Let K be a number field, and let F be a symmetric bilinear form in 2N variables over K. Let Z be a subspace of K . A classical theorem of Witt states that the bilinear space (Z,F ) can be decomposed into an orthogonal sum of hyperbolic planes, singular, and anisotropic components. We prove the existence of such a decomposition of small height, where all bounds on height are explicit in terms of...

In this paper, we present a novel bilinear invariant representation for multimedia information classification and retrieval. We introduce the concept of kernel space from functional analysis to show that null space invariants are only the special case when the transformation is linear. Subsequently, we derive the exact invariant basis for one of the important applications for kernel space: bili...

Pairings are particular bilinear maps, and as any bilinear maps they factor through the tensor product as group homomorphisms. Besides, nothing seems to prevent us to construct pairings on other abelian groups than elliptic curves or more general abelian varieties. The point of view adopted in this contribution is based on these two observations. Thus we present an elliptic curve free study of ...

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional KadomtsevPetviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by whic...

We compare new time-series methods for estimating the death rate of an emerging and re-emerging disease and our approach is based on One-Dimensional Integrated Autoregressive Bilinear Time Series Model and Generalized Integrated Autoregressive Bilinear Time Series Model. The parameters of the proposed models are estimated using Newton-Raphson iterative method and statistical properties of the d...

An algebraic extended bilinear Hilbert semispace H∓ is proposed as being the natural representation space for the algebras of von Neumann. This bilinear Hilbert semispace has a well defined structure given by the representation space Repsp(GLn(Lv ×Lv)) of an algebraic general bilinear semigroup GLn(Lv ×Lv) over the product of sets of completions characterized by increasing ranks. This represent...

This paper investigates a cylindrical nonlinear Schrödinger (cNLS) equation, which describes the cylindrically diverging quasi-plane envelope waves in a nonlinear medium. With the Hirota method and symbolic computation, bilinear form and N-soliton solutions in the form of an Nth-order polynomial in N exponentials are obtained for the cNLS equation. By means of the properties of double Wronskian...

This paper presents a voice conversion technique based on bilinear models and introduces the concept of contextual modeling. The bilinear approach reformulates the spectral envelope representation from line spectral frequencies feature to a two-factor parameterization corresponding to speaker identity and phonetic information, the so-called style and content factors. This decomposition offers a...

A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear Calderón-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact.

This note introduces bilinear estimates intended as a step towards an L∞-endpoint Kato-Ponce inequality. In particular, a bilinear version of the classical Gagliardo-Nirenberg interpolation inequalities for a product of functions is proved.