q qa qf qk qn qq qr qs qt qu qw qz

Перевод: quadratic

[прилагательное]
квадратный;
[существительное]
квадратное уравнение; уравнение второй степени

Тезаурус:

1. Thus, since If we express a quadratic form in terms of another set of variables y given by the linear substitution x = By, then where and we observe that C, like A, is symmetric.
2. This quadratic form is not, as previously, a sum of squares; but provided it is not zero we could choose di to make the element unity, when we should have (with X for Xd) On account of the properties established here, it is usual to say that the modes of a system are orthogonal to each other.
3. This may be done in various ways, but one simple and useful device is to adopt two auxiliary variables: and to write the equations in the form Then if we now write and proportional to exp and again seek the complementary function, the four equations may be written, with a little rearrangement, This equation can clearly be written in partitioned form as or where The quartic determinantal equation obtained from this first-order set of equations may be seen by inspection to be identical with that obtained from the quadratic formulation.
4. Various sources claim that before age 20 he had amongst other things, rediscovered and proved the law of quadratic reciprocity, discovered the double periodicity of elliptic functions, proved that every positive integer is a sum of 3 triangular numbers (these are integers of the form where n Z+), formulated the principle of least squares and conjectured the prime number theorem (itself not proved until 1896).
5. During this stage quadratic harmonic potentials were included for the covalent geometry, a square-well quadratic term was used for the distances and dihedral restraints, and a quartic potential was used for the van der Waals term ( F- repel).
6. The quadratic equation, y = ax , can be plotted to form a parabola symmetrical about the y axis.
7. One boy was solving a quadratic equation, another was engaged with Euclid.
8. In number theory too there ws interest in representing whole numbers by, amongst other things, binary quadratic forms and in quantities such as which remain unchanged when in are replaced by where , , , are integers and - = 1.
9. Now the ith diagonal element of where the bracketed term is the quadratic form obtained from C with the ith eigenvector xi.
10. A quadratic form and the matrix A within f, are said to be positive definite (pos. def.) if for all real, non-null vectors x.
11. 1.11 BILINEAR AND QUADRATIC FORMS
12. Gauss' most influential contribution is probably his Disquisitiones Arithmeticae (1801), a work in which appear his 17-gon (see Section 4.6), his introduction of the notation of congruence (see Section 2.2), his proof that all the roots of are expressible in radicals, and a proof of the quadratic reciprocity law.