相关论文: Multiple Exchange Property for M$^\natural$-concav…
Some differential implications of classical Marx-Strohh\"acker theorem are extended for multivalent functions. These results are also generalized for functions with fixed second coefficient by using the theory of first order differential…
In this paper, we introduce new properties of the relative interior calculus for nearly convex sets, functions, and set-valued mappings. These properties are important for the development of duality theory in optimization. Then we…
We consider the class of valuations on indivisible items called gross-substitute (GS). This class was introduced by Kelso and Crawford (1982) and is widely used in studies of markets with indivisibilities. GS is a condition on the…
Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making…
We derive a general quantum exchange fluctuation theorem for multipartite systems with arbitrary coupling strengths by taking into account the informational contribution of the back-action of the quantum measurements, which contributes to…
We study exchange couplings in the organic magnets copper(II) phthalocyanine (Cu(II)Pc) and manganese(II) phthalocyanine (Mn(II)Pc) by a combination of Green's function perturbation theory and \textsl{ab initio} density-functional theory…
We investigate polyconvexity of the double well function $f(X)\,:= |X-X\_1|^2|X-X\_2|^2$ for given matrices $X\_1, X\_2 \in \R^{n \times n}$. Such functions are fundamental in the modeling of phase transitions in materials, but their…
The phenomenon of many-body localisation received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at non-zero temperature as well as in the context of the…
In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation derived from the Dyson equation under the…
We provide a simple proof for the Fenchel duality between strong convexity and Lipschitz continuous gradient. To this end, we first establish equivalent conditions of convexity for a general function that may not be differentiable. By…
Various authors have been generalizing some unital ring properties to nonunital rings. We consider properties related to cancellation of modules (being unit-regular, having stable range one, being directly finite, exchange, or clean) and…
Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, and the invariant $\mathcal G$ introduced by the first author, are valuative. In this paper we construct…
Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optimization, and combinatorial geometry, where linear structure…
We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjecture similarity over discrete valuation rings can be descent…
The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of…
The demand for pseudopotentials constructed for a given exchange-correlation (XC) functional far exceeds the supply, necessitating the use of those commonly available. The number of XC functionals currently available is in the hundreds, if…
In recent years, combinatorial reconfiguration problems have attracted great attention due to their connection to various topics such as optimization, counting, enumeration, or sampling. One of the most intriguing open questions concerns…
By generalizing Ledrappier's criterion for the $K$-property of equilibrium states, we extend the criterion to subadditive potentials. We apply this result to the singular value potentials of matrix cocycles, and show that equilibrium states…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
Wei's celebrated Duality Theorem is generalized in several ways, expressed as duality theorems for linear codes over division rings and, more generally, duality theorems for matroids. These results are further generalized, resulting in two…