Related papers: Linear sets in the projective line over the endomo…

Let H be a closed subgroup of a linear algebraic group G defined over a field F. There is an equivalence of categories between the category of linear finite-dimensional representations of H and the category of finite rank G-homogeneous…

We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection…

Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…

Given finite posets $P$ and $Q$, we consider a specific ideal $L(P,Q)$, whose minimal monomial generators correspond to order-preserving maps $\phi:P\rightarrow Q$. We study algebraic invariants of those ideals. In particular, sharp lower…

The paper deals with the interplay between boundedness, order and ring structures in function lattices on the line and related metric spaces. It is shown that the lattice of all Lipschitz functions on a normed space $E$ is isomorphic to its…

We prove that the set of orthogonal projections on a Hilbert space equipped with the length metric is $\frac\pi2$-geodesic. As an application, we consider the problem of variation of spectral subspaces for bounded linear self-adjoint…

We study automorphisms of the affine line over rings like ZZ/p^n.

For L a finite lattice, let C(L) denote the set of pairs g = (g_0,g_1) such that g_0 is a lower cover of g_1 and order it as follows: g <= d iff g_0 <= d_0, g_1 <= d_1, but not g_1 <= d_0. Let C(L,g) denote the connected component of g in…

We consider the Andr\'e/Bruck-Bose representation of the projective plane $\mathrm{PG}(2,q^n)$ in $\mathrm{PG}(2n,q)$. We investigate the representation of $\mathbb{F}_{q^k}$-sublines and $\mathbb{F}_{q^k}$-subplanes of…

We establish a new decomposition formula for two orthogonal projections P and Q on a separable Hilbert space V. This formula yields an orthogonal direct sum decomposition of V into invariant subspaces under P and Q, each of which is either…

A linear system is a pair $(P,\mathcal{L})$ where $\mathcal{L}$ is a family of subsets on a ground finite set $P$, such that $|l\cap l^\prime|\leq 1$, for every $l,l^\prime \in \mathcal{L}$. The elements of $P$ and $\mathcal{L}$ are called…

Following \cite{B2}, we introduce a notion of para-products associated to a semi-group. We do not use Fourier transform arguments and the background manifold is doubling, endowed with a sub-laplacian structure. Our main result is a…

We give two presentations for bordisms of $S^2$ in the 3-dimensional oriented bordism category $\operatorname{Cob}(3) $, encoding the algebraic structures on $S^2$. After passing through topological field theories, we define two kinds of…

The projective space $\mathbb{P}_q(n)$, i.e. the set of all subspaces of the vector space $\mathbb{F}_q^n$, is a metric space endowed with the subspace distance metric. Braun, Etzion and Vardy argued that codes in a projective space are…

We consider the Grassman manifold $G(E)$ as the subset of all orthogonal projections of a given Euclidean space $E$ and obtain some explicit formulas concerning the differential geometry of $G(E)$ as a submanifold of $L(E,E)$ endowed with…

Let $\ell$ be a prime and let $q$ be a prime power not divisible by $\ell$. Put $G=\mathrm{GL}_n(\mathrm{F}_q)$ and fix an irreducible cuspidal representation, $\bar{\pi}$, of $G$ over a sufficiently large finite field, $k$, of…

In this work, we study the well-posedness of certain sparse regularized linear regression problems, i.e., the existence, uniqueness and continuity of the solution map with respect to the data. We focus on regularization functions that are…

In our companion work \cite{Stojnicl1RegPosasymldp} we revisited random under-determined linear systems with sparse solutions. The main emphasis was on the performance analysis of the $\ell_1$ heuristic in the so-called asymptotic regime,…

A structure $\cal S$ is quasi-projective if for every structure $\cal T$, for every homomorphism $f : {\cal S} \rightarrow {\cal T}$ and every epimorphism $j: {\cal S}\rightarrow {\cal T}$ there is an endomorphism $\phi$ of $\cal S$ such…

Scattering of electromagnetic fields by a defect layer embedded in a slow-light periodically layered ambient medium exhibits phenomena markedly different from typical scattering problems. In a slow-light periodic medium, constructed by…