Related papers: On differential equations invariant under two-vari…
We give a survey on eta invariants including methods of computation and applications in differential topology.
We present a theoretical framework and numerical methods for predicting the large-scale properties of solutions of partial differential equations that are too complex to be properly resolved. We assume that prior statistical information…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
Here we develop a technique of computing the invariants of $n-$ary forms and systems of forms using the discriminants of corresponding multilinear forms built of their partial derivatives, which should be cosidered as analogues of classical…
The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop…
We discuss invariants in equivariant birational geometry.
We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…
A general expression for a relative invariant of a linear ordinary differential equations is given in terms of the fundamental semi-invariant and an absolute invariant. This result is used to established a number of properties of relative…
We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
Point transformations for the ordinary differential equations of the form $y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) (y')^2+S(x,y) (y')^3$ are considered. Some classical results are resumed. Solution for the equivalence problem for the equations of…
Invariant foliations are complicated random sets useful for describing and understanding the qualitative behaviors of nonlinear dynamical systems. We will consider invariant foliations for stochastic partial differential equation with…
We study some conformally invariant integral equations using the method of moving spheres.
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
The general notion of distance dependent statistics in anyon-like systems is discussed. The two-body problem for such statistics is considered, the general formula for the second virial coefficient is derived and it is shown that in the…
Here, Darboux's classical results about transformations with differential substitutions for hyperbolic equations are extended to the case of parabolic equations of the form $L u = \big(D^2_{x} + a(x,y) D_x + b(x,y) D_y + c(x,y)\big)u=0$. We…