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
In this paper,we give the double inequalities of a special quasi-arithmetic mean E(a,b)and the Seifert-like elliptic integral mean V(a,b)under the combination of generalized Heronian mean Hw(a,b),harmonic mean H(a,b)a...In this paper,we give the double inequalities of a special quasi-arithmetic mean E(a,b)and the Seifert-like elliptic integral mean V(a,b)under the combination of generalized Heronian mean Hw(a,b),harmonic mean H(a,b)and arithmetic mean A(a,b).As applications,we obtain two new optimal bounds for the second kind of complete elliptic integral".Finally,numerical experiments are performed to compare these with some known bounds of",and the improved effect is verified.展开更多
In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operato...In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.展开更多
Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic...Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.展开更多
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.
文摘In this paper,we give the double inequalities of a special quasi-arithmetic mean E(a,b)and the Seifert-like elliptic integral mean V(a,b)under the combination of generalized Heronian mean Hw(a,b),harmonic mean H(a,b)and arithmetic mean A(a,b).As applications,we obtain two new optimal bounds for the second kind of complete elliptic integral".Finally,numerical experiments are performed to compare these with some known bounds of",and the improved effect is verified.
基金Supported by National Natural Science Foundation of China(12161078)Foundation for Innovative Fundamental Research Group Project of Gansu Province(24JRRA778)Project of Northwest Normal University(20240010)。
文摘In this paper,we studyλ-biharmonic hypersurfaces M_(r)^(5) of 6-dimensional pseudo Riemannian space form N_(p)^(6)(c)with the indexs 0≤p≤6,r=p−1 or p,and constant curvature c.It was proved that if the shape operator of M_(r)^(5) is diagonalizable,then the mean curvature is a constant.As an application,we find some types of biharmonic hypersurfaces of N_(p)^(6)(c)are minimal.
文摘Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.
