相关论文: Commutators of flows and fields

A generalized reciprocal theorem is formulated for the motion and hydrodynamic force moments of an active particle in an arbitrary background flow of a (weakly nonlinear) complex fluid. This formalism includes as special cases a number of…

On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…

In this paper, we study the asymptotic expansion of the flow X(t, x) solution to the nonlinear ODE: X (t, x) = b X(t, x) with X(0, x) = x $\in$ R d , where b is a regular Z dperiodic vector field in R d. More precisely, we provide various…

The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…

Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly…

Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and…

We start with a (q,t)-generalization of a binomial coefficient. It can be viewed as a polynomial in t that depends upon an integer q, with combinatorial interpretations when q is a positive integer, and algebraic interpretations when q is…

The traditional first approach to fractional calculus is via the Riemann-Liouville differintegral $_{a}D_{x}^{k}$. The intent of this paper will be to create a space $K$, pair of maps $g: C^{\omega}(\mathbb{R}) \to K$ and $g': K \to…

In this paper we study geometric aspects of dynamics generated by Young differential equations (YDE) driven by $\alpha$-H\"older trajectories with $\alpha \in (1/2, 1)$. We present a number of properties and geometrical constructions on…

We consider regular open curves in R^n with fixed boundary points and moving according to the L^{2}-gradient flow for a generalisation of the Helfrich functional. Natural boundary conditions are imposed along the evolution. More precisely,…

Using the asymmetric fractional calculus of variations, we derive a fractional Lagrangian variational formulation of the convection-diffusion equation in the special case of constant coefficients.

Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in (\frac13, \frac12)$ and $f$ is a continuously…

$ $Let $k$ be a field of characteristic zero. If $c_1, c_2\in k\setminus \{0\}, s,t\geq 1$ and $u\geq 0$, then it is shown that the $k$-derivations $\partial_x + x^u(c_1x^ty^s+c_2)\partial_y$ and $\partial_x +…

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum…

The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to…

Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric…

An exact functional renormalization group flow equation is derived for the divergence functional which is a generalization of the Kullback-Leibler divergence to quantum field theories in the Euclidean domain. It compares distributions with…

We study the $p$-tuples of holomorphic vector fields $(X_1,X_2,\ldots,X_p)$ satisfying the barycentric property $\displaystyle\sum_k\exp tX_k=p\cdot\mathrm{id}$, where $\exp tX$ denotes the flow of $X$.

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional…

Transport of scalar fields in compressible flow is investigated. The effective equations governing the transport at scales large compared to those of the advecting flow are derived by using multi-scale techniques. Ballistic transport…