Related papers: Pairings between bounded divergence-measure vector…
In this paper we investigate the relationship between the properties of a compact set $\sigma \subseteq \mathbb{C}$ and the structure of the space $BV(\sigma)$ of functions of bounded variation (in the sense of Ashton and Doust) defined on…
The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and…
The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…
We investigate the 1D Riemann-Liouville fractional derivative focusing on the connections with fractional Sobolev spaces, the space $BV$ of functions of bounded variation, whose derivatives are not functions but measures and the space…
We study a version of the Lebesgue differentiation theorem in which the integral averages are replaced with medians over Busemann--Feller differentiation bases. Our main result gives several characterizations for the differentiation…
Let $G=(U \cup V, E)$ be a bipartite graph, where $U$ represents jobs and $V$ represents machines. We study a new variant of the bipartite matching problem in which each job in $U$ can be matched to at most one machine in $V$, and the…
We present an overview of the mathematical structure of geminal theory within the seniority formalism and bi-variational principle. Named after the constellation, geminal wavefunctions provide the mean-field like representation of…
An extension of the notion of classical equivalence of equivalence in the Batalin--(Fradkin)--Vilkovisky (BV) and (BFV) framework for local Lagrangian field theory on manifolds possibly with boundary is discussed. Equivalence is phrased in…
The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series
Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean…
Given bounded vector field $b : \mathbb R^d \to \mathbb R^d$, scalar field $u : \mathbb R^d \to \mathbb R$ and a smooth function $\beta : \mathbb R \to \mathbb R$ we study the characterization of the distribution $\mathrm{div}(\beta(u)b)$…
The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate…
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…
Extending the notion of bounded variation, a function $u \in L_c^1(\mathbb R^n)$ is of bounded fractional variation with respect to some exponent $\alpha$ if there is a finite constant $C \geq 0$ such that the estimate \[ \biggl|\int u(x)…
Starting from the linearized BdG-equation we make the simple observation that pairing can occur between particles with total momenta different from zero, e.g., with equal momentum and opposite spin, in cases of an effective interaction…
For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining points via characteristic functions of different boundary…
We study a class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few…
We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…
The generating functionals of Green's functions with composite and external fields are considered in the framework of BV and BLT quantization methods for general gauge theories. The corresponding Ward identities are derived and the gauge…
The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the…