Related papers: On the local integrability condition for generalis…
In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms…
We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its…
The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace…
We consider affine control systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions of local controllability around this equilibrium, involving the iterated Lie…
We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizability are obtained for (1,-1,1), (2,-1,1) and…
Melting is analyzed dynamically as a problem of localization at a liquid-solid interface. A Lindemann-like criterion of melting is derived in terms of particular vibrational amplitudes, which turn out to equal a universal quotient (about…
We investigate the stability conditions for remote state estimation of multiple linear time-invariant (LTI) systems over multiple wireless time-varying communication channels. We answer the following open problem: what is the fundamental…
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any…
We give necessary and sufficient conditions for both square integrability and smoothness for densities of a probability measure on a compact connected Lie group.
We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schr\"odinger model with general on-site nonlinearity. Analytic conditions for existence of exact compact three-site…
It is argued that the (traditional) global level statistics which determines localization and coherent transport properties of disordered systems at zero temperature (e.g. the Anderson model) becomes inappropriate when it comes to…
This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the…
We consider lattice gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas…
In this paper we investigate the affect of various acceptance conditions on recogniser membrane systems without dissolution. We demonstrate that two particular acceptance conditions (one easier to program, the other easier to prove…
I derive a general set of boundary conditions for quasiclassical transport theory of metals and superconductors that is valid for equilibrium and non-equilibrium situations and includes multi-band systems, weakly and strongly spin-polarized…
We propose a new inference framework called localized conformal prediction. It generalizes the framework of conformal prediction by offering a single-test-sample adaptive construction that emphasizes a local region around this test sample,…
We prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general…