相关论文: Algebroid Mappings and Their Equidistribution Theo…
It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this…
A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…
Let g be a nonconstant rational map from the projective line to itself that has degree greater than one and is defined over a number field. The map g gives rise to generalized Mahler measures for polynomials in one variable. We use…
First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for…
Early in 1970s, Carlson-Griffiths made a significant progress in the study of Nevanlinna theory, who devised equi-distribution theory for holomorphic mappings from $\mathbb C^m$ into a projective algebraic manifold intersecting divisors. In…
We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…
The elliptic-matrix quantum Olshanetsky-Perelomov problem is introduced for arbitrary root systems by means of an elliptic generalization of the Dunkl operators. Its equivalence with the double affine generalization of the…
We investigate the value distribution of holomorphic maps defined on one class of K\"ahler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main…
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a…
The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction of an explicit basis of the space of…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
This paper establishes a version of Nevanlinna theory based on Askey-Wilson divided difference operator for meromorphic functions of finite logarithmic order in the complex plane $\mathbb{C}$. A second main theorem that we have derived…
The authors proposed a general way to find particular solutions for overdetermined systems of PDEs previously, where the number of equations is greater than the number of unknown functions. In this paper, we propose an algorithm for finding…
A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.
A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in…
The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…
In his work on deformation quantization of algebraic varieties Kontsevich introduced the notion of algebroid as a certain generalization of a sheaf of algebras. We construct algebroids which are given locally by NC-smooth thickenings in the…
Ehrhart theory is the study of the enumeration of lattice points in lattice polytopes. Equivariant Ehrhart theory is a generalization of Ehrhart theory that takes into account the action of a finite group acting via affine transformations…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…