Related papers: On the Hamilton-Waterloo Problem with a single fac…

For an even integer t \geq 2, the Matchings Connecivity matrix H_t is a matrix that has rows and columns both labeled by all perfect matchings of the complete graph K_t on t vertices; an entry H_t[M_1,M_2] is 1 if M_1\cup M_2 is a…

This is the full and extended version of the brief note arXiv:1908.00938. A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to the asymptotic theory of partial differential equations. The…

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…

Given $N$ cities and $R < N^2 - N$ directed (unidirectional/one way) roads does there exist a tour of all $N$ cities stopping at each city exactly once using the given roads (a Hamiltonian cycle)? This Hamiltonian cycle problem (HCP) is an…

We characterize possible pairs $(u_\varepsilon,c)\in C(\mathbb{R}^n\backslash\varepsilon\mathbb{Z}^n,\mathbb{R})\times\mathbb{R}$ addressing the homogenization problem for Hamilton--Jacobi equations $$ H\left(\frac{x}{\varepsilon}, d…

The Hamiltonian coupled-mode theory (HCMT), recently derived by Athanassoulis and Papoutsellis [1], provides an efficient new approach for solving fully nonlinear water-wave problems over arbitrary bathymetry. In HCMT, heavy use is made of…

In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…

This article study the fractional Hamiltonian systems \begin{eqnarray}\label{00} {_{t}}D_{\infty}^{\alpha}({_{-\infty}}D_{t}^{\alpha}u) + \lambda L(t)u = \nabla W(t, u), \;\;t\in \mathbb{R}, \end{eqnarray} where $\alpha \in (1/2, 1)$,…

In this paper we consider the existence of Hamilton cycles and perfect matchings in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are…

Given a weighted graph $G$ with $n$ vertices and $m$ edges, and a positive integer $p$, the Hamiltonian $p$-median problem consists in finding $p$ cycles of minimum total weight such that each vertex of $G$ is in exactly one cycle. We…

We introduce a way of implementing Wilson renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized $G$--matrix and is independent of any…

In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…

We consider |\Delta F| = 1 (F = S,C or B) nonleptonic effective hamiltonian in a renormalization scheme which allows to consistently use fully anticommuting gamma_5 at any number of loops, but at the leading order in the Fermi coupling G_F.…

A unitary perfect number is a positive integer n satisfying \sigma^*(n)=2n, where \sigma^* sums unitary divisors. Only five examples are known, and no sixth has been found. We revisit the Subbarao-Warren problem by keeping the seed factor…

The present work is a study of the unitarity problem for Quantum Mechanics at Planck Scale considered as Quantum Mechanics with Fundamental Length (QMFL).In the process QMFL is described as deformation of a well-known Quantum Mechanics…

We study the complexity of a problem "Common Eigenspace" -- verifying consistency of eigenvalue equations for composite quantum systems. The input of the problem is a family of pairwise commuting Hermitian operators H_1,...,H_r on a Hilbert…

This paper proposes a hybrid quantum-classical algorithm to solve a fundamental power system problem called unit commitment (UC). The UC problem is decomposed into a quadratic subproblem, a quadratic unconstrained binary optimization (QUBO)…

In this paper, we give first constant factor approximation for capacitated knapsack median problem (CKM) for hard uniform capacities, violating the budget only by an additive factor of $f_{max}$ where $f_{max}$ is the maximum cost of a…

Based on the three rules developed from the Roe-type scheme, the mechanisms of the classical and preconditioned Harten-Lax-van Leer (HLL) schemes are analyzed. For the classical HLL scheme, the accuracy problem is attributable to the…

The decision problems of the existence of a Hamiltonian cycle or of a Hamiltonian path in a given graph, and of the existence of a truth assignment satisfying a given Boolean formula $C$, are well-known {\it NP}-complete problems. Here we…