相关论文: Every 1D Persistence Module is a Restriction of So…

We compare several classes of biparameter persistence modules: $\gamma$-products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem, and modules of projective dimension at most 1. We…

We develop a stability theory for minimal projective resolutions of $\mathbf{P}$-modules, where $\mathbf{P}$ is a finite metric poset. We use the G\"ulen-McCleary distance on $\mathbf{P}$-modules together with a new complex matching…

Assume that $k$ is an algebraically closed field and $A$ is a finite-dimensional wild $k$-algebra. Recently, L. Gregory and M. Prest proved that in this case the width of the lattice of all pointed $A$-modules is undefined and hence there…

When working with (multi-parameter) persistence modules, one usually makes some type of tameness assumption in order to obtain better control over their algebraic behavior. One such notion is Ezra Millers notion of finite encodability,…

We prove a generalised version of finiteness of skein modules for 3-manifolds by including boundary. We show that internal skein modules are holonomic modules over the internal skein algebra of the boundary - a property including finite…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

A residual design ${\cal{D}}_B$ with respect to a block $B$ of a given design $\cal{D}$ is defined to be linearly embeddable over $GF(p)$ if the $p$-ranks of the incidence matrices of ${\cal{D}}_B$ and $\cal{D}$ differ by one. A sufficient…

We consider persistent homology obtained by applying homology to the open Rips filtration of a compact metric space $(X,d)$. We show that each decrease in zero-dimensional persistence and each increase in one-dimensional persistence is…

An exact solution is presented for the resistance of an orifice in a 2D membrane separating two infinitely large conductive reservoirs and obstructed by an infinitely long cylinder. The solution is obtained by constructing a curvilinear…

It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…

On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends…

We prove that every distinct covering system has a modulus divisible by either 2 or 3.

This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…

A cone spherical metric is called irreducible if any developing map of the metric does not have monodromy in ${\rm U(1)}$. By using the theory of indigenous bundles, we construct on a compact Riemann surface $X$ of genus $g_X \geq 1$ a…

We study the problem of constructing bulk and surface embedded modes (EMs) inside the quasi-continuum band of a square lattice, using a potential engineering approach \`a la Wigner and von Neumann. Building on previous results for the…

We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…

We construct new families of U_q(gl_n)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object - admissible set of relations defined in \cite{FRZ}. More precisely, we prove…

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…

For any prime p, we construct, and simultaneously count, all of the complex Specht modules in a given p-block of the symmetric group which remain irreducible when reduced modulo p. We call the Specht modules with this property p-irreducible…

A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-parameter persistence modules. One such invariant is the minimal…