Results 21 to 30 of about 4,252 (197)

Maximal functions with polynomial densities in lacunary directions [PDF]

Transactions of the American Mathematical Society, 2002
In the plane, the authors consider the maximal operator \[ M_p f(x_1,x_2)= \sup_{h>0, i,j\in\mathbb{Z}} {1\over h} \int^h_0|f(x_1- 2^i p(t),\;x_2- 2^j p(t))|dt, \] where a real one variable polynomial \(p(t)\) with \(p(0)= 0\) is given. They prove that \(M_p\) is bounded on \(L^p(\mathbb{R}^2)\) for \(q> 1\) with bounds that only depend on the degree ...
Kathryn E. Hare, Fulvio Ricci
openalex   +4 more sources

Application of f-lacunary statistical convergence to approximation theorems [PDF]

Journal of Inequalities and Applications, 2018
The concept of f-lacunary statistical convergence which is, in fact, a generalization of lacunary statistical convergence, has been introduced recently by Bhardwaj and Dhawan (Abstr. Appl. Anal. 2016:9365037, 2016).
Vinod K Bhardwaj, Shweta Dhawan
doaj   +2 more sources

Generalized Rough Cesaro and Lacunary Statistical Triple Difference Sequence Spaces in Probability of Fractional Order Defined by Musielak-Orlicz Function

International Journal of Analysis and Applications, 2018
We generalized the concepts in probability of rough Ces$\grave{a}$ro and lacunary statistical by introducing the difference operator $\Delta^{\alpha}_{\gamma}$ of fractional order, where $\alpha$ is a proper fraction and $\gamma=\left(\gamma_{mnk}\right)$
A. Esi, N. Subramanian
doaj   +5 more sources

Spatial distribution of 6s² lone electron pair in Pb₄Na(PO₄)₃ and stereochemical activity of the 6s² electron cloud in lead-bearing apatites. [PDF]

Acta Crystallogr B Struct Sci Cryst Eng Mater
In lacunary apatite structure‐type Pb4Na(PO4)3, residual density attributable to the deformed 6s2 electron cloud is found in the vicinity of A2‐site Pb2+ on regular A2 triangle normal to c. Systematic comparison on the size of the A2 triangle with other apatite‐type compounds indicates limited stereochemical activity of the orbital.Single crystals of ...
Hirano K, Okudera H.
europepmc   +2 more sources

Asymptotically Lacunary I-Invariant Statistical Equivalence of Sequences of Sets Defined By A Modulus Function

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018
Inthis paper, we introduce the concepts of strongly asymptotically lacunary I-invariant equivalence, f-asymptoticallylacunary I-invariant equivalence, strongly f-asymptotically lacunary I-invariant equivalence and asymptotically lacunary I-invariant ...
Erdinç Dundar, Nimet P. Akın, Uğur Ulusu   +2 more
doaj   +2 more sources

In Situ Observation of Polyoxometalate Formation by Vibrational Spectroscopy. [PDF]

Chemistry
In‐situ IR and Raman spectroscopy were employed to observe the formation of polyoxometalates (POMs) in aqueous solution. Thereby key intermediates were identified, and better understanding of POM formation enabled the development of an improved method for the synthesis of vanadium‐substituted phosphomolybdates, which are important catalysts for ...
Krueger JH, Raabe JC, Yusufzadeh Z, Berger A, Albert J, Poller MJ.   +5 more
europepmc   +2 more sources

Biomimetic Hierarchical Construction of Anti-Tumor Polyoxopalladates for Cancer Therapy. [PDF]

Angew Chem Int Ed Engl
Engineering of lacunary polyoxopalladates resulted in a hierarchical assembly that resembles the construction of biomacromolecules. An ordered structural evolution from monomer via dimer to supramolecular aggregates was achieved by cooperative covalent and supramolecular bonding effects, resulting in enhanced anti‐tumor activity via DNA damage ...
Zhao Y, Liu Z, Qin Z, Wen Q, Du J, Ren XY, Chen CQ, Peng X, Kortz U, Yang P.   +9 more
europepmc   +3 more sources

Recent Advances in Polyoxometalate‒Metal Nanocluster Hybrids. [PDF]

Chemistry
POMs are gaining attention in metal nanocluster synthesis for their ability to impart unique structural and functional roles. This review highlights recent advances in POM–metal nanocluster hybrids, categorized as follows: (a) hybrids of POMs and metal nanoclusters stabilized by organic ligands, (b) metal nanoclusters stabilized by POMs as ligands, and
Yonesato K, Yanai D, Yamaguchi K, Suzuki K.   +3 more
europepmc   +2 more sources

Fractional differentiation of functions with lacunary Fourier series [PDF]

Proceedings of the American Mathematical Society, 1968
Grant V. Welland
openalex   +3 more sources

Surface-Exposed Pd Nanocluster Confined within a Ring-Shaped Polyoxometalate for Selective Hydrogenation. [PDF]

Adv Sci (Weinh)
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 ...
Xi R, Yonesato K, Yatabe T, Koizumi Y, Kikkawa S, Yamazoe S, Harano K, Yamaguchi K, Suzuki K.   +8 more
europepmc   +2 more sources