Kimura diffusions serve as a stochastic model for the evolution of gene frequencies in population genetics. Their infinitesimal generator is an elliptic differential operator whose second-order coefficients matrix degenerates on the boundary of the domain. In this article, we consider the inhomogeneous initial-value problem defined by generators of Kimura diffusions, and we establish C-estimate...

This paper performs an in-depth qualitative analysis of the dynamic behavior a diffusive Lotka-Volterra type competition system with advection terms under homogeneous Dirichlet boundary condition. First, we obtain existence, multiplicity and explicit structure spatially nonhomogeneous steady-state solutions by using implicit function theorem Lyapunov-Schmidt reducti...

For any compact oriented manifold M , we show that that the top degree multi-vector fields transverse to the zero section of ∧TM are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of its zero locus and a finite number of numerical invariants. The group governing the infinitesimal deformations of such multi-vector fields is computed, and an e...

In this paper, the Lie group analysis method is applied to the geometric average Asian option pricing equation in financial problems. Firstly, the complete Lie symmetry group and infinitesimal generators of this equation are derived. Then the optimal system with one parameter for the Lie symmetry algebra are obtained, which gives the possibility to describe a complete set of invariant solutions...

Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent z = 1, none of the known variants of conformal invariance can act as its dynamical symmetry. In d = 1 spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal gene...

Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, ·} and L = G(q, p)∂q + F (q, p)∂p, which are used in equations of motion, are derivative operators. We consider fractional derivatives on a set of classical observables as fractional powers of derivative operators. As ...

The continuous extension of the discrete duality symmetry of the SchwarzSen model is studied. The corresponding infinitesimal generator Q turns out to be local, gauge invariant and metric independent. Furthermore, Q commutes with all the conformal group generators. We also show that Q is equivalent to the non—local duality transformation generator found in the Hamiltonian formulation of Maxwell...

A presentation of the problem of calculating the vector coupling coefficients for SU3 ⊃ SU2⊗U1 is made, in the spirit of traditional treatments of SU2 coupling. The coefficients are defined as the overlap matrix element between product states and a coupled state with good SU3 quantum numbers. A technique for resolution of the outer degeneracy problem, based upon actions of the infinitesimal gen...

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau’s theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions...

Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups thermodynamic processes. We characterise a wide class GKSL-generators for quantum maps within thermal operations and argue that every infinitesimal generator (a one-parameter semigroup of) Markovian belongs to this class. completely classify visualise them their non-Markovian counterparts case single...