Sentence examples for genus 1 from inspiring English sources

C looks like a hollow sphere with g hollow handles attached and finitely many points pinched together a sphere has genus 0, a torus has genus 1, and so forth.

Furthermore, the proposed approach can easily treat a multiply connected domain of genus 1 as shown in Fig. 1.

In 1965, Willmore proposed the problem of minimizing the Willmore energy among surfaces of genus (1).

We present an algorithm to mesh point clouds sampled from a closed manifold surface of genus 1.

More generally, we show that any minimal surface of genus (1) which is Alexandrov immersed must be rotationally symmetric.

Suppose that (F: Sigma rightarrow S^3) is a minimal immersion of a genus (1) surface into (S^3).

For quite some time, studies in Burkholderia encompassed only species of clinical interest; however, the recent identification of nitrogen-fixing species has provided an ecological and biotechnological context for the genus [ 1, 5, 6, 20, 22, 30].

The taxonomy of Bauhinia is especially complicated, and it has been recognized either as a large genus [ 1- 3, 5, 7- 9], or as 8-9 distinct genera [ 4, 6, 10].

(Choe and Soret [14]) There exists a family of embedded minimal surfaces (Sigma _{m,l}) in (S^3) of genus (1+4m m-1 l).

Recently, acylphloroglucinols and their derivatives, including adducts of a phloroglucinol moiety coupled with its derivative or a terpenoid unit, have been extensively obtained from this genus [1, 2, 3, 4, 5, 6, 7, 8].

The minimal surfaces described in Theorem 1.1 come in 1-parameter families, they have finite genus ≥1, they meet orthogonally the boundary of the ball only along the middle boundary curve.