Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userIterated paraproducts and iterated commutator estimates in Besov spaces
193
0
0.0
(
0
)
Authors
Masato Hoshino
Ask ChatGPT about the research
No Arabic abstract
We extend the results in [6] to Besov spaces $B_{p,q}^alpha$ with $p,qin[1,infty]$ and $0<alpha<1$.
rate research
Read More
We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provides an analytical expression for the MFS as a formal expansion in terms of the thermodynamic mean values of successively higher commutators of the Hamiltonian with the operator involved through the control parameter. That expression is naturally divided into two parts: the usual isothermal susceptibility and a constituent in the form of an infinite series of thermodynamic mean values which encodes the noncommutativity in the problem. If the symmetry properties of the Hamiltonian are given in terms of the generators of some (finite dimensional) algebra, the obtained expansion may be evaluated in a closed form. This issue is tested on several popular models, for which it is shown that the calculations are much simpler if they are based on the properties from the representation theory of the Heisenberg or SU(1, 1) Lie algebra.
It is well known since Stasheffs work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads. The combinatorics of these higher homotopies is well understood and is extremely useful. For $n ge 2$ the theory of symmetric operads encapsulated the corresponding higher homotopies, yet hid the combinatorics and it has remain a mystery for almost 40 years. However, the recent developments in many fields ranging from algebraic topology and algebraic geometry to mathematical physics and category theory show that this combinatorics in higher dimensions will be even more important than the one dimensional case. In this paper we are going to show that there exists a conceptual way to make these combinatorics explicit using the so called higher nonsymmetric $n$-operads.
We give a new proof of the equivalence between two of the main models for $(infty,n)$-categories, namely the $n$-fold Segal spaces of Barwick and the $Theta_{n}$-spaces of Rezk, by proving that these are algebras for the same monad on the $infty$-category of $n$-globular spaces. The proof works for a broad class of $infty$-categories that includes all $infty$-topoi.
We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation between the Haar measure and the Hausdorff measure is clarified. Finally, we discus an example in ${Bbb R}times{Bbb Q}sb 2$ and calculate upper and lower bounds for its Hausdorff dimension.
We consider the compressible Navier-Stokes-Korteweg system describing the dynamics of a liquid-vapor mixture with diffuse interphase. The global solutions are established under linear stability conditions in critical Besov spaces. In particular, the sound speed may be greater than or equal to zero. By fully exploiting the parabolic property of the linearized system for all frequencies, we see that there is no loss of derivative usually induced by the pressure for the standard isentropic compressible Navier-Stokes system. This enables us to apply Banachs fixed point theorem to show the existence of global solution. Furthermore, we obtain the optimal decay rates of the global solutions in the $L^2(mathbb{R}^d)$-framework.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
