Norm convergence of partial sums of H1 functions

AbstractA formula is given for assigning sums to divergent series where the ratio of adjacent terms varies slowly along the series. This formula consistş of a weighted average of partial sums and is shown to be a general formula which can be easily calculated using a simple recurrence relation. It appears to be more powerful than a repeated Aitken or Shankse1process as long as the transformed series remains divergent and it is also compared with the Padé approximants. It is demonstrated on a factorial series, on a nearly geometric divergent series and for the extrapolation of a velocity formula for small amplitudes of motion.

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On the variance of the maximum of partial sums of n-exchangeable random variables with applications

Journal of Applied Probability ◽

10.1017/s0021900200047252 ◽

1980 ◽

Vol 17 (02) ◽

pp. 432-439

Author(s):

A. A. Anis ◽

M. Gharib

Keyword(s):

General Formula ◽

Random Variables ◽

Partial Sums ◽

Direct Relevance ◽

Exchangeable Random Variables ◽

Hurst Effect

A general formula is obtained for the variance of the maximum of partial sums of n-exchangeable random variables, derived from a result of Spitzer's. The formula is applied in particular to obtain the variance of the maximum of adjusted rescaled partial sums of normal summands. This is of direct relevance to the Hurst effect.

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On the variance of the maximum of partial sums of n-exchangeable random variables with applications

Journal of Applied Probability ◽

10.2307/3213032 ◽

1980 ◽

Vol 17 (2) ◽

pp. 432-439

Author(s):

A. A. Anis ◽

M. Gharib

Keyword(s):

General Formula ◽

Random Variables ◽

Partial Sums ◽

Direct Relevance ◽

Exchangeable Random Variables ◽

Hurst Effect

A general formula is obtained for the variance of the maximum of partial sums of n-exchangeable random variables, derived from a result of Spitzer's. The formula is applied in particular to obtain the variance of the maximum of adjusted rescaled partial sums of normal summands. This is of direct relevance to the Hurst effect.

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A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space

Georgian Mathematical Journal ◽

10.1515/gmj.2011.0001 ◽

2011 ◽

Vol 18 (1) ◽

pp. 67-81

Author(s):

Ushangi Goginava

Keyword(s):

Fourier Series ◽

Hardy Space ◽

Weak Type ◽

Type Inequality ◽

Partial Sums ◽

Two Dimensional ◽

Fejér Means ◽

Weak Type Inequality

Abstract Define the two dimensional diagonal Sunouchi operator where S 2 n , 2 n ƒ and σ 2 n ƒ are the (2 n , 2 n )th cubic-partial sums and 2 n th Marcinkiewicz–Fejér means of a two-dimensional Walsh–Fourier series. The main aim of this paper is to prove that the operator is bounded from the Hardy space H 1/2 to the weak L 1/2 space and is not bounded from the Hardy space H 1/2 to the space L 1/2.

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A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces

Georgian Mathematical Journal ◽

10.1515/gmj-2018-0045 ◽

2019 ◽

Vol 26 (3) ◽

pp. 351-360

Author(s):

István Blahota ◽

Karoly Nagy ◽

Lars-Erik Persson ◽

George Tephnadze

Keyword(s):

Fourier Series ◽

Hardy Space ◽

Hardy Spaces ◽

Lebesgue Space ◽

Maximal Operators ◽

Partial Sums ◽

Boundedness Result

Abstract The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space {H_{p}} to the Lebesgue space {L_{p}} for all {0<p\leq 1} . We also prove that the result is sharp in a particular sense.

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Norm approximation by Taylor polynomials in Hardy and Bergman spaces

International Journal of Mathematics ◽

10.1142/s0129167x21500373 ◽

2021 ◽

pp. 2150037

Author(s):

Inyoung Park ◽

Jian Zhao ◽

Kehe Zhu

Keyword(s):

Unit Ball ◽

Bergman Spaces ◽

Weighted Bergman Spaces ◽

Partial Sums ◽

Taylor Polynomial ◽

Norm Convergence ◽

Positive Formula ◽

Hardy And Bergman Spaces ◽

Taylor Polynomials ◽

Norm Approximation

For positive [Formula: see text] and real [Formula: see text] let [Formula: see text] denote the weighted Bergman spaces of the unit ball [Formula: see text] introduced in [R. Zhao and K. Zhu, Theory of Bergman Spaces on the Unit Ball in [Formula: see text], Mémoires de la Société Mathématique de France, Vol. 115 (2008)]. It is well known that, at least in the case [Formula: see text], all functions in [Formula: see text] can be approximated in norm by their Taylor polynomials if and only if [Formula: see text]. In this paper we show that, for [Formula: see text] with [Formula: see text], we always have [Formula: see text] as [Formula: see text], where [Formula: see text] and [Formula: see text] is the [Formula: see text]th Taylor polynomial of [Formula: see text]. We also show that for every [Formula: see text] in the Hardy space [Formula: see text], [Formula: see text], we always have [Formula: see text] as [Formula: see text], where [Formula: see text]. This generalizes and improves a result in [J. McNeal and J. Xiong, Norm convergence of partial sums of [Formula: see text] functions, Internat. J. Math. 29 (2018) 1850065, 10 pp.].

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ON THE FOURTH MOMENT OF THE MAXIMUM OF PARTIAL SUMS OF $n$-EXCHANGEABLE RANDOM VARIABLES WITH APPLICATIONS

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.27.1996.4341 ◽

1997 ◽

Vol 27 (3) ◽

pp. 247-256

Author(s):

M. GHARIB

Keyword(s):

Time Series ◽

Stochastic Processes ◽

General Formula ◽

Random Variables ◽

Partial Sums ◽

Fourth Moment ◽

Direct Relevance ◽

Exchangeable Random Variables ◽

Reservoir Design

A general formula is obtained for the fourth moment of the maximum of partial sums of $n$-exchangeable random variables derived from a result of Spitzer. The formula is applied in particular to obtain the fourth moment of the maximum of adjusted partial sums of normal summands. This is of direct relevance to reservoir design and the analysis of the structure of stochastic processes and time series.

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The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2008.1053 ◽

2008 ◽

Vol 45 (3) ◽

pp. 321-331

Author(s):

István Blahota ◽

Ushangi Goginava

Keyword(s):

Fourier Series ◽

Hardy Space ◽

Maximal Operator ◽

Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

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X-ray Structure Refinement and Vibrational Spectroscopy of Ca8Gd2 (PO4)6 O2

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v12i10.5520 ◽

2013 ◽

Vol 12 (10) ◽

pp. 719-726

Author(s):

R. Ayadi ◽

Mohamed Boujelbene ◽

T. Mhiri

Keyword(s):

Solid State ◽

General Formula ◽

Vibrational Spectroscopy ◽

Powder Diffraction ◽

Infrared Spectra ◽

Solid State Reaction ◽

Structure Refinement ◽

Unit Cell ◽

Cell Group ◽

X Ray

The present paper is interested in the study of compounds from the apatite family with the general formula Ca10 (PO4)6A2. It particularly brings to light the exploitation of the distinctive stereochemistries of two Ca positions in apatite. In fact, Gd-Bearing oxyapatiteCa8 Gd2 (PO4)6O2 has been synthesized by solid state reaction and characterized by X-ray powder diffraction. The site occupancies of substituents is0.3333 in Gd and 0.3333 for Ca in the Ca(1) position and 0. 5 for Gd in the Ca (2) position. Besides, the observed frequencies in the Raman and infrared spectra were explained and discussed on the basis of unit-cell group analyses.

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Opportunities for treating opportunistic vaginal infections during pregnancy

GYNECOLOGY ◽

10.26442/2079-5696_19.6.11-15 ◽

2017 ◽

Vol 19 (6) ◽

pp. 11-15 ◽

Cited By ~ 1

Author(s):

T E Karapetyan ◽

V V Muravieva ◽

A S Ankirskaya ◽

L A Lyubasovskaya ◽

T V Priputnevich

Keyword(s):

Positive Result ◽

Pregnant Women ◽

Early Pregnancy ◽

Premature Birth ◽

Local Treatment ◽

Vaginal Infections ◽

Aerobic Vaginitis ◽

Early Gestation ◽

Early Stages ◽

Intrauterine Infections

The aim of the study was to evaluate the effectiveness of treatment of women with opportunistic vaginal infections during pregnancy. Materials and methods. A prospective cohort study included 330 pregnant women, of whom 151 were diagnosed with bacterial vaginosis (BV), 37 had aerobic vaginitis (AB), 109 had vulvovaginal candidiasis (VC), 20 had a combination of VC + BV. When carrying out antibiotic therapy in the early stages of pregnancy, the principle of local treatment was observed. Results. Most often (46.0%), vaginal infections were detected when women were treated early in pregnancy. In the treatment of BV in the early stages of pregnancy with antiseptic chlorhexidine, a positive result of therapy was noted in 97.6% of women. Therapy with metronidazole or clindamycin BV in women who applied in the II and III trimesters, gave a positive result, respectively, in 90.0% and 89.5% of cases. The course of therapy with chlorhexidine pregnant women with AB was effective in 91.7% of cases with treatment in the first trimester and 92.0% in treatment in the II and III trimesters. In the treatment of VC in early pregnancy, natamycin was effective in 95.0% of women. In the II and III trimesters, econazole treatment was successful in 88.2% and 88.6%, respectively. In the treatment of combination of BV + VC in early gestation, the complex course of chlorhexidine + natamycin was effective in 76.5% of women, in II and III trimesters Neo-Penotran Forte was effective in 93.8% of pregnant women. Relapses of vaginal infections were observed in 34 pregnant women (10.3%). Superinfection with fungi was noted in 9.3% of cases of BV treatment and in 8.1% of pregnant women with AB. Among women observed from early pregnancy, there were no cases of premature birth, manifestations of intrauterine infections were noted in 5.3% of newborns. At treatment in the II and III trimesters, premature birth was in 6.5% and 13.5% of women, and manifestations of intrauterine infections - in 15.3% of newborns. Thus, microbiological monitoring of timely detection and treatment of opportunistic vaginal infections in pregnant at-risk groups showed the advisability of treating these infections in early gestation.

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