Related papers: Isotone projection cones and Q-matrices
We prove the conjectural relation between the Stokes matrix for the quantum cohomology and an exceptional collection generating the derived category of coherent sheaves in the case of smooth cubic surfaces. The proof is based on a toric…
We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by…
Let $(P_n)_n$ and $(Q_n)_n$ be two sequences of monic polynomials linked by a type structure relation such as $$ Q_{n}(x)+r_nQ_{n-1}(x)=P_{n}(x)+s_nP_{n-1}(x)+t_nP_{n-2}(x)\;, $$ where $(r_n)_n$, $(s_n)_n$ and $(t_n)_n$ are sequences of…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
We consider the structure of classes of curves on a projective simply connected surface for which fundamental groups of the complements admit free quotients having rank greater than one with irreducible components belonging to a selected…
Several recent developments point to the fact that rational maps from n-punctured spheres to the null cone of D dimensional momentum space provide a natural language for describing the scattering of massless particles in D dimensions. In…
Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a…
In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means…
We study the geometry of $\mathcal{Q}$-conic arrangements in the complex projective plane. These are arrangements consisting of smooth conics and they admit certain quasi-homogeneous singularities. We show that such $\mathcal{Q}$-conic…
For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\mathrm{rep}(Q)$ of pointwise finite dimensional representations. We show that an object in…
We define the concept of an affinized projective variety and show how one can, in principle, obtain q-identities by different ways of computing the Hilbert series of such a variety. We carry out this program for projective varieties…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
The tensor product of two ordered vector spaces can be ordered in more than one way, just as the tensor product of normed spaces can be normed in multiple ways. Two natural orderings have received considerable attention in the past, namely…
In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the…
Let $V$ be a vector space endowed with a non-degenerate quadratic form $Q$. If the base field $\mathbb{F}$ is different from $\mathbb{F}_2$, it is known that every isometry can be written as a product of reflections. In this article, we…
Let $p\neq 2$, and let $R$ be a smooth affine algebra of dimension $3$ over $\overline{F}_p$ and $P, Q$ be projective $R$-modules of rank $2$, each with trivial determinant. We prove: $P$ is isomorphic to $Q$ if and only if there is an…
We apply the theory of cotorsion pairs to study closure properties of classes of modules with finite projective dimension with respect to direct limit operations and to filtrations. We also prove that if the ring is an order in an…
We study touching cones of a (not necessarily closed) convex set in a finitedimensional real Euclidean vector space and we draw relationships to other concepts in Convex Geometry. Exposed faces correspond to normal cones by an antitone…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
The structure of cones of positive and k-positive maps acting on a finite-dimensional Hilbert space is investigated. Special emphasis is given to their duality relations to the sets of superpositive and k-superpositive maps. We characterize…