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We investigate equivalences between the categories of perfects complexes of the quotients of two smooth projective schemes by the action of a finite group. As a result we give a necessary and sufficient condition for an equivalence between…

We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.

Parity is ubiquitous, but not always identified as a simplifying tool for computations. Using parity, having in mind the example of the bosonic/fermionic Fock space, and the framework of Z_2-graded (super) algebra, we clarify relationships…

In this paper we consider arbitrary intervals in the left weak order on the symmetric group $S_n$. We show that the Lehmer codes of permutations in an interval form a distributive lattice under the product order. Furthermore, the…

We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M…

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some homological data and takes values in the free abelian group…

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be…

We say that a Euclidean lattice in $\mathbb R^n$ is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group $S_n$, i.e., if the lattice is closed under the action of some non-identity elements…

Given discrete groups $\Gamma \subset \Delta$ we characterize $(\Gamma,\sigma)$-invariant spaces that are also invariant under $\Delta$. This will be done in terms of subspaces that we define using an appropriate Zak transform and a…

This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target…

We classify irreducible homogeneous almost Hermite-Lorentz spaces of complex dimension 3.

This paper investigates a novel connection between reductions of companion matrices associated with a symmetric family of certain binomial ideals in the coordinate ring of affine n-space and permutation matrices. Specifically, for fixed…

This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…

For a Reproducing Kernel Hilbert Space on a complex domain we give a formula that describes the Hermitean metrics on the domain which are pull-backs of some metric on the (dual of) the RKHS via the evaluation map. Then we consider the…

Two Bayesian models with different sampling densities are said to be marginally equivalent if the joint distribution of observables and the parameter of interest is the same for both models. We discuss marginal equivalence in the general…

Using evaluation at appropriately chosen points, we propose a Gr\"obner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the…

This is the first part of a series of papers. The whole series aims to develop the tools for the study of all almost Hermitian symmetric structures in a unified way. In particular, methods for the construction of invariant operators, their…