相关论文: The ideal trefoil knot

In this note we will determine which contact structures on manifolds obtained by certain surgeries on the right handed trefoil are Stein fillable and which are not. This continues a long line of research and shows that there seems to be few…

There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to receive uniformly convergent series. There is also proposed…

The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…

We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincar\'e conjecture;…

We investigate the effects of Rashba and intrinsic spin-orbit couplings in graphynes. First, we develop a general method to address spin-orbit couplings within the tight-binding theory. Then, we apply this method to $\alpha$, $\beta$, and…

A new classification theorem for links by the authors and Roger Fenn leads to computable link invariants. As an illustration we distinguish the left and right trefoils and recover the result of Carter et al that the 2-twist-spun trefoil is…

Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the…

In this paper the new model of plastic deformation is constructed. For classification of plastic statuses the theory of knot is used.

We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides…

In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…

Surface tension and contact angle measurements are fundamental characterization techniques relevant to thermal and fluidic applications. Drop shape analysis techniques for the measurement of interfacial tension are powerful, versatile and…

Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…

It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended…

Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…

Recently, there have been several breakthroughs in the classification of tight contact structures. We give an outline on how to exploit methods developed by Ko Honda and John Etnyre to obtain classification results for specific examples of…

The aim of this paper is to study the skein exact sequence for knot Floer homology. We prove precise graded version of this sequence, and also one using $\HFm$. Moreover, a complete argument is also given purely within the realm of grid…

Approximately 1% of the known protein structures display knotted configurations in their native fold but their function is not understood. It has been speculated that the entanglement may inhibit mechanical protein unfolding or transport,…

Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay;…

Tensor-ring decomposition of tensors plays a key role in various applications of tensor network representation in physics as well as in other fields. In most heuristic algorithms for the tensor-ring decomposition, one encounters the problem…

We show that the knot quandle of the $3$-, $4$-, or $5$-twist-spun trefoil is isomorphic to a quandle related to the $16$-, $24$-, or $600$-cell respectively. We further show that the cardinality of the knot quandle of the $m$-twist-spun…