Related papers: Monotone Comparative Statics for Equilibrium Probl…
We review and develop the classical theory of moments of configurations of weighted points with a focus on systems with an identically vanishing first moment. The latter condition produces equations for equilibrium configurations of systems…
The derivation of determinant representations for the space-, time-, and temperature-dependent correlation functions of the impenetrable Gaudin-Yang model in the presence of a trapping potential is presented. These representations are valid…
For a dynamic system consisting of $n$ point vortices in an ideal plane fluid with a steady, incompressible and} irrotational background flow, a more physically significant definition of a fixed equilibrium configuration is suggested. Under…
By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schr\"odinger equations is found, and an open problem in…
Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated…
We revisit the classical monotone-follower problem and consider it in a generalized formulation. Our approach is based on a compactness substitute for nondecreasing processes, the Meyer-Zheng weak convergence, and the maximum principle of…
In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *--weakly convex graph and we prove some fixed point theorems for these…
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a…
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with…
This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the…
We show that if a numerical method is posed as a sequence of operators acting on data and depending on a parameter, typically a measure of the size of discretization, then consistency, convergence and stability can be related by a…
We study competitive equilibria in the classic Shapley-Shubik assignment model with indivisible goods and unit-demand buyers, with budget constraints: buyers can specify a maximum price they are willing to pay for each item, beyond which…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…
We study the linear and nonlinear stability of relative equilibria in the planar N-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological…
We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…
This paper studies a one-dimensional Mean-Field Planning (MFP) system with a non-local, rank-based coupling. Using a potential formulation, we rewrite the system as an associated scalar partial differential equation. We prove an equivalence…
We present a stabilizing output-feedback controller for nonlinear finite and infinite-dimensional control systems governed by monotone operators that respects given input constraints. In particular, we show under a detectability-like…
We investigate numerically a recent BGK-type model for a multi-component mixture of monatomic gases, undergoing a reversible bimolecular chemical reaction. The model replaces each collisional term of the Boltzmann equation with a relaxation…
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is…