Related papers: A revised pre-order principle and set-valued Ekela…

We prove a conditional expectation bang-bang principle. Based on properties of the conditional expectation vector measure, we establish that the conditional expectation of a set-valued mapping coincides with the conditional expectation of…

We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated $\Pi^1_1$-comprehension and the existence of admissible sets, over weak…

In this paper, we develop a variational perturbation (VP) scheme for calculating vacuum expectation values (VEVs) of local fields in quantum field theories. For a comparatively general scalar field model, the VEV of a comparatively general…

Rerandomization utilizes modern computing ability to improve covariate balance while adhering to the randomization principle originally advocated by RA Fisher. Affinely invariant rerandomization has the ``Equal Percent Variance Reducing''…

We propose novel high-order algorithms for a class of $\ell_p$-structured non-monotone variational inequalities. In particular, work by Diakonikolas et al. (2021), which introduced the weak Minty variational inequality (weak-MVI) setting,…

This paper addresses a large class of vector optimization problems in infinite-dimensional spaces with respect to two important binary relations derived from domination structures. Motivated by theoretical challenges as well as by…

For proper lower semi-continuous functionals bounded below which do not increase upon polarization, an improved version of Ekeland's variational principle can be formulated in Banach spaces, which provides almost symmetric points.

We present a higher well-ordering principle which is equivalent (over Simpson's set theoretic version of $\text{ATR}_0$) to the existence of transitive models of Kripke-Platek set theory, and thus to $\Pi^1_1$-comprehension. This is a…

We introduce a new logic, called \emph{cluster first-order logic}, a restricted fragment of first-order logic specifically designed to study order invariance. An order-invariant formula is one on a vocabulary that contains an order;…

Phase transition is one of the most important phenomena in nature and plays a central role in materials design. All phase transitions are characterized by suitable order parameters, including the order-disorder phase transition. However,…

We develop a first-order theory of ordered transexponential fields in the language $\{+,\cdot,0,1,<,e,T\}$, where $e$ and $T$ stand for unary function symbols. While the archimedean models of this theory are readily described, the study of…

Recently there has been an increased interest in unsupervised learning of disentangled representations using the Variational Autoencoder (VAE) framework. Most of the existing work has focused largely on modifying the variational cost…

A general nonlinear regularity model for a set-valued mapping $F:X\times R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves.…

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when…

The variational principle (VP) is designed to generate non-folding grids (diffeomorphisms) with prescribed Jacobian determinant (JD) and curl. Its solution pool of the original VP is based on an additive formulation and, consequently, is…

Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…

We consider large-order perturbative expansions in QED and QCD. The coefficients of the expansions are known to be dominated by the so called ultraviolet (UV) renormalons which arise from inserting a chain of vacuum-polarization graphs into…

The inference of a hidden variable's historical value, based on observations before and after the fact, is a controversial subject in quantum mechanics. Here I address the controversy by proposing a formalism that unifies and generalizes…

Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \[ \langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0. \] Here…

In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li, Shi, J. Math. Anal. Appl. 246, 308-319 (2000), clarify the assumptions and conclusions of their Theorem 1 as…