Related papers: A global invariant for path structures and second …
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
We give here a covariant definition of the path integral formalism for the Lagrangian, which leaves a freedom to choose anyone of many possible quantum systems that correspond to the same classical limit without adding new potential terms…
We compute the best constants in some second order dilation invariant inequalities, with weights being powers of the distance from the origin.
In this paper we mainly study the global structure of the quaternion Bernoulli equations $\dot q=aq+bq^n$ for $q\in \mathbb H$ the quaternion field and also some other form of cubic quaternion differential equations. By using the…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
A notion of the generalized invariant manifold for a nonlinear integrable lattice is considered. Earlier it has been observed that this kind objects provide an effective tool for evaluating the recursion operators and Lax pairs. In this…
In this paper we describe what should perhaps be called a `type-2' Vassiliev invariant of knots S^2 -> S^4. We give a formula for an invariant of 2-knots, taking values in Z_2 that can be computed in terms of the double-point diagram of the…
This short survey, which was written to accompany a minicourse at the BIRS conference "Topology in dimension 4.5", concerns invariants of knotted $2$-spheres in $S^4$, also known as $2$-knots. It covers invariants extracted from the…
We define a computable topological invariant $\mu(\gamma)$ for generic closed planar regular curves $\gamma$, which gives an effective lower bound for the number of inflection points on a given generic closed planar curve. Using it, we…
In [LP] the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kahler surface X with p_g>0 are a sum of such local GW invariants. This paper describes how the local…
This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the equivalence, local and global, of transitive structures.…
This paper treats some basic points in general relativity and in its perturbative analysis. Firstly a systematic classification of global SO(n) invariants, which appear in the weak-field expansion of n-dimensional gravitational theories, is…
For an adjoint action of a Lie group G (or its subgroup) on Lie algebra Lie(G) we suggest a method for construction of invariants. The method is easy in implementation and may shed the light on algebraical independence of invariants. The…
We define a two-variable polynomial invariant of finite quandles. In many cases this invariant completely determines the algebraic structure of the quandle up to isomorphism. We use this polynomial to define a family of link invariants…
The spectral flow of the overlap operator is computed numerically along a particular path in gauge field space. The path connects two gauge equivalent configurations which differ by a gauge transformation in the non-trivial class of…
Based on the gauge invariant variables proposed in [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], general framework of the second order gauge invariant perturbation theory on arbitrary background spacetime is considered. We derived…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…