Related papers: Multi-linear forms, structure of graphs and Lebesg…

This is an exposition of results on the existence problem of $\pi_1$-injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are…

The algebraic connectivity of a graph $G$ in a finite dimensional real normed linear space $X$ is a geometric counterpart to the Fiedler number of the graph and can be regarded as a measure of the rigidity of the graph in $X$. We analyse…

Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving…

In this article, we introduce a class of multilinear strongly singular integral operators with generalized kernels on the RD-space. The boundedness of these operators on weighted Lebesgue spaces is established. Moreover, two types of…

Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on $\ell^r$-valued extensions of linear operators. We show that for certain $1 \leq p, q_1, \dots, q_m, r \leq \infty$, there is a constant $C\geq 0$…

Given a finite regular graph G=(V,E) and a metric space (X,d_X), let $gamma_+(G,X) denote the smallest constant $\gamma_+>0$ such that for all f,g:V\to X we have: \frac{1}{|V|^2}\sum_{x,y\in V} d_X(f(x),g(y))^2\le \frac{\gamma_+}{|E|}…

Consider a system of $N$ electrons projected onto the lowest Landau level (LLL) with filling factor of the form $n/(2pn\pm1)<1/2$ and $N$ a multiple of $n$. We show that there always exists a two-dimensional symmetric correlation factor…

A method of classification of integrable equations on quad-graphs is discussed based on algebraic ideas. We assign a Lie ring to the equation and study the function describing the dimensions of linear spaces spanned by multiple commutators…

When ${\cal{D}}: E \rightarrow F$ is a linear differential operator of order $q$ between the sections of vector bundles over a manifold $X$ of dimension $n$, it is defined by a bundle map $\Phi: J_q(E) \rightarrow F=F_0$ that may depend,…

The Orlicz $\left( \ell_{2},\ell_{1}\right) $-mixed inequality states that $$ \left( \sum_{j_{1}=1}^{n}\left( \sum_{j_{2}=1}^{n}\left\vert A(e_{j_{1} },e_{j_{2}})\right\vert \right) ^{2}\right) ^{\frac{1}{2}}\leq\sqrt {2}\left\Vert…

Let $\mathcal{F}$ be a family of graphs, and let $p,r$ be nonnegative integers. The \textsc{$(p,r,\mathcal{F})$-Covering} problem asks whether for a graph $G$ and an integer $k$, there exists a set $D$ of at most $k$ vertices in $G$ such…

For a semibounded sesquilinear form ${\mathfrak t}$ in a Hilbert space ${\mathfrak H}$ there exists a representing map $Q$ from ${\mathfrak H}$ to another Hilbert space ${\mathfrak K}$, such that ${\mathfrak t}[\varphi, \psi]-c(\varphi,…

Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…

Let $(X,d,\mu)$ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions. In this paper, the boundedness of multilinear fractional integral operator in this setting is…

We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for…

In this paper, we study the adjoint foliated structures of the form $K_{\mathcal{F}}+D$ on algebraic surfaces, with particular focus on their minimal and canonical models. We investigate the effective behavior of the multiple linear system…

In this paper, we prove the pointwise convergence and the rate of pointwise convergence for a family of singular integral operators in two-dimensional setting in the following form: \begin{equation*} L_{\lambda }\left( f;x,y\right)…

For positive integers $K$ and $L$, we introduce and study the notion of $K$-multiplicative dependence over the algebraic closure $\overline{\mathbb{F}}_p$ of a finite prime field $\mathbb{F}_p$, as well as $L$-linear dependence of points on…

Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics, and group theory. In this paper we initiate the study of the…