Related papers: U-Invariants for forms of higher degree
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
We consider Open Gromov-Witten invariants for noncompact Calabi-Yau in the case the Lagrangian has the topology of $\R^2 \times S^1$. The definition of the invariant involves the choice of a frame for the Lagrangian, in accord with string…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
The Eynard-Orantin invariants of a plane curve are multilinear differentials on the curve. For a particular class of genus zero plane curves these invariants can be equivalently expressed in terms of simpler expressions given by polynomials…
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…
We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.
The first part of this paper completes the classification of Whitney towers in the 4-ball that was started in three related papers. We provide an algebraic framework allowing the computations of the graded groups associated to geometric…
We develop the version of the $J$-invariant for hermitian forms over quadratic extensions in a similar way Alexander Vishik did it for quadratic forms. This discrete invariant contains informations about rationality of algebraic cycles on…
In this paper the structures of the generalised Euler-Lagrange equations and their associated conserved quantities are derived for one-dimensional Herglotz variational problems of order $n$. Their derivations use the framework of moving…
We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree $n \le 4$ to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree $n$, an $n \times n$ alternating…
We define invariants for colored oriented spatial graphs by generalizing CM invariants, which were defined via non-integral highest weight representations of $U_q(sl_2)$. We apply the same method to define Yokota's invariants, and we call…
In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find such a classical form in 2 variables, which differs from…
There exists and is unique up to multiplication by a constant function a form of the highest dimension on the manifold of n-dimensional continued fractions in the sense of Klein, such that the form is invariant under the natural action of…
We develop an inversive geometry for anisotropic quadradic spaces, in analogy with the classical inversive geometry of a Euclidean plane.
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
Invertible disformal transformations serve as a useful tool to explore ghost-free scalar-tensor theories. In this paper, we construct a generalization of invertible disformal transformations that involves arbitrary higher-order covariant…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
It is classically known that generic smooth maps of R^2 into R^3 admit only cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap…