Results 41 to 50 of about 3,883 (229)
Two Erdos problems on lacunary sequences: Chromatic number and Diophantine approximation
, 2007 Let ${n_k}$ be an increasing lacunary sequence, i.e., $n_{k+1}/n_k>1+r$ for some $r>0$. In 1987, P. Erdos asked for the chromatic number of a graph $G$ on the integers, where two integers $a,b$ are connected by an edge iff their difference $|a-b|$ is in ...
Peres, Yuval, Schlag, Wilhelm
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012 In this article, we introduce the lacunary difference sequence spaces w0(M, θ, Δnm, p, q), w1(M, θ, Δnm, p, q) and w∞(M, θ, Δnm, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define
Tripathy Binod Chandra, Dutta Hemen
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Star Discrepancy Bounds of Double Infinite Matrices induced by Lacunary Systems [PDF]
, 2014 In 2001 Heinrich, Novak, Wasilkowski and Wo\'zniakowski proved that the inverse of the star discrepancy satisfies $n(d,\varepsilon)\leq c_{\abs}d \varepsilon^{-2}$ by showing that there exists a set of points in $[0,1)^d$ whose star-discrepancy is ...
Löbbe, Thomas
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On Metric Ramsey-type Dichotomies
, 2002 The classical Ramsey theorem, states that every graph contains either a large clique or a large independent set. Here we investigate similar dichotomic phenomena in the context of finite metric spaces.
Bartal, Yair +3 more
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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The Cesáro Lacunary Ideal bounded linear operator of χ2 - of φ-statistical vector valued defined by a bounded linear operator of interval numbers [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2017 Let uv mn A be a sequence of bounded linear operators from a separable Banach metric space of (X , 0) into a Banach metric space (Y, 0). Suppose that φ ∈ Φ is a countable fundamental set of X and the ideal I - of subsets \mathbb{N} x \mathbb{N ...
Deepmala +2 more
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A pointwise ergodic theorem along return times of rapidly mixing systems
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3730-3748, December 2025.Abstract We introduce a new class of sparse sequences that are ergodic and pointwise universally L2$L^2$‐good for ergodic averages; that is, sequences along which the ergodic averages converge almost surely to the projection to invariant functions.
Sebastián Donoso +2 more
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Advanced Science, Volume 12, Issue 38, October 13, 2025.A small Pd nanocluster is successfully prepared within a ring‐shaped polyoxometalate via a mild solid‐state reduction process. The resulting surface‐exposed Pd nanocluster functions as a robust heterogeneous reusable catalyst, enabling highly chemoselective hydrogenation of substrates containing multiple reducible functional groups via selective ...
Rui Xi +8 more
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Ferrimagnetic Structure of 3C Pyrrhotite (Fe7S8) From Neutron Diffraction
Geochemistry, Geophysics, Geosystems, Volume 26, Issue 9, September 2025.Abstract Pyrrhotite is a paleomagnetically important magnetic mineral in many geological settings. It forms numerous polytypes with different stacking patterns of the NiAs structure along the crystallographic c axis to produce different vacancy‐ordered superstructures.
Chin‐Wei Wang +2 more
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ChemCatChem, Volume 17, Issue 15, August 7, 2025.The computational study, sustained by experimental data, of the catalytic activity of [PW11O39{Zn(H2O)}]5− in CO2 cycloaddition to epoxide highlights how the carbonic anhydrase‐like character of this complex couples to the versatile binding properties of the polyoxometalate in this reaction pathway. Abstract The intertwined experimental and theoretical
Jingjing Ren +3 more
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