关于G-Matlis自反模的换环定理

设Ｒ和Ｔ是Ｎｏｅｔｈｅｒ完备半局部环，Ｒ→Ｔ是环同态．本文证明了，若Ｔ是有限生成或ＡｒｔｉｎＲ－模，Ｍ为Ｇ－Ｍａｔｌｉｓ自反Ｒ－模，则对所有ｎ≥０，Ｅｘｔ^Ｒ_ｎ（Ｔ，Ｍ），Ｅｘｔ^Ｒ_ｎ（Ｍ，Ｔ），Ｔｏｒ^Ｒ_ｎ（Ｔ，Ｍ）以及Ｔｏｒ^Ｒ_ｎ（Ｍ，Ｔ）均是Ｇ－Ｍａｔｌｉｓ自反Ｔ－模．所得结果推广了Ｒ．Ｂｅｌｓｈｏｆ的结果．     

超空间2x的局部覆盖性质

本文讨论了超空间２^x的某些局部覆盖性质，并给出下面二个结果：定理１设Ｘ是Ｔ₂空间，则２^x紧当且仅当２^x是局部ｍｅｔａ－Ｌｉｎｄｅｌｏｆ空间．定理２₁设Ｘ是Ｔ¹空间，则２^xｍ－紧当且仅当２^x是局部ｍ－紧。     

范畴 RMRl上的一个函子及范畴A Grn0

本文定义了一个由范畴 _RM_R^l到范畴Ａ G_rn⁰ 的函子Ｇ，并证明了函子Ｇ保持分量正合及全正合，关于范畴ＡＧG_rn⁰ 证明了定理：     

关于CVD 矩阵的n- 宽度

本文证明了d_2k =δ_2k =d^2k ≥b_2k，其中d_2k ,δ_2k , b_2k分别表示Ａ（Ｂｌ^M_p）在ｌ^N_q下的Ｋｏｌｍｏｇｏｒｏｖ，线性，Ｂｅｒｎｓｔｅｉｎ ２ｋ－宽度，ｄ^2k 表示Ａ^Ｔ（Ｂｌ^N相似文献   

Gorenstein AC亏范畴*

作者定义了Gorenstein AC导出范畴 D^b_gac(R)并且和导出范畴作了一些比较.作者定义了Gorenstein AC奇点范畴 D^b_gacsg(R),在这个范畴中具有有限Gorenstein AC- 投射维数的模都是零对象.同时, 作者给出了由Gorenstein AC- 投射模构成的稳定范畴到奇点范畴的三角嵌入 F : GAC → D^b_sg(R) .通过作函子 F 的商引入Gorenstein AC亏范畴 D^b_gacd(R),并且给出三角等价 D^b_gacd(R) = D^b_gacsg(R)     

一类超临界椭圆方程正解的存在性

本文讨论了球上半线性椭圆Ｄｉｒｉｃｈｌｅｔ问题Δｕ＋λｕ^ｑ＋ｕ^p＝０正解的存在性,其中,λ∈Ｒ,０〈ｑ〈１,ｐ〉ｐ_ｃ≡(Ｎ＋２)/(Ｎ－２)（Ｎ〉２）．在条件Ｎ≤６或Ｎ〉６,ｐ〈ｐ_Ｎ≡（Ｎ＋１－(２Ｎ－３)^1/2）／（Ｎ－３－(２Ｎ－３)^1/2）下,证明了存在唯一的λ₀,λ₀〉０,当λ＝λ₀时,有唯一的径向奇异解及无穷多个正解。     

三角域上分片二次函数Bernstein多项式的退化性

设Ｓ_２（Ｔ）为三角域Ｔ的二阶剖分，本文给出在Ｓ_２（Ｔ）下分片二次函数f(P)∈Ｃ¹（Ｔ）的Ｂｅｒｎｓｔｃｉｎ多项式的退化性及递推公式。这里的条件Ｓ_２（Ｔ）及Ｃ¹（Ｔ）类都是重要的。我们举例说明更一般情况下分片二次函数Ｂｅｒｎｓｔｃｉｎ多项式的复杂性。     

关于ut= div(|▽u|p-2▽u)方程解的梯度H?lder连续性的一个注记

对文献［１－３］中的结果：u_t= div(|▽u|^p-2▽u)在ΩＴ＝Ω×（０，Ｔ）上弱解的空间梯度是Ｈ?ｌｄｅｒ连续的做一个补充．在这个注记里，讨论了条件ｐ＞ｍａｘ｛１，２Ｎ/Ｎ＋２｝是怎样由ｕ的性质所决定的．属于L^N_loc(Ω_T)空间解的梯度是Ｈ?ｌｄｅｒ连续的条件仅仅是ｐ＞１．     

交换群上Hopf路余代数的结构分类

设G是群, kG是域k上的群代数. 对任意Hopf箭向Q=(G, r), 利用右kZ_u(C) -模的直积范畴∏_C∈K(G) MkZ_u(C)与kG-Hopf双模范畴^kG_kG M^kG_kG之间的同构, 可由^u(C)(kQ₁)¹上的右kZ_u(C) -模结构导出在箭向余模kQ₁上的kG-Hopf双模结构. 该文讨论在群G分别是2阶循环群与克莱茵四元群时的Hopf路余代数kQ^c的同构分类及其子Hopf代数kG[kQ₁]结构.     

基于xL（a）n－1（x）之零点的（0，1，…，m－2，m）插值

本文给出了基于xL^（a）_n－1（x）之零点的（０，１，…，ｍ－２，ｍ）插值的正则性的充要条件，其中xL^（a）_n－1（x）为（ｎ－１）次Ｌａｇｕｅｒｒｅ多项式。同时基函数（若存在的话）的明显表达式也在文中给出。再者，还证明了，若该插值问题有无穷多个解，则其解的一般形式为ｆ₀（ｘ）＋Ｃｆ₁（ｘ）这里Ｃ为任意常数。     

PreT 2 Objects in Topological Categories

In previous papers, two notions of pre-Hausdorff (PreT ₂) objects in a topological category were introduced and compared. The main objective of this paper is to show that the full subcategory of PreT ₂ objects is a topological category and all of T ₀, T ₁, and T ₂ objects in this topological category are equivalent. Furthermore, the characterizations of pre-Hausdorff objects in the categories of filter convergence spaces, (constant) local filter convergence spaces, and (constant) stack convergence spaces are given and as a consequence, it is shown that these categories are homotopically trivial.     

Morita Equivalence of Sketches

Equivalence of sketches S and T means the equivalence of their categories Mod_S and Mod_T of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category Mod_T. For general sketches, we show that an analogous result holds provided that Mod_T is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is (Mod_T), the free product completion of Mod_T.     

Monomorphism Operator and Perpendicular Operator

For a quiver Q, a k-algebra A, and an additive full subcategory 𝒳 of A-mod, the monomorphism category Mon(Q, 𝒳) is introduced. The main result says that if T is an A-module such that there is an exact sequence 0 → T _m  → … → T ₀ → D(A _A ) → 0 with each T _i  ∈ add(T), then Mon(Q, ^⊥ T) =^⊥(kQ ? _k T); and if T is cotilting, then kQ ? _k T is a unique cotilting Λ-module, up to multiplicities of indecomposable direct summands, such that Mon(Q, ^⊥ T) =^⊥(kQ ? _k T).

As applications, the category of the Gorenstein-projective (kQ ? _k A)-modules is characterized as Mon(Q, 𝒢𝒫(A)) if A is Gorenstein; the contravariantly finiteness of Mon(Q, 𝒳) can be described; and a sufficient and necessary condition for Mon(Q, A) being of finite type is given.     

A Rank Theorem of Operators between Banach Spaces

Suppose that E and F are two Banach spaces and that B(E, F) is the space of all bounded linear operators from E to F. Let T ₀∈B(E, F) with a generalized inverse T ₀ ⁺∈B(F, E). This paper shows that, for every T∈B(E, F) with ‖T ₀ ⁺ (T−T ₀)‖<1, B ≡ (I + T ₀ ⁺(T−T ₀))⁻¹ T ₀ ⁺ is a generalized inverse of T if and only if (I−T ₀ ⁺ T ₀)N(T) = N(T ₀), where N(·) stands for the null space of the operator inside the parenthesis. This result improves a useful theorem of Nashed and Cheng and further shows that a lemma given by Nashed and Cheng is valid in the case where T ₀ is a semi-Fredholm operator but not in general.     

Almost stable spectra and limits of similarities

Suppose that {D _n } is a sequence of invertible operators on a Hilbert space, andD _n T D _n ^–1 converges in norm toT ₀. Recently, H. Bercovici, C. Foias, and A. Tannenbaum have shown that if {D _n ^±1 n=1, 2,...} is contained in a finite dimensional subspace of operators, thenT andT ₀ must have the same spectral radius. Using this result, R. Teodorescu proved that the resolvents ofT andT ₀ have the same unbounded component. We show that in fact the spectra differ only by certain eigenvalues ofT ₀, and the spectrum ofT ₀ is obtained by filling in holes in the spectrum ofT; i.e., by adjoining (all, some, or none of the) bounded components of the resolvent ofT to the spectrum ofT.     

On Homeomorphisms of Effective Topological Spaces

We study effective presentations and homeomorphisms of effective topological spaces. By constructing a functor from the category of computable models into the category of effective topological spaces, we show in particular that there exist homeomorphic effective topological spaces admitting no hyperarithmetical homeomorphism between them and there exist effective topological spaces whose autohomeomorphism group has the cardinality of the continuum but whose only hyperarithmetical autohomeomorphism is trivial. It is also shown that if the group of autohomeomorphisms of a hyperarithmetical topological space has cardinality less than 2 then this group is hyperarithmetical. We introduce the notion of strong computable homeomorphism and solve the problem of the number of effective presentations of T ₀-spaces with effective bases of clopen sets with respect to strong homeomorphisms.     

An Elementary Approach to Exponentiable Maps

Originally, exponentiable maps in the category Top of topological spaces were described by Niefield in terms of certain fibrewise Scott-open sets. This generalizes the first characterization of exponentiable spaces by Day and Kelly, which was improved thereafter by Hofmann and Lawson who described them as core-compact spaces.Besides various categorical methods, the Sierpinski-space is an essential tool in Niefield's original proof. Therefore, this approach fails to apply to quotient reflective subcategories of Top like Haus, the category of Hausdorff spaces. A recent generalization of the Hofmann–Lawson improvement to exponentiable maps enables now to reprove the characterization in a completely different and very elementary way. This approach works for any nontrivial quotient reflective subcategory of Top or Top/ _T , the category of all spaces over a fixed base space T, as well as for exponentiable monomorphisms with respect to epi-reflective subcategories.An important special case is the category Sep_Top/ _T of separated maps, i.e. distinct points in the same fibre can be separated in the total space by disjoint open neighbourhoods. The exponentiable objects in Sep turn out to be the open and fibrewise locally compact maps. The same holds for Haus/ _T , T a Hausdorff space. In this case, a similar characterization was obtained by Cagliari and Mantovani.     

Quasicoherent sheaves on complex noncommutative two-tori

We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus T as an ind-object in the category of holomorphic vector bundles on T. Extending the results of [10] and [9] we prove that the derived category of quasicoherent sheaves on T is equivalent to the derived category of usual quasicoherent sheaves on the corresponding elliptic curve. We define the rank of a quasicoherent sheaf on T that can take arbitrary nonnegative real values. We study the category Qcoh(η _T ) obtained by taking the quotient of the category of quasicoherent sheaves by the subcategory of objects of rank zero (called torsion sheaves). We show that projective objects of finite rank in Qcoh(η _T ) are classified up to an isomorphism by their rank. We also prove that the subcategory of objects of finite rank in Qcoh(η _T ) is equivalent to the category of finitely presented modules over a semihereditary algebra.     

A conglomerate of exponential supercategories of the category of finitely generated topological spaces

Summary For every ordinaln > 1 we define a categoryT _n of topological spaces in ech's sense which is isomorphic to a category ofn-ary monorelational systems. We show that every categoryT _n is an exponential supercategory of the categoryB of finitely generated topological spaces, which means that well-behaved function spacesG ^H can be defined inT _n wheneverG B.     

On the MacNeille Completion of the Category of Partially Ordered Topological Spaces

Preordered topological spaces for which the order has a closed graph form a topological category. Within this category we identify the MacNeille completions (coinciding with the universal initial completions) of five monotopological subcategories, namely those of the T₀(T₁, T₂) preordered spaces and the (completely regular) partially ordered spaces. We also show that a functor due to L. NACHBIN from the quasi-uniform spaces to the preordered spaces preserves initial sources.