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  • The cyclicity problem for Albert algebras
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Maneesh Thakur

    Addressing a long-standing question of Albert dating back to 1965, we show that every Albert division algebra has an isotope that contains a cyclic cubic subfield.

    更新日期:2021-01-15
  • Bad oracles in higher computability and randomness
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Laurent Bienvenu, Noam Greenberg, Benoit Monin

    Many constructions in computability theory rely on “time tricks”. In the higher setting, relativising to some oracles shows the necessity of these. We construct an oracle A and a set X, higher Turing reducible to X, but for which ψ(A) ≠ X for any higher functional ψ which is consistent on all oracles. We construct an oracle A relative to which there is no universal higher ML-test. On the other hand

    更新日期:2021-01-15
  • L 2 vanishing theorem on some Kähler manifolds
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Teng Huang

    Let E be a Hermitian vector bundle over a complete Kähler manifold (X, ω), dimℂX = n, with a d(bounded) Kähler form ω, and let dA be a Hermitian connection on E. The goal of this article is to study the L2-Hodge theory on the vector bundle E. We extend the results of Gromov [18] to the Hermitian vector bundle. Finally, as an application, we prove a gap result for the Yang-Mills connection on the bundle

    更新日期:2021-01-15
  • Almost formality of quasi-Sasakian and Vaisman manifolds with applications to nilmanifolds
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Beniamino Cappelletti-Montano, Antonio De Nicola, Juan Carlos Marrero, Ivan Yudin

    We provide models that are as close as possible to being formal for a large class of compact manifolds that admit a transversely Kähler structure, including Vaisman and quasi-Sasakian manifolds. As an application we are able to classify the corresponding nilmanifolds.

    更新日期:2021-01-15
  • Homological identities and dualizing complexes of commutative differential graded algebras
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Hiroyuki Minamoto

    In this paper we study a connective commutative differential graded algebra (CDGA) which is piecewise Noetherian. The principal aim is to analyze a dualizing complex of CDGA’s and investigate a Gorenstein CDGA. We also establish many other results which can be expected to play basic roles in the study of a CDGA, such as the Auslaner-Buchsbaum formula and Bass formula without any unnecessary assumptions

    更新日期:2021-01-15
  • The destruction of the axiom of determinacy by forcings on ℝ when Θ Is regular
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    William Chan, Stephen Jackson

    ZF + AD proves that for all nontrivial forcings \(\mathbb{P}\) on a wellorderable set of cardinality less than Θ, \({1_\mathbb{P}}{ \Vdash _\mathbb{P}}\,\neg {\rm{AD}}\). ZF + AD + Θ is regular proves that for all nontrivial forcing \(\mathbb{P}\) which is a surjective image of ℝ, \({1_\mathbb{P}}{ \Vdash _\mathbb{P}}\,\neg {\rm{AD}}\). In particular, ZF + AD + V = L(ℝ) proves that for every nontrivial

    更新日期:2021-01-15
  • A Whitehead theorem for periodic homotopy groups
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Tobias Barthel, Gijs Heuts, Lennart Meier

    We show that vn-periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes.

    更新日期:2021-01-15
  • Identities for the special linear Lie algebra with the Pauli and Cartan gradings
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Claudemir Fidelis, Diogo Diniz, Franciélia Limeira de Sousa

    Let \(\mathbb{K}\) be a field of characteristic zero. We study the graded identities of the special linear Lie algebra with the Pauli and Cartan gradings. Given a prime number p we provide a finite basis for the graded identities of \(s{l_p}\left(\mathbb{K}\right)\) with the Pauli grading by the group ℤp × ℤp and compute its graded codimensions. We also prove that \({{\mathop{\rm var}} ^{{\mathbb{Z}_p}

    更新日期:2021-01-15
  • Existentially closed exponential fields
    Isr. J. Math. (IF 0.894) Pub Date : 2021-01-15
    Levon Haykazyan, Jonathan Kirby

    We characterise the existentially closed models of the theory of exponential fields. They do not form an elementary class, but can be studied using positive logic. We find the amalgamation bases and characterise the types over them. We define a notion of independence and show that independent systems of higher dimension can also be amalgamated. We extend some notions from classification theory to positive

    更新日期:2021-01-15
  • Retraction Note of “Baire property and axiom of choice”
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Saharon Shelah

    I hereby retract the paper [1] as the proof has an irreparable gap.

    更新日期:2020-11-02
  • Counting projections of rational curves
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Matteo Gallet, Josef Schicho

    Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of them. We show that, under suitable assumptions on the degree of the curves and the dimensions of the two given ambient projective spaces, the number of curves and projections fulfilling the requirements is finite. Using standard

    更新日期:2020-10-30
  • Rigidity with few locations
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Karim Adiprasito, Eran Nevo

    Graphs triangulating the 2-sphere are generically rigid in 3-space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a finite subset A in 3-space so that the vertices of each graph G as above can be mapped into A to make the resulted embedding of G infinitesimally rigid. This assertion extends to the triangulations of any fixed compact connected surface, where the upper bound obtained on the size

    更新日期:2020-10-30
  • Spatio-temporal Poisson processes for visits to small sets
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Françoise Pène, Benoît Saussol

    for many measure preserving dynamical systems (Ω,T, μ) the successive hitting times to a small set is well approximated by a Poisson process on the real line. In this work we define a new process obtained from recording not only the successive times n of visits to a set A, but also the position Tn (x)in A of the orbit, in the limit where μ(A) → 0. We obtain a convergence of this process, suitably normalized

    更新日期:2020-10-30
  • A family of q -hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Victor J. W. Guo, Michael J. Schlosser

    We prove a two-parameter family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Crucial ingredients in our proof are George Andrews’ multiseries extension of the Watson transformation, and a Karlsson—Minton-type summation for very-well-poised basic hypergeometric series due to George Gasper. The new family of q-congruences is then used to prove two conjectures posed

    更新日期:2020-10-30
  • A new lattice invariant for lattices in totally disconnected locally compact groups
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek

    We introduce and explore a natural rank for totally disconnected locally compact groups called the bounded conjugacy rank. This rank is shown to be a lattice invariant for lattices in sigma compact totally disconnected locally compact groups; that is to say, for a given sigma compact totally disconnected locally compact group, some lattice has bounded conjugacy rank n if and only if every lattice has

    更新日期:2020-10-30
  • Notes on the Szegő minimum problem. II. Singular measures
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Alexander Borichev, Anna Kononova, Mikhail Sodin

    In this note, we prove several quantitative results concerning the Szegő minimum problem for classes of measures on the unit circle concentrated on small subsets. As a by-product, we refute a long-standing conjecture of Nevai. This note can be read independently from the first one.

    更新日期:2020-10-30
  • Notes on the Szegő minimum problem. I. Measures with deep zeroes
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Alexander Borichev, Anna Kononova, Mikhail Sodin

    The classical Szegő polynomial approximation theorem states that the polynomials are dense in the space L2(ρ), where ρ is a measure on the unit circle, if and only if the logarithmic integral of the measure ρ diverges. In this note we give a quantitative version of Szegő’s theorem in the special case when the divergence of the logarithmic integral is caused by deep zeroes of the measure ρ on a sufficiently

    更新日期:2020-10-30
  • Exterior square gamma factors for cuspidal representations of GL n : Finite field analogs and level-zero representations
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Rongqing Ye, Elad Zelingher

    We follow Jacquet-Shalika [7], Matringe [12] and Cogdell-Matringe [3] to define exterior square gamma factors for irreducible cuspidal representations of \({\rm{G}}{{\rm{L}}_n}({\mathbb{F}_q})\). These exterior square gamma factors are expressed in terms of Bessel functions associated to the cuspidal representations. We also relate our exterior square gamma factors over finite fields to those over

    更新日期:2020-10-30
  • Fusion rules for ℤ 2 -orbifolds of affine and parafermion vertex operator algebras
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Cuipo Jiang, Qing Wang

    This paper is about the orbifold theory of affine and parafermion vertex operator algebras. It is known that the parafermion vertex operator algebra K(sl2,k) associated to the integrable highest weight modules for the affine Kac—Moody algebra \(A_1^{(1)}\) is the building block of the general parafermion vertex operator K(\(K(\mathfrak{g},k)\),k) for any finite-dimensional simple Lie algebra \(\mathfrak{g}\)

    更新日期:2020-10-30
  • Uniform distribution of Kakutani partitions generated by substitution schemes
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Yotam Smilansky

    Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which include the sequence of partitions of the unit interval considered by Kakutani as a special case. Using our recent path counting results for directed weighted graphs,

    更新日期:2020-10-30
  • Pressure metrics and Manhattan curves for Teichmüller spaces of punctured surfaces
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Lien-Yung Kao

    In this paper, we extend the construction of pressure metrics to Teichmüller spaces of surfaces with punctures. This construction recovers Thurston’s Riemannian metric on Teichmüller spaces. Moreover, we prove the real analyticity and convexity of Manhattan curves of finite area type-preserving Fuchsian representations, and thus we obtain several related entropy rigidity results. Lastly, relating the

    更新日期:2020-10-30
  • Distances and trees in dense subsets of ℤ d
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Neil Lyall, Ákos Magyar

    In [4] Furstenberg, Katznelson and Weiss establish that all sufficiently large distances can always be attained between pairs of points from any given measurable subset of ℝ2 of positive upper (Banach) density. A second proof of this result, as well as a stronger “pinned variant”, was given by Bourgain in [2] using Fourier analytic methods. In [8] the second author adapted Bourgain’s Fourier analytic

    更新日期:2020-10-30
  • Measures of intermediate entropies for star vector fields
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Ming Li, Yi Shi, Shirou Wang, Xiaodong Wang

    We prove that all star vector fields, including Lorenz attractors and multi-singular hyperbolic vector fields, admit the intermediate entropy property. To be precise, if X is a star vector field with htop(X) > 0, then for any h ∈ [0, htop(X)), there exists an ergodic invariant measure μ of X such that hμ(X)= h. Moreover, we show that the topological entropy is lower semi-continuous for star vector

    更新日期:2020-10-30
  • Nonlinear descent on moduli of local systems
    Isr. J. Math. (IF 0.894) Pub Date : 2020-10-27
    Junho Peter Whang

    We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.

    更新日期:2020-10-30
  • Normal subgroups of powerful p -groups
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    James Williams

    In this note we show that if p is an odd prime and G is a powerful p-group with N ≤ Gp and N normal in G, then N is powerfully nilpotent. An analogous result is proved for p = 2 when N ≤ G4.

    更新日期:2020-09-23
  • Centers of Sylow subgroups and automorphisms
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    George Glauberman, Robert Guralnick, Justin Lynd, Gabriel Navarro

    Suppose that p is an odd prime and G is a finite group having no normal non-trivial p′-subgroup. We show that if a is an automorphism of G of p-power order centralizing a Sylow p-group of G, then a is inner.

    更新日期:2020-09-23
  • Universal differentiability sets in Carnot groups of arbitrarily high step
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Andrea Pinamonti, Gareth Speight

    We show that any Carnot group \(\mathbb{G}\) with sufficiently many deformable directions contains a measure zero set N such that every Lipschitz map \(f:\mathbb{G}\rightarrow \mathbb{R}\) is differentiable at some point of N. We also prove that model filiform groups satisfy this condition, extending some previous results to a class of Carnot groups of arbitrarily high step. Essential to our work is

    更新日期:2020-09-23
  • A structure theorem for almost low-degree functions on the slice
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Nathan Keller, Ohad Klein

    The Fourier-Walsh expansion of a Boolean function f: {0, 1}n → {0, 1} is its unique representation as a multilinear polynomial. The Kindler-Safra theorem (2002) asserts that if in the expansion of f, the total weight on coefficients beyond degree k is very small, then f can be approximated by a Boolean-valued function depending on at most O(2k) variables. In this paper we prove a similar theorem for

    更新日期:2020-09-23
  • Slice Dirac operator over octonions
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Ming Jin, Guangbin Ren, Irene Sabadini

    The slice Dirac operator over octonions is a slice counterpart of the Dirac operator over quaternions. It involves a new theory of stem functions, which is the extension from the commutative O(1) case to the non-commutative O(3) case. For functions in the kernel of the slice Dirac operator over octonions, we establish the representation formula, the Cauchy integral formula (and, more in general, the

    更新日期:2020-09-23
  • Product systems of C*-correspondences and Takai duality
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Elias Katsoulis

    We establish the Hao–Ng isomorphism for generalized gauge actions of locally compact abelian groups on product systems over abelian lattice orders and we then use it to explore Takai duality in this context. As an application we generalize some recent work of Schafhauser.

    更新日期:2020-09-23
  • Complex interpolation of families of Orlicz sequence spaces
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Willian Hans Goes Corrêa

    We study the complex interpolation and derivation process induced by a family of Orlicz sequence spaces. We present a concrete example of an interpolation family of three spaces inducing a centralizer that cannot be obtained from complex interpolation of two spaces.

    更新日期:2020-09-23
  • The complete enumeration of 4-polytopes and 3-spheres with nine vertices
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Moritz Firsching

    We describe an algorithm to enumerate polytopes. This algorithm is then implemented to give a complete classification of combinatorial spheres of dimension 3 with 9 vertices and decide polytopality of those spheres. In order to decide polytopality, we generate polytopes by adding suitable points to polytopes with less than 9 vertices and therefore realize as many as possible of the combinatorial spheres

    更新日期:2020-09-23
  • Invariants related to the tree property
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Nicholas Ramsey

    We consider cardinal invariants related to Shelah’s model-theoretic tree properties and the relations that obtain between them. From strong colorings, we construct theories T with κcdt(T) > κsct(T) + κinp(T). We show that these invariants have distinct structural consequences, by investigating their effect on the decay of saturation in ultrapowers. This answers some questions of Shelah.

    更新日期:2020-09-23
  • Lipschitz free p -spaces for 0 < p < 1
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-23
    Fernando Albiac, José L. Ansorena, Marek Cúth, Michal Doucha

    This paper initiates the study of the structure of a new class of p-Banach spaces, 0

    更新日期:2020-09-23
  • Intersection of unit balls in classical matrix ensembles
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Zakhar Kabluchko, Joscha Prochno, Christoph Thäle

    We study the volume of the intersection of two unit balls from one of the classical matrix ensembles GOE, GUE and GSE, as the dimension tends to infinity. This can be regarded as a matrix analogue of a result of Schechtman and Schmuckenschläger for classical ℓp-balls [Schechtman and Schmuckenschläger, GAFA Lecture Notes, 1991]. The proof of our result is based on two ingredients, which are of independent

    更新日期:2020-09-02
  • Realizing ergodic properties in zero entropy subshifts
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Van Cyr, Bryna Kra

    A subshift with linear block complexity has at most countably many ergodic measures, and we continue the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity is arbitrarily close to linear but have uncountably many ergodic measures, we show that this behavior fails as soon as the block complexity is superlinear. With a different

    更新日期:2020-09-02
  • Structure theorems in tame expansions of o-minimal structures by a dense set
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Pantelis E. Eleftheriou, Ayhan Günaydin, Philipp Hieronymi

    We study sets and groups definable in tame expansions of o-minimal structures. Let \(\widetilde{\cal M} = \left\langle {{\cal M},P} \right\rangle \) be an expansion of an o-minimal \({\cal L}\)-structure \({\cal M}\) by a dense set P. We impose three tameness conditions on \(\widetilde{\cal M}\) and prove a structure theorem for definable sets and functions in analogy with the cell decomposition theorem

    更新日期:2020-09-02
  • Counting lattice points and weak admissibility of a lattice and its dual
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Niclas Technau, Martin Widmer

    We prove a counting theorem concerning the number of lattice points for the dual lattices of weakly admissible lattices in an inhomogeneously expanding box. The error term is expressed in terms of a certain function ν(Γ⊥, ·) of the dual lattice Γ⊥, and we carefully analyse the relation of this quantity with ν(Γ, ·). In particular, we show that ν(Γ⊥, ·) = ν(Γ, ·) for any unimodular lattice of rank 2

    更新日期:2020-09-02
  • Lyapunov exponents, holomorphic flat bundles and de Rham moduli space
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Matteo Costantini

    We consider Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We refine a lower bound obtained by Eskin, Kontsevich, Möller and Zorich showing that the sum of the first k exponents is greater than or equal to the sum of the degree of any rank k holomorphic subbundle of the flat bundle and the asymptotic degree of its equivariant developing

    更新日期:2020-09-02
  • Hall algebras and graphs of Hecke operators for elliptic curves
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Roberto Alvarenga

    The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms over a global function field. These graphs were introduced by Lorscheid in [16] for PGL2 and generalized to GLn in [1]. After reviewing some general properties, we explain the connection to the Hall algebra of the function field. In the case of an elliptic function field, we can use structure

    更新日期:2020-09-02
  • Quite free complicated abelian groups, pcf and Black Boxes
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Saharon Shelah

    We would like to build Abelian groups (or R-modules) which on the one hand are quite free, say ℵω+1-free, and on the other hand are complicated in a suitable sense. We choose as our test problem one having no nontrivial homomorphism to ℤ (known classically for ℵ1-free, recently for ℵn-free). We succeed to prove the existence of even \({\aleph _{{\omega _1} \cdot n}}\)-free ones. This requires building

    更新日期:2020-09-02
  • Domination, almost additivity, and thermodynamic formalism for planar matrix cocycles
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Balázs Bárány, Antti Käenmäki, Ian D. Morris

    In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of self-affine sets, and the theory of random matrix products, it has often been found useful to assume positivity of the matrix entries in order to simplify or make feasible certain types of calculation. It is natural to ask how positivity may be relaxed or generalised in a way which enables similar calculations

    更新日期:2020-09-02
  • Locally analytic representations in the étale coverings of the Lubin-Tate moduli space
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Mihir Sheth

    The Lubin-Tate moduli space \(X_0^{{\rm{rig}}}\) is a p-adic analytic open unit polydisc which parametrizes deformations of a formal group H0 of finite height defined over an algebraically closed field of characteristic p. It is known that the natural action of the automorphism group Aut(H0)on \(X_0^{{\rm{rig}}}\) gives rise to locally analytic representations on the topological duals of the spaces

    更新日期:2020-09-02
  • Almost everywhere convergence of spline sequences
    Isr. J. Math. (IF 0.894) Pub Date : 2020-09-02
    Paul F. X. Müller, Markus Passenbrunner

    We prove the analogue of the Martingale Convergence Theorem for polynomial spline sequences. Given a natural number k and a sequence (ti) of knots in [0, 1] with multiplicity ≤ k − 1, we let Pn be the orthogonal projection onto the space of spline polynomials in [0, 1] of degree k − 1 corresponding to the grid \(\left( {{t_i}} \right)_{i = 1}^n\). Let X be a Banach space with the Radon—Nikodým property

    更新日期:2020-09-02
  • Gelfand-Tsetlin theory for rational Galois algebras
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez, Pablo Zadunaisky

    In the present paper we study Gelfand-Tsetlin modules defined in terms of BGG differential operators. The structure of these modules is described with the aid of the Postnikov-Stanley polynomials introduced in [PS09]. These polynomials are used to identify the action of the Gelfand-Tsetlin subalgebra on the BGG operators. We also provide explicit bases of the corresponding Gelfand-Tsetlin modules and

    更新日期:2020-07-27
  • On Benjamini-Schramm limits of congruence subgroups
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Arie Levit

    A sequence of orbifolds corresponding to pairwise non-conjugate congruence lattices in a higher rank semisimple group over zero characteristic local fields is Benjamini-Schramm convergent to the universal cover.

    更新日期:2020-07-27
  • Finite groups, 2-generation and the uniform domination number
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Timothy C. Burness, Scott Harper

    Let G be a finite 2-generated non-cyclic group. The spread of G is the largest integer k such that for any nontrivial elements x1, …, xk, there exists y ∈ G such that G = 〈xi, y〉 for all i. The more restrictive notion of uniform spread, denoted u(G), requires y to be chosen from a fixed conjugacy class of G, and a theorem of Breuer, Guralnick and Kantor states that u(G) ⩾ 2 for every non-abelian finite

    更新日期:2020-07-27
  • Ergodicity and central limit theorem for random interval homeomorphisms
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Klaudiusz Czudek, Tomasz Szarek

    The central limit theorem for Markov chains generated by iterated function systems consisting of orientation-preserving homeomorphisms of the interval is proved. We study also ergodicity of such systems.

    更新日期:2020-07-27
  • Unconditional Schauder frames of translates in L p (ℝ d )
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Miguel Berasategui, Daniel Carando

    We show that, for 1 < p ≤ 2, the space Lp(ℝd) does not admit unconditional Schauder frames {fi, f′i}i∈ℕ where {fi} is a sequence of translates of finitely many functions and {f′i} is seminormalized. In fact, the only subspaces of Lp(ℝd) admitting such Banach frames are those isomorphic to ℓp. On the other hand, if 2 < p < +∞ and {λi}i∈ℕ ⊆ ℝd is an unbounded sequence, there is a subsequence {λi}i∈ℕ

    更新日期:2020-07-27
  • Metric properties of the product of consecutive partial quotients in continued fractions
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Lingling Huang, Jun Wu, Jian Xu

    In the one-dimensional Diophantine approximation, by using the continued fractions, Khintchine’s theorem and Jarnik’s theorem are concerned with the growth of the large partial quotients, while the improvability of Dirichlet’s theorem is concerned with the growth of the product of consecutive partial quotients. This paper aims to establish a complete characterization on the metric properties of the

    更新日期:2020-07-27
  • Boundedness of hyperbolic components of Newton maps
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Hongming Nie, Kevin M. Pilgrim

    We investigate boundedness of hyperbolic components in the moduli space of Newton maps. For quartic maps, (i) we prove hyperbolic components possessing two distinct attracting cycles each of period at least two are bounded, and (ii) we characterize the possible points on the boundary at infinity for some other types of hyperbolic components. For general maps, we prove hyperbolic components whose elements

    更新日期:2020-07-27
  • On subspaces spanned by freely independent random variables in noncommutative L p -spaces
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Yong Jiao, Fedor Sukochev, Dmitriy Zanin

    This paper deals with new phenomena appearing in the structure of Banach spaces arising in noncommutative integration theory. Let E be a fully symmetric Banach function space on [0, 1] and M be a finite von Neumann algebra. Let [xk] be the closed subspace spanned by a sequence (xk) of freely independent mean zero random variables from E(ℳ). The subspace [xk] is complemented in E(ℳ) if and only if the

    更新日期:2020-07-27
  • The Schur-Erdős problem for sesmi-algebraic colorings
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Jacob Fox, János Pach, Andrew Suk

    We consider m-colorings of the edges of a complete graph, where each color class is defined semi-algebraically with bounded complexity. The case m = 2 was first studied by Alon et al., who applied this framework to obtain surprisingly strong Ramsey-type results for intersection graphs of geometric objects and for other graphs arising in computational geometry. Considering larger values of m is relevant

    更新日期:2020-07-27
  • Quaternion distinguished generic representations of GL 2n
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-27
    Miyu Suzuki

    Let E/F be a quadratic extension of non-Archimedean local fields of characteristic 0. Let D be the unique quaternion division algebra over F and fix an embedding of E to D. Then, GLm(D) can be regarded as a subgroup of GL2m(E). Using the method of Matringe, we classify irreducible generic GLm(D)-distinguished representations of GL2m(E) in terms of Zelevinsky classification. Rewriting the classification

    更新日期:2020-07-27
  • Detecting structural properties of finite groups by the sum of element orders
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
    Marius Tărnăuceanu

    In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.

    更新日期:2020-07-08
  • Random walks on linear groups satisfying a Schubert condition
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
    Weikun He

    We study random walks on GLd(ℝ) whose proximal dimension r is larger than 1 and whose limit set in the Grassmannian Grr,d(ℝ) is not contained any Schubert variety. These random walks, without being proximal, behave in many ways like proximal ones. Among other results, we establish a Hölder-type regularity for the stationary measure on the Grassmannian associated to these random walks. Using this and

    更新日期:2020-07-08
  • On Erdős-Ginzburg-ZIV inverse theorems for dihedral and dicyclic groups
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
    Jun Seok Oh, Qinghai Zhong

    Let G be a finite group and exp(G) = lcm{ord(g) ∣ g ∈ G}. A finite unordered sequence of terms from G, where repetition is allowed, is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. We denote by s(G)(or E(G) respectively) the smallest integer ℓ such that every sequence of length at least ℓ has a product-one subsequence of length exp(G)(or

    更新日期:2020-07-08
  • Popular products and continued fractions
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
    Nikolay Moshchevitin, Brendan Murphy, Ilya Shkredov

    We prove bounds for the popularity of products of sets with weak additive structure, and use these bounds to prove results about continued fractions. Namely, considering Zaremba’s set modulo p, that is the set of all a such that \({a \over p} = [{a_1}, \ldots ,{a_s}]\) has bounded partial quotients, aj ⩽ M, we obtain a sharp upper bound for the cardinality of this set.

    更新日期:2020-07-08
  • Proof of the Kalai-Meshulam conjecture
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
    Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl

    Let G be a graph, and let fG be the sum of (−1)∣A∣, over all stable sets A. If G is a cycle with length divisible by three, then fG = ±2. Motivated by topological considerations, G. Kalai and R. Meshulam [8] made the conjecture that, if no induced cycle of a graph G has length divisible by three, then ∣fG∣ ≤ 1. We prove this conjecture.

    更新日期:2020-07-08
  • Families of superelliptic curves, complex braid groups and generalized Dehn twists
    Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
    Filippo Callegaro, Mario Salvetti

    We consider the universal family Edn of superelliptic curves: each curve Σdn in the family is a d-fold covering of the unit disk, totally ramified over aset P of n distinct points; \(\Sigma _n^d \hookrightarrow E_n^d \to {{\rm{C}}_n}\) is a fiber bundle, where Cn is the configuration space of n distinct points. We find that Edn is the classifying space for the complex braid group of type B(d, d, n)

    更新日期:2020-07-08
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