Related papers: On the Annihilation of Thin Sets
Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic $K$-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when…
Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyse the effective entanglement, i.e. entanglement…
We exhibit an asymmetry phenomenon for uniqueness sets in $\ell^q$. Specifically, we construct sets that do not support measures with $\ell^q$-summable Fourier coefficients, yet simultaneously support measures whose positive frequencies…
Based on SU(3) flavor symmetry, many of the quark-graph amplitudes in two-body nonleptonic decays of charmed mesons can be extracted from experiment, which enable us to see the relevance and importance of weak annihilation topologies and to…
A general discussion is given for first-kind (FK) and quantum non-demolition (QND) measurements. The general conditions for these measurements are derived, including the most general one (called the weak condition), an intermediate one, and…
We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory…
We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of…
A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of 'forbidden patterns', to be strongly aperiodic if all point…
A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…
We consider the set of monic irreducible polynomials $P$ over a finite field $\mathbb{F}_q$ such that the multiplicative order modulo $P$ of some a in $\mathbb{F}_q(T)$ is divisible by a fixed positive integer $d$. Call $R_q(a,d)$ this set.…
We show that if a closed discrete subset $A \subseteq \mathbf{R}^d$ is denser than a certain critical threshold, then $A$ is a Fourier uniqueness set, while if $A$ is sparser, then uniqueness fails and one can prescribe arbitrary values for…
Dark matter annihilation in so-called ``spikes'' near black holes is believed to be an important method of indirect dark matter detection. In the case of circular particle orbits, the density profile of dark matter has a plateau at small…
In theories with long-range forces like QED or perturbative gravity, only rates that include emitted soft radiation are non-vanishing. Independently of detector resolution, finite observables can only be obtained after integrating over the…
Let $\mathcal{S} = \{ \tau_n \}_{n=1}^\infty \subset (0,T)$ be an arbitrary countable (dense) set. We show that for any given initial density and momentum, the compressible Euler system admits (infinitely many) admissible weak solutions…
Let $R$ be a ring and $n$, $k$ two non-negative integers. In this paper, we introduce the concepts of $n$-weak injective and $n$-weak flat modules and via the notion of special super finitely presented modules, we obtain some…
In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are…
We use currently available data of nonleptonic charmless 2-body $B\to MM$ decays ($MM = PP, PV, VV$) that are mediated by $b\to (d, s)$ QCD- and QED-penguin operators to study weak annihilation and new-physics effects in the framework of…
The main goal of this note is to prove the following theorem. If $A_n$ is a sequence of measurable sets in a $\sigma$-finite measure space $(X, \mathcal{A}, \mu)$ that covers $\mu$-a.e. $x \in X$ infinitely many times, then there exists a…
We prove that if $T$ is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for $T$ and strict independence relations for $T^{\text{eq}}$. We use this observation…
Semi-annihilation is a generic feature of dark matter theories with symmetries larger than Z_2. We explore a model based on a Z_4-symmetric dark sector comprised of a scalar singlet and a "wino"-like fermion SU(2)_L triplet. This is the…