Results 81 to 90 of about 3,272,186 (195)
Discatenated and lacunary recurrences [PDF]
Notes on Number Theory and Discrete MathematicsRecursive sequences with gaps have been studied previously. This paper considers some elementary properties of such sequences where the gaps have been created on a regular basis from sequence to sequence – ‘discatenated’ (systematic gaps) and ‘lacunary’
Hakan Akkuş +3 more
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Extremal discrepancy behavior of lacunary sequences [PDF]
Monatshefte für Mathematik, 2014 In 1975 Walter Philipp proved the law of the iterated logarithm (LIL) for the discrepancy of lacunary sequences: for any sequence $(n_k)_{k \geq 1}$ satisfying the Hadamard gap condition $n_{k+1} / n_k \geq q > 1,~k \geq 1,$ we have $$ \frac{1}{4 \sqrt{2}} \leq \limsup_{N \to \infty} \frac{N D_N(\{ n_1 x \}, \dots, \{n_N x\})}{\sqrt{2 N \log \log N}}
Aistleitner, Christoph, Fukuyama, Katusi
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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
wiley +1 more source
On the fractional parts of lacunary sequences
MATHEMATICA SCANDINAVICA, 2006 In this paper, we prove that if $t_0, t_1, t_2, \dots$ is a lacunary sequence, namely, $t_{n+1}/t_n\geq 1+r^{-1}$ for each $n\geq 0$, where $r$ is a fixed positive number, then there are two positive constants $c(r)=\max(1-r, 2(3r+6)^{-2})$ and $\xi=\xi(t_0, t_1,\dots)$ such that the fractional parts $\{\xi t_n\}$, $n=0,1,2,\dots$, all belong to a ...
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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
wiley +1 more source
, 2014 The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space.
M. Aiyub
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Variations on strong lacunary quasi-Cauchy sequences
Journal of Nonlinear Sciences and Applications, 2016 We introduce a new function space, namely the space of Nθ (p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions for each positive integer p. Nθα(p)-ward continuity is also introduced and investigated for any fixed 0 < α ≤ 1, and for any fixed positive integer p. A real valued function f defined on a
Kaplan, Huseyin, Cakalli, Huseyin
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A metric discrepancy result for lacunary sequences [PDF]
Proceedings of the American Mathematical Society, 2012 In 1975, [Acta Arith. 26, 241--251 (1975; Zbl 0263.10020)] \textit{W. Philipp} proved the bounded law of the iterated logarithm (LIL) for the discrepancy of lacunary sequences. In 2008, the first author of the present paper under review developed a new technique to calculate the exact value of the limsup in the LIL for special lacunary sequences; it ...
Fukuyama, Katusi, Watada, Tetsujin
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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
wiley +1 more source