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Publisher: Springer-Verlag (Total: 2354 journals)

 Archiv der Mathematik   [SJR: 0.597]   [H-I: 29]   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1420-8938 - ISSN (Online) 0003-889X    Published by Springer-Verlag  [2354 journals]
• On graded characterizations of finite dimensionality for algebraic
algebras
• Authors: Edward S. Letzter
Pages: 499 - 503
Abstract: We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring $${{\text {gr}}}{R}$$ is right noetherian, if and only if $${{\text {gr}}}{R}$$ has right Krull dimension, if and only if $${{\text {gr}}}{R}$$ satisfies a polynomial identity.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1090-8
Issue No: Vol. 109, No. 6 (2017)

• High-rank ternary forms of even degree
• Authors: Alessandro De Paris
Pages: 505 - 510
Abstract: We exhibit, for each positive even degree, a ternary form of rank strictly greater than the maximum rank of monomials. Together with an earlier result in the odd case, this gives a lower bound of \begin{aligned} \left\lfloor \frac{d^2+2d+5}{4}\right\rfloor \;, \end{aligned} for $$d\ge 2$$ , on the maximum rank of degree d ternary forms with coefficients in an algebraically closed field of characteristic zero.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1105-5
Issue No: Vol. 109, No. 6 (2017)

• Unirationality of the Hurwitz space $$\varvec{\mathcal {H}_{9,8}}$$ H 9 ,
8
• Authors: Hamid Damadi; Frank-Olaf Schreyer
Pages: 511 - 519
Abstract: In this paper we prove that the Hurwitz space $$\mathcal {H}_{9,8}$$ , which parameterizes 8-sheeted covers of $${\mathbb P }^1$$ by curves of genus 9, is unirational. Our construction leads to an explicit Macaulay2 code, which will randomly produce a nodal curve of degree 8 of geometric genus 9 with 12 double points and together with a pencil of degree 8.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1095-3
Issue No: Vol. 109, No. 6 (2017)

• Irreducibility of the Hilbert scheme of smooth curves in $$\mathbb {P}^4$$
P 4 of degree $$g+2$$ g + 2 and genus g
• Authors: Changho Keem; Yun-Hwan Kim
Pages: 521 - 527
Abstract: We denote by $$\mathcal {H}_{d,g,r}$$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in $$\mathbb {P}^r$$ . In this note, we show that any non-empty $$\mathcal {H}_{g+2,g,4}$$ is irreducible, generically smooth, and has the expected dimension $$4g+11$$ without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006), in which several low genus $$g\le 10$$ cases have been left untreated.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1083-7
Issue No: Vol. 109, No. 6 (2017)

• Closure and connected component of a planar global semianalytic set
defined by analytic functions definable in o-minimal structure
• Authors: Masato Fujita
Pages: 529 - 538
Abstract: We consider a global semianalytic set defined by real analytic functions definable in an o-minimal structure. When the o-minimal structure is polynomially bounded, we show that the closure of this set is a global semianalytic set defined by definable real analytic functions. We also demonstrate that a connected component of a planar global semianalytic set defined by real analytic functions definable in a substructure of the restricted analytic field is a global semianalytic set defined by definable real analytic functions.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1107-3
Issue No: Vol. 109, No. 6 (2017)

• On functional equations for meromorphic functions and applications
• Authors: Ha Huy Khoai; Vu Hoai An; Pham Ngoc Hoa
Pages: 539 - 549
Abstract: In this paper we investigate some functional equations of the form $$P(f)=Q(g),$$ where P, Q are Yi’s polynomials, and f, g are meromorphic functions. Then we apply the obtained results to study the uniqueness problem for meromorphic functions sharing two subsets, and to give an analogue of Ritt’s decomposition theorem for a class of polynomials of Fermat-Waring type in meromorphic functions.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1093-5
Issue No: Vol. 109, No. 6 (2017)

• The G-invariant spectrum and non-orbifold singularities
• Authors: Ian M. Adelstein; M. R. Sandoval
Pages: 563 - 573
Abstract: We consider the G-invariant spectrum of the Laplacian on an orbit space M/G where M is a compact Riemannian manifold and G acts by isometries. We generalize the Sunada–Pesce–Sutton technique to the G-invariant setting to produce pairs of isospectral non-isometric orbit spaces. One of these spaces is isometric to an orbifold with constant sectional curvature whereas the other admits non-orbifold singularities and therefore has unbounded sectional curvature. We conclude that constant sectional curvature and the presence of non-orbifold singularities are inaudible to the G-invariant spectrum.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1089-1
Issue No: Vol. 109, No. 6 (2017)

• Constant angle surfaces in the Lorentzian Heisenberg group
• Authors: Irene I. Onnis; Paola Piu
Pages: 575 - 589
Abstract: In this paper, we define and, then, we characterize constant angle spacelike and timelike surfaces in the three-dimensional Heisenberg group, equipped with a 1-parameter family of Lorentzian metrics. In particular, we give an explicit local parametrization of these surfaces and we produce some examples.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1104-6
Issue No: Vol. 109, No. 6 (2017)

• Universal inequalities on complete noncompact smooth metric measure spaces
• Authors: Yanli Li; Feng Du
Pages: 591 - 598
Abstract: In this paper, we obtain universal inequalities for the eigenvalues of the Dirichlet problem and clamped plate problem of drifting Laplacian on ( $$n+1$$ )-dimensional ( $$n\ge 4$$ ) complete noncompact simply connected smooth metric measure spaces which meet some conditions of the sectional curvature and radial weighted Ricci curvature.
PubDate: 2017-12-01
DOI: 10.1007/s00013-017-1099-z
Issue No: Vol. 109, No. 6 (2017)

• Metric ultraproducts of classical groups
• Authors: John S. Wilson
Pages: 407 - 412
Abstract: Simple non-discrete metric ultraproducts of classical groups are geodesic spaces with respect to a natural metric.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1087-3
Issue No: Vol. 109, No. 5 (2017)

• Endpoint estimates of positive operators in a filtered measure space
• Authors: Yahui Zuo; Lian Wu; Yong Jiao
Pages: 477 - 488
Abstract: In a filtered measure space, a necessary and sufficient Sawyer type condition is given under which a positive operator is bounded from $$L^1(d\mu )$$ to $$L^{q,\infty }(d\mu )$$ with $$1<q <\infty$$ . This result can be recognized as the endpoint case of Tanaka and Terasawa (Arch Math (Basel) 101:559–568, 2013, Theorem 1.1). We also establish a similar weak type inequality for generalized Doob’s maximal operators.
PubDate: 2017-11-01
DOI: 10.1007/s00013-017-1079-3
Issue No: Vol. 109, No. 5 (2017)

• Noether’s problem for cyclic groups of prime order
• Authors: Ming-chang Kang
Abstract: Let k be a field and $$k(x_0,\ldots ,x_{p-1})$$ be the rational function field of p variables over k where p is a prime number. Suppose that $$G=\langle \sigma \rangle \simeq C_p$$ acts on $$k(x_0,\ldots ,x_{p-1})$$ by k-automorphisms defined as $$\sigma :x_0\mapsto x_1\mapsto \cdots \mapsto x_{p-1}\mapsto x_0$$ . Denote by P the set of all prime numbers and define $$P_0=\{p\in P:\mathbb {Q}(\zeta _{p-1})$$ is of class number one $$\}$$ where $$\zeta _n$$ a primitive n-th root of unity in $$\mathbb {C}$$ for a positive integer n; $$P_0$$ is a finite set by Masley and Montgomery (J Reine Angew Math 286/287:248–256, 1976). Theorem. Let k be an algebraic number field and $$P_k=\{p\in P: p$$ is ramified in $$k\}$$ . Then $$k(x_0,\ldots ,x_{p-1})^G$$ is not stably rational over k for all $$p\in P\backslash (P_0\cup P_k)$$ .
PubDate: 2017-11-21
DOI: 10.1007/s00013-017-1123-3

• On generalized Toeplitz and little Hankel operators on Bergman spaces
• Authors: Jari Taskinen; Jani Virtanen
Abstract: We find a concrete integral formula for the class of generalized Toeplitz operators $$T_a$$ in Bergman spaces $$A^p$$ , $$1<p<\infty$$ , studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an $$L^2$$ -symbol a such that $$T_{ a }$$ fails to be bounded in $$A^2$$ , although $$T_a : A^2 \rightarrow A^2$$ is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense.
PubDate: 2017-11-21
DOI: 10.1007/s00013-017-1124-2

• On the horizontal diameter of the unit sphere
• Authors: Yi Shi; Zhiqi Xie
Abstract: For a singular Riemannian foliation $$\mathcal {F}$$ on a Riemannian manifold M, a curve is called horizontal if it meets the leaves of $$\mathcal {F}$$ perpendicularly. For a singular Riemannian foliation $$\mathcal {F}$$ on a unit sphere $$\mathbb {S}^{n}$$ , we show that if $$\mathcal {F}$$ satisfies some properties, then the horizontal diameter of $$\mathbb {S}^{n}$$ is $$\pi$$ , i.e., any two points in $$\mathbb {S}^{n}$$ can be connected by a horizontal curve of length $$\le \pi$$ .
PubDate: 2017-11-21
DOI: 10.1007/s00013-017-1118-0

• Standard Jordan partitions with three parameters
• Authors: Michael J. J. Barry
Abstract: We extend previous work on standard two-parameter Jordan partitions by Barry (Commun Algebra 43:4231–4246, 2015) to three parameters. Let $$J_r$$ denote an $$r \times r$$ matrix with minimal polynomial $$(t-1)^r$$ over a field F of characteristic p. For positive integers $$n_1$$ , $$n_2$$ , and $$n_3$$ satisfying $$n_1 \le n_2 \le n_3$$ , the Jordan canonical form of the $$n_1 n_2 n_3 \times n_1 n_2 n_3$$ matrix $$J_{n_1} \otimes J_{n_2} \otimes J_{n_3}$$ has the form $$J_{\lambda _1} \oplus J_{\lambda _2} \oplus \cdots \oplus J_{\lambda _m}$$ where $$\lambda _1 \ge \lambda _2 \ge \cdots \ge \lambda _m>0$$ and $$\sum _{i=1}^m \lambda _i=n_1 n_2 n_3$$ . The partition $$\lambda (n_1,n_2,n_3:p)=(\lambda _1, \lambda _2,\ldots , \lambda _m)$$ of $$n_1 n_2 n_3$$ , which depends on $$n_1$$ , $$n_2$$ , $$n_3$$ , and p, will be called a Jordan partition. We will define what we mean by a standard Jordan partition and give necessary and sufficient conditions for its existence.
PubDate: 2017-11-20
DOI: 10.1007/s00013-017-1125-1

• Modules over cluster-tilted algebras that do not lie on local slices
• Authors: Ibrahim Assem; Ralf Schiffler; Khrystyna Serhiyenko
Abstract: We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.
PubDate: 2017-11-18
DOI: 10.1007/s00013-017-1121-5

• On certain generalized isometries of the special orthogonal group
• Authors: Marcell Gaál
Abstract: In this paper we explore the structure of certain generalized isometries of the special orthogonal group SO(n) which are transformations that leave any member of a large class of generalized distance measures invariant.
PubDate: 2017-11-18
DOI: 10.1007/s00013-017-1122-4

• Localisation uniforme des espaces de Besov et de Lizorkin–Triebel
• Authors: Salah Eddine Allaoui; Gérard Bourdaud
Abstract: Résumé On établit des caractérisations intrinsèques des versions localisées-uniformes des espaces de Besov $${B_{{p},{q}}^{s}({\mathbb R}^n)}$$ , avec $$p,q\in [1,+\infty ]$$ , et de Lizorkin–Triebel $${F_{{p},{q}}^{s}({\mathbb R}^n)}$$ avec $$q\in [1,+\infty ]$$ et $$p\in [1,+\infty [$$ , quel que soit le nombre réel $$s>0$$ .
PubDate: 2017-10-03
DOI: 10.1007/s00013-017-1096-2

• Reduction of the Small Cohen–Macaulay Conjecture to excellent unique
factorization domains
• Authors: Ehsan Tavanfar
Abstract: In this article, applying the quasi-Gorenstein analogous of the Ulrich’s deformation of certain Gorenstein rings to unique factorization domains, we show that the Small Cohen–Macaulay Conjecture reduces to excellent unique factorization domains.
PubDate: 2017-09-22
DOI: 10.1007/s00013-017-1103-7

• Strict comparison theorems under sublinear expectations
• Authors: Xinpeng Li; Yiqing Lin
Abstract: In this paper, we consider strict comparison theorems in the framework of G-expectation, which is a type of sublinear expectation associated with fully nonlinear parabolic partial differential equations. In particular, we first apply Krylov–Safonov estimates to establish the strict comparison theorem for functions from the Lipschitz class $$Lip(\Omega )$$ . Then we prove generalized strict comparison theorems on the enlarged space $$L_G^1(\Omega )$$ , which is the Banach completion of $$Lip(\Omega )$$ under the G-expectation.
PubDate: 2017-09-22
DOI: 10.1007/s00013-017-1098-0

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