Non-hyperbolic Closed Characteristics on Non-degenerate Star-shaped Hypersurfaces in R~(2n)

In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface ∑ R~(2 n), there exist at least n non-hyperbolic closed characteristics with even Maslovtype indices on E when n is even. When n is odd, there exist at least n closed characteristics with odd Maslov-type indices on ∑ and at least(n-1) of them are non-hyperbolic. Here we call a compact star-shaped hypersurface ∑ R~(2 n) index perfect if it carries only finitely many geometrically distinct prime closed characteristics, and every prime closed characteristic(τ,y) on ∑ possesses positive mean index and whose Maslov-type index i(y,m) of its m-th iterate satisfies i(y,m)≠-1 when n is even,and i(y,m){-2,-1,0} when n is odd for all m∈N.     

On the number of P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in R~(2n)

In this paper, let n 2 be an integer, P = diag(-In-κ, Iκ,-In-κ, Iκ) for some integer κ∈ [0, n),and Σ∈ R2 nbe a partially symmetric compact convex hypersurface, i.e., x ∈Σ implies P x ∈Σ. We prove that if Σ is(r, R)-pinched withRr2~(1/2), then there exist at least n- κ geometrically distinct P-symmetric closed characteristics on Σ, as a consequence, Σ carry at least n geometrically distinct P-invariant closed characteristics.     

本刊英文版Vol.38(2022),No.1论文摘要（英文）北大核心CSCD

The Non-contractibility of Closed Geodesics on Finsler RP;Hua Gui DUAN Hui LIU Abstract Let（RP;,F） be a bumpy and irreversible Finsler n-dimensional real projective space with reversibility λ and flag curvature K satisfying(λ/（1+λ）);相似文献   

The Non-contractibility of Closed Geodesics on Finsler RPn

Let(RPⁿ,F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)²n,F),then all of them are non-contractible,which coincides with the Katok’s examples.     

FIVE LIMIT CYCLES TO A CLASS OF SYSTEMS IN R~3

In this paper, a bridge between near-homogeneous and homogeneous vector fields in R 3 is found. By the relationship between homogeneous vector fields and the induced tangent vector fields of two-dimensional manifold S 2 , we prove the existence of at least 5 isolated closed orbits for a class of n + 1 (n ≥ 2) systems in R 3 , which are located on the five invariant closed cones of the system.     

Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in ℝ<Superscript>2<Emphasis Type="Italic">n</Emphasis></Superscript> under a pinching condition

In this paper, let Σ R2n be a symmetric compact convex hypersurface which is ( r, R )- pinched with R/r (5/3)1/2 . Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least E [ n-1/2 ] + E [ n-1/3 ] non-hyperbolic symmetric closed characteristics.     

强正则自补图的一个注记

Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k 1, where 4k 1=x2 y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k 1 orders.     

Entropy,Periodicity, and Graphs with Zero Euler Characteristic

Let G be a graph which contains exactly one simple closed curve. We prove that a continuous map f : G → G has zero topological entropy if and only if there exist at most k ≤ |(Edg(G) End(G) 3)/2] different odd numbers n1,...,nk such that Per(f) is contained in ∪i=1^k ∪j=0^∞ ni2^j, where Edg(G) is the number of edges of G and End(G) is the number of end points of G.     

BOUNDS OF EIGENVALUES OF A GRAPH

Let G be a simple graph with n vertices.We denote by λ_i(G) the i-th largest eigenvalue of G.In this paper,several results are presented concerning bounds on the eigenvalues of G.In particular,it is shown that -1≤λ_2(G)≤(n-2)/2,and the left hand equality holds if and only if G is a complete graph with at least two vertices;the right hand equality holds if and only if n is even and G?2K_(n/2).     

On Z3-Actions on Spin 4-Manifolds

Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to 2 k(-E_8)⊕lH, where H is the hyperbolic form. In this paper, the authors prove that if there exists a locally linear pseudofree Z_3-action on X,then Sign(g, X) ≡-k mod 3. They also investigate the smoothability of locally linear Z_3-action satisfying above congruence. In particular, it is proved that there exist some nonsmoothable locally linear Z_3-actions on certain elliptic surfaces.     

Characterizations of Best L_p(1≤p≤+ ∞) Approximation With Restricted Ranges of Derivatives

Let [a,b] be a compact set containing at least n + 1 points. If Φ_n = span(φ_1, φ_2,…, φ_n) is an n-dimensional subspace of L,[a, b] m φ_1~(s), φ_2~(s)…, φ_n~(s)exist (s≥0is an integer) and have a maximal linearly independent subset which is an extendedChebyshev system of order rs on [a,b], then write     

GENERALIZED TORUS IN R WITH PRESCRIBED MEAN CURVATURE

Let H be a given function satisfying two conditions on some region N in R~3.It,isproved that there exists a closed surface in N which is homeomorphic to a torus such thatits mean curvature is equal to H.     

EXISTENCE OF SOLUTIONS TO 2m-ORDER PERIODIC BOUNDARY VALUE PROBLEM

In this paper, we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem. By the infinite dimensional Morse theory, under some conditions on nonlinear term, we obtain that there exist at least two nontrivial solutions.     

Multivariate probabilistic approximation in wavelet structure

Letotherwiseand F(x,y).be a continuous distribution function on R~2.Then there exist linear wavelet operators L_n(F,x,y)which are also distribution functionand where the defining them mother wavelet is(x,y).These approximate F(x,y)in thesupnorm.The degree of this approximation is estimated by establishing a Jackson typeinequality.Furthermore we give generalizations for the case of a mother wavelet ≠,whichis just any distribution function on R~2,also we extend these results in R~r,r>2.     

PATHS AND CYCLES EMBEDDING ON FAULTY ENHANCED HYPERCUBE NETWORKS

Let Qn,k(n≥3,1≤k≤n-1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges,fv and fe be the numbers of faulty vertices and faulty edges,respectively.In this paper,we give three main results.First,a fault-free path P [u,v] of length at least 2n-2fv-1(respectively,2n-2fv-2) can be embedded on Qn,k with fv+fe≤n-1 when d Qn,k(u,v) is odd(respectively,d Qn,k(u,v) is even).Secondly,an Qn,k is(n-2) edgefault-free hyper Hamiltonian-laceable when n(≥3) and k have the same parity.Lastly,a fault-free cycle of length at least 2n-2fv can be embedded on Qn,k with fe≤n-1 and fv+fe≤2n-4.     

Topology of Certain Closed Submanifolds in Euclidean Space

Recently P.F,Leung has investigated the topological characters of certaincompact oriented submanifolds minimally immersed in the unit sphere S~(n+p).It iswell known that a immersed submanifold in S~(n+p) can be always regarded as a sub-manifold in n+p+1-dimensional Euclidean space R~(n+p+1) and there is no minimalclosed submanifold in R~(n+p+1).Thus,it is a natural and important problem tostudy the topological properties of general closed submanifolds in R~N. Through     

本刊英文版Vol.30(2014),No.11论文摘要(英文)北大核心CSCD

On Equivalence of Simple Closed Curves in Flat Surfaces Zong Liang SUN Abstract By explicit constructions,we give direct proofs of the following results:for any distinct homotopy classes of simple closed curvesαandβin a closed surface of genus g>1,there exist a hyperbolic structure X and a holomorphic quadratic differential q on X such     

Vertex-transitive Diameter Two Graphs

We investigate the family of vertex-transitive graphs with diameter 2. Let Γ be such a graph.Suppose that its automorphism group is transitive on the set of ordered non-adjacent vertex pairs. Then either Γ is distance-transitive or Γ has girth at most 4. Moreover, if Γ has valency 2, then Γ≌ C₄ or C₅; and for any integer n ≥ 3, there exist such graphs Γ of valency n such that its automorphism group is not transitive on the set of arcs. Also, we determine this family of grap...     

On k-ordered Graphs Involved Degree Sum

Abstract A graph G is k-ordered Hamiltonian,2≤k≤n,if for every ordered sequence S of k distinctvertlces of G,there exists a Hamiltonian cycle that encounters S in the given order. In this article, we provethat if G is a graph on n vertices with degree sum of nonadjacent vertices at least n+3k-9/2,then G is k-orderedHamiltonian for k=3,4,…,[n/19].We also show that the degree sum bound can be reduced to n+2[k/2]-2 ifk(G)≥3k-1/2 or δ(G)≥5k-4.Several known results are generalized.     

On higher analogues of Courant algebroids

In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle TM ⊕∧nT*M for an m-dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an (n + 1)-vector field π is closed under the higher-order Dorfman bracket iff π is a Nambu-Poisson structure. Consequently, there is an induced Leibniz algebroid structure on ∧nT*M. The graph of an (n+1)-form ω is closed under...