More on correct condition to generalize monotonicity in <italic>L</italic><sup>1</sup>-convergence of sine series

2012 ◽  
Vol 42 (6) ◽  
pp. 593-602
Author(s):  
SongPing ZHOU
Keyword(s):  
Sine Series ◽  
Correct Condition ◽  
Generalize Monotonicity

scholarly journals Fractal fits to Riemann zeros

2007 ◽  
Vol 85 (4) ◽  
pp. 345-357 ◽  
Author(s):  
P B Slater
Keyword(s):  
Potential Model ◽  
Sine Series ◽  
Dominant Term ◽  
One Dimensional ◽  
Smooth Potential ◽  
Smooth Part ◽  
Least Squares Fit ◽  
The One ◽  
Higher Order Corrections ◽  
03.65 Sq

Wu and Sprung (Phys. Rev. E, 48, 2595 (1993)) reproduced the first 500 nontrivial Riemann zeros, using a one-dimensional local potential model. They concluded — as did van Zyl and Hutchinson (Phys. Rev. E, 67, 066211 (2003)) — that the potential possesses a fractal structure of dimension d = 3/2. We model the nonsmooth fluctuating part of the potential by the alternating-sign sine series fractal of Berry and Lewis A(x,γ). Setting d = 3/2, we estimate the frequency parameter (γ), plus an overall scaling parameter (σ) that we introduce. We search for that pair of parameters (γ,σ) that minimizes the least-squares fit Sn(γ,σ) of the lowest n eigenvalues — obtained by solving the one-dimensional stationary (nonfractal) Schrodinger equation with the trial potential (smooth plus nonsmooth parts) — to the lowest n Riemann zeros for n = 25. For the additional cases, we study, n = 50 and 75, we simply set σ = 1. The fits obtained are compared to those found by using just the smooth part of the Wu–Sprung potential without any fractal supplementation. Some limited improvement — 5.7261 versus 6.392 07 (n = 25), 11.2672 versus 11.7002 (n = 50), and 16.3119 versus 16.6809 (n = 75) — is found in our (nonoptimized, computationally bound) search procedures. The improvements are relatively strong in the vicinities of γ = 3 and (its square) 9. Further, we extend the Wu-Sprung semiclassical framework to include higher order corrections from the Riemann–von Mangoldt formula (beyond the leading, dominant term) into the smooth potential. PACS Nos.: 02.10.De, 03.65.Sq, 05.45.Df, 05.45.Mt

scholarly journals On the uniform convergence of double sine series

2009 ◽  
Vol 193 (1) ◽  
pp. 79-97 ◽  
Author(s):  
Péter Kórus ◽  
Ferenc Móricz
Keyword(s):  
Uniform Convergence ◽  
Sine Series

scholarly journals On Some Sufficient Conditions for L1-Convergence of Double Sine Series

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Xhevat Z. Krasniqi
Keyword(s):  
Sufficient Conditions ◽  
Two Dimensional ◽  
Double Sequences ◽  
Sine Series

Abstract In this paper we introduce some numerical classes of double sequences. Such classes are used to show some sufficient conditions for L1 −convergence of double sine series. This study partially extends very recent results of Leindler, and particularly those of Zhou, from single to two-dimensional sine series.

LEBESGUE INTEGRABILITY OF DOUBLE COSINE AND SINE SERIES

Analysis ◽  
1993 ◽  
Vol 13 (4) ◽  
pp. 321-350
Author(s):  
Ferenc Móricz
Keyword(s):  
Sine Series ◽  
Lebesgue Integrability

scholarly journals Prediction of solar activity on the basis of spectral characteristics of sunspot number

2004 ◽  
Vol 22 (6) ◽  
pp. 2239-2243 ◽  
Author(s):  
E. Echer ◽  
N. R. Rigozo ◽  
D. J. R. Nordemann ◽  
L. E. A. Vieira
Keyword(s):  
Solar Activity ◽  
Sunspot Number ◽  
Confidence Level ◽  
Spectral Characteristics ◽  
Solar Cycles ◽  
Sine Series ◽  
Maximum Peak ◽  
Spectral Components ◽  
Sunspot Series

Abstract. Prediction of solar activity strength for solar cycles 23 and 24 is performed on the basis of extrapolation of sunspot number spectral components. Sunspot number data during 1933-1996 periods (solar cycles 17-22) are searched for periodicities by iterative regression. The periods significant at the 95% confidence level were used in a sum of sine series to reconstruct sunspot series, to predict the strength of solar cycles 23 and 24. The maximum peak of solar cycles is adequately predicted (cycle 21: 158±13.2 against an observed peak of 155.4; cycle 22: 178

scholarly journals Torsional vibration of cracked carbon nanotubes with torsional restraints using Eringen’s nonlocal differential model

2018 ◽  
Vol 38 (1) ◽  
pp. 70-87 ◽  
Author(s):  
Mustafa Ö Yayli ◽  
Suheyla Y Kandemir ◽  
Ali E Çerçevik
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Torsional Vibration ◽  
Nonlocal Boundary ◽  
Coefficient Matrix ◽  
Vibration Frequencies ◽  
Sine Series ◽  
Differential Model ◽  
Fourier Sine ◽  
Fourier Sine Series

Free torsional vibration of cracked carbon nanotubes with elastic torsional boundary conditions is studied. Eringen’s nonlocal elasticity theory is used in the analysis. Two similar rotation functions are represented by two Fourier sine series. A coefficient matrix including torsional springs and crack parameter is derived by using Stokes’ transformation and nonlocal boundary conditions. This useful coefficient matrix can be used to obtain the torsional vibration frequencies of cracked nanotubes with restrained boundary conditions. Free torsional vibration frequencies are calculated by using Fourier sine series and compared with the finite element method and analytical solutions available in the literature. The effects of various parameters such as crack parameter, geometry of nanotubes, and deformable boundary conditions are discussed in detail.

On sine series with positive coefficients

1962 ◽  
Vol 80 (1) ◽  
pp. 382-383
Author(s):  
R. P. Boas
Keyword(s):  
Sine Series ◽  
Positive Coefficients
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