Related papers: Lattice-like operations and isotone projection set…

We study an extreme scenario of the Mastrand projection theorem for which a fractal has the property that its orthogonal projection is the same as the orthogonal projection of its convex hull. We extend results in current literature and…

Orthogonal projections of the uniform measure on the Sierpinski triangle form a family of self similar measures with overlaps. The main result of this work is to make a connection between the dimension theory of these measures and the…

Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…

This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…

Part I proved that for every quasivariety K of structures (which may have both operations and relations) there is a semilattice S with operators such that he lattice of quasi-equational theories of K (the dual of the lattice of…

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that…

We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…

For a convex body $K\subset\R^n$ and $i\in\{1,...,n-1\}$, the function assigning to any $i$-dimensional subspace $L$ of $\R^n$, the $i$-dimensional volume of the orthogonal projection of $K$ to $L$, is called the $i$-th projection function…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…

In this paper, we establish equivariant mirror symmetry for the weighted projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017].…

Given an idempotent operator $E$ in a complex Hilbert space ${\mathcal H}$, one can associate to it two orthogonal projections: - The polar decomposition $2E-1=(2P-1)|2E-1|$ provides an orthogonal projection $P$. That the unitary part in…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

This paper aims to develop a Newton-type method to solve a class of nonconvex composite programs. In particular, the nonsmooth part is possibly nonconvex. To tackle the nonconvexity, we develop a notion of strong prox-regularity which is…

We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of `peak projections', and in the…

Motivated by connections to random matrices, Littlewood-Richardson coefficients and tilings, we study random discrete concave functions on an equilateral lattice. We show that such functions having a periodic Hessian of a fixed average…

A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is…

In this paper, we will show how the Caratheodory Extension process is intimately related to the metric completion process. In particular, it will be shown how one is able to construct a lattice on the completion and to obtain an isomorphism…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

It is proved that the linearity of metric projections on subspaces and the convexity of the polars of the convex cones in the uniformly convex and uniformly smooth Banach space are equivalent, and both of them is equivalent with the fact…

Given a two-dimensional quantum lattice model with an abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a…