Related papers: Projective functions
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…
In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and gives many more. The theorem depends on a formal approach to…
For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use this to show that every such dynamical system over a number…
Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative…
This article studies optional and predictable projections of integrands and convex-valued stochastic processes. The existence and uniqueness are shown under general conditions that are analogous to those for conditional expectations of…
We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves to be the dualizable objects in the derived infinity-category…
In this paper, we consider a wider class of simulation functions and present some coincidence and common fixed point results in metric spaces. Results obtained in this paper extend, generalize and unify some well-known fixed and common…
In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly…
We prove that one may approximate parametric suprema of constructible and power-constructible functions using functions within the same class. This resolves a conjecture by Adiceam and Cluckers, which was posited after studying a question…
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of `peak projections', and in the…
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…
We characterize stability under composition, inversion, and solution of ordinary differential equations for ultradifferentiable classes, and prove that all these stability properties are equivalent.
Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…
Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove…
We study the stability of a class of action functionals induced by gradients of convex functions with respect to Mosco convergence, under mild assumptions on the underlying space.
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
In this paper we introduce ternary modules over ternary algebras and using fixed point methods, we prove the stability and super-stability of ternary additive, quadratic, cubic and quartic derivations and $\sigma$-homomorphisms in such…