Related papers: Strongly proper forcing and some problems of Forem…
Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper $\omega^\omega$-bounding poset with $\aleph_2$-cc that forces continuum many pairwise different cardinal…
Motivated by recent results on the dual formulation of optimal stopping problems, we investigate in this short paper how the knowledge of an approximating dual martingale can improve the efficiency of primal methods. In particular, we show…
Let $R$ be a commutative ring and $S \subseteq R$ be a multiplicative subset. We introduce and study the concept of $S$-purity based on the notion of $S$-strongly flat modules. The class of $S$-pure injective modules will be studied. We…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
We prove that \textsf{P}-points (even strong P-points) and Gruff ultrafilters exist in any forcing extension obtained by adding fewer than $\aleph_{\omega}% $-many random reals to a model of \textsf{CH. }These results improve and correct…
We set the foundation and formulate the Perfect (Ideal) Hyperfluid. The latter represents the natural generalization of the usual perfect fluid structure where now the microscopic characteristics of matter (spin, shear, dilation) are also…
This paper is concerned with the structure of solutions to the elliptic problem for an Henon type equation with a forcing term. Under suitable assumptions on the forcing term, we give a complete classification of the existence/nonexistence…
Our goal is to finally settle the persistent problem in Diophantine Approximation of finding best linear approximates. Classical results from the theory of continued fractions provide the solution for the special homogeneous case in the…
We introduce an operation on modules over an $F$-finite ring of characteristic $p$. We call this operation \emph{tight interior}. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight…
Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven,…
We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal achievement sets with the notion of ideally supported sum…
We give a brief survey on the interplay between forcing axioms and various other non-constructive principles widely used in many fields of abstract mathematics, such as the axiom of choice and Baire's category theorem. First of all we…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
This paper focuses on infinite-horizon optimal control problems for dissipative systems and the relations to their finite-horizon formulations. We show that, for a large class of problems, dissipativity of the state equation, when a…
For a polarized family of complex projective manifolds, we identify the algebraic obstructions that govern the existence of approximate solutions to the Wess-Zumino-Witten equation. When this is specialized to the fibration associated with…
Let A be a commutative ring, and let \a be a weakly proregular ideal in A. (If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category of cohomologically \a-torsion complexes. We prove…
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
The Cauchy problem for metric-affine f(R)-gravity `a la Palatini and with torsion, in presence of perfect fluid matter acting as source, is discussed following the well-known Bruhat prescriptions for General Relativity. The problem results…
We formalize the theory of forcing in the set theory framework of Isabelle/ZF. Under the assumption of the existence of a countable transitive model of ZFC, we construct a proper generic extension and show that the latter also satisfies…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…