相关论文: Another Relation Between Approaches to the Schottk…
Transformation optics establishes an equivalence relationship between gradient media and curved space, unveiling intrinsic geometric properties of gradient media. However, this approach based on curved spaces is concentrated on…
This work lies across three areas (in the title) of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link consists of a single…
The determination of Jacobi sums, their congruences and cyclotomic numbers have been the object of attention for many years and there are large number of interesting results related to these in the literature. This survey aims at reviewing…
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…
We study the McKay correspondence for representations of the cyclic group of order $p$ in characteristic $p$. The main tool is the motivic integration generalized to quotient stacks associated to representations. Our version of the change…
Given a canonical genus three curve $X=\{F=0\}$, we construct, emulating Mumford discussion for hyperelliptic curves, a set of equations for an affine open subset of the jacobian $JX$. We give explicit algorithms describing the law group in…
For a family of Jacobians of smooth pointed curves there is a notion of tautological algebra. There is an action of $\mathfrak{sl}_2$ on this algebra. We define and study a lifting of the Polishchuk operator, corresponding to $f\in…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
We define Jacobi forms with complex multiplication. Analogous to modular forms with complex multiplication, they are constructed from Hecke characters of the associated imaginary quadratic field. From this construction we obtain a Jacobi…
In the work we discuss two invariants of conjugacy classes of braids. The first invariant is the conformal module which occurred in connection with the interest in the 13th Hilbert Problem. The second is a popular dynamical invariant, the…
We give a criterion to distinguish between a genus three Jacobian and its [-1] twist in terms of the product of the 36 even theta nulls. We also express the product of the 36 theta nulls in terms of the discriminant of a genus three curve.…
The main purpose of this paper is to give an overview over the theory of abelian varieties, with main focus on Jacobian varieties of curves reaching from well-known results till to latest developments and their usage in cryptography. In the…
A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and complementary new families of solutions are characterized. Such families are very general,…
In this paper we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the…
The factorization problem for the group of canonical transformations close to the identity and the corresponding twistor equations for an ample family of canonical variables are considered. A method to deal with these reductions is…
We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to…
The purpose of this paper is twofold. The first is to apply the method introduced in the works of Nakayashiki and Smirnov on the Mumford system to its variants. The other is to establish a relation between the Mumford system and the…
In previous works, the second author defined directional Robin constants associated to a compact, nonpolar subset $K$ of an algebraic curve $A$ in $\mathbb{C}^N$ and related these to a natural class of Chebyshev constants for $K$. We define…
The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood from the multiplication in the space of…