相关论文: Function theory on the Neil parabola

Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The…

We develop complex function theory within certain algebras of holomorphic functions on coverings of Stein manifolds. This, in particular, includes the results on holomorphic extension from complex submanifolds, corona type theorems,…

We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection…

Function theory of Cayley-Dickson variables is applied to Fermat's last theorem. For this the homotopy theorem, Rouch\'e's theorem and residues of meromorphic functions over Cayley-Dickson algebras are used. A special meromorphic function…

We present the first example of an interacting Carroll supersymmetric field theory with both temporal and spatial derivatives, belonging to the Galileon class, where the non-linear field equation remains second-order in derivative. To…

We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus…

We say that a contact manifold is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). Generalizing results of Milnor and Giroux, we associate to each holomorphic function f…

By means of the property of effective local connectivity, the computability of finding the Carath\'eodory extension of a conformal map of a Jordan domain onto the unit disk is demonstrated.

We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function…

A class is studied of complex valued functions defined on the unit disk (with a possible exception of a discrete set) with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. Functions…

Given a matrix-valued function $\mathcal{F}(\lambda)=\sum_{i=1}^d f_i(\lambda) A_i$, with complex matrices $A_i$ and $f_i(\lambda)$ entire functions for $i=1,\ldots,d$, we discuss a method for the numerical approximation of the distance to…

Given a link in $S^3$ we will use invariants derived from the Alexander module and the Blanchfield pairing to obtain lower bounds on the Gordian distance between links, the unlinking number and various splitting numbers. These lower bounds…

In this paper we develop an algebraic theory to study the problem of finding the minimum distance point from an algebraic variety with respect to the Hermitian distance function. The theory generalizes the Euclidean Distance degree…

We investigate properties of holomorphic extensions in the one-variable case of Whitney's Approximation Theorem on intervals. Improving a result of Gauthier-Kienzle, we construct tangentially approximating functions which extend…

We show that the parabola is of strong Khintchine type for convergence, which is the first result of its kind for curves. Moreover, Jarnik type theorems are established in both the simultaneous and the dual settings, without monotonicity on…

In this paper we present a generalization in the context of multilinear Muckenhoupt classes of the endpoint extrapolation theorem on restricted weights due to Carro, Grafakos and Soria. Moreover, our main result is obtained on limited…

In practical purposes for some geometrical problems in computer science we have as information the coordinates of some finite points in surface instead of the whole body of a surface. The problem arised here is: "How to define a distance…

Let Y be an infinite covering space of a projective manifold M in P^N of dimension n geq 2. Let C be the intersection with M of at most n-1 generic hypersurfaces of degree d in P^N. The preimage X of C in Y is a connected submanifold. Let…

In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the…

We prove that the Nielsen zeta function is a rational function or a radical of a rational function for orientation preserving homeomorphisms on closed orientable 3-dimensional manifolds which are special Haken or Seifert manifolds. In the…