相关论文: Commutators of flows and fields
This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It implies then easily the existence of global solutions to linear non-autonomous ODE's, with a standard…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
Complete sets of commutation relations for arbitrary pairs of quantum minors are computed, with explicit coefficients in closed form.
In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial…
We introduce a Yamabe-type flow \begin{align*} \left\{ \begin{array}{ll} \frac{\partial g}{\partial t} &=(r^m_{\phi}-R^m_{\phi})g \\ \frac{\partial \phi}{\partial t} &=\frac{m}{2}(R^m_{\phi}-r^m_{\phi}) \end{array} \right. ~~\mbox{ in }M…
Let $F(X_1,X_2)\in\mathbb{Z}[X_1,X_2] $ be an irreducible binary form of degree $3$ and $h$ an arithmetic function. We give some estimates for the average order $\sum_{\substack{|n_1|\leq x,|n_2|\leq x}}h(F(n_1,n_2))$ when $h$ satisfy…
The detailed fluctuation theorems of the exact form $P(A)/P(-A)=e^A$ exist only for a handful of variables $A$, namely for work (Crooks theorem), for total entropy change (Seifert's theorem), etc. However, the so-called modified detailed…
In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional…
Viscous fluid dynamical calculations require no-slip boundary conditions. Numerical calculations of turbulence, as well as theoretical turbulence closure techniques, often depend upon a spectral decomposition of the flow fields. However,…
The first part of the paper will describe a recent result of K. Retert in (\cite{Ret}) for $k[x_1,\ldots,x_n]$ and $k[[x_1,\ldots,x_n]]$. This result states that if $\mathfrak{D}$ is a set of commute $k$-derivations of $k[x,y]$ such that…
The Fluctuation Theorem (FT) gives an analytic expression for the probability, in a nonequilibrium system of finite size observed for a finite time, that the dissipative flux will flow in the reverse direction to that required by the Second…
First, we prove a local spectral flow formula (Theorem 3.7) for a differentiable curve of selfadjoint Fredholm operators. This formula enables us to prove in a simple way a general spectral flow formula. Secondly, we prove a splitting…
In this paper, the author considers the fractional mean field equation on a finite graph $G=(V,E)$, say \begin{equation*} (-\Delta)^s u=\rho\left(\dfrac{he^u}{\int_V he^ud\mu}-\dfrac{1}{|V|}\right),\quad\forall\,x\in V, \end{equation*}…
The average of densities of currents and charges, induced by a weak electromagnetic field in spatially inhomogeneous are calculated at final temperatures. The Kubo formula for a conductivity tensor is generalized for spatially inhomogeneous…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
From the paper "Formality Conjecture" (Ascona 1996): "I am aware of only one such a class, it corresponds to simplest good graph, the complete graph with $4$ vertices $($and $6$ edges$)$. This class gives a remarkable vector field on the…
Shown is a new duality for the moduli spaces of Yang-Mills connections over noncommutative vector bundles, using which one sees that total data of quantum field theory are preserved by dimension reduction.
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…
We determine the most general form of the covariant drag force exerted on a quark moving through a fluid dynamical flow. Up to first order in derivative expansion, our general formula requires the specification of seven coefficient…
Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83--109] prove an extension of It\^{o}'s formula for $F(X_t,t)$, where $F(x,t)$ has a locally square-integrable derivative in $x$ that satisfies a mild continuity condition in $t$ and…