# Solubility of Systems of Quadratic Forms

## Related Articles

- Polynomial Deformations of sl(2, R) in a Three-Dimensional Invariant Subspace of Monomials. Debergh, N.; Ndimubandi, J.; van den Bossche, B. // Modern Physics Letters A;5/20/2003, Vol. 18 Issue 15, p1013
New finite-dimensional representations of specific polynomial deformations of sl(2; R) are constructed. The corresponding generators can be, in particular, realized through linear differential operators preserving a finite-dimensional subspace of monomials. We concentrate on three-dimensional...

- Sharp inequalities for approximations of classes of periodic convolutions by odd-dimensional subspaces of shifts. Vinogradov, O. // Mathematical Notes;Apr2009, Vol. 85 Issue 3/4, p544
Sharp Akhiezer-Krein-Favard-type inequalities for classes of periodic convolutions with kernels that do not increase oscillation are obtained. A large class of approximating odd-dimensional subspaces constructed from uniform shifts of one function with extremal widths is specified. As a...

- ON THE NUMBER OF SQUARES REPRESENTED BY A PRODUCT OF TWO TERNARY QUADRATIC FORMS. MUNSHI, RITABRATA // Quarterly Journal of Mathematics;Mar2011, Vol. 62 Issue 1, p157
In the context of Manin's conjecture it is an important problem to estimate the number of times a ternary quartic form represents a square. In this paper we give good estimates for this counting problem when the quartic form is a product of two ternary quadratic forms.

- On quasi-reduced quadratic forms. Dubois, E.; Levesque, C. // Acta Mathematica Sinica;Aug2010, Vol. 26 Issue 8, p1425
With the help of continued fractions, we plan to list all the elements of the set of quasi-reduced quadratic forms of fundamental discriminant ?. As a matter of fact, we show that for each reduced quadratic form f = aX2 + bXY + cY2 = < a, b, c> of discriminant ? > 0 (and of sign s( f) equal to...

- THE CROSS-CORRELATION DISTRIBUTION OF A p-ARY m-SEQUENCE OF PERIOD p2k - 1 AND ITS DECIMATED SEQUENCE BY (pk+1)2/2(pe+1). YUHUA SUN; ZILONG WANG; HUI LI; TONGJIANG YAN // Advances in Mathematics of Communications;Nov2013, Vol. 7 Issue 4, p409
Families of m-sequences with low correlation property have important applications in communication systems. In this paper, for a prime pâ‰¡ 1 mod 4 and an odd integer k, we study the cross correlation between a p-ary m-sequence {st} of period pn -1 and its decimated sequence {sdt}, where d =...

- Diophantine analysis Mathematics. // Dictionary of Theories;2002, p150
A definition of the term "diophantine analysis" is presented. It refers a mathematical named after Greek mathematician Diophantus of Alexandria. This theory is also known as Diophantine approximation. It is the area of Number Theory whose principal concern is the solubility of inequalities in...

- An Effective Schmidtâ€™s Subspace Theorem for Projective Varieties Over Function Fields. Ru, Min; Wang, Julie Tzu-Yueh // IMRN: International Mathematics Research Notices;Jan2012, Vol. 2012 Issue 3, p651
We deduce an effective version of Schmidtâ€™s subspace theorem on a smooth projective variety over a function field of characteristic zero for divisors of coming from hypersurfaces in .

- Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction. Han, Jeong // Journal of Mechanical Science & Technology;Apr2012, Vol. 26 Issue 4, p1115
In this paper, we examine an efficient calculation of the approximate frequency response (FR) for large-size finite element (FE) models using the Krylov subspace-based model order reduction (MOR) and its direct design sensitivity analysis with respect to design variables for sizing. Information...

- Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method. Artale Harris, Pietro; Garra, Roberto // Nonlinear Studies;2013, Vol. 20 Issue 4, p471
In this paper we study the analytic solutions of Burgers type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the time-fractional Burgers equation. Some generalizations linked to the forced...