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  • 1.
    Balletti, Gabriele
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Higashitani, Akihiro
    Universal inequalities in Ehrhart theory2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 227, no 2, p. 843-859Article in journal (Refereed)
    Abstract [en]

    In this paper, we show the existence of universal inequalities for the h*-vector of a lattice polytope P, that is, we show that there are relations among the coefficients of the h*-polynomial that are independent of both the dimension and the degree of P. More precisely, we prove that the coefficients h* (1) and h* (2) of the h*-vector (h* (0), h* (1),..., h* (d) ) of a lattice polytope of any degree satisfy Scott's inequality if h* (3) = 0.

  • 2.
    Berglund, Alexander
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hess, Kathryn
    Homotopical Morita theory for corings2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 227, no 1, p. 239-287Article in journal (Refereed)
    Abstract [en]

    A coring (A,C) consists of an algebra A in a symmetric monoidal category and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf-Galois extensions and descent theory, as well as in the study of Hopf algebroids. In this paper, we address the question of when two corings (A,C) and (B,D) in a symmetric monoidal model category V are homotopically Morita equivalent, i.e., when their respective categories of comodules V (C)(A) and V (D)(B) are Quillen equivalent. As an illustration of the general theory, we examine homotopical Morita theory for corings in the category of chain complexes over a commutative ring.

  • 3.
    Bergner, Julia
    et al.
    University of California, Riverside, USA.
    Hackney, Philip
    Stockholm University, Faculty of Science, Department of Mathematics. University of California, Riverside, USA.
    Group actions on Segal operads2014In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 202, no 1, p. 423-460Article in journal (Refereed)
    Abstract [en]

    We give a Quillen equivalence between model structures for simplicial operads, described via the theory of operads, and Segal operads, thought of as certain reduced dendroidal spaces. We then extend this result to give a Quillen equivalence between the model structures for simplicial operads equipped with a group action and the corresponding Segal operads.

  • 4.
    Björner, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Wachs, Michelle
    Welker, Volkmar
    ON SEQUENTIALLY COHEN-MACAULAY COMPLEXES AND POSETS2009In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 169, no 1, p. 295-316Article in journal (Refereed)
    Abstract [en]

    The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for posets is given. Finally, in an appendix we outline connections with ring-theory and survey some uses of sequential Cohen-Macaulayness in commutative algebra.

  • 5. Bogart, Tristram
    et al.
    Haase, Christian
    Hering, Milena
    Lorenz, Benjamin
    Nill, Benjamin
    Stockholm University, Faculty of Science, Department of Mathematics.
    Paffenholz, Andreas
    Rote, Günter
    Santos, Francisco
    Schenck, Hal
    Finitely many smooth d-polytopes with n lattice points2015In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 207, no 1, p. 301-329Article in journal (Refereed)
    Abstract [en]

    We prove that for fixed n there are only finitely many embeddings of ℚ-factorial toric varieties X into ℙ n that are induced by a complete linear system. The proof is based on a combinatorial result that implies that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with ≤ 12 lattice points.

  • 6.
    Coulembier, Kevin
    et al.
    Univ Ghent, Dept Math Anal, Krijgslaan 281, B-9000 Ghent, Belgium..
    Mazorchuk, Volodymyr
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Dualities and derived equivalences for category O2017In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 219, no 2, p. 661-706Article in journal (Refereed)
    Abstract [en]

    We determine the Ringel duals for all blocks in the parabolic versions of the BGG category associated to a reductive finite-dimensional Lie algebra. In particular, we find that, contrary to the original category and the specific previously known cases in the parabolic setting, the blocks are not necessarily Ringel self-dual. However, the parabolic category as a whole is still Ringel self-dual. Furthermore, we use generalisations of the Ringel duality functor to obtain large classes of derived equivalences between blocks in parabolic and original category . We subsequently classify all derived equivalence classes of blocks of category in type A which preserve the Koszul grading.

  • 7. Dao, Hailong
    et al.
    Smirnov, Ilya
    Stockholm University, Faculty of Science, Department of Mathematics.
    On generalized Hilbert–Kunz function and multiplicity2020In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511Article in journal (Refereed)
  • 8.
    Gustafsson, Björn
    et al.
    KTH, Superseded Departments, Mathematics.
    Putinar, M.
    Linear analysis of quadrature domains. II2000In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 119, p. 187-216Article in journal (Refereed)
    Abstract [en]

    The natural correspondence between bounded planar quadrature domains, in the terminology of Aharonov-Shapiro, and certain square matrices with a distinguished cyclic vector is further exploited. Two different cubature formulas on quadrature domains, that is the computation of the integral of a real polynomial, are presented. The minimal defining polynomial of a quadrature domain is decomposed uniquely into a linear combination of moduli squares of complex polynomials. The geometry of a canonical rational embedding of a quadrature domain into the projective complement of a real affine ball is also investigated. Explicit computations on order-two quadrature domains illustrate the main results.

  • 9.
    Johansson, Anders
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Jordan, Thomas
    Bristol University.
    Öberg, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Pollicott, Mark
    Multifractal analysis of non-uniformly hyperbolic systems2010In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 177, no 1, p. 125-144Article in journal (Refereed)
    Abstract [en]

    We prove a multifractal formalismfor Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.

  • 10.
    Johansson, Anders
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Jordan, Thomas
    Department of Mathematics, University of Bristol, Bristol, United Kingdom.
    Öberg, Anders
    Department of Mathematics, Uppsala Universitet, Uppsala, Sweden.
    Pollicott, Mark
    Mathematics Institute, University of Warwick, Coventry, United Kingdom.
    Multifractal analysis of non-uniformly hyperbolic systems2010In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 177, no 1, p. 125-144Article in journal (Refereed)
    Abstract [en]

    We prove a multifractal formalism for Birkhoff averages of continuous functions in the case of some non-uniformly hyperbolic maps, which includes interval examples such as the Manneville-Pomeau map.

  • 11.
    Josefson, Bengt
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Subspaces of l(infinity)(Gamma) without quasicomplements2002In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 130, p. 281-283Article in journal (Refereed)
    Abstract [en]

    J. Lindenstrauss proves in [L] that c(0)(Gamma) is not quasicomplemented in L-infinity(Gamma) while H. P. Rosenthal in [R] proves that subspaces, whose dual balls are weak* sequentially compact and weak* separable, are quasicomplemented in l(infinity)(Gamma). In this note it is proved that weak* separability of the dual is the precise condition determining whether a subspace, without isomorphic copies of l(1) and whose dual balls are weak* sequentially compact, is quasicomplemented or not in l(infinity)(Gamma). Especially spaces isomorphic to l(p)(Gamma), for 1 < p < infinity, have no quasicomplements in l(infinity)(Gamma) if Gamma is uncountable.

  • 12.
    Kaminska, Anna
    et al.
    University of Memphis.
    Maligranda, Lech
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On Lorentz spaces Γp,w2004In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, no 140, p. 285-318Article in journal (Refereed)
    Abstract [en]

    We study Lorentz spaces Γp,w where 0 < p < ∞, and w is a nonnegative measurable weight function. We first present some results concerning new formulas for the quasi-norm, duality, embeddings and Boyd indices. We then show that, whenever Γp,w does not coincide with L1 + L∞, it contains an order isomorphic and complemented copy of lp. We apply this result to determine criteria for order convexity and concavity as well as for lower and upper estimates. Finally, we characterize the type and cotype of Γp,w.

  • 13.
    Kiessling, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Properties of cellular classes of chain complexes2012In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 191, no 1, p. 483-505Article in journal (Refereed)
    Abstract [en]

    In this paper we prove certain properties of cellular and acyclic classes of chain complexes of modules over a commutative Noetherian ring. In particular, we show that if X is finite and belongs to some cellular class C, then Σ nH nX also belongs to C, for every n.

  • 14. Kurlberg, Pär
    The distribution of spacings between quadratic residues, II2000In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 120, p. 205-224Article in journal (Refereed)
    Abstract [en]

    We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for square free Q is Poissonian, this paper extends the result to arbitrary Q.

  • 15. Matousek, Jiri
    et al.
    Sedgwick, Eric
    Tancer, Martin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Charles University, Czech Republic.
    Wagner, Uli
    UNTANGLING TWO SYSTEMS OF NONCROSSING CURVES2016In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 212, no 1, p. 37-79Article in journal (Refereed)
    Abstract [en]

    We consider two systems (alpha(1), ... ,alpha(m)) and (beta(1), ... , beta(n)) of simple curves drawn on a compact two-dimensional surface M with boundary. Each alpha(i) and each beta(j) is either an arc meeting the boundary of M at its two endpoints, or a closed curve. The a, are pairwise disjoint except for possibly sharing endpoints, and similarly for the beta(j). We want to "untangle" the beta(j) from the alpha(i) by a self-homeomorphism of M; more precisely, we seek a homeomorphism phi: M -> M fixing the boundary of M pointwise such that the total number of crossings of the a, with the phi(beta(j)) is as small as possible. This problem is motivated by an application in the algorithmic theory of embeddings and 3 -manifolds. We prove that if M is planar, i.e., a sphere with h >= 0 boundary components ("holes"), then O(mn) crossings can be achieved (independently of h), which is asymptotically tight, as an easy lower bound shows. In general, for an arbitrary (orientable or nonorientable) surface M with h holes and of (orientable or nonorientable) genus g >= 0, we obtain an O((m + n)(4)) upper bound, again independent of h and g. The proofs rely, among other things, on a result concerning simultaneous planar drawings of graphs by Erten and Kobourov.

  • 16.
    Nystedt, Patrik
    et al.
    Högskolan Väst, SWE.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences. Blekinge Inst Technol, Dept Math & Nat Sci, SE-37179 Karlskrona, Sweden..
    Richter, Johan
    Mälardalens högskola, SWE.
    NON-ASSOCIATIVE ORE EXTENSIONS2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 224, no 1, p. 263-292Article in journal (Refereed)
    Abstract [en]

    We introduce non-associative Ore extensions, S = R[X; sigma, delta], for any non-ssociative unital ring R and any additive maps sigma, delta : R -> R satisfying sigma(1) = 1 and delta(1) = 0. In the special case when delta is either left or right R-delta-linear, where R-delta = ker(delta), and R is delta-simple, i.e. {0} and R are the only delta-invariant ideals of R, we determine the ideal structure of the non-associative differential polynomial ring D = R[X; id(R),delta]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z(D) = R-delta[p] for a monic p is an element of R-delta [X], unique up to addition of elements from Z(R)(delta) . Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is delta-simple and Z(D) equals the field R-delta boolean AND Z(R). This provides us with a non-associative generalization of a result by Oinert, Richter and Silve-strov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field R-delta boolean AND Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces.

  • 17.
    Nystedt, Patrik
    et al.
    Högskolan Väst, Sweden.
    Öinert, Johan
    Blekinge Tekniska Högskola, Sweden.
    Richter, Johan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Non-associative Ore extensions2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 224, no 1, p. 263-292Article in journal (Refereed)
    Abstract [en]

    We introduce non-associative Ore extensions, S = R[X; σ, δ], for any nonassociative unital ring R and any additive maps σ, δ: R → R satisfying σ(1) = 1 and δ(1) = 0. In the special case when δ is either left or right Rδ-linear, where Rδ = ker(δ), and R is δ-simple, i.e. {0} and R are the only δ-invariant ideals of R, we determine the ideal structure of the nonassociative differential polynomial ring D = R[X; idR, δ]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z(D) = Rδ[p] for a monic p ∈ Rδ[X], unique up to addition of elements from Z(R)δ. Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is δ-simple and Z(D) equals the field Rδ ∩ Z(R). This provides us with a non-associative generalization of a result by Öinert, Richter and Silvestrov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field Rδ ∩ Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces. 

  • 18.
    Nystedt, Patrik
    et al.
    University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.
    Öinert, Johan
    Blekinge Institute of Technology, Department of Mathematics and Natural Sciences, Karlskrona, Sweden.
    Richter, Johan
    Mälardalen University, Academy of Education, Culture and Communication,Västerås, Sweden.
    Non-associative Ore extensions2018In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 224, no 1, p. 263-292Article in journal (Refereed)
    Abstract [en]

    We introduce non-associative Ore extensions, S = R[X; sigma, delta], for any non-ssociative unital ring R and any additive maps sigma, delta : R -> R satisfying sigma(1) = 1 and delta(1) = 0. In the special case when delta is either left or right R-delta-linear, where R-delta = ker(delta), and R is delta-simple, i.e. 0 and R are the only delta-invariant ideals of R, we determine the ideal structure of the non-associative differential polynomial ring D = R[X; id(R),delta]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z(D) = R-delta[p] for a monic p is an element of R-delta [X], unique up to addition of elements from Z(R)(delta) . Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is delta-simple and Z(D) equals the field R-delta boolean AND Z(R). This provides us with a non-associative generalization of a result by Oinert, Richter and Silve-strov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field R-delta boolean AND Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces.

  • 19. Schippers, Eric
    et al.
    Staubach, Wolfgang
    Variation of Neumann and Green functions under homotopies of the boundary2009In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 173, p. 279-303Article in journal (Refereed)
  • 20.
    Shapiro, Boris
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Holst, Thomas
    Stockholm University, Faculty of Science, Department of Mathematics.
    On higher heine-stieltjes polynomials2011In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 183, no 1, p. 321-345Article in journal (Refereed)
    Abstract [en]

    Take a linear ordinary differential operator d(z) = Pk i=1 Qi(z) di dzi with polynomial coefficients and set r = maxi=1,...,k(degQi(z) − i). If d(z) satisfies the conditions: i) r   0 and ii) degQk(z) = k + r we call it a non-degenerate higher Lam´e operator. Following the classical examples of E. Heine and T. Stieltjes we initiated in [6] the study of the following multiparameter spectral problem: for each positive integer n find polynomials V (z) of degree at most r such that the equation: d(z)S(z) + V (z)S(z) = 0 has a polynomial solution S(z) of degree n. We have shown that under some mild non-degeneracy assumptions on T there exist exactly `n+r n ´ spectral polynomials Vn,i(z) of degree r and their corresponding eigenpolynomials Sn,i(z) of degree n. Localization results of [6] provide the existence of abundance of converging as n ! 1 sequences of normalized spectral polynomials {eVn,in (z)} where eVn,in (z) is the monic polynomial proportional to Vn,in(z). Below we calculate for any such converging sequence {eVn,in(z)} the asymptotic rootcounting measure of the corresponding family {Sn,in (z)} of eigenpolynomials. We also conjecture that the sequence of sets of all normalized spectral polynomials {eVn,i(z)} having eigenpolynomials S(z) of degree n converges as n ! 1to the standard measure in the space of monic polynomials of degree r which depends only on the leading coefficient Qk(z).

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