Authors:Banerjee; Abhishek Pages: 703 - 714 Abstract: Let be a small preadditive category, viewed as a “ring with several objects.” A right -module is an additive functor from to the category of abelian groups. We show that every hereditary torsion theory on the category of right -modules must be differential. PubDate: 2019-04-08 DOI: 10.4153/S0008439518000656

Authors:Deng; Guotai, Liu, Chuntai, Ngai, Sze-Man Pages: 727 - 740 Abstract: We construct a family of self-affine tiles in ( ) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in , and its extension to by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible. PubDate: 2019-05-03 DOI: 10.4153/S0008439519000237

Authors:Gauthier P. M. Pages: 767 - 779 Abstract: In 1895, Cantor showed that between every two countable dense real sets, there is an order isomorphism. In fact, there is always such an order isomorphism that is the restriction of a universal entire function. PubDate: 2019-04-10 DOI: 10.4153/S0008439519000158

Authors:Geng; Pengbo, Chen, Wengu, Ge, Huanmin Pages: 780 - 797 Abstract: The Orthogonal Least Squares (OLS) algorithm is an efficient sparse recovery algorithm that has received much attention in recent years. On one hand, this paper considers that the OLS algorithm recovers the supports of sparse signals in the noisy case. We show that the OLS algorithm exactly recovers the support of -sparse signal from in iterations, provided that the sensing matrix satisfies the restricted isometry property (RIP) with restricted isometry constant (RIC) , and the minimum magnitude of the nonzero elements of satisfies some constraint. On the other hand, this paper demonstrates that the OLS algorithm exactly recovers the support of the best -term approximation of an almost sparse signal in the general perturbations case, which means both and are perturbed. We show that the support of the best ... PubDate: 2019-03-22 DOI: 10.4153/S0008439519000134

Authors:Koşan; M. Tamer, Yildirim, Tülay, Zhou, Y. Pages: 810 - 821 Abstract: This paper is about rings for which every element is a sum of a tripotent and an element from the Jacobson radical . These rings are called semi-tripotent rings. Examples include Boolean rings, strongly nil-clean rings, strongly 2-nil-clean rings, and semi-boolean rings. Here, many characterizations of semi-tripotent rings are obtained. Necessary and sufficient conditions for a Morita context (respectively, for a group ring of an abelian group or a locally finite nilpotent group) to be semi-tripotent are proved. PubDate: 2019-03-15 DOI: 10.4153/S0008439519000092

Authors:Koca; Caner, Lejmi, Mehdi Pages: 822 - 840 Abstract: We classify up to automorphisms all left-invariant non-Einstein solutions to the Einstein–Maxwell equations on four-dimensional Lie algebras. PubDate: 2019-05-09 DOI: 10.4153/S0008439519000249

Authors:Kuo; Wentang, Liu, Yu-Ru, Ribas, Sávio, Zhou, Kevin Pages: 841 - 855 Abstract: We construct a shifted version of the Turán sieve method developed by R. Murty and the second author and apply it to counting problems on tournaments. More precisely, we obtain upper bounds for the number of tournaments which contain a fixed number of restricted -cycles. These are the first concrete results which count the number of cycles over “all tournaments”. PubDate: 2019-04-11 DOI: 10.4153/S000843951900016X

Authors:Raghavan; Dilip, Verner, Jonathan L. Pages: 856 - 868 Abstract: It is proved that the Continuum Hypothesis implies that any sequence of rapid P-points of length that is increasing with respect to the Rudin–Keisler ordering is bounded above by a rapid P-point. This is an improvement of a result from B. Kuzeljevic and D. Raghavan. It is also proved that Jensen’s diamond principle implies the existence of an unbounded strictly increasing sequence of P-points of length in the Rudin–Keisler ordering. This shows that restricting to the class of rapid P-points is essential for the first result. PubDate: 2019-02-18 DOI: 10.4153/S0008439519000043

Authors:Sáez; Pablo, Vidaux, Xavier, Vsemirnov, Maxim Pages: 876 - 885 Abstract: Given a prime and an integer , we show that there exists an integer such that for any quadratic polynomial with coefficients in the ring of integers modulo , such that is not a square, if a sequence is a sequence of squares, then is at most . We also provide some explicit formulas for the optimal . PubDate: 2019-04-26 DOI: 10.4153/S0008439519000225

Authors:Steinberg; Benjamin Pages: 886 - 895 Abstract: We say that two elements of a group or semigroup are -linear conjugates if their images under any linear representation over are conjugate matrices. In this paper we characterize -linear conjugacy for finite semigroups (and, in particular, for finite groups) over an arbitrary field . PubDate: 2019-01-29 DOI: 10.4153/S0008439519000031

Authors:Bu; Shangquan, Cai, Gang Pages: 715 - 726 Abstract: In this paper, by using operator-valued -Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the -well-posedness for the third order differential equations , ( ), where are closed linear operators on a Banach space such that , and . PubDate: 2018-10-15 DOI: 10.4153/S0008439518000048

Authors:Deza; Antoine, Pournin, Lionel Pages: 741 - 755 Abstract: We investigate how the Minkowski sum of two polytopes affects their graph and, in particular, their diameter. We show that the diameter of the Minkowski sum is bounded below by the diameter of each summand and above by, roughly, the product between the diameter of one summand and the number of vertices of the other. We also prove that both bounds are sharp. In addition, we obtain a result on polytope decomposability. More precisely, given two polytopes and , we show that can be written as a Minkowski sum with a summand homothetic to if and only if has the same number of vertices as its Minkowski sum with . PubDate: 2018-12-17 DOI: 10.4153/S0008439518000668

Authors:Farhat; Yasser, Gourdeau, Frédéric Pages: 756 - 766 Abstract: We consider the unital Banach algebra and prove directly, without using cyclic cohomology, that the simplicial cohomology groups vanish for all . This proceeds via the introduction of an explicit bounded linear operator which produces a contracting homotopy for . This construction is generalised to unital Banach algebras , where and is a subgroup of . PubDate: 2018-12-17 DOI: 10.4153/S0008439518000644

Authors:Hare; Kathryn E., Yang, Robert (Xu) Pages: 798 - 809 Abstract: In his seminal work on Sidon sets, Pisier found an important characterization of Sidonicity: A set is Sidon if and only if it is proportionally quasi-independent. Later, it was shown that Sidon sets were proportionally “special” Sidon in several other ways. Here, we prove that Sidon sets in torsion-free groups are proportionally -degree independent, a higher order of independence than quasi-independence, and we use this to prove that Sidon sets are proportionally Sidon with Sidon constants arbitrarily close to one, the minimum possible value. PubDate: 2018-12-11 DOI: 10.4153/S0008439518000620

Authors:Roy; Damien, Schleischitz, Johannes Pages: 869 - 875 Abstract: In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set and by rational numbers outside of that set. We consider more general missing digit sets and construct numbers in that are arbitrarily well approximable by rationals in , but badly approximable by rationals outside of . More precisely, we construct them so that all but finitely many of their convergents lie in . PubDate: 2018-12-03 DOI: 10.4153/S0008439518000450

Authors:Ueyama; Kenta Pages: 896 - 911 Abstract: We study the structure of the stable category of graded maximal Cohen–Macaulay module over where is a graded ( )-skew polynomial algebra in variables of degree 1, and . If is commutative, then the structure of is well known by Knörrer’s periodicity theorem. In this paper, we prove that if , then the structure of is determined by the number of irreducible components of the point scheme of which are isomorphic to . PubDate: 2018-12-03 DOI: 10.4153/S0008439518000607

Authors:Wang; Yaning Pages: 912 - 922 Abstract: In this paper, we prove that if an almost co-Kähler manifold of dimension greater than three satisfying -Einstein condition with constant coefficients is a Ricci soliton with potential vector field being of constant length, then either the manifold is Einstein or the Reeb vector field is parallel. Let be a non-co-Kähler almost co-Kähler 3-manifold such that the Reeb vector field is an eigenvector field of the Ricci operator. If is a Ricci soliton with transversal potential vector field, then it is locally isometric to Lie group of rigid motions of the Minkowski 2-space. PubDate: 2018-12-07 DOI: 10.4153/S0008439518000632

Authors:Yang; Qi, Zong, Chuanming Pages: 923 - 929 Abstract: In 1885, Fedorov discovered that a convex domain can form a lattice tiling of the Euclidean plane if and only if it is a parallelogram or a centrally symmetric hexagon. This paper proves the following results. Except for parallelograms and centrally symmetric hexagons, there are no other convex domains that can form two-, three- or four-fold lattice tilings in the Euclidean plane. However, there are both octagons and decagons that can form five-fold lattice tilings. Whenever , there are non-parallelohedral polytopes that can form five-fold lattice tilings in the -dimensional Euclidean space. PubDate: 2018-11-16 DOI: 10.4153/S0008439518000103