Related papers: Indexes of vector fields for mixed functions

This paper is part of an ongoing series of works on the study of foliations on algebraic varieties via derived algebraic geometry. We focus here on the specific case of globally defined vector fields and the global behaviour of their…

An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence…

We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different…

An invertible polynomial is a quasihomogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search…

Topological indices are parameters associated with graphs that have many applications in different areas such as mathematical chemistry. Among various topological indices, the Wiener index is classical \cite{w}. In this paper, we prove a…

A signed graph is a graph with edges marked positive and negative; it is unbalanced if some cycle has negative sign product. We introduce the concept of vector valued switching function in signed graphs, which extends the concept of…

Let $X=\{x_i\}_{i=1}^m$ be a set of unit vectors in $\RR^n$. The coherence of $X$ is $\coh(X):=\max_{i\not=j}|\langle x_i, x_j\rangle|$. A vector $x\in X$ is said to be isolable if there are no unit vectors $x'$ arbitrarily close to $x$…

We consider a real analytic map $F=(f_1,...,f_k) : (\mathbb{R}^n,0) \rightarrow (\mathbb{R}^k,0)$, $2 \le k \le n-1$, that satisfies Milnor's conditions (a) and (b) introduced by D. Massey. This implies that every real analytic…

Recently, a bond-additive topological descriptor, named as the Mostar index, has been introduced as a measure of peripherality in networks. For a connected graph $G$, the Mostar index is defined as $Mo(G) = \sum_{e=uv \in E(G)} |n_u(e) -…

In a multi-index model with $k$ index vectors, the input variables are transformed by taking inner products with the index vectors. A transfer function $f: \mathbb{R}^k \to \mathbb{R}$ is applied to these inner products to generate the…

Let $f:\mathbb{C}^{n+1} \to \mathbb{C}$ be a germ of hypersurface with isolated singularity. One can associate to $f$ a polarized variation of mixed Hodge structure $\mathcal{H}$ over the punctured disc, where the Hodge filtration is the…

The mixed metric dimension ${\rm mdim}(G)$ of a graph $G$ is the cardinality of a smallest set of vertices that (metrically) resolves each pair of elements from $V(G)\cup E(G)$. We say that $G$ is a max-mdim graph if ${\rm mdim}(G) = n(G)$.…

In this paper, we propose one index $i_1(f)-i_2(f)$ which measures how well-behaved a given finitely determined multigerm $f: (\mathbb{K}^n,S)\to (\mathbb{K}^p,0)$ $(n\le p)$ of corank at most one is from the viewpoint of liftable vector…

We consider a sequence of random vectors on \(\mathbb{R}^d, \ d\geq 1\). We consider the record values based on the simultaneous strict inequality of the coordinates. The indicator record variable (irv) of the j-th observation is the…

In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the…

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…

In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to…

The Graovac-Pisanski index, also called the modified Wiener index, was introduced in 1991 and represents an extension of the original Wiener index, because it considers beside the distances in a graph also its symmetries. Similarly as…

Let $f_{{\bf a},\{bf b}}({\bf z},\bar{\bf z})=z_1^{a_1+b_1}\bar z_1^{b_1}+...+z_n^{a_n+b_n}\bar z_n^{b_n}$ be a polar weighted homogeneous mixed polynomial with $a_j>0,b_j\ge 0$, $j=1,..., n$ and let $f_{{\bf a}}({\bf…

The vector notation adopted by GNU Octave plays a significant role as a tool for introspection, aligning itself with the vision of Kenneth E. Iverson. He believed that, just like mathematics, a programming language should be an effective…