Related papers: One-sided epsilon-approximants
The notion of weak cyclic monotonicity of set-valued maps generalizing the cyclic monotonicity is introduced. The existence of solutions of differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides…
We prove weak approximation for smooth cubic hypersurfaces of dimension at least 2 defined over the function field of a complex curve.
Let $\mathcal{P}$ be the set of the primes. We consider a class of random multiplicative functions $f$ supported on the squarefree integers, such that $\{f(p)\}_{p\in\mathcal{P}}$ form a sequence of $\pm1$ valued independent random…
This paper addresses the weak-strong uniqueness property and singular limit for the compressible Primitive Equations (PE). We show that a weak solution coincides with the strong solution emanating from the same initial data. On the other…
A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…
Pach showed that every $d+1$ sets of points $Q_1,\dotsc,Q_{d+1} \subset \mathbb{R}^d$ contain linearly-sized subsets $P_i\subset Q_i$ such that all the transversal simplices that they span intersect. We show, by means of an example, that a…
In this paper, approximate optimality conditions and sensitivity analysis in nearly convex optimization are discussed. More precisely, as in the spirit of convex analysis, we introduce the concept of $\varepsilon$-subdifferential for nearly…
The tight span $T_d$ of a metric $d$ on a finite set is the subcomplex of bounded faces of an unbounded polyhedron defined by~$d$. If $d$ is generic then $T_d$ is known to be dual to a regular triangulation of a second hypersimplex. A tight…
This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…
This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. Our approach entails analyzing the rational connectivity of the smooth locus of…
A convex subset X of a linear topological space is called compactly convex if there is a continuous compact-valued map $\Phi:X\to exp(X)$ such that $[x,y]\subset\Phi(x)\cup \Phi(y)$ for all $x,y\in X$. We prove that each convex subset of…
We define a weakly threshold sequence to be a degree sequence $d=(d_1,\dots,d_n)$ of a graph having the property that $\sum_{i \leq k} d_i \geq k(k-1)+\sum_{i > k} \min\{k,d_i\} - 1$ for all positive $k \leq \max\{i:d_i \geq i-1\}$. The…
We develop the parabolic weak porosity to characterize the parabolic Muckenhoupt $A_1$ weights with time-lag. Our main result shows that a nonempty closed set is parabolic weakly porous if and only if the parabolic distance function of the…
We study the closure of approximating sequences of some diffusion equations under certain weak convergence. A specific description of the closure under weak $H^1$-convergence is given, which reduces to the original equation when the…
We show that badly approximable vectors are exactly those that cannot, for any inhomogeneous parameter, be inhomogeneously approximated at every monotone divergent rate. This implies in particular that Kurzweil's Theorem cannot be…
Closed expressions are derived for the quantum measurement statistics of pre-and postselected gaussian particle beams. The weakness of the pre-selection step is shown to compete with the non-orthogonality of post-selection in a transparent…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…
Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the pre-selection and the post-selection should…
We extend the definition of weak symmetric continuity to be applicable for functions defined on any nonempty subset of $\R$. Then we investigate basic properties of weakly symmetrically continuous functions and compare them with those of…
We show that for every $k\in\mathbb{N}$ and $\varepsilon>0$, for large enough alphabet $R$, given a $k$-CSP with alphabet size $R$, it is NP-hard to distinguish between the case that there is an assignment satisfying at least…