Related papers: Difference Index of Quasi-Prime Difference Algebra…

In the problem of semialgebraic range searching, we are to preprocess a set of points in $\mathbb{R}^D$ such that the subset of points inside a semialgebraic region described by $O(1)$ polynomial inequalities of degree $\Delta$ can be found…

We establish existence and uniqueness results for the singular initial value problem associated with a class of quasilinear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an…

We introduce a notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertex operator algebra has a modular invariance…

In this short note we prove a lemma about the dimension of certain algebraic sets of matrices. This result is needed in our paper arXiv:1201.1672. The result presented here has also applications in other situations and so it should appear…

We introduce families of quasi-rectifiable vector fields and study their geometric and algebraic aspects. Then, we analyse their applications to systems of partial differential equations. Our results explain, in a simpler manner, previous…

In this work, the set of quasi-primary ideals of a commutative ring with identity is equipped with a topology and is called quasi-primary spectrum. Some topological properties of this space are examined. Further, a sheaf of rings on the…

We introduced the quasicentral modulus to study normed ideal perturbations of operators. It is a limit of condenser quasicentral moduli in view of a recently noticed analogy with capacity in nonlinear potential theory. We prove here some…

The Hilbert function, its generating function and the Hilbert polynomial of a graded ring R have been extensively studied since the famous paper of Hilbert: Ueber die Theorie der algebraischen Formen [Hil90]. In particular, the coefficients…

We show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize…

Almost difference sets have emerged as a fascinating and important area of research as they can produce functions with optimal nonlinearity, cyclic codes, and binary sequences with optimal autocorrelation. This study aims to investigate the…

In this book super interval matrices using the special type of intervals of the form [0, a] are introduced. Several algebraic structures like semigroups, groups, semirings, rings, semivector spaces and vector spaces are introduced. Special…

The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…

We introduce the notion of bounded quasi-inversion closed semiprime f-algebras and we prove that, if A is such an algebra, then any intermediate algebra in A is an order ideal of A. This extends a recent result by Dominguez who has dealt…

In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the…

In this paper, a general setting is proposed to define a class of modules over nonsemisimple Lie algebras $\mathfrak{g}$ induced by a nonperfect ideal $\mathfrak{p}$. This class of Lie algebras includes many well-known Lie algebras, and…

In this paper we consider a special class of arithmetic quotients of bounded symmetric domains which can roughly be described as higher- dimensional analogues of the Hilbert modular varities. The algebraic groups are defined as the unitary…

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…

In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…

This paper gives a geometric interpretation of the notion of quasi-symmetric representation and uses this to show that the discriminant locus associated to such a representation is a hyperplane arrangement. Moreover, we identify this…