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The quadratic function and quadratic equations
1985The function f(x), where f(x) = ax2 + bx + c, and a, b, c are constants, a ≠ 0, is called a quadratic function, or sometimes a quadratic polynomial. From elementary algebra $${(x + d)^2} \equiv {x^2} + 2dx + {d^2}.$$ Using this, we write $$a{x^2} + bx + c \equiv a\left( {{x^2} + \frac{b}{a}x + \frac{c}{a}} \right) \equiv a\left[ {{{\left( {x
J. E. Hebborn, C. Plumpton
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Quadratic programming with quadratic constraints
Naval Research Logistics Quarterly, 1972AbstractA program with a quadratic objective function and quadratic constraints is considered. Two duals to such programs are provided, and an algorithm is presented based upon approximations to the duals. The algorithm consists of a sequence of linear programs and programs involving the optimization of a quadratic function either unconstrained or ...
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Management Science, 1971
A procedure based on Lemke's algorithm is developed which either computes stationary points for general quadratic programs or else shows that the program has no optimum. If a general quadratic program has an optimum and satisfies a non-degeneracy condition then it is demonstrated that there are an odd number of stationary points.
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A procedure based on Lemke's algorithm is developed which either computes stationary points for general quadratic programs or else shows that the program has no optimum. If a general quadratic program has an optimum and satisfies a non-degeneracy condition then it is demonstrated that there are an odd number of stationary points.
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1984
Von den Ecken eines Quadrats aus werden Verbindungsgeraden zu den Mittelpunkten (geeigneter) Seiten gezogen (Bild 91). Man beweise das uberraschende Ergebnis, das die Flache des dabei entstehenden kleineren Quadrates gleich einem Funftel der Flache des ursprunglichen Quadrates ist.
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Von den Ecken eines Quadrats aus werden Verbindungsgeraden zu den Mittelpunkten (geeigneter) Seiten gezogen (Bild 91). Man beweise das uberraschende Ergebnis, das die Flache des dabei entstehenden kleineren Quadrates gleich einem Funftel der Flache des ursprunglichen Quadrates ist.
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British Journal of Mathematical and Statistical Psychology, 1970
An axiom set for similarities is presented together with a set‐theoretic definition of multidimensional similarity consistent with the axioms. A special case of relative similarity judgement, involving the simultaneous comparison of three stimulus pairs, called ‘quadratic similarities’, is empirically illustrated and related to the theory. The goodness
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An axiom set for similarities is presented together with a set‐theoretic definition of multidimensional similarity consistent with the axioms. A special case of relative similarity judgement, involving the simultaneous comparison of three stimulus pairs, called ‘quadratic similarities’, is empirically illustrated and related to the theory. The goodness
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Quadratic forms and quadratic fields
1991Dedekind realised that one can give a clear presentation of Gauss’s theory of quadratic forms (Chapter 2), and particularly the composition of classes of forms, when one goes from forms to modules in quadratic fields. Here we consider the modules first and then give the connection between modules and forms.
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SIAM Journal on Numerical Analysis, 1974
Quadratic approximation is a three-dimensional analogue of the two-dimensional Pade approximation. The advantages of employing quadratic approximation are demonstrated by several examples. With automatic computers having a relatively inexpensive square root instruction, quadratic approximation is an attractive alternative to Pade approximation if ...
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Quadratic approximation is a three-dimensional analogue of the two-dimensional Pade approximation. The advantages of employing quadratic approximation are demonstrated by several examples. With automatic computers having a relatively inexpensive square root instruction, quadratic approximation is an attractive alternative to Pade approximation if ...
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Quadratic Residues and Quadratic Reciprocity
2021Gove Effinger, Gary L. Mullen
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On quadratic and quartic characters of quadratic units
The science reports of the Kanazawa University, 1981Furuta, Yoshiomi, Kaplan, Pierre
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Universal approximation with quadratic deep networks
Neural Networks, 2020Ge Wang, Jinjun Xiong, Fenglei Fan
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