二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

具有可变时滞的非线性非自治差分方程的振动性及其应用

本文获得了一类具有可变时滞的非线性非自治差分方程的振动准则,建立了这类差分方程的几个线性化振动性定理,并得到了具有可变时滞的离散型非自治广义Logistic方程关于其正平衡点振动的一系列充分条件.     

一类具变号系数的二阶非线性变时滞微分方程的振动性

研究一类二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0的振动性,对振动因子p(t)可变符号的情况,通过两个引理,得出了方程振动的两个充分性定理.所得结论推广了二阶非线性变时滞微分方程当系数不变号时的振动性结论.     

一类二阶自共轭矩阵微分系统的区间振动定理

本文运用单调泛函和广义区间平均方法,获得了一类二阶自共轭矩阵微分系统[P(t)X'(t)]'+Q(t)X(t)=0的一些新的区间振动定理.     

一类二阶广义Emden-Fowler型微分方程的振动性

研究了具非线性中立项的一类二阶广义Emden-Fowler型泛函微分方程的振动性,考虑方程是非正则的情形(即∫_(t_0)~(+∞)a~(-1/β)(t)dt+∞的情形),利用广义黎卡提变换技术及不等式技巧,获得了方程振动的几个新型的判别准则.     

一类时标上的二阶变时滞动力系统的振动性

利用H(t,s)k(s)函数、广义Riccati变换和完全平方技巧获得了一类时标上的二阶非线性变时滞动力系统的新的振动准则.     

三阶非线性中立型方程的Philos型振动定理

研究三阶中立型分布时滞微分方程(r(t)[x(t)+p(t)x(r(t))]″)′+∫_a~b q(t,ξ)f(x[g(t,ξ)])dσ(ξ)=0的振动性.利用广义Riccati变换和积分平均技巧,建立了保证此方程一切解振动或者收敛到零的若干新的充分条件.     

带次线性中立项的二阶广义Emden-Fowler微分方程的Philos型振动准则

研究一类带次线性中立项的二阶非线性广义Emden-Fowler时滞微分方程的振动性.利用Riccati变换和不等式技巧,在非正则条件下建立了该类方程多个简便的Philos型和Kamenev型新振动准则.所得定理也适应于包括经典Euler方程等线性非中立型方程,推广和改进了已有文献中的相应结果.最后还给出应用实例展示了所...     

二阶非线性脉冲时滞微分方程的振动性

利用广义黎卡提变换得到了一类二阶非线性脉冲时滞微分方程所有解振动的充分条件,推广了Dz∨urina和Stavroulakis中关于非脉冲方程的相关结果.     

时标上的二阶变时滞动力方程的振动准则

利用广义Riccati技巧及完全平方技巧,讨论了一类时标上的二阶非线性变时滞动力方程的振动性,得到了一些新的振动准则.     

Generic Flatness and the Jacobson Conjecture

A result of Artin, Small, and Zhang is used to show that a Noetherian algebra over a commutative, Noetherian Jacobson ring will be Jacobson if the algebra possesses a locally finite, Noetherian associated graded ring. This result is extended to show that if an algebra over a commutative Noetherian ring has a locally finite, Noetherian associated graded ring, then the intersection of the powers of the Jacobson radical is nilpotent. The proofs rely on a weak generalization of generic flatness and some observations about G-rings.     

Primitive noetherian algebras with big centers

Recent work of Artin, Small, and Zhang extends Grothendieck's classical commutative algebra result on generic freeness to a large family of non-commutative algebras. Over such an algebra, any finitely-generated module becomes free after localization at a suitable central element. In this paper, a construction is given of primitive noetherian algebras, finitely generated over the integers or over algebraic closures of finite fields, such that the faithful, simple modules don't satisfy such a freeness condition. These algebras also fail to satisfy a non-commutative version of the Nullstellensatz.

     

A Depth Formula for Generic Singularities and Their Weak Normality

Let X be a smooth projective variety of dimension r and π:X → ?^m a generic projection with r + 1 ≤ m ≤ 2r. It is shown that, at any point on X′ = π(X) of multiplicity μ, off a closed subset of the triple locus of codimension four, the depth of the local ring is equal to r ? (μ ? 1)(m ? r ? 1). This leads to some improvements on the affirmation of a conjecture of Andreotti–Bombieri–Holm on the weak normality of X′ and a conjecture of Piene on the weak normality of Sing(X′).     

Forcing axioms via ground model interpretations

We study principles of the form: if a name σ is forced to have a certain property φ, then there is a ground model filter g such that ${\sigma }^g$ satisfies φ. We prove a general correspondence connecting these name principles to forcing axioms. Special cases of the main theorem are:

• •Any forcing axiom can be expressed as a name principle. For instance, $\mathsf{PFA}$ is equivalent to:

  • A principle for rank 1 names (equivalently, nice names) for subsets of ${\omega }_1$.

  • A principle for rank 2 names for sets of reals.
• •λ-bounded forcing axioms are equivalent to name principles. Bagaria's characterisation of $\mathsf{BFA}$ via generic absoluteness is a corollary.

We further systematically study name principles where φ is a notion of largeness for subsets of ${\omega }_1$ (such as being unbounded, stationary or in the club filter) and corresponding forcing axioms.     

Mapping resolutions of length three I

We produce some interesting families of resolutions of length three by describing certain open subsets of the spectrum of the generic ring for such resolutions constructed in [6].     

Universally meager sets and principles of generic continuity and selection in Banach spaces

In this paper we use large cardinals to address some problems about generic continuity and generic selection that occur in the study of fragmentability and differentiability in the context of Banach spaces.     

Coincidence of Two Classes of Universal Laurent Series

There exist functions, called U.L.S. (Universal Laurent Series), holomorphic on finitely connected domains Ω in C, whose Laurent-type partial sums approximate everything we can hope for, on compact subsets outside Ω ∪ {a ₁,…,a}, for certain prescribed points a ₁,…,a _k. In this paper we prove that, under additional assumptions, for every U.L.S. there exists a subsequence of its Laurent-type partial sums, which converges to the function itself in the whole of Ω and which approximates everything we can hope for outside Ω ∪ {a ₁,…,a, _k}.     

The Connectedness of Space Curve Invariants

In this paper we will give necessary conditions for a Borel-fixed monomial ideal to be the generic initial ideal of a reduced, irreducible, non-degenerate curve in P³.     

On a fragment of the universal Baire property for sets

There is a well-known global equivalence between sets having the universal Baire property, two-step generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of sets being -cc-universally Baire, which is below . In a model obtained, there is a set which is weakly -universally Baire but not -universally Baire.

     

Generic Picard–Vessiot Extensions for Nonconnected Groups

Let K be a differential field with algebraically closed field of constants 𝒞 and G a linear algebraic group over 𝒞. We provide a characterization of the K-irreducible G-torsors for nonconnected groups G in terms of the first Galois cohomology H¹(K, G) and use it to construct Picard–Vessiot extensions which correspond to nontrivial torsors for the infinite quaternion group, the infinite multiplicative and additive dihedral groups and the orthogonal groups. The extensions so constructed are generic for those groups.