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.     

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.     

本刊英文版Vol.34(2018),No.1论文摘要（英文）

正Non-hyperbolic Closed Characteristics on Non-degenerate Star-shaped Hypersurfaces in R~(2n)Hua Gui DUAN Hui LIU Yi Ming LONG Wei WANGAbstract In this paper,we prove that for every index perfect non-degenerate compact starshaped hypersurface∑(?)R~(2n),there exist at least n non-hyperbolic closed characteristics with even Maslov-type indices on E when n is even.When n is odd,there exist at least n closed     

强symmetric环

为了统一交换环和约化环的层表示,Lambek引进了Symmetric环.继续symmetric环的研究,定义引入了强symmetric环的概念,研究它的一些扩张性质.证明环R是强symmetric环当且仅当R[x]是强symmetric环当且仅当R[x;x~(-1)]是强symmetric环.也证明对于右Ore环R的经典右商环Q,R是强symmetric环当且仅当Q是强symmetric环.     

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.     

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.     

Non-naturally reductive Einstein metrics on Sp(n)

We prove that Sp(2k+l)admits at least two non-naturally reductive Einstein metrics which are Ad(Sp(k)×Sp(k)×Sp(l))-invariant ifk<1.It implies that every compact simple Lie group Sp(n)for n≥4 admits at least 2[(n-1)/3]non-naturally reductive left-invariant Einstein metrics.     

MULTIPLE POSITIVE SOLUTIONS OF A SINGULAR (n-1,1) CONJUGATE BOUNDARY VALUE PROBLEM WITH DELAY

§ 1　IntroductionThe study of boundary value problems(abbr.as BVP) for ordinary differential equa-tions has a long history and there are many papers and wonderful results about it(for ex-ample,refer to [1～ 5] and the references therein) .Recently,[3 ] discussed the existenceproblem of at least one positive solution for some(n-1 ,1 ) conjugate boundary value prob-lem as follows:u(n) (t) a(t) f(u) =0 ,(0 相似文献   

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-Poincaré inequality for general symmetric forms

Lp Poincare inequalities for general symmetric forms are established by new Cheeger＇s isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger＇s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.     

Three symmetric positive solutions for second-order nonlocal boundary value problems

Using the Leggett-Williams fixed point theorem,we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u(t)+g(t)f(t,u(t))=0,0相似文献   

ON MULTIPLE POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM IN R^N

61. IntroductionConsider the semilinear elliptic problemwhere p E (1, ac) for N 2 3, and p E (l, co) for N = 1, 2, 0 S a(x) E C(R"), A > 0 is areal parameter.The existence and uniqueness of solution for such problems have been considered by mailyauthors recently (see [l--4] and references therein). In I3], T. Bartsch and Wang, Z. Q. provedthat with more genaral nolilineaxities (1.1) has at least one solution for A large under someconditions on a(x), one of which is that a--1 (0) has non…     

等距节点上(0,3)插值五次样条

§1.引言 设f(x)是定义在[0,1]上的连续函数,n是自然数。记h=1/n, f_v~((r))=f~((r))(vh),v=0,1,…,n;r=0,1,…,5, f_(v 1/2)~((r))=f~((r))((v 1/2)h),v=0,1,…,n-1;r=0,1,…,5, ω_r(j)=max |f~((r))(x_1)-f~((r))(x_2)|,r=0,1,…,6. |x_1-x_2|≤h 0≤x_1,x_2≤1又设s(x)是[0,1]上满足(i)s(x)∈C~3[0,1],(ii)在[vh,(v 1)h]上s(x)∈∏_5,v=0,1,…,n-1的五次样条.它们的全体记为?_(n5)~((3)) .     

Oscillation of second-order quasilinear neutral delay difference equations

By using the Riccati transformation and mathematical analytic methods,some sufficient conditions are obtained for oscillation of the second-order quasilinear neutral delay difference equations Δ[r n |Δz n | α-1 Δ z n ] + q n f (x n-σ)=0,where z n=x n + p n x n τ and ∞ Σ n=0 1 /r n 1/α < ∞.     

Distortion theorem for Bloch mappings on the unit ball <Emphasis Type="Italic">ℬ</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1 - ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.     

Exact Solution to an Extremal Problem on Graphic Sequences with a Realization Containing Every 2-Tree on k Vertices

A simple graph G is a 2-tree if G=K_3,or G has a vertex v of degree 2,whose neighbors are adjacent,and G-v is a 2-tree.Clearly,if G is a 2-tree on n vertices,then |E(G)|=2 n-3.A non-increasing sequence π=(d_1,...,d_n) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices.[Acta Math.Sin.Engl.Ser.,25,795-802(2009)] proved that if k≥2,n≥9/2 k~2+19/2 k and π=(d_1,...,d_n) is a graphic sequence with∑_(i=1)~n di(k-2)n,then π has a realization containing every 1-tree(the usual tree) on k vertices.Moreover,the lower bound(k-2)_n is the best possible.This is a variation of a conjecture due to Erdos and Sos.In this paper,we investigate an analogue problem for 2-trees and prove that if k≥3 is an integer with k≡i(mod 3),n≥ 20[k/3] ~2+31[k/3]+12 and π=(d_1,...,d_n) is a graphic sequence with ∑_(i=1)~n d_imax{k-1)(n-1), 2 [2 k/3] n-2 n-[2 k/3] ~2+[2 k/3]+1-(-1)~i}, then π has a realization containing every 2-tree on k vertices.Moreover,the lower bound max{(k-1)(n-1), 2[2 k/3]n-2 n-[2 k/3] ~2+[2 k/3]+1-(-1)~i}is the best possible.This result implies a conjecture due to [Discrete Math.Theor.Comput.Sci.,17(3),315-326(2016)].     

RIGIDITY THEOREMS OF CLIFFORD TORUS

In this article, we prove that the Clifford torus S1(1-r2~(1/2)) × Sn-1(r) is the only closed hypersurface in the unit sphere Sn+1(1) with infinite fundamental group, which satisfy r2 ≥ (n-1)/n, RicM ≤ C-(H), and S ≤ S+(H). Moreover, we give a characterization of Clifford torus S1(1-r2~(1/2)) × Sn-1(r) with r2 = 2(n-1)+nH2±|H| n2H2+4(n-1)(1/2)/2n(1+H2) .     

A QP-FREE AND SUPERLINEARLY CONVERGENT ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

1 IntroductionConsider tl1e optimizatioll problemndn{f(x): gj(x) 5 0, j e I, x E R"}, j1)where f(x), gj(x): R" - R, j E I = {l,2,...,m}.We know tl1e quasi-Newton meth.d[1]'[9]1[5]1[1O1 is one of the most effective methods to solveproblenl (1) due to its property of superlinear convergence and is still all hot topic at presenttime, which attracts a Iot of authors to make iInprovemellt both in theory a1ld app1ication.Fechinei and Lucidi[3] in 1995 proposed a locally superlinearly convergell…     

EXISTENCE AND NONEXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS TO RIEMANN PROBLEM FOR DAMPED P-SYSTEM

In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M) when p≥3/2, where , there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1相似文献   

Stability of Periodic Orbits and Return Trajectories of Continuous Multi-valued Maps on Intervals

Let I be a compact interval of real axis R, and(I, H) be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f : I → I be a continuous multi-valued map. Assume that Pn =(x_0, x_1,..., xn) is a return tra jectory of f and that p ∈ [min Pn, max Pn] with p ∈ f(p). In this paper, we show that if there exist k(≥ 1) centripetal point pairs of f(relative to p)in {(x_i; x_i+1) : 0 ≤ i ≤ n-1} and n = sk + r(0 ≤ r ≤ k-1), then f has an R-periodic orbit, where R = s + 1 if s is even, and R = s if s is odd and r = 0, and R = s + 2 if s is odd and r 0. Besides,we also study stability of periodic orbits of continuous multi-valued maps from I to I.     

具有对称自同态的环及其扩张

Let R be a ring with an endomorphism α and an α-derivation δ. We introduce the notions of symmetric α-rings and weak symmetric α-rings which are generalizations of symmetric rings and weak symmetric rings, respectively, discuss the relations between symmetricα-rings and related rings and investigate their extensions. We prove that if R is a reduced ring and α(1) = 1, then R is a symmetric α-ring if and only if R[x]/(x n) is a symmetric ˉα-ring for any positive integer n. Moreover, it is proven that if R is a right Ore ring, α an automorphism of R and Q(R) the classical right quotient ring of R, then R is a symmetric α-ring if and only if Q(R) is a symmetric ˉα-ring. Among others we also show that if a ring R is weakly 2-primal and(α, δ)-compatible, then R is a weak symmetric α-ring if and only if the Ore extension R[x; α, δ] of R is a weak symmetric ˉα-ring.