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In this article we classify indecomposable objects of the derived categories of finitely-generated modules over certain infinite-dimensional algebras. The considered class of algebras (which we call nodal algebras) contains such well-known…
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total…
We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories $C_Q^{(t)}$ $(t=1,2,3)$, $\mathscr{C}_{\mathscr{Q}}^{(1)}$ and…
We consider $m$-th order linear recurrences that can be thought of as generalizations of the Lucas sequence. We exploit some interplay with matrices that again can be considered generalizations of the Fibonacci matrix. We introduce the…
This paper studies global a priori gradient estimates for divergence-type equations patterned over the $p$-Laplacian with first-order terms having polynomial growth with respect to the gradient, under suitable integrability assumptions on…
We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its…
A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of…
We construct a finite-dimensional algebra derived equivalent to the example of Kershaw--Rickard. For the Kershaw--Rickard example the delooping level and the sub-derived delooping level are both infinite, while for our algebra both…
We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.
In one of his papers, the author introduces the class of Farkas-related vectors for which a version of Farkas' lemma over integers is derived. In this paper, two similar classes are introduced and studied.
We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence…
We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians…
In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were…
$\lambda$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.
We investigate the algebraic structure of integrable hierarchies that, we propose, underlie models of $W$-gravity coupled to matter. More precisely, we concentrate on the dispersionless limit of the topological subclass of such theories, by…
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function…
When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for…
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…
We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.