Related papers: Spherical Preferences
The bending energy of any freely deformable closed surface is quadratic in its curvature. In the absence of constraints, it will be minimized when the surface adopts the form of a round sphere. If the surface is confined within a…
Polarization independent Mie scattering of building blocks is foundational for constructions of optical systems with robust functionalities. Conventional studies for such polarization independence are generally restricted to special states…
We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth…
One widely-existed state --``harmony with diversity" in which individuals freely express various viewpoints to sustain integration of social diversity, but at the same time shared values ensure social coherence, can be considered as the…
In this paper we develop a novel approach to relaxing Arrow's axioms for voting rules, addressing a long-standing critique in social choice theory. Classical axioms (often styled as fairness axioms or fairness criteria) are assessed in a…
We study balanced exchange problems in which agents with responsive preferences are endowed with multiple indivisible objects and can trade without transfers (e.g. shift exchange, time-banking). Eliciting full preferences over bundles is…
We introduce a new flatness index for the boundary of an open subset $\Omega$ of $\mathbb{R}^n$, $n\ge 2$. This index provides a necessary condition for $\partial\Omega$ to be a harmonic pseudosphere and sufficient conditions for a harmonic…
Consider the object allocation (one-sided matching) model of Shapley and Scarf (1974). When final allocations are observed but agents' preferences are unknown, when might the allocation be in the core? This is a one-sided analogue of the…
An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the…
Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a…
We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are…
Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic…
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally…
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…
In the paper two important theorems about complete affine spheres are generalized to the case of statistical structures on abstract manifolds. The assumption about constant sectional curvature is replaced by the assumption that the…
Motivated by questions in inverse scattering theory, we develop free boundary methods in obstacle problems where both the solution and the right hand side of the equation may have varying sign. The key condition that prevents the appearance…
In the landscape, if there is to be any prospect of scientific prediction, it is crucial that there be states which are distinguished in some way. The obvious candidates are states which exhibit symmetries. Here we focus on states which…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
We revisit a classical question of how individual consumer preferences and incomes shape aggregate behavior. We develop a method that applies to populations with homothetic preferences and reduces the hard problem of aggregation to simply…
In this paper, we introduce concepts of separable functions in balls and in the whole space, and develop a new method to investigate the qualitative properties of separable functions. We first study the axial symmetry and monotonicity of…