Related papers: The Langberg-M\'{e}dard Multiple Unicast Conjectur…

We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer…

Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…

A multi-stream instability is observed experimentally in a longitudinally expanding electron beam in a storage ring. The instability is observed when the beam expands such that its length is several times the circumference of the ring, and…

Let (A,B) and (C,D) denote Leonard pairs on V. We say these pairs are adjacent whenever each basis for V which is standard for (A,B) (resp. (C,D)) is split for (C,D) (resp. (A,B)). Our main results are as follows: Theorem 1. There exists at…

From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…

As a common generalization of previously solved optimization problems concerning bipartite stable matchings, we describe a strongly polynomial network flow based algorithm for computing $\ell$ disjoint stable matchings with minimum total…

We introduce and study a new model that we call the {\em matching model}. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be {\em matched}. There is a finite…

We consider the stability of a laminar flow $U\in C^4([-1,1])$ in the two-dimensional channel $\mathbb{R} \times[-1,1]$ in the large Reynolds number limit. Assuming that $U$ is strictly monotone but allowing $U^{\prime\prime}$ to vanish, we…

The classical Benjamin and Lighthill conjecture about steady water waves states that the non-dimensional flow force constant of a solution is bounded by the corresponding constants of the supercritical and subcritical uniform streams…

We study Pandharipande-Thomas's stable pair theory on $K3$ fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of Kawai-Yoshioka's formula for the Euler…

In this paper, we prove several stability theorems for multiplicities of naturally defined representations of symmetric groups. The first such theorem states that if we consider the diagonal action of the symmetric group $S_{m+r}$ on $k$…

Aharoni and Howard, and, independently, Huang, Loh, and Sudakov proposed the following rainbow version of Erd\H{o}s matching conjecture: For positive integers $n,k,m$ with $n\ge km$, if each of the families $F_1,\ldots, F_m\subseteq…

W. Mader [J. Graph Theory 65 (2010), 61--69] conjectured that for any tree $T$ of order $m$, every $k$-connected graph $G$ with $\delta(G)\geq\lfloor\frac{3k}{2}\rfloor+m-1$ contains a tree $T'\cong T$ such that $G-V(T')$ remains…

We prove an existence result for the steady state flow of gas mixtures on networks. The basis of the model are the physical principles of the isothermal Euler equation, coupling conditions for the flow and pressure, and the mixing of…

It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…

We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…

We demonstrate the truth of the sunflower conjecture by showing that a family $\mathcal{F}$ of sets each of cardinality at most $m$ includes a $k$-sunflower, if $|\mathcal{F}| > ( c k )^{2m}$ for a constant $c>0$ independent of $m$ and $k$,…

We consider the problem of creating a long-distance entangled state between two stations of a network, where neighboring nodes are connected by noisy quantum channels. We show that any two stations can share an entangled pair if the…

Hasunuma [J. Graph Theory 102 (2023) 423-435] conjectured that for any tree $T$ of order $m$, every $k$-connected (or $k$-edge-connected) graph $G$ with minimum degree at least $k+m-1$ contains a tree $T'\cong T$ such that $G-E(T')$ is…

Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…