values of a coefficient A of a quadratic term, a coefficient B of a linear term, and a constant term C of a quadratic equation in order to derive one of two roots of the quadratic equation, simple addition and subtraction using values stored in these registers, and a simp...