相关论文: Which are the Maximal Ideals ?
We consider degenerated nonlinear PDE of elliptic type: $$ - \mathrm{div}(a(|x|)|\nabla w(x)|^{p-2} \nabla w(x)) + h(|x|,w(x),\langle\nabla w(x),\frac{x}{|x|}\rangle)=\phi(w(x)), $$ where $x$ belongs to the ball in $\bf{R}^n$. Using the…
The main result in this paper is to supply a recursive formula, on the number of minimal primes, for the colength of a fractional ideal in terms of the maximal points of the value set of the ideal itself. The fractional ideals are taken in…
This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a…
The maximum principle forms an important qualitative property of second order elliptic equations, therefore its discrete analogues, the so-called discrete maximum principles (DMPs) have drawn much attention. In this paper DMPs are…
For a joint probability density function f(x) of a random vector X the mixed partial derivatives of log f(x) can be interpreted as limiting cumulants in an infinitesimally small open neighborhood around x. Moreover, setting them to zero…
The paper suggests a new --- to the best of the author's knowledge --- characterization of decisions which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a…
A universal differential equation is a nontrivial differential equation the solutions of which approximate to arbitrary accuracy any continuous function on any interval of the real line. On the other hand, there has been much interest in…
Optimal approximation and optimal interpolation problems on the classes of periodic functions that are determined by restrictions on several higher derivatives of the functions are solved.
We study almost complete intersections ideals whose Rees algebras are extremal in the sense that some of their fundamental metrics---depth or relation type---have maximal or minimal values in the class. The focus is on those ideals that…
We prove some new results on existence of solutions to first--order ordinary differential equations with deviating arguments. Delay differential equations are included in our general framework, which even allows deviations to depend on the…
It is well known that the only proper non-trivial norm-closed ideal in the algebra L(X) for X=\ell_p (1 \le p < \infty) or X=c_0 is the ideal of compact operators. The next natural question is to describe all closed ideals of…
We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…
We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…
We systematically introduce an approach to the analysis and (numerical) solution of a broad class of nonlinear unconstrained optimal control problems, involving ordinary and distributed systems. Our approach relies on exact representations…
Reduced ideals have been defined in the context of integer rings in quadratic number fields, and they are closely tied to the continued fraction algorithm. The notion of this type of ideal extends naturally to number fields of higher…
We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler-Lagrange…
The paper considers the overdetermined system of PDE that describes a special type of two-dimensional motion of an ideal fluid. The analysis of the compatibility of the system was performed. All solutions of the system are obtained in a…
This paper exhibits some new examples of the behavior of the Castelnuovo-Mumford regularity of homogeneous ideals in polynomial rings. More precisely, we present new examples of homogenous ideals with large regularity compared to the…
Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such powers are linearly…
We develop the duality theory between ideals of multilinear operators and tensor norms that arises from the geometric approach of $\Sigma$-operators. To this end, we introduce and develop the notions of $\Sigma$-ideals of multilinear…