Related papers: Laws of inertia in higher degree binary forms

If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.

Varieties of Sums of Powers describe the additive decompositions of an homogeneous polynomial into powers of linear forms. Despite their long history, going back to Sylvester and Hilbert, few of them are known for special degrees and number…

Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras.

It is known that the Jebsen-Birkhoff theorem is valid for vacuum solutions to Einstein's equation, as well as some of its generalizations. Using symmetry inheritance properties we investigate in detail the additional constraints that fields…

In this paper we obtain the linear Weyl gravity in de Sitter background. Its linear form in five-dimensional ambient space notation has also been obtained. From the group theoretical point of view, we show that this conformal invariant…

Quantum lattice models describe a wide array of physical systems, and are a canonical way to numerically solve the Schrodinger equation. Here we prove the potential inversion theorem, which says that wavefunction probability in these models…

A positive definite and integral quadratic form $f$ is called irrecoverable if there is a quadratic form $F$ such that it represents all proper subforms of $f$, whereas it does not represent $f$ itself. In this case, $F$ is called an…

We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…

We study the general form of the possible kinetic terms for 2-form fields in four dimensions, under the restriction that they have a semibounded energy density. This is done by using covariant symplectic techniques and generalizes previous…

This study establishes consistency conditions and a general solution for a coupled system that consists of five two-sided Sylvester-like tensor equations in ten quaternion variables throughout the Einstein tensor product. Certain specific…

A number field $k$ admits a binary integral quadratic form which represents all integers locally but not globally if and only if the class number of $k$ is bigger than one. In this case, there are only finitely many classes of such binary…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

We state and prove an identity which represents the most general eta-products of weight 1 by binary quadratic forms. We discuss the utility of binary quadratic forms in finding a multiplicative completion for certain eta-quotients. We then…

We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.

We give partial generalizations of the classical Descartes' rule of signs to multivariate polynomials (with real exponents), in the sense that we provide upper bounds on the number of connected components of the complement of a hypersurface…

We revisit recent work of Heath-Brown on the average order of the quantity r(L_1)r(L_2)r(L_3)r(L_4), for suitable binary linear forms L_1,..., L_4, for integers ranging over quite general regions. In addition to improving the error term in…

We say that a field extension $L/F$ has the descent property for isometry (resp. similarity) of quadratic or symmetric bilinear forms if any two forms defined over $F$ that become isometric (resp. similar) over $L$ are already isometric…

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of…

Current approaches to the problem of inertia attempt to explain the inertial properties of matter by expressing the inertial mass appearing in Newton's second law of motion in terms of some other more fundamental interaction. One…