Related papers: An Example of a Right Loop Admitting Only Discrete…
This is a review and tutorial paper which discusses the fundamental limitations on the maximal power which can be received, absorbed, and scattered by an electrically small electrically polarizable particle and infinite periodical arrays of…
Potentialism is the view that objects are successively generated in an incompletable process. A strict version of the view adds that truths are successively determined. Strict potentialism can be analyzed using two modalities: one for the…
The polarization phenomenon for a single source is extended to a framework with multiple correlated sources. It is shown in addition to extracting the randomness of the source, the polar transforms takes the original arbitrary dependencies…
A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected…
If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.
The lambda Pi calculus can be extended with rewrite rules to embed any functional pure type system. In this paper, we show that the embedding is conservative by proving a relative form of normalization, thus justifying the use of the lambda…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
We show that classical chaining bounds on the suprema of random processes in terms of entropy numbers can be systematically improved when the underlying set is convex: the entropy numbers need not be computed for the entire set, but only…
Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…
We show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by any increasing sequence of mixing shifts of finite type,…
We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler…
We present and study the Pool model in $\mathbb{R}^2$, a rotationally symmetric analogue of Multi-Particle Diffusion-Limited Aggregation (MDLA), in which particles ("droplets") perform continuous-time random walks and are absorbed upon…
Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only…
Polynomial closure is a standard operator which is applied to a class of regular languages. In the paper, we investigate three restrictions called left (LPol), right (RPol) and mixed polynomial closure (MPol). The first two were known while…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…
We give an elementary proof of a monotone selection principle which allows to pass from increasing nets to increasing sequences in the Hermitian part of a $\sigma$-finite von Neumann algebra. This is to be seen as a ``monotone version'' of…
We give a criterion for a real divisor to be rational and semiample.
In a branching process, the number of particles increases exponentially with time, which makes numerical simulations for large times difficult. In many applications, however, only the region close to the extremal particles is relevant (the…
Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e., the…
For the model Hamiltonian describing the electron-nuclear dynamics of a quantum dot, we obtained an exact expression for the limiting nuclear polarization as a function of the number of groups of equivalent nuclei. It is shown that the…