Related papers: How to distinguish a local semigroup from a global…
A network of locally interacting agents can be thought of as performing a distributed computation. But not all computations can be faithfully distributed. This paper investigates which global, linear transformations can be computed using…
We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; i.e., over one variable function fields over complete discretely valued fields. We provide conditions on the group and the…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…
We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…
The short-time and global behaviour are studied for an autonomous linear evolution equation, which is defined by a generator inducing a uniformly bounded holomorphic semigroup in a Hilbert space. A general necessary and sufficient condition…
We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…
Let F be the function field of a curve over a complete discretely valued field K. Let G be a semisimple simply connected linear algebraic group over F of type An. We give a description of the obstruction to local global principle for…
We compare different local-global principles for torsors under a reductive group G defined over a semiglobal field F. In particular if the F-group G s a retract rational F-variety, we prove that the local global principle holds for the…
We study the `local entanglement' remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of…
In this work we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced…
In this paper we consider systems of vectors in a Hilbert space $\mathcal{H}$ of the form $\{g_{jk}: j \in J, \, k\in K\}\subset \mathcal{H}$ where $J$ and $K$ are countable sets of indices. We find conditions under which the local…
The short-time and global behaviour are studied for autonomous linear evolution equations defined by generators of uniformly bounded holomorphic semigroups in a Hilbert space. A general criterion for log-convexity in time of the norm of the…
A multipartite system comprised of $n$ subsystems, each of which is described with `local variables' in ${\mathbb Z}(d)$ and with a $d$-dimensional Hilbert space $H(d)$, is considered. Local Fourier transforms in each subsystem are defined…
For some Maltsev conditions $\Sigma$ it is enough to check if a finite algebra $\mathbf A$ satisfies $\Sigma$ locally on subsets of bounded size, in order to decide, whether $\mathbf A$ satisfies $\Sigma$ (globally). This local-global…
In this paper we prove a theorem of global time-extension for the local classical solution of Navier-Stokes's evolution problem in $\Real^n$ with $n\geqslant2$ for incompressible fluids subjected to external forces and regular initial…
Time-local master equations are more generally applicable than is often recognised, but at first sight it would seem that they can only safely be used in time intervals where the time evolution is invertible. Using the Jaynes-Cummings…
We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.
For a large class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors.
Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality, and a central question is to determine…
We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…