Cyclic normal subgroups of generalized Baumslag–Solitar groups

The centers and cyclic radicals of generalized Baumslag–Solitar groups (GBS-groups) are studied. Criteria for their non-triviality are found and an algorithm to compute the center and cyclic radical is given. In addition, for each unimodular GBS-group, a GBS-cover, i.e., a GBS-group in whose underlying graph the weights around each vertex are constant in absolute value, is constructed. These groups are then characterized by a minimality property.     

A new class of generalized f-projected dynamical system in Banach spaces

In this article, a new class of generalized f-projected dynamical systems is introduced and studied in Banach spaces. A global existence and uniqueness result of generalized f-projected dynamical system is proved, which generalizes the existence result of Xia and Vincent [Y.S. Xia and T.L. Vincent, On the stability of global projected dynamical systems, J. Optim. Theory Appl. 106 (2009), pp. 129–150]. The global convergence stability of the generalized f-projected dynamical system and the sensitivity result of solutions set with perturbations of the constraint sets are also obtained under some suitable conditions.     

A generalization of generalized Fibonacci and generalized Pell numbers

This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which are recently developed are deduced as special cases. Moreover, some other interesting identities involving the celebrated Fibonacci, Lucas, Pell and Pell–Lucas numbers are also deduced.     

A note on invariant generators for generalized subbundles

This note studies invariant generators for a certain class of invariant smooth generalized subbundles of exact Courant algebroids, which generalizes existing results for invariant vector subbundles of exact Courant algebroids. As a result, we provide a simple and geometric proof for Theorem 1 in [1].     

On quotients of generalized Euclidean group rings

Let R = ?[C] be the integral group ring of a finite cyclic group C. Dennis et al. [4 Dennis, K., Magurn, B., Vaserstein, L. (1984). Generalized Euclidean group rings. J. Reine Angew. Math. 351:113–128.[Web of Science ®] , [Google Scholar]] proved that R is a generalized Euclidean ring in the sense of Cohn [3 Cohn, P. M. (1966). On the structure of the GL₂ of a ring. Inst. Hautes Études Sci. Publ. Math. 30:5–53.[Crossref] , [Google Scholar]], i.e., SL_n(R) is generated by the elementary matrices for all n. We prove that every proper quotient of R is also a generalized Euclidean ring.     

Group invertible block matrices

Let M=(ABCD) (A and D are square) be a 2 × 2 block matrix over a skew field, where A is group invertible. Let S=D-CA^#B denote the generalized Schur complement of M. We give the representations and the group invertibility of M under each of the following conditions:(1)S=0; (2) S is group invertible and CA^πB=0, where A^π=I-AA^#. And the second result generalizes a result of C. Bu et al. [Appl. Math. Comput., 2009, 215: 132–139]     

Characterization of generalized Chernikov groups among groups with involutions

The class of generalized Chernikov groups is characterized, i.e., the class of periodic locally solvable groups with the primary ascending chain condition. The name of the class is related to the fact that the structure of such groups is close to that of Chernikov groups. Namely, a Chernikov group is defined as a finite extension of a direct product of finitely many quasi-cyclic groups, and a generalized Chernikov group is a layer-finite extension of a direct productA of quasi-cyclicp-groups with finitely many factors for each primep such that each of its elements does not commute elementwise with only finitely many Sylow subgroups ofA. A theorem that characterizes the generalized Chernikov groups in the class of groups with involution is proved. Translated fromMatematicheskie Zametki, Vol. 62, No 4, pp. 577–587, October, 1997. Translated by A. I. Shtern     

Generalized quadraticity of linear combination of two generalized quadratic matrices

It is investigated the necessary and sufficient conditions for the generalized quadraticity of a linear combination of any two generalized quadratic matrices. The main result obtained is, in a sense, a generalization of the main results given in [Uç M, Özdemir H, Özban AY. On the quadraticity of linear combinations of quadratic matrices. Linear Multilinear Algebra. 2015;63:1125–1137.] which contains many of the results in the literature related to idempotency or involutivity of the linear combinations of idempotent and/or involutive matrices, to the generalized quadratic matrices.     

The fundamental group of period domains over finite fields

We determine the fundamental group of period domains over finite fields. This answers a question of M. Rapoport raised in [M. Rapoport, Period domains over finite and local fields, in: Proc. Sympos. Pure Math., vol. 62, part 1, 1997, pp. 361-381].     

Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity

We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of the Colombeau simplified model. This generalizes the notion of G^∞-regularity introduced by M. Oberguggenberger. A key point is that these regularities can be characterized, for compactly supported generalized functions, by a property of their Fourier transform. This opens the door to microanalysis of singularities of generalized functions, with respect to these regularities. We present a complete study of this topic, including properties of the Fourier transform (exchange and regularity theorems) and relationship with classical theory, via suitable results of embeddings.     

Covers of generalized quadrangles, 2. Kantor-Knuth covers and embedded ovoids

In this paper, which is a sequel to [12], we proceed with our study of covers and decomposition laws for geometries related to generalized quadrangles. In particular, we obtain a higher decomposition law for all Kantor-Knuth generalized quadrangles which generalizes one of the main results in [12]. In a second part of the paper, we study the set of all Kantor-Knuth ovoids (with given parameter) in a fixed finite parabolic quadrangle, and relate this set to embeddings of parabolic quadrangles into Kantor-Knuth quadrangles. This point of view gives rise to an answer of a question posed in [11].     

Multiplicity formulas for finite dimensional and generalized principal series representations

The article presents two results. (1) Let a be a reductive Lie algebra over ℂ and let b be a reductive subalgebra of a. The first result gives the formula for multiplicity with which a finite dimensional irreducible representation of b appears in a given finite dimensional irreducible representation of a in a general situation. This generalizes a known theorem due to Kostant in a special case. (2) LetG be a connected real semisimple Lie group andK a maximal compact subgroup ofG. The second result is a formula for multiplicity with which an irreducible representation ofK occurs in a generalized representation ofG arising not necessarily from fundamental Cartan subgroup ofG. This generalizes a result due to Enright and Wallach in a fundamental case.     

THE MULTI-PARAMETERS OVERRELAXATION METHOD

1.IntroductionRecently,manymathematicalliteratureshaveprovidedsomenewiterativemeth-odsforsolvingthelinearsystem.Kuang[2]presentedatwo-parameteriterativemethodcalledTORmethod,whichiseffectivetogivethenumericalsolutionofpartialdif-ferentialequations.Wang[,']extendedtheTORmethodtotheGTORmethedandimprovessomeresultsof[3,11,12].In[5],LialsodiscussedtheGTORmethod,andextendedthecorrespondingresultsof[10,11].Recently3SongandDai[9]presentedthemulti-parametersoverrelaxation(MPOR)method,whosespe…     

Entries of the group inverse of the Laplacian matrix for generalized Johnson graphs

In this paper, we use graph theoretic properties of generalized Johnson graphs to compute the entries of the group inverse of Laplacian matrices for generalized Johnson graphs. We then use these entries to compute the Zenger function for the group inverse of Laplacian matrices of generalized Johnson graphs.     

关于K_（1，r）－free图的连通因子

本文证明了每个连通的Ｋ１，ｒ－ｆｒｅｅ图Ｇ，如果有［ｆ，ｇ］－因子Ｆ，则它就有包含Ｆ的［ｆ，ｇ＋ｒ－１］连通因子．     

Smallest graphs with given generalized quaternion automorphism group

For , a smallest graph whose automorphism group is isomorphic to the generalized quaternion group is constructed. If , then such a graph has vertices and edges. In the special case when , a smallest graph has 16 vertices but 44 edges.     

Generalized quadrangles admitting a sharply transitive Heisenberg group

All known finite generalized quadrangles that admit an automorphism group acting sharply transitively on their point set arise by Payne derivation from thick elation generalized quadrangles of order s with a regular point. In these examples only two groups occur: elementary abelian groups of even order and odd order Heisenberg groups of dimension 3. In [2] the authors determined all generalized quadrangles admitting an abelian group with a sharply transitive point action. Here, we classify thick finite generalized quadrangles admitting an odd order Heisenberg group of dimension 3 acting sharply transitively on the points. In fact our more general result comes close to a complete solution of classifying odd order Singer p-groups.      

A fundamental representation of quantum generalized Kac-Moody algebras with one imaginary simple root

We consider the Borcherds-Cartan matrix obtained from a symmetrizable generalized Cartan matrix by adding one imaginary simple root. We extend the result of Gebert and Teschner [Lett. Math. Phys., 1994, 31: 327-334] to the quantum case. Moreover, we give a connection between the irreducible dominant representations of quantum Kac-Moody algebras and those of quantum generalized Kac-Moody algebras. As the result, a large class of irreducible dominant representations of quantum generalized Kac-Moody algebras were obtained from representations of quantum Kac-Moody algebras through tensor algebras.     

Transient solutions of Markov processes and generalized continued fractions

In 1974 J. A. Murphy and M. R. O'Donohoe numerically approximatedthe minimal solution of the Kolmogorov forward equation forthe generalized birth and death process by use of continuedfractions. This paper generalizes this approach by suggestingan algorithm for q-matrices of lower band structure (n, 1).This is achieved by analogy with generalized continued fractions.Applications involving q-matrices of this type include, forexample, many types of queueing systems with batch processingor birth–death–catastrophe population processesin biology.     

可行策略对应的图像拓扑下广义博弈Nash平衡的稳定性

以往关于广义博弈Nash平衡的稳定性的研究,均利用可行策略映射之间的一致度量.现考虑在更弱的度量下,利用可行策略映射图像之间的Hausdorff距离定义度量.在此弱图像拓扑下,证明了广义博弈空间的完备性,以及Nash平衡映射的上半连续性和紧性,进而得到广义博弈Nash平衡的通有稳定性.即在Baire分类的意义下,大多数的广义博弈都是本质的.