• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Jun Wang, Xiao Yao

Let f be a meromorphic function in the complex plane. A value θ ∈ [0, 2π) is called a Julia limiting direction of f if there is an unbounded sequence {zn} in the Julia set J(f) satisfying limn→∞ arg zn = θ (mod 2π). We denote by L(f) the set of all Julia limiting directions of f. Our main result is that, for any non-empty compact set E ⊆ [0, 2π) and ρ ∈ [0, ∞], there are an entire function f of infinite

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Sheldy Ombrosi, Carlos Pérez, Ezequiel Rela, Israel P. Rivera-Ríos

In this note we generalize the definition of the Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, Aweak∞ and Cp, in terms of BMO type spaces suited to them. We will provide as well some self improvement properties for some of those generalized BMO spaces and some quantitative estimates for Bloom’s BMO type spaces.

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Matija Bucić, Matthew Kwan, Alexey Pokrovskiy, Benny Sudakov, Tuan Tran, Adam Zsolt Wagner

How long a monotone path can one always find in any edge-ordering of the complete graph Kn? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n2/3-o(1)

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-07-07
Danijela Damjanović, Disheng Xu

We prove global smooth classification results for Anosov ℤk actions on general compact manifolds, under certain irreduciblity conditions and the presence of sufficiently many Anosov elements. In particular, we remove all the uniform control assumptions which were used in all the previous results towards the Katok-Spatzier global rigidity conjecture on general manifolds. The main idea is to create a

更新日期：2020-07-08
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
William Woods

Let p > 2 be a prime, k a finite field of characteristic p, and G a nilpotent-by-finite compact p-adic analytic group. Write kG for the completed group ring of G over k. We show that kG is a catenary ring.

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Sergei V. Kislyakov, Ilya K. Zlotnikov

Let (X, μ) be a space with a finite measure μ, let A and B be w*-closed subalgebras of L∞(μ), and let C and D be closed subspaces of Lp(μ) (1 < p < ∞) that are modules over A and B, respectively. Under certain additional assumptions, the couple (C ∩ D, C ∩ D ∩ L∞>(μ)) is K-closed in (Lp(μ), L∞(μ)). This statement covers, in particular, two cases analyzed previously: that of Hardy spaces on the two-dimensional

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Antonio Giambruno, Daniela La Mattina

In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T*-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Carl Bürger, Max Pitz

In 1978, Richard Rado showed that every edge-coloured complete graph of countably infinite order can be partitioned into monochromatic paths of different colours. He asked whether this remains true for uncountable complete graphs and a notion of generalised paths. In 2016, Daniel Soukup answered this in the affirmative and conjectured that a similar result should hold for complete bipartite graphs

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Junehyuk Jung

We prove Polterovich’s conjecture concerning the growth of the number of nodal domains for eigenfunctions on a unit square domain, under the assumption that the eigenfunctions do not have any singular points.

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Boris Bukh, Christopher Cox

How can d+k vectors in ℝd be arranged so that they are as close to orthogonal as possible? In particular, define θ(d, k) := minX maxx≠y∈X |〈x, y〉 | where the minimum is taken over all collections of d + k unit vectors X ⊆ ℝd. In this paper, we focus on the case here k is fixed and d → ∞. In establishing bounds on θ(d, k), we find an intimate connection to the existence of systems of $$\left(\begin{array}{c}k+1\\ 更新日期：2020-06-05 • Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05 Barbara Anna Balázs, Szabolcs Mészáros We prove an Amitsur–Levitzki-type theorem for Grassmann algebras, stating that the minimal degree of a standard identity that is a polynomial identity of the ring of n × n matrices over the m-generated Grassmann algebra is at least \(2\lfloor\frac{m}{2}\rfloor+4n-4$$ for all n, m ≥ 2 and this bound is sharp for m = 2,3 and any n ≥ 2. The arguments are purely combinatorial, based on computing sums of

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Juan Bès, Dimitris Papathanasiou

We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff’s operator also has this property on the space of complex-valued smooth functions on the real line.

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Andrey Gogolev, Boris Kalinin, Victoria Sadovskaya

We study the regularity of the conjugacy between an Anosov automorphism L of a torus and its small perturbation. We assume that L has no more than two eigenvalues of the same modulus and that L4 is irreducible over ℚ. We consider a volume-preserving C1-small perturbation f of L. We show that if Lyapunov exponents of f with respect to the volume are the same as Lyapunov exponents of L, then f is C1+Hölder

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-06-05
Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré

Extending the model of the interval, we explicitly define for each n ≥ 0 a free complete differential graded Lie algebra $$\mathfrak{L}_n$$ generated by the simplices of Δn, with desuspended degrees, in which the vertices are Maurer-Cartan elements and the differential extends the simplicial chain complex of the standard n-simplex. The family $$\{\mathfrak{L{_\bullet}}\}_{n\geq0}$$ is endowed with

更新日期：2020-06-05
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Richard Lechner, Pavlos Motakis, Paul F. X. Müller, Thomas Schlumprecht

We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach spaces in which the Haar system is strategically reproducible: multi-parameter Lebesgue spaces, mixed-norm Hardy spaces and most significantly the space

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Leo Margolis, Ofir Schnabel

Similarly to how the classical group ring isomorphism problem asks, for a commutative ring R, which information about a finite group G is encoded in the group ring RG, the twisted group ring isomorphism problem asks which information about G is encoded in all the twisted group rings of G over R. We investigate this problem over fields. We start with abelian groups and show how the results depend on

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Soumitra Ghara

Let Möb denote the group of biholomorphic automorphisms of the unit disc and (Möb · T) be the orbit of a Hilbert space operator T under the action of Möb. If the quotient , where is the similarity between two operators is a singleton, then the operator T is said to be weakly homogeneous. In this paper, we obtain a criterion to determine if the operator Mz of multiplication by the coordinate function

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Eliana Barriga

We study definably compact definably connected groups definable in a sufficiently saturated real closed field R. Our main result is that for such a kind of groups G that are also abelian, there is a Zariski-connected R-algebraic group H such that the o-minimal universal covering group of G is, up to a locally definable isomorphism, an open connected locally definable subgroup $$\mathcal{W}$$ of the

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Hidefumi Ohsugi, Akiyoshi Tsuchiya

Stanley introduced a lattice polytope $$\mathscr{C}_P$$ arising from a finite poset P, which is called the chain polytope of P. The geometric structure of $$\mathscr{C}_P$$ has good relations with the combinatorial structure of P. In particular, the Ehrhart polynomial of $$\mathscr{C}_P$$ is given by the order polynomial of P. In the present paper, associated to P, we introduce a lattice polytope ℰP

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Michael Lieberman, Jiří Rosický, Sebastien Vasey

Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from [LRV19b], we examine set-theoretic problems related to internal sizes and prove several Löwenheim–Skolem theorems for accessible categories. For example, assuming the singular cardinal hypothesis, we show that a large accessible category has an object in all

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Hezi Halawi, Avner Segal

In this paper, we study the reducibility of degenerate principal series of the simple, simply-connected exceptional group of type E6. Furthermore, we calculate the maximal semi-simple subrepresentation and quotient of these representations.

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Konrad Engel, Themis Mitsis, Christos Pelekis, Christian Reiher

Let n be an integer with n ≥ 2. A set A ⊆ ℝn is called an antichain (resp. weak antichain) if it does not contain two distinct elements x = (x1, …, xn) and y = (y1, …, yn) satisfying xi ≤ yi (resp. xi < yi) for all i ∈ {1, …, n}. We show that the Hausdorff dimension of a weak antichain A in the n-dimensional unit cube [0, 1]n is at most n − 1 and that the (n − 1)-dimensional Hausdorff measure of A

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Andreas Maurischat

This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative differential field which is finitely generated over its algebraically closed field of constants. We also introduce the notion of equivalence of iterative derivations on a

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-20
Moti Gitik

We deal with some questions related to κ-compact cardinals.

更新日期：2020-05-20
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Mahir Bilen Can, Yonah Cherniavsky

We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number of blocks, we introduce and investigate “Stirling posets.” As we show, the Stirling posets have a hierarchy and they glue together to give the whole set partition

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Anton A. Klyachko, Maria A. Ryabtseva

The Gordon-Rodriguez-Villegas theorem says that, in a finite group, the number of solutions to a system of coefficient-free equations is divisible by the order of the group if the rank of the matrix composed of the exponent sums of the j-th unknown in the i-th equation is less than the number of unknowns. We obtain analogues of this and similar facts for algebraic groups. In particular, our results

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Ilijas Farah, Ilan Hirshberg, Alessandro Vignati

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character ℵ1 embed into the Calkin algebra, Q(H). Together with other results, this shows that each of the following assertions is relatively consistent with ZFC: (i) Q(H) is a 2ℵ0-universal C*-algebra. (ii) There exists a 2ℵ0-universal C*-algebra, but Q(H) is not 2ℵ0-universal, (iii) A 2ℵ0-universal

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Cheryl E. Praeger, Jacqui Ramagge, George A. Willis

It is shown that a flat subgroup, H, of the totally disconnected, locally compact group G decomposes into a finite number of subsemigroups on which the scale function is multiplicative. The image, P, of a multiplicative semigroup in the quotient, H/H(1), of H by its uniscalar subgroup has a unique minimal generating set which determines a natural Cayley graph structure on P. For each compact, open

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Hailong Dao, Ilya Smirnov

Let (R, m) be a local ring of characteristic p > 0 and M a finitely generated R-module. In this note we consider the limit $$\mathop {\lim }\limits_{n \to \infty } \frac{{l(H_m^0({F^n}(M)))}}{{{p^{n\dim R}}}}$$ where F(-) is the Peskine-Szpiro functor. A consequence of our main results shows that the limit always exists when R is excellent, equidimensional and has an isolated singularity. Furthermore

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Will Grodzicki

We realize the non-split Bessel model of Novodvorsky and Piatetski-Shapiro in [22] as a generalized Gelfand-Graev representation of GSp(4), as suggested by Kawanaka in [17]. With uniqueness of the model already established in [22], we establish existence of a Bessel model for unramified principal series representations. We then connect the Iwahori-fixed vectors in the Bessel model to a linear character

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo

We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e., they have full density with respect to counting in balls for the word metric in the Cayley graph) and translation length grows linearly. We provide applications to a large class of relatively hyperbolic groups and graph products

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Sebastián Reyes-Carocca

In this article we study compact Riemann surfaces with a non-large group of automorphisms of maximal order, namely, compact Riemann surfaces of genus g with a group of automorphisms of order 4g–4. Under the assumption that g–1 is prime, we provide a complete classification of them and determine isogeny decompositions of the corresponding Jacobian varieties.

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Udayan B. Darji, Kende Kalina, Márton Elekes, Viktor Kiss, Zoltán Vidnyánszky

In order to understand the structure of the “typical” element of a homeomorphism group, one has to study how large the conjugacy classes of the group are. When typical means generic in the sense of Baire category, this is well understood; see, e.g., the works of Glasner and Weiss, and Kechris and Rosendal. Following Dougherty and Mycielski we investigate the measure theoretic dual of this problem,

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-05-14
Samuel M. Corson

We prove that groups for which every countable subgroup is free (ℵ1-free groups) are n-slender, cm-slender, and lcH-slender. In particular, every homomorphism from a completely metrizable group to an ℵ1-free group has an open kernel. We also show that ℵ1-free abelian groups are lcHslender, which is especially interesting in light of the fact that some ℵ1-free abelian groups are neither n-slender nor

更新日期：2020-05-14
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Daniele Puglisi

Let Ω ⊆ ℝn be a non-empty open bounded set and h: Ω → ℝ be a non-negative continuous function. We prove that for any u ∈ C2(Ω) ∩ C1($$\overline{\Omega}$$) solution of the Monge–Ampère equation $${\rm{det}}(D^2u)=h\;\;{\rm{in}}\;\Omega,$$ , then ∇u satisfies the convex hull property: ∇u(Ω) ⊆ conv(∇u(∂Ω)).

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Iwona Chlebicka

Under various conditions on the data we analyze how the appearance of lower order terms affects the gradient estimates on solutions to a general nonlinear elliptic equation of the form $$- {\rm{div}}\;a\left( {x,Du} \right) + b\left( {x,u} \right) = \mu$$ with data μ not belonging to the dual of the natural energy space but to Lorentz/Morrey-type spaces. The growth of the leading part of the operator

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Philipp Lücke

We study partition properties for uncountable regular cardinals that arise by restricting partition properties defining large cardinal notions to classes of simply definable colourings. We show that both large cardinal assumptions and forcing axioms imply that there is a homogeneous closed unbounded subset of ω1 for every colouring of the finite sets of countable ordinals that is definable by a Σ1-formula

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Costantino Delizia, Urban Jezernik, Primož Moravec, Chiara Nicotera

We show that there is a positive constant δ < 1 such that the probability of satisfying either the 2-Engel identity [X1, X2, X2] = 1 or the metabelian identity [[X1, X2], [X3, X4]] = 1 in a finite group is either 1 or at most δ

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Christopher Goodrich, Carlos Lizama

We utilize a new definition for the fractional delta operator and prove that it is equivalent by translation to the more commonly used operator. By means of the convolution operation we demonstrate that this new operator is strongly connected to the positivity, monotonicity, and convexity of the functions on which it operates. We also analyze the case of compositions of discrete fractional operators

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Igor E. Chyzhykov

We propose a new approach for studying asymptotic behaviour of pth means of the logarithmic potential and classes of analytic and subharmonic functions in the unit disc. In particular, we generalize a criterion due to G. MacLane and L. Rubel of boundedness of the L2-norm of log |B|, where B is a Blaschke product, in several directions. We describe growth and decrease of pth means, p ∈ (1,∞), for nonpositive

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Sherwood Hachtman, Dima Sinapova

For an inaccessible cardinal κ, the super tree property (ITP) at κ holds if and only if κ is supercomact. However, just like the tree property, it can hold at successor cardinals. We show that ITP holds at the successor of the limit of ω many supercompact cardinals. Then we show that it can consistently hold at ℵω+1. We also consider a stronger principle, ISP and certain weaker variations of it. We

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Artem Dudko, Rostislav Grigorchuk

We study the question of whether or not it is possible to determine a finitely generated group G up to some notion of equivalence from the spectrum sp(G) of G. We show that the answer is “No” in a strong sense. As a first example we present the collection of amenable 4-generated groups Gω, ω ∈ {0, 1, 2}ℕ, constructed by the second author in 1984. We show that among them there is a continuum of pairwise

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Pablo Cubides Kovacsics, Françoise Delon

In this article we study definable functions in tame expansions of algebraically closed valued fields. For a given definable function we have two types of results: type (I), which hold in a neighborhood of infinity, and type (II), which hold locally for all but finitely many points in the domain of the function. In the first part of the article, we show type (I) and (II) results concerning factorizations

更新日期：2020-04-04
• Isr. J. Math. (IF 0.894) Pub Date : 2020-04-04
Yair Hayut, Asaf Karagila

We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the Axiom of Choice this is equivalent to measurability, but it is wellknown that Choice is necessary for the equivalence. Oddly enough, this central notion was never investigated on its own before. We prove a technical criterion for lifting elementary embeddings

更新日期：2020-04-04
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