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Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An…
We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…
Conflict of interest is the permanent companion of any population of agents (computational or biological). For that reason, the ability to compromise is of paramount importance, making voting a key element of societal mechanisms. One of the…
We utilize an event-by-event relativistic hydrodynamic calculation performed at a number of different incident beam energies to investigate the creation of hot and dense QCD matter near the critical point. Using state-of-the-art analysis…
We study a class of weakly coupled systems of Hamilton{Jacobi equations at the critical level. We associate to it a family of scalar discounted equation. Using control{theoretic tech- niques we construct an algorithm which allows obtaining…
We use variational methods to study the existence of nontrivial and radially symmetric solutions to the H\`enon-Lane-Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative…
We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of…
We tackle a stochastic version of the Critical Node Problem (CNP) where the goal is to minimize the pairwise connectivity of a graph by attacking a subset of its nodes. In the stochastic setting considered, the attacks on nodes can fail…
Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the…
The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its…
Pairing plays a central role in nuclear systems. The simplest model for the pairing is the constant-pairing Hamiltonian. The aim of the present paper is to include the continuum single particle level density in the constant pairing…
In the computation of compressible fluid flows, numerical boundary conditions are always necessary for all physical variables at computational boundaries while just partial physical variables are often prescribed as physical boundary…
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in $\mathbb{R}^d (d \geq 1)$. The particles perform random jumps with pair wise repulsion, in the…
We present a model of coupling between a point wise particle and a compressible inviscid fluid following the Euler equations. The interaction between the fluid and the particle is achieved through a drag force. It writes as the product of a…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also we will…
This paper analyses the numerical solution of a class of non-linear Schr\"odinger equations by Galerkin finite elements in space and a mass- and energy conserving variant of the Crank-Nicolson method due to Sanz-Serna in time. The novel…
The tensorial equations for non trivial fully interacting fixed points at lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and $3-\varepsilon$ dimensions are analysed for $N$-component fields and corresponding multi-index…
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…