Related papers: Nested nodal loops of biharmonic functions

An $n$-list $\lambda:=\left(r; \lambda_2, \ldots, \lambda_n\right)$ of complex numbers with $r>0,$ is said to be realizable if $\lambda$ is the spectrum of $n\times n$ nonnegative matrix $A$ and in this case $A$ is said to be a nonnegative…

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4, and 2.6), biharmonic maps between…

Let $G$ be a simple, connected graph on $n$ vertices, and further assume that $G$ has disjoint cycles. Let $h$ be a real symmetric matrix supported on $G$ (for example, a discrete Schr\"odinger operator). The eigenvalues of $h$ are ordered…

This article proves a conjecture by Zuber about the enumeration of fully packed loops (FPLs). The conjecture states that the number of FPLs whose link pattern consists of two noncrossing matchings which are separated by $m$ nested arches is…

It has recently been suggested that in certain special nonsupersymmetric type II string compactifications, at least the first two perturbative contributions to the cosmological constant $\Lambda$ vanish. Support for perturbative vanishing…

The confluent binomial posets with the atomic function A(n) = max (1,2^(n-2)) are classified. In particular, it is shown that in general there are non-isomorphic intervals of the same length.

We describe a general framework for studying duality between different phase spaces which share the same symmetry group $\mathrm{H}$. Solutions corresponding to collective dynamics become dual in the sense that they are generated by the…

We consider nested variational inequalities con- sisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. This class of hierarchical equilibrium…

This work is focused on the study of the nonlinear elliptic higher order equation \begin{equation}\nonumber \left( -\Delta \right)^m u = S_k[-u] + \lambda f, \qquad x \in \mathbb{R}^N, \end{equation} where the $k-$Hessian $S_k[u]$ is the…

Given a function f: [a,b] -> R, if f(a) < 0 and f(b)> 0 and f is continuous, the Intermediate Value Theorem implies that f has a root in [a,b]. Moreover, given a value-oracle for f, an approximate root of f can be computed using the…

Let $\Lambda^{\ast}$ be the free monoid of (finite) words over a not necessarily finite alphabet $\Lambda$, which is equipped with some (partial) order. This ordering lifts to $\Lambda^{\ast}$, where it extends the divisibility ordering of…

A theorem of Cohn and Lempel [J. Combin. Theory Ser. A 13 (1972), 83-89] gives an equality relating the number of circuits in a directed circuit partition of a 2-in, 2-out digraph to the GF(2)-nullity of an associated matrix. This equality…

Each extreme edge of the Newton diagram of a plurisubharmonic polynomial on $\mathbb{C}^2$ gives rise to a plurisubharmonic polynomial. It is tempting to believe that the union of the extreme edges or the convex hull of said union will do…

We use the nested loop approach to investigate loop models on random planar maps where the domains delimited by the loops are given two alternating colors, which can be assigned different local weights, hence allowing for an explicit Z_2…

Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested…

Let $k\geq 2$ be a fixed natural number. We establish the existence of infinitely many pairs of consecutive primes $p_n$, $p_{n+1}$ satisfying $$ p_{n+1}-p_n\geq c\:\frac{\log p_n\: \log_2 p_n\: \log_4 p_n}{\log_3 p_n}\:,$$ with $c$ being a…

We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a…

Let NG0 denote the category of all pointed numerically generated spaces and continuous maps preserving base-points. In [SYH], we described a passage from bivariant functors to generalized homology and cohomology theories. In this paper, we…

A net in $\mathbb{P}^2$ is a configuration of lines $\mathcal A$ and points $X$ satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac-Moody…

This work is a continuation of [13]. We study the linear disjointness between higher-order oscillating sequences and nonlinear dynamical systems. Specifically, we prove that any oscillating sequence of order $m=d+k-1$ and any simple…