Related papers: Cancellation problem via locally nilpotent derivat…
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
We consider here the local existence of strong solutions for the Zakharov-Kuznestov (ZK) equation posed in a limited domain (0,1)_{x}\times(-pi /2, pi /2)^d, d=1,2. We prove that in space dimensions 2 and 3, there exists a strong solution…
The principal theorem of Sz.-Nagy on dilation of a positive definite Hilbert space operator valued function has played a central role in the development of the non-self-adjoint operator theory. In this paper we introduce the positive…
We first introduce a weak type of Zariski decomposition in higher dimensions: an $\R$-Cartier divisor has a weak Zariski decomposition if birationally and in a numerical sense it can be written as the sum of a nef and an effective…
In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation…
The continuity of the inverse Klain map is investigated and the class of centrally symmetric convex bodies at which every valuation depends continuously on its Klain function is characterized. Among several applications, it is shown that…
We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite…
In a 1962 paper, Zariski introduced the decomposition theory that now bears his name. Although it arose in the context of algebraic geometry and deals with the configuration of curves on an algebraic surface, we have recently observed that…
We study the maximum likelihood degree of linear concentration models in algebraic statistics. We relate the geometry of the reciprocal variety to that of semidefinite programming. We show that the Zariski closure in the Grassmanian of the…
In this note I give a description of Lyubeznik's local cohomology invariants for a certain natural class of local rings, namely the ones which have the same local cohomology vanishing as one expects from an isolated singularity. This…
Let $\L_m$ be the scheme of the laws defined by the Jacobi's identities on $\K^m$ with $\K$ a field. A deformation of $\g\in\L_m$, parametrized by a local $\K$-algebra $\A$, is a local $\K$-algebra morphism from the local ring of $\L_m$ at…
If $\bar\rho$ is an automorphic modulo $p$ Galois representation, it is natural to wonder if automorphic points are Zariski dense in the deformation space of $\bar\rho$. We prove new results in this direction in the case of a unitary group…
In this paper, we study for the first time topological defects in the context of nonlocal field theories in which Lagrangians contain infinite-order differential operators. In particular, we analyze domain walls. Despite the complexity of…
We explore some of the cosmological implications of the recent classical nonlocal generalization of Einstein's theory of gravitation in which nonlocality is due to the gravitational memory of past events. In the Newtonian regime of this…
We consider the Cauchy problem for the kinetic derivative nonlinear Schr\"odinger equation on the torus: \[ \partial_t u - i \partial_x^2 u = \alpha \partial_x \big( |u|^2 u \big) + \beta \partial_x \big[ H \big( |u|^2 \big) u \big] , \quad…
We give a simple algorithm showing that the reduction of the multiplicity of a characteristic p>0 hypersurface singularity along a valuation is possible if there is a finite linear projection which is defectless. The method begins with the…
We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kahler potential on…
In the present paper, local derivations and local automorphisms of five-dimensional naturally graded nilpotent associative algebras are studied. Namely, a general form of the matrices of local derivations and local automorphisms of algebras…
For the Hamiltonian operator H = -{\Delta}+V(x) of the Schr\"odinger Equation with a repulsive potential, the problem of local decay is considered. It is analyzed by a direct method, based on a new, L^2 bounded, propagation observable. The…
We use Pauli-Villars regularization to evaluate the conformal and chiral anomalies in the effective field theories from Z3 and Z7 compactifications of the heterotic string without Wilson lines. We show that parameters for Pauli-Villars…