并素元有限生成格的弱直积分解

本文建立了并素元有限生成格的弱直积分解,并给出一个解决并素元生成的完全Heyting代数的直积分解问题的新方法;作为弱直积分解的应用,证明了并素元有限生成的完全Heyting代数必然同构于有限个既约的完全Heyting代数的直积,证明了并素元有限生成格是Boole代数的充要条件是它同构于某有限集的幂集格.     

L-Fuzzy子群的L-Fuzzy直积的新刻画

研究L-fuzzy正规子群的性质,借助于L-fuzzy集A的水平截集A(a)和A[a],给出当L是完全分配格时L-fuzzy子群的L-fuzzy直积的若干等价刻画。     

Stability conditions on Kuznetsov components of Gushel–Mukai threefolds and Serre functor

We show that the stability conditions on the Kuznetsov component of a Gushel–Mukai threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre functor, up to the action of the universal cover of ${\text{GL}}_2^{+}(\mathbb{R})$. As application, we construct stability conditions on the Kuznetsov component of special Gushel–Mukai fourfolds.     

Affine Completeness and Lexicographic Product Decompositions of Abelian Lattice Ordered Groups

In this paper it is proved that an abelian lattice ordered group which can be expressed as a nontrivial lexicographic product is never affine complete. This work was supported by VEGA grant 2/1131/21.     

Decompositions of complete bipartite and tripartite graphs into selfcomplementary factors with finite diameters

We completely determine the spectrum of the complete bipartite and tripartite graphs that are decomposable into two isomorphic factors with a finite diameter.1991 Mathematics Subject Classification. 05C70     

Note on Direct Products of Certain Classes of Finite Groups

Direct products of solvable groups in which Sylow-permutability is a transitive relation are analyzed. Such groups are called 𝒫𝒮𝒯 groups, and it is well known that if the orders of two 𝒫𝒮𝒯 groups are relatively prime, then their direct product is again a 𝒫𝒮𝒯 group. Examples suggest that for solvable groups it is not necessary to have relatively prime orders to stay in the class. Some characterizations are provided, and also direct products of some other classes are discussed.     

半模的张量积

本文引入了半模的张量积的泛性定义，给出了半模范畴中的有向正向系的上极限以及任意一个半模同态的上核，讨论了半模张量积的若干性质，主要结果是：证明了张量函子保持半模的右正合性和上积，并且上积保持半模的平坦性，半模范畴中的张量函子保持上极限和上核．     

On constructing normal and non-normal Cayley graphs

Bamberg and Giudici (2011) showed that the point graphs of certain generalised quadrangles of order $(q?1,q+1)$, where $q=p^k$ is a prime power with $p\ge 5$, are both normal and non-normal Cayley graphs for two isomorphic groups. We call these graphs BG-graphs. In this paper, we show that the Cayley graphs obtained from a finite number of BG-graphs by Cartesian product, direct product, and strong product also possess the property of being normal and non-normal Cayley graphs for two isomorphic groups.     

Finitely Presented Wreath Products and Double Coset Decompositions

We characterize which permutational wreath products $G \ltimes W^{(X)}We characterize which permutational wreath products are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X ². On the one hand, this extends a result of G. Baumslag about infinite presentation of standard wreath products; on the other hand, this provides nontrivial examples of finitely presented groups. For instance, we obtain two quasi-isometric finitely presented groups, one of which is torsion-free and the other has an infinite torsion subgroup. Motivated by the characterization above, we discuss the following question: which finitely generated groups can have a finitely generated subgroup with finitely many double cosets? The discussion involves properties related to the structure of maximal subgroups, and to the profinite topology.      

Spline approximation,Kronecker products and multilinear forms

Sums of Kronecker products occur naturally in high‐dimensional spline approximation problems, which arise, for example, in the numerical treatment of chemical reactions. In full matrix form, the resulting non‐sparse linear problems usually exceed the memory capacity of workstations. We present methods for the manipulation and numerical handling of Kronecker products in factorized form. Moreover, we analyze the problem of approximating a given matrix by sums of Kronecker products by making use of the equivalence to the problem of decomposing multilinear forms into sums of one‐forms. Greedy algorithms based on the maximization of multilinear forms over a torus are used to obtain such (finite and infinite) decompositions that can be used to solve the approximation problem. Moreover, we present numerical considerations for these algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Quiver varieties and Lusztig's algebra

We study preprojective algebras of graphs and their relationship to module categories over representations of quantum SL(2). As an application, ADE quiver varieties of Nakajima are shown to be subvarieties of the variety of representations of a certain associative algebra introduced by Lusztig.     

The Kernel of the Adjoint Representation of a p-Adic Lie Group Need Not Have an Abelian Open Normal Subgroup

Let G be a p-adic Lie group with Lie algebra 𝔤 and Ad: G → Aut(𝔤) be the adjoint representation. It was claimed in the literature that the kernel K?ker(Ad) always has an abelian open normal subgroup. We show by means of a counterexample that this assertion is false. It can even happen that K = G, but G has no abelian subnormal subgroup except for the trivial group. The arguments are based on auxiliary results on subgroups of free products with central amalgamation.     

q-Weighted log-concavity and q-product theorem on the normality of posets

We show that q-weighted log-concavity and the strict normalized matching property are preserved under the q-direct product over weighted posets. As consequences, two classes of weighted posets including the finite linear lattices are strictly q-weighted log-concave and strictly normal.     

关于模糊拓扑环的直积

给出模糊拓扑环族直积的定义,研究它的性质,及任意模糊拓扑环族直积、与其模糊拓扑子环,与其模糊拓扑剩余环之间的同构问题.并对(QU)型模糊拓扑环关于上述问题进行研究.     

Small Cycle Double Covers of Products II: Categorical and Strong Products with Paths and Cycles

We continue the study of small cycle double covers of products of graphs that began in [7], concentrating here on the categorical product and the strong product. Under the assumption that G has an SCDC, we show that G × P _m has an SCDC for all m ≠ 3, and that G × C _m has an SCDC for all m ≥ 3. For the strong product we use results about the categorical product and the Cartesian product [7] to show that if G has an SCDC, then so does G ⊠ C _m , m ≥ 5. Some results are also given for G ⊠ P _m , but require additional assumptions about the SCDC of G. The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.     

Some Remarks on Normal Measures and Measurable Cardinals

We prove two theorems which in a certain sense show that the number of normal measures a measurable cardinal κ can carry is independent of a given fixed behavior of the continuum function on any set having measure 1 with respect to every normal measure over κ . First, starting with a model V ⊨ “ZFC + GCH + o(κ) = δ*” for δ* ≤ κ⁺ any finite or infinite cardinal, we force and construct an inner model N ⊆ V [G] so that N ⊨ “ZF + (∀δ < κ) [DC_δ] + ¬AC_κ + κ carries exactly δ* normal measures + 2^δ = δ⁺⁺ on a set having measure 1 with respect to every normal measure over κ”. There is nothing special about 2^δ = δ here, and other stated values for the continuum function will be possible as well. Then, starting with a modelV ⊨ “ZFC + GCH + κis supercompact”, we force and construct models of AC in which, roughly speaking, regardless of the specified behavior of the continuum function below κ on any set having measure 1 with respect to every normal measure over κ, κ can in essence carry any number of normal measures δ* ≥ κ⁺⁺.