A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable...A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.展开更多
In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for t...In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.展开更多
In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface...In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.展开更多
Let G=(V,E)be a connected graph.For an integer h≥0,a subset F■V(G)(resp.F■E(G))of G,if any,is called an h-restricted vertex cut(resp.h-restricted edge cut)of G,if G-F is disconnected and every vertex in G-F has at ...Let G=(V,E)be a connected graph.For an integer h≥0,a subset F■V(G)(resp.F■E(G))of G,if any,is called an h-restricted vertex cut(resp.h-restricted edge cut)of G,if G-F is disconnected and every vertex in G-F has at least h neighbors.The cardinality of a minimum h-restricted vertex-cut(resp.h-restricted edge cut)of G is the h-restricted connectivity(resp.h-restricted edge connectivity)of G,and denoted by κ^(h)(G)(resp.λ^(h)(G)).The enhanced hypercube Q_(n,κ)(1≤k≤n)is a variant of the hypercube Q_(n).In this paper,we consider the h-restricted connectivity of Q_(n,κ) for 2≤k≤n-1.Our main results are as follows:(1)κ^(h)(Q_(n,κ))=2^(h)(n-h+1)for 4≤k≤n-1 and 0≤h≤n-3,λ^(h)(Q_(n,κ))=2^(h)(n-h+1)for 2≤k≤n-1 and 0≤h≤n-2.(2)κ^(h)(Q_(n,3))=2^(h-1)(n-h+1)for n≥5 and 4≤h≤n-1,κ^(h)(Q_(n,2))=2^(h-1)(n-h+1)for n≥4 and 3≤h≤n-1.(3)κ^(3)(Q_(n,3))=6n-16 for n≥5,κ^(2)(Q_(n,3))=4n-8 for n≥4 and κ^(2)(Q_(n,2))=3n-5 for n≥3,κ^(1)(Q_(n,3))=2n and κ^(3)(Q_(n,2))=2n-2 for n≥3.展开更多
基金supported by Fujian Provincial Natural Science Foundation of China(2024J02022)the NSFC(11571158)+1 种基金supported by the NSFC(12071199)supported by the Young and middle-aged project in Fujian Province(JAT190397)。
文摘A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.
基金Supported by Science and Technology Development Plan Project of Jilin Province China(Grant No.20260102245JC)Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.
文摘In Minkowski 3-space,we construct a surfaces family interpolating the involute of a spacelike curve as a common line of curvature,geodesic or asymptotic curve.Moreover,the conditions are examined for the ruled surface to be developable.And we support our conclusion with some examples.
文摘Let G=(V,E)be a connected graph.For an integer h≥0,a subset F■V(G)(resp.F■E(G))of G,if any,is called an h-restricted vertex cut(resp.h-restricted edge cut)of G,if G-F is disconnected and every vertex in G-F has at least h neighbors.The cardinality of a minimum h-restricted vertex-cut(resp.h-restricted edge cut)of G is the h-restricted connectivity(resp.h-restricted edge connectivity)of G,and denoted by κ^(h)(G)(resp.λ^(h)(G)).The enhanced hypercube Q_(n,κ)(1≤k≤n)is a variant of the hypercube Q_(n).In this paper,we consider the h-restricted connectivity of Q_(n,κ) for 2≤k≤n-1.Our main results are as follows:(1)κ^(h)(Q_(n,κ))=2^(h)(n-h+1)for 4≤k≤n-1 and 0≤h≤n-3,λ^(h)(Q_(n,κ))=2^(h)(n-h+1)for 2≤k≤n-1 and 0≤h≤n-2.(2)κ^(h)(Q_(n,3))=2^(h-1)(n-h+1)for n≥5 and 4≤h≤n-1,κ^(h)(Q_(n,2))=2^(h-1)(n-h+1)for n≥4 and 3≤h≤n-1.(3)κ^(3)(Q_(n,3))=6n-16 for n≥5,κ^(2)(Q_(n,3))=4n-8 for n≥4 and κ^(2)(Q_(n,2))=3n-5 for n≥3,κ^(1)(Q_(n,3))=2n and κ^(3)(Q_(n,2))=2n-2 for n≥3.
