非光滑边界条件下具时滞的Rotenberg方程主算子的谱分析

该文考虑细胞分裂的时滞性,引入了具时滞的Rotenberg迁移方程,在L₁空间中非光滑边界条件下(边界算子无界),证明迁移算子生成C₀-半群,并进一步分析迁移算子的谱,得到该迁移算子的谱在区域Γ=σ(A_H)∩{λ∈C|Reλ>γ}(γ>max{λ₀,-σ₀})中仅由有限个具有有限代数重数的离散本征值组成等结果(λ₀,-σ₀的具体意义见正文).     

次临界Choquard方程的多解

该文考虑次临界Choquard方程■(0.1)多解的存在性,其中N> 3,λ是正实参数,p_ε=2_μ^*-ε,ε> 0,0 <μμ^*=(2N-μ)/(N-2)是Hardy-Littlewood-Sobolev不等式意义下的临界指数.假定Ω:=int V^-1(0)是R^N中非空带光滑边界的有界区域,利用Lusternik-Schnirelman定理,该文证明了当λ足够大及ε充分小时,方程(0.1)至少有cat_Ω(Ω)个正解.     

含参数拟线性薛定谔方程的特征值问题

本文考虑如下拟线性薛定谔方程:-Δu+(κu)/2△u²=λ|u|^p-2u,x∈Ω,这里u∈H(Ω),20,N≥3且Ω是有界区域.结合变分方法和摄动讨论,作者证明了存在常数κ₀> 0,使得对任何的κ∈(0,κ₀),这类特征值问题有解(λ,u).特别地,如果限制|u|_p^p=α,作者发现对任何的κ> 0,存在α₀> 0,使得在α <α₀时,该特征值问题的解总是存在的.此外,作者采用不同于Morse迭代的方法构造出了常数κ₀和α₀的精确表达式.     

基于自组织理论的技术创新系统演化机理及模型分析

创新是人类财富之源,是经济发展的巨大动力。本文从复杂系统理论角度说明了技术创新系统的自组织特性;分析了创新过程的不稳定性、分岔、突变和随机"涨落"等演化特征和作用机理;随后结合进化经济学理论,构建了技术创新系统自组织竞争与协同演化过程的定量模型,并对模型的稳定性和演化趋势进行分析,应用统计和数学工具软件对模型的参数变化进行函数模拟,对模拟结果进行了讨论;随后以我国通信产业发展为例进行了相关案例分析。此研究旨在通过自然科学与社会科学的有效结合,对技术创新系统的演化机理及过程提供一种新的研究思路。     

Diophantine Inequality by Unlike Powers of Primes*

Suppose that λ₁, · · ·, λ₅ are nonzero real numbers, not all of the same sign,satisfying that λ₁/λ₂is irrational. Then for any given real number η and ε > 0, the inequality |λ₁p₁+ λ₂p₂~2+ λ₃p₃~3+ λ₄p₄~4+ λ₅p₅~5+ η| <(■)^-19/756+ε has infinitely many solutions in prime variables p₁, · · ·, p₅. This result co...     

Brake Orbits of a Reversible Even Hamiltonian System Near an Equilibrium

In this paper,we consider the brake orbits of a reversible even Hamiltonian system near an equilibrium.Let the Hamiltonian system(H S)x=J H(x)satisfies H(0)=0,H(0)=0,reversible and even conditions H(Nx)=H(x)and H(-x)=H(x)for all x∈R²ⁿ.Suppose the quadratic form Q(x)=1/2 is non-degenerate.Fixτ₀>0 and assume that R²ⁿ=E⊕F decomposes into linear subspaces E and F which are invariant under the flow associated to the linear system x=J H'(0)x and such that each solution of the above linear system in E isτ₀-periodic whereas no solution in F{0}isτ₀-periodic.Writeσ(τ₀)=σ_Q(τ₀)for the signature of Q|E.Ifσ(τ₀)≠=0,we prove that either there exists a sequence of brake orbits x_k→0 withτk-periodic on the hypersurface H^-1(0)whereτ_k→τ₀;or for eachλclose to 0 withλ_σ(τ₀)>0 the hypersurface H-1(λ)contains at least 1/2|σ(τ₀)|distinct brake orbits of the Hamiltonian system(HS)near 0 with periods nearτ₀.Such result for periodic solutions was proved by Bartsch in 1997.     

一类非线性动力系统混沌运动的研究

讨论了含二次和三次非线性项的受迫振动系统 -λ₁T+λ₂T2+λ₃T3=ε(gcosωt-ε'T)的混沌运动,利用Melnikov函数法给出了发生混沌的临界条件,结合相平面轨迹、时程曲线和Poincaré映射判定系统是否发生混沌.     

具有次线性和超线性项的非线性椭圆型方程组最小正解的存在性

证明了对每一λ∈(0,Λ),当Λ>0时半线性椭圆型方程组。有最小正解(λ_u,λ_v)。其中ΩRN(N≥2)为具有光滑边界的有界区域,0<q<1u,λ_v关于λ是严格递增的。     

双挠积复Finsler流形的局部对偶平坦性

设(M₁,F₁)和(M₂,F₂)是两个强凸的复Finsler流形,λ₁和λ₂是乘积流形M=M₁×M₂上的光滑实值函数,双挠积复Finsler流形(M₁×(λ₁,λ₂) M2,F)是在乘积流形上赋予了复Finsler度量F²=λ₁²F₁²+λ₂²F₂²的复Finsler流形.本文给出了双挠积复Finsler流形是局部对偶平坦流形的充要条件.     

Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem

In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^N is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev growth term with respect to φ.Under appropriate conditions on φ,ψ and φ,we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation,for λ∈(0,λ₀),where λ₀> 0 is a fixed constant.     

Degrevlex Gröbner bases of generic complete intersections

In this paper, we study the Hilbert–Samuel function of a generic standard graded K-algebra

K[X₁,…,X_n]/(g₁,…,g_m)

when refined by an (ℓ)-adic filtration, ℓ being a linear form. From this we obtain a structure theorem which describes the stairs of a generic complete intersection for the degree-reverse-lexicographic order. We show what this means for generic standard (or Gröbner) bases for this order; in particular, we consider an “orderly filling up” conjecture, and we propose a strategy for the standard basis algorithm which could be useful in generic-like cases.     

Forbidden minors to graphs with small feedback sets

Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the graph minor theorem. In this paper we characterize several families of graphs with small feedback sets, namely k₁-F V S , k₂-F E S and (k₁,k₂)-F V /E S , for small integer parameters k₁ and k₂. Our constructive methods can compute obstruction sets for any minor-closed family of graphs, provided the pathwidth (or treewidth) of the largest obstruction is known.     

Inverse geophysical problems for some noncompactly supported inhomogeneities

Let[²+k²n(x₁,x₃)]u(x₁,x₂,x₃)=−δ(x₁,y₁δ(x₂,y₂)δ(x₃,y₃) in R³₊. Assume that u(x₁,x₂,x₃=0,y₁,y₂=0,y₃=0,k) is measured at the plane P {x:x₃=0} for all positions of the source on the line y = (y₁,y₂ = 0,y₃ = 0), -∞ < y₁ < ∞, and receiver on the plane(x₁,x₂,x₃ − <x₁,x₂ < ∞, and for low-frequencies 0 < k <k₀, k₀ > 0 is an arbitrary small wave number. Assume thatn(x₁,x₃) is an arbitrary bounded piecewise-continuous function. The basic result is: the above low-frequency surface data determinen(x₁,x₃)uniquely.     

Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R₀, is derived. If R₀  1, the disease-free equilibrium is globally stable and the disease always dies out. If R₀ > 1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique endemic equilibrium when ₁ = ₂ = 0 and the disease persists at an endemic equilibrium state if it initially exists.     

Partition of a directed bipartite graph into two directed cycles

Let D = (V₁, V₂; A) be a directed bipartite graph with |V₁| = |V₂| = n 2. Suppose that d_D(x) + d_D(y) 3n + 1 for all x ε V₁ and y ε V₂. Then D contains two vertex-disjoint directed cycles of lengths 2n₁ and 2n₂, respectively, for any positive integer partition n = n₁ + n₂. Moreover, the condition is sharp for even n and nearly sharp for odd n.     

More limit theory for the sample correlation function of moving averages

Let X_t = Σ^∞_j=-∞ c_jZ_{t - j} be a moving average process where {Z_t} is iid with common distribution in the domain of attraction of a stable law with index , 0 < < 2. If 0 < < 2, E|Z₁| < ∞ and the distribution of |Z₁|and |Z₁Z₂| are tail equivalent then the sample correlation function of {X₁} suitably normalized converges in distribution to the ratio of two dependent stable random variables with indices and /2. This is in sharp contrast to the case E|Z₁| ^{= ∞} where the limit distribution is that of the ratio of two independent stable variables. Proofs rely heavily on point process techniques. We also consider the case when the sample correlations are asymptotically normal and extend slightly the classical result.     

Irreducible Wakimoto-like Modules for the Lie Superalgebra <Emphasis Type="Italic">D</Emphasis>(2, 1;α)

By using the idea of Wakimoto's free field, we construct a class of representations for the Lie superalgebra D(2, 1; α) on the tensor product of a polynomial algebra and an exterior algebra involving one parameter λ. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact, the representation is irreducible if and only if the parameter λ satisfies (λ + m)(λ-(1+α/α)≠m)=0 for any m ∈ Z₊.     

On the degree of regularity of some equations

In this paper we investigate the behaviour of the solutions of equations Σ_I=1ⁿ a_ix_i = b, where Σ_i=1ⁿ, a_i = 0 and b ≠ 0, with respect to colorings of the set N of positive integers. It turns out that for any b ≠ 0 there exists an 8-coloring of N, admitting no monochromatic solution of x₃ − x₂ = x₂ − x₁ + b. For this equation, for b odd and 2-colorings, only an odd-even coloring prevents a monochromatic solution. For b even and 2-colorings, always monochromatic solutions can be found, and bounds for the corresponding Rado numbers are given. If one imposes the ordering x₁ < x₂ < x₃, then there exists already a 4-coloring of N, which prevents a monochromatic solution of x₃ − x₂ = x₂ − x₁ + b, where b ε N.     

带有临界增长的分数阶Kirchhoff方程的半经典解

本文研究如下带有临界增长的分数阶Kirchhoff方程ε^2s(ε^2s-3∫∫R³×R³|u(x)-u(y)/|²|x-y|^3+2s),x∈R³,其中M是一个连续正的Kirchhoff函数,λ>0是一个参数,3/40充分小和λ足够大时,我们首先证明了上述问题正基态解的存在性.其次,证明了基态解集中在一个由位势函数所刻画的特定集合中.最后,研究了基态解的衰减估计.