相关论文: Rationality and computability of the covering radi…

We study how the number $c(X)$ of components of a graph $X$ can be expressed through the number and properties of the components of a quotient graph $X/\sim.$ We partially rely on classic qualifications of graph homomorphisms such as…

We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.

We define a notion of (one-sided) shift spaces over infinite alphabets. Unlike many previous approaches to shift spaces over countable alphabets, our shift spaces are compact Hausdorff spaces. We examine shift morphisms between these shift…

We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…

In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…

In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…

- An algorithm for calculating the radiation field of a charged point particle performing a spiral motion in an infinite cylindrical waveguide with a multilayer side wall is found. The number of layers and their filling is arbitrary. The…

We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by…

We consider the problem of taking an opaque forest and determining the regions that are covered by it. We provide a tight upper bound on the complexity of this problem, and an algorithm for computing this area, which is worst-case optimal.

We investigate the computability (in the sense of computable analysis) of the topological pressure $P_{\rm top}(\phi)$ on compact shift spaces $X$ for continuous potentials $\phi:X\to {\mathbb R}$. This question has recently been studied…

We study the product structure on the Chow ring (with rational coefficients) of a cubic hypersurface in projective space and prove that the image of the product map is as small as possible.

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

The Cayley--Salmon theorem implies the existence of a 27-sheeted covering space specifying lines contained in smooth cubic surfaces over $\mathbb{C}$. In this paper we compute the rational cohomology of the total space of this cover, using…

A graph is periodic if it can be obtained by joining identical pieces in a cyclic fashion. It is shown that the limit crossing number of a periodic graph is computable. This answers a question of Benny Pinontoan and Bruce Richter (2004).

We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.

The purpose of this paper is to analysis the Harnack part of some truncated shifts whose $\rho$-numerical radius equal one in the finite dimensional case. As pointed out in Theorem 1.17 [12], a key point is to describe the null spaces of…

We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which the real locus is connected and the intermediate Jacobian…

In terms of complex radio environments especially in dense urban areas, a very interesting topic is considered - the utilization of reconfigurable intelligent surfaces. Basically, based on simple controls of the angle of reflection of the…

In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by…

We determine the exact value of the biclique covering number for all grid graphs.