相关论文: Model knot solutions for the twisted Bogomolny equ…

Twisted Alexander invariants have been defined for any knot and linear representation of its group. The invariants are generalized for any periodic representation of the commutator subgroup of the knot group. Properties of the new twisted…

We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…

We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology thus answering in the positive the 1987 conjecture by J.Przytycki concerning the existence of knots without matched diagrams.

Twisted knot theory, introduced by M.O.Bourgoin, is a generalization of virtual knot theory. It is easily shown that any virtual knot can be deformed into a trivial knot by a finite sequence of generalized Reidemeister moves and two…

The paper proves existence of renormalized stationary solutions for a dense class of discrete velocity Boltzmann equations in the plane with given ingoing boundary values. The proof is based on the construction of a sequence of…

We revisit Dimofte-Gaiotto-Gukov's construction of 3d gauge theories associated to 3-manifolds with a torus boundary. After clarifying their construction from a viewpoint of compactification of a 6d $\mathcal{N}=(2,0)$ theory of $A_1$-type…

We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…

A physically natural potential energy for simple closed curves in $\bold R^3$ is shown to be invariant under M\"obius transformations. This leads to the rapid resolution of several open problems: round circles are precisely the absolute…

We prove some new results regarding the boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may contain time-dependent…

We discuss a semi-implicit numerical scheme that allows for minimizing the bending energy of curves within certain isotopy classes. To this end we consider a weighted sum of the bending energy and the tangent-point functional. Based on…

A transverse knot is a knot that is transverse to the planes of the standard contact structure on real 3-space. In this paper we prove the Markov Theorem for transverse braids, which states that two transverse closed braids that are…

In this paper we analyze symmetries, hidden symmetries, and commensurability classes of $(\epsilon, d_L)$-twisted knot complements, which are the complements of knots that have a sufficiently large number of twists in each of their twist…

We present a new paradigm for three dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension three is the existence of singularities. We show how to use knot…

This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers with no or little background in this area, and…

For a prime knot $K$, we give sufficient conditions for the existence of a component $\mathcal{C}$ of the irreducible ${\rm SL}(2,\mathbb{C})$-character variety of $K$ with $\dim\mathcal{C}>1$, and give a lower bound for $\dim\mathcal{C}$.…

We present a large family of {\it{exact}} solitary wave solutions of the one dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain/loss, in both expulsive and regular parabolic confinement regimes. The…

We investigate the existence of positive solutions for a class of Minkowski-curvature equations with indefinite weight and nonlinear term having superlinear growth at zero and super-exponential growth at infinity. As an example, for the…

In this work we present some classes of models whose the corresponding two coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. In these cases the so-called trial orbit method is…

Let $\ix$ be a smooth Deligne-Mumford stack over the complex numbers. One can define twisted orbifold Gromov-Witten invariants of $\ix$ by considering multiplicative invertible characteristic classes of various bundles on the moduli spaces…

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to…