Acta Mathematica Hungarica最新文献

We study the Haagerup property of certain semigroup crossed products. Let P be a left Ore semigroup. Then P generates a group G. We assume that there is an action (alpha) of G on a unital ({rm C}^*)-algebra A. If A has an (alpha)-invariant state (tau) and (D^G_P) has a GP-invariant state, then (tau) induces a state (tau') on the reduced semigroup crossed product (Artimes_{alpha,r} P). If ((Artimes_{alpha,r} P,tau')) has the Haagerup property, then both ((A,tau)) and G have the Haagerup property. Conversely, the Haagerup property of ((A,tau)) implies that of ((Artimes_{alpha,r} P,tau')), when G is amenable.

We show it is consistent with (ZFC) that there is an everywhere Kurepa line which is order isomorphic to all of its dense (aleph_2)-dense suborders.Moreover, this Kurepa line does not contain any Aronszajn suborder.We also show it is consistent with (ZFC) that there is a minimal Kurepa line which does not contain any Aronszajn suborder.

For the Grassmann manifold (widetilde G_{n,4}) of oriented 4-planes in (mathbb{R}^{n}) nofull description of its cohomology ring with coefficients in the two element field (mathbb {Z}_{2})is available. It is known however that it contains a subring that can be identifiedwith a quotient of a polynomial ring by a certain ideal. Examining this quotientring by means of Gröbner bases we are able to determine the (mathbb {Z}_{2})-cup-length of (widetilde G_{n,4}) for (n=2^t,2^t-1,2^t-2)for all (t geq 4).

Consider a nonstandard multidimensional risk model in whichthe claim sizes from all lines of businesses, sharing a common claim-arrival renewalprocess, constitute a sequence of independent and identically distributednonnegative random vectors, the common inter-arrival times are assumed to bearbitrarily dependent and the dependence between claim size vectors and theirwaiting times are also allowed to be arbitrary. Moreover, the claim sizes fromdifferent lines of businesses are supposed to be extended negatively dependent.Under some mild conditions, this paper achieves some vector-type precise largedeviation formulae for aggregate claims of such multidimensional risk model in thepresence of dominatedly-varying claim sizes. The obtained results extend someexisting ones in the literature.

Based on work of P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba [5], we show that if a covering system has distinctsquarefree moduli, then the minimum modulus is at most 118. We also showthat in general the (k)-th smallest modulus in a covering system with distinct moduli (provided it is required for the covering) is bounded by an absolute constant.

The study aims to investigate the weak convergence of nearestneighbor random walks in one-dimensional space, with the assumption that thetransition probabilities tend towards a constant within the range ([ 0, 1/2 ]). Thepaper will demonstrate limit theorems based on the bias or balance of the randomwalk, utilizing the method of moments.

A Schmidt group is a non-nilpotent group whose every proper subgroup is nilpotent. A subgroup A of a group G is called OS-propermutablein G if there is a subgroup B such that (G = NG(A)B), where AB is a subgroup of G and A permutes with all Schmidt subgroups of B. We proved (p)-solubility of a group in which a Sylow (p)-subgroup is OS-propermutable, where (pgeq 7) 7. For (p < 7) all non-Abelian composition factors of such group are listed.

In [18], we showed that the Boolean prime ideal theorem ((mathsf{BPI})) suffices to prove the celebrated theorem of R. Ellis, which states: ``Every compact Hausdorff right topological semigroup has an idempotent element''. However, the natural and intriguing question of the status of the reverse implication remained open until now. We resolve this open problem in the setting of (mathsf{ZFA}) (Zermelo–Fraenkel set theory with atoms), namely we establish that Ellis' theorem does not imply (mathsf{BPI}) in (mathsf{ZFA}), and thus is strictly weaker than (mathsf{BPI}) in (mathsf{ZFA}). From the above paper, we also answer two more open questions and strengthen some theorems.

Typical results are:

1. Ellis' theorem is true in the Basic Fraenkel Model, and thus Ellis' theorem does not imply (mathsf{BPI}) in (mathsf{ZFA}).

2. In (mathsf{ZF}) (Zermelo–Fraenkel set theory without the Axiom of Choice ((mathsf{AC}))), if (S) is a compact Hausdorff right topological semigroup with (S) well orderable, then every left ideal of (S) contains a minimal left ideal and a minimal idempotent element. In addition, every such semigroup (S) has a maximal idempotent element.

3. In (mathsf{ZF}), if (S) is a compact Hausdorff right topological abelian semigroup, then every left ideal of (S) contains a minimal left ideal.

4. In (mathsf{ZF}), (mathsf{BPI}) implies ``Every compact Hausdorff right topological abelian semigroup (S) has a minimal idempotent element''.

5. In (mathsf{ZFA}), the Axiom of Multiple Choice ((mathsf{MC})) implies ``Every compact Hausdorff right topological abelian semigroup (S) has a minimal idempotent element''.

6. In (mathsf{ZFA}), (mathsf{MC}) implies ``Every compact Hausdorff right topological semigroup (S) with (S) linearly orderable, has a minimal idempotent element''.

A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat [1] and the Polymath REU (2020), continues to investigate representations of convex geometries with small convex dimension by convex shapes on the plane and in spaces of higher dimension. In particular, we answer in the negative the question raised by Polymath REU (2020): whether every convex geometry of convex dimension 3 is representable by circles on the plane. We show there are geometries of convex dimension 3 that cannot be represented by spheres in any (mathbb{R}^k), and this connects to posets not representable by spheres from the paper of Felsner, Fishburn and Trotter [44]. On the positive side, we use the result of Kincses [55] to show that every finite poset is an ellipsoid order.

Many remarkable results have been obtained on important problems combining arithmetic properties of the integers and some restricted conditions of their digits in a given base. Maynard considered the number of the polynomial values with missing digits and gave an asymptotic formula. In this paper we study truncated polynomials with restricted digits by using the estimates for character sums and exponential sums modulo prime powers. In the case where the polynomials are monomial we further give exact identities.