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Publisher: Springer-Verlag   (Total: 2329 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  [2329 journals]
• Analytic isolation of newforms of given level
• Authors: Paul D. Nelson
Pages: 555 - 568
Abstract: We describe a method for understanding averages over newforms on $$\Gamma _0(q)$$ in terms of averages over all forms of some level. The method is simplest when q is divisible by the cubes of its prime divisors.
PubDate: 2017-06-01
DOI: 10.1007/s00013-017-1039-y
Issue No: Vol. 108, No. 6 (2017)

• On Cohen–Macaulay modules over the plane curve singularity of type
$$\varvec{T_{44}}$$ T 44
• Authors: Yuriy A. Drozd; Oleksii Tovpyha
Pages: 569 - 579
Abstract: For a wide class of Cohen–Macaulay modules over the local ring of the plane curve singularity of type $$T_{44}$$ , we explicitly describe the corresponding matrix factorizations. The calculations are based on the technique of matrix problems, in particular, representations of bunches of chains.
PubDate: 2017-06-01
DOI: 10.1007/s00013-017-1034-3
Issue No: Vol. 108, No. 6 (2017)

• On some spectral spaces associated to tensor triangulated categories
• Authors: Abhishek Banerjee
Pages: 581 - 591
Abstract: We consider a closure operator c of finite type on the space $$SMod(\mathcal M)$$ of thick $$\mathcal K$$ -submodules of a triangulated category $$\mathcal M$$ that is a module over a tensor triangulated category $$(\mathcal K,\otimes ,1)$$ . Our purpose is to show that the space $$SMod^c(\mathcal M)$$ of fixed points of the operator c is a spectral space that also carries the structure of a topological monoid.
PubDate: 2017-06-01
DOI: 10.1007/s00013-017-1025-4
Issue No: Vol. 108, No. 6 (2017)

• Irreducibility of the Hilbert scheme of smooth curves in $$\mathbb {P}^3$$
P 3 of degree g and genus g
• Authors: Changho Keem; Yun-Hwan Kim
Pages: 593 - 600
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 $$\mathcal {H}_{g,g,3}$$ is irreducible without any restriction on the genus g. This extends the result obtained earlier by Iliev (Proc Am Math Soc 134:2823–2832, 2006).
PubDate: 2017-06-01
DOI: 10.1007/s00013-016-1017-9
Issue No: Vol. 108, No. 6 (2017)

• On the fundamental group of compact homogeneous manifolds carrying an
invariant fat distribution
• Authors: A. Lotta
Pages: 625 - 628
Abstract: We show that a homogeneous space of a compact Lie group carrying an invariant fat distribution must have finite fundamental group.
PubDate: 2017-06-01
DOI: 10.1007/s00013-017-1021-8
Issue No: Vol. 108, No. 6 (2017)

• Uniform approximation of the heat kernel on a manifold
• Authors: Evelina Shamarova; Alexandre B. Simas
Pages: 485 - 494
Abstract: We approximate the heat kernel h(x, y, t) on a compact connected Riemannian manifold M without boundary uniformly in $$(x,y,t)\in M\times M\times [a,b]$$ , $$a>0$$ , by n-fold integrals over $$M^n$$ of the densities of Brownian bridges. Moreover, we provide an estimate for the uniform convergence rate. As an immediate corollary, we get a uniform approximation of solutions of the Cauchy problem for the heat equation on M.
PubDate: 2017-05-01
DOI: 10.1007/s00013-017-1032-5
Issue No: Vol. 108, No. 5 (2017)

• Bach-flat noncompact steady quasi-Einstein manifolds
• Authors: M. Ranieri; E. Ribeiro
Pages: 507 - 519
Abstract: The goal of this article is to study the geometry of Bach-flat noncompact steady quasi-Einstein manifolds. We show that a Bach-flat noncompact steady quasi-Einstein manifold $$(M^{n},\,g)$$ with positive Ricci curvature such that its potential function has at least one critical point must be a warped product with Einstein fiber. In addition, the fiber has constant curvature if $$n = 4$$ .
PubDate: 2017-05-01
DOI: 10.1007/s00013-016-1014-z
Issue No: Vol. 108, No. 5 (2017)

• Born–Infeld solitons, maximal surfaces, and Ramanujan’s
identities
• Authors: Rukmini Dey; Rahul Kumar Singh
Pages: 527 - 538
Abstract: We show that a Born–Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. We also obtain some exact solutions of the Born–Infeld equation from already known solutions to the maximal surface equation. Further we present a method to construct a one parameter family of complex solitons from a given one parameter family of maximal surfaces. Finally, using Ramanujan’s identities and the Weierstrass–Enneper representation of maximal surfaces, we derive further non-trivial identities.
PubDate: 2017-05-01
DOI: 10.1007/s00013-016-1011-2
Issue No: Vol. 108, No. 5 (2017)

• On finite groups for which the lattice of S -permutable subgroups is
distributive
• Authors: Alexander N. Skiba
Abstract: A subgroup A of a finite group G is said to permute with a subgroup B if $$AB=BA$$ . If A permutes with all Sylow subgroups of G, then A is called S-permutable in G. We characterize finite groups with modular and distributive lattice of S-permutable subgroups.
PubDate: 2017-05-20
DOI: 10.1007/s00013-017-1051-2

• Muckenhoupt–Wheeden conjectures for sparse operators
• Authors: Cong Hoang; Kabe Moen
Abstract: We provide an explicit example of a pair of weights and a dyadic sparse operator for which the Hardy–Littlewood maximal function is bounded from $$L^p(v)$$ to $$L^p(u)$$ and from $$L^{p'}(u^{1-p'})$$ to $$L^{p'}(v^{1-p'})$$ while the sparse operator is not bounded on the same spaces. Our construction also provides an example of a single weight for which the weak-type endpoint does not hold for sparse operators.
PubDate: 2017-05-17
DOI: 10.1007/s00013-017-1046-z

• On just infinite periodic locally soluble groups
• Authors: R. Grigorchuk; P. Shumyatsky
Abstract: We construct an uncountable family of periodic locally soluble groups which are hereditarily just infinite. We also show that the associated full $$C^*$$ -algebra $$C^*(G)$$ is just infinite for many groups G in this family.
PubDate: 2017-05-16
DOI: 10.1007/s00013-017-1043-2

• Some remarks on energy inequalities for harmonic maps with potential
• Authors: Volker Branding
Abstract: In this note we discuss how several results characterizing the qualitative behavior of solutions to the nonlinear Poisson equation can be generalized to harmonic maps with potential between complete Riemannian manifolds. This includes gradient estimates, monotonicity formulas, and Liouville theorems under curvature and energy assumptions.
PubDate: 2017-05-16
DOI: 10.1007/s00013-017-1049-9

• Groups with finiteness conditions on the lower central series of
non-normal subgroups
• Authors: Fausto De Mari
Abstract: It is known that any locally graded group with finitely many derived subgroups of non-normal subgroups is finite-by-abelian. This result is generalized here, by proving that in a locally graded group G the subgroup $$\gamma _{k}(G)$$ is finite if the set $$\{\gamma _{k}(H)\; \;H\le G,\,H\ntriangleleft G\}$$ is finite. Moreover, locally graded groups with finitely many kth terms of lower central series of infinite non-normal subgroups are also completely described.
PubDate: 2017-05-16
DOI: 10.1007/s00013-017-1050-3

• Rigidity of complete manifolds with parallel Cotton tensor
• Authors: Yawei Chu; Shouwen Fang
Abstract: The aim of this paper is to show some rigidity results for complete Riemannian manifolds with parallel Cotton tensor. In particular, we prove that any compact manifold of dimension $$n\ge 3$$ with parallel Cotton tensor and positive constant scalar curvature is isometric to a finite quotient of $${\mathbb {S}}^n$$ under a pointwise or integral pinching condition. Moreover, a rigidity theorem for stochastically complete manifolds with parallel Cotton tensor is also given. The proofs rely mainly on curvature elliptic estimates and the weak maximum principle.
PubDate: 2017-05-16
DOI: 10.1007/s00013-017-1047-y

• Relating the Frobenius and Morita-Frobenius numbers of blocks of finite
groups
• Authors: Matthias Klupsch
Abstract: Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.
PubDate: 2017-04-25
DOI: 10.1007/s00013-017-1042-3

• Corona problem with data in ideal spaces of sequences
• Authors: Dmitry V. Rutsky
Abstract: Let E be a Banach lattice on $${\mathbb {Z}}$$ with order continuous norm. We show that for any function $$f = \{f_j\}_{j \in {\mathbb {Z}}}$$ from the Hardy space $$\mathrm H_{\infty }\left( E \right)$$ such that $$\delta \leqslant \Vert f (z)\Vert _E \leqslant 1$$ for all z from the unit disk  $${\mathbb {D}}$$ there exists some solution $$g = \{g_j\}_{j \in {\mathbb {Z}}} \in \mathrm H_{\infty }\left( E' \right)$$ , $$\Vert g\Vert _{\mathrm H_{\infty }\left( E' \right) } \leqslant C_\delta$$ of the Bézout equation $$\sum _j f_j g_j = 1$$ , also known as the vector-valued corona problem with data in  $$\mathrm H_{\infty }\left( E \right)$$ .
PubDate: 2017-04-25
DOI: 10.1007/s00013-017-1045-0

• Inequalities for combinatorial sums
• Authors: Horst Alzer; Man Kam Kwong
Abstract: For $$k,l\in \mathbf {N}$$ , let \begin{aligned}&P_{k,l}=\Bigl (\frac{l}{k+l}\Bigr )^{k+l} \sum _{\nu =0}^{k-1} {k+l\atopwithdelims ()\nu } \Bigl (\frac{k}{l}\Bigr )^{\nu }\\&\quad \text{ and }\quad Q_{k,l}=\Bigl (\frac{l}{k+l}\Bigr )^{k+l} \sum _{\nu =0}^{k} {k+l\atopwithdelims ()\nu } \Bigl (\frac{k}{l}\Bigr )^{\nu }. \end{aligned} We prove that the inequality \begin{aligned} \frac{1}{4}\le P_{k,l} \end{aligned} is valid for all natural numbers k and l. The sign of equality holds if and only if $$k=l=1$$ . This complements a result of Vietoris, who showed that \begin{aligned} P_{k,l}<\frac{1}{2} \quad {(k,l\in \mathbf {N})}. \end{aligned} An immediate corollary is that \begin{aligned} \frac{1}{4}\le P_{k,l}<\frac{1}{2} <Q_{k,l}\le \frac{3}{4} \quad {(k,l\in \mathbf {N})}. \end{aligned} The constant bounds are sharp.
PubDate: 2017-04-24
DOI: 10.1007/s00013-017-1024-5

• A reverse isoperimetric inequality for embedded starshaped plane curves
• Authors: Jianbo Fang
Abstract: In this note, we present a reverse isoperimetric inequality for embedded starshaped closed plane curves, which states that if K is a starshaped domain with perimeter p(K) and area a(K), then one gets \begin{aligned} p(K)^2 \le 4\pi \Big ((a(K)+\tilde{a}(K)\Big ), \end{aligned} where $$\tilde{a}(K)$$ denotes the oriented area of the domain enclosed by $$\beta$$ (defined in Section 2), and equality holds if and only if K is a disc.
PubDate: 2017-04-24
DOI: 10.1007/s00013-017-1048-x

• Normes cyclotomiques naïves et unités logarithmiques
• Authors: Jean-François Jaulent
Abstract: Résumé Nous déterminons le rang du sous-groupe $$\widetilde{E}_K$$ des éléments du groupe multiplicatif d’un corps de nombres K qui sont normes à chaque étage fini de sa $${\mathbb {Z}}_\ell$$ -extension cyclotomique $$K^c$$ ; et nous comparons son $$\ell$$ -adifié $${\mathbb {Z}}_\ell \otimes _{\mathbb {Z}}\widetilde{E}_K$$ avec le $$\ell$$ -groupe des unités logarithmiques $$\,\widetilde{\varepsilon }_K$$ . Nous donnons à cette occasion une preuve très facile de la conjecture de Gross–Kuz’min en $$\ell$$ pour les extensions K / k d’un corps abélien dans lesquelles les places au-dessus de $$\ell$$ ne se décomposent pas.
PubDate: 2017-04-13
DOI: 10.1007/s00013-017-1038-z

• A remark on orbital free entropy
• Authors: Yoshimichi Ueda
Abstract: A lower estimate of the orbital free entropy $$\chi _\mathrm {orb}$$ under unitary conjugation is proved, and it together with Voiculescu’s observation shows that the conjectural exact formula relating $$\chi _\mathrm {orb}$$ to the free entropy $$\chi$$ breaks in general in contrast to the case when given random multi-variables are all hyperfinite.
PubDate: 2017-04-06
DOI: 10.1007/s00013-017-1035-2

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