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Artykuły w czasopismach na temat „Remainder term”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

TAKAHASHI, FUTOSHI. "AN ISOPERIMETRIC INEQUALITY WITH REMAINDER TERM." Communications in Contemporary Mathematics 08, no. 03 (2006): 401–10. http://dx.doi.org/10.1142/s0219199706002167.

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We prove a version of the isoperimetric inequality for mappings with remainder term. Let S = (32π)1/3 and Q(u) = ∫R2 u · ux1 ∧ ux2dx for a mapping u : R2 → R3 in a function space [Formula: see text] defined below. Let [Formula: see text] be a set of functions in [Formula: see text] for which we have equality in the classical isoperimetric inequality S|Q(u)|2/3 ≤ ∫R2 |∇u|2dx. We show that for some positive constant C > 0, [Formula: see text] holds for any [Formula: see text]. Here, [Formula: see text] denotes the distance of u from [Formula: see text] in [Formula: see text].

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2

Dyda, Bartłomiej. "Fractional Hardy inequality with a remainder term." Colloquium Mathematicum 122, no. 1 (2011): 59–67. http://dx.doi.org/10.4064/cm122-1-6.

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3

Alvino, Angelo, Roberta Volpicelli, and Bruno Volzone. "On Hardy inequalities with a remainder term." Ricerche di Matematica 59, no. 2 (2010): 265–80. http://dx.doi.org/10.1007/s11587-010-0086-5.

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4

Stănilă, Elena-Dorina. "The Remainder Term in an Optimal Differentiation Formula." Results in Mathematics 53, no. 3-4 (2009): 445–52. http://dx.doi.org/10.1007/s00025-008-0356-7.

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5

CHANG, XIRONG, FENG DAI, and KUNYANG WANG. "Estimations of the remainder of spherical harmonic series." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 1 (2008): 243–55. http://dx.doi.org/10.1017/s030500410800131x.

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AbstractAn asymptotic estimate is obtained for the error in approximation of functions by partial sums of spherical harmonic expansions. The precise constant in the main term is found and the order of growth of the remainder term is given.

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6

Roginsky, Allen L. "A central limit theorem by remainder term for renewal processes." Advances in Applied Probability 24, no. 2 (1992): 267–87. http://dx.doi.org/10.2307/1427692.

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Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

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7

Behncke, Horst. "The remainder term in asymptotic summation of linear difference systems." Journal of Difference Equations and Applications 19, no. 5 (2013): 850–62. http://dx.doi.org/10.1080/10236198.2012.697160.

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8

Schira, Thomas. "The remainder term for analytic functions of Gauss-Lobatto quadratures." Journal of Computational and Applied Mathematics 76, no. 1-2 (1996): 171–93. http://dx.doi.org/10.1016/s0377-0427(96)00100-8.

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9

Cuomo, Salvatore, and Adamaria Perrotta. "On best constants in Hardy inequalities with a remainder term." Nonlinear Analysis: Theory, Methods & Applications 74, no. 16 (2011): 5784–92. http://dx.doi.org/10.1016/j.na.2011.05.069.

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10

Roginsky, Allen L. "A central limit theorem by remainder term for renewal processes." Advances in Applied Probability 24, no. 02 (1992): 267–87. http://dx.doi.org/10.1017/s0001867800047522.

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Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

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11

Schira, Thomas. "The remainder term for analytic functions of symmetric Gaussian quadratures." Mathematics of Computation 66, no. 217 (1997): 297–311. http://dx.doi.org/10.1090/s0025-5718-97-00798-9.

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12

Foust, Henry. "An Adaptive Time Step Scheme based on Taylor's Remainder Term." Journal of Management Science and Business Intelligence 1, no. 1 (2016): 53–61. https://doi.org/10.5281/zenodo.376751.

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An adaptive time step method was developed based on the Taylor series remainder term associated with Euler’s method, which is utilized to solve initial value problems involving ordinary differential equations. The accuracy and stability of the developed method was determined for three test cases where one of the test cases was stiff. It is also show that the accuracy of the developed method compares well with Runge Kutta 2. In future research, this method will be applied to explicit and implicit versions of Runge Kutta 2 to include Calahan’s method, which is a variation of the Rosenbrock’s sch

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13

Nair, Kumari Sreeja S. "Rapidly Convergent Series from Positive Term Series." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 3 (2023): 79–86. http://dx.doi.org/10.17762/ijritcc.v11i3.6204.

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In this paper we shall give description about the extraction of a rapidly decaying remainder from Euler series and telescoping series. Then we apply the procedure to generalised telescoping series. The new positive term series obtained with rapidly decaying remainder will converge faster than the original series. We shall apply the procedure to generalised telescoping series also. The introduction of such remainder will give a better approximation for the series.

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14

Petrova, Tatiana Nikolaevna, Olga Nikolaevna Krasnorutsky, and Daniel Yuryevich Bugrimov. "Morphofunctional state estimation of the thyroid remainder after thyroid gland resection." Journal of Experimental and Clinical Surgery 4, no. 1 (2011): 118–21. http://dx.doi.org/10.18499/2070-478x-2011-4-1-118-121.

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The morphofunctional dynamics of the thyroid remainder after the thyroid gland resection on occasion the colloid goiter are considered and analysed. The technique of the patients rehabilitation in early postoperation term including the complexes therapy of multivitaminous complex Vitrum with combination of correction the hormonal status is proposed. The application of rehabilitation scheme in comparison with traditional observation after operating term permits to prevent the development of postoperation complication to reduce the term of temporal invalidity and to improve the quality life of t

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15

Sitaramachandrarao, R. "An integral involving the remainder term in the Piltz divisor problem." Acta Arithmetica 48, no. 1 (1987): 89–92. http://dx.doi.org/10.4064/aa-48-1-89-92.

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16

Lau, Yuk-Kam, and Kai-Man Tsang. "Mean square of the remainder term in the Dirichlet divisor problem." Journal de Théorie des Nombres de Bordeaux 7, no. 1 (1995): 75–92. http://dx.doi.org/10.5802/jtnb.131.

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17

Alvino, Angelo, Roberta Volpicelli, and Adele Ferone. "Sharp Hardy inequalities in the half space with trace remainder term." Nonlinear Analysis: Theory, Methods & Applications 75, no. 14 (2012): 5466–72. http://dx.doi.org/10.1016/j.na.2012.04.051.

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18

Kaczorowski, Jerzy, and Kazimierz Wiertelak. "Oscillations of the remainder term related to the Euler totient function." Journal of Number Theory 130, no. 12 (2010): 2683–700. http://dx.doi.org/10.1016/j.jnt.2010.06.010.

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19

Milovanović, Gradimir V., Miodrag M. Spalević, and Miroslav S. Pranić. "On the remainder term of Gauss–Radau quadratures for analytic functions." Journal of Computational and Applied Mathematics 218, no. 2 (2008): 281–89. http://dx.doi.org/10.1016/j.cam.2007.01.037.

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20

Berkane, D., O. Bordellès, and O. Ramaré. "Explicit upper bounds for the remainder term in the divisor problem." Mathematics of Computation 81, no. 278 (2011): 1025–51. http://dx.doi.org/10.1090/s0025-5718-2011-02535-4.

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21

Abdellaoui, Boumediene, Ireneo Peral, and Ana Primo. "A remark on the fractional Hardy inequality with a remainder term." Comptes Rendus Mathematique 352, no. 4 (2014): 299–303. http://dx.doi.org/10.1016/j.crma.2014.02.003.

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22

Skrabutėnas, Rimantas. "The effective use of remainder term estimation in the limit theorems." Lietuvos matematikos rinkinys 43 (December 22, 2003): 79–83. http://dx.doi.org/10.15388/lmr.2003.32323.

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We investigate the asymptotic behavior of mean value of multiplicative arithmetic function from the class M1(G). In the present paper the asymptotic formula under special condition on prime elements of Knopfmacher’s semigroup G is obtained.

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23

Pahirya, M. M. "Evaluation of the remainder term for the Thiele interpolation continued fraction." Ukrainian Mathematical Journal 60, no. 11 (2008): 1813–22. http://dx.doi.org/10.1007/s11253-009-0171-7.

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24

Mahir, M. Sabzaliev, and M. Sabzalieva Ilhama. "Asymptotics of Solution of a Boundary Value Problem for Quasilinear Non-Classical Type Differential Equation of Arbitrary Odd Order." British Journal of Mathematics & Computer Science 22, no. 4 (2017): 1–19. https://doi.org/10.9734/BJMCS/2017/33704.

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In a rectangle domain, a boundary value problem is considered for a singularly perturbed quasilinear non-classical type equation of arbitrary odd order, degenerating into a hyperbolic equation. Asymptotic expansion of the generalized solution of the problem under consideration is constructed to within any positive degree of a small parameter, and the residual term is estimated.

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25

Shutov, Anton Vladimirovich. "On some analogue of the Gelfond problem for Zeckendorf representations." Chebyshevskii Sbornik 25, no. 5 (2025): 195–215. https://doi.org/10.22405/2226-8383-2024-25-5-195-215.

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A.O. Gelfond proved that if 𝑏−1 and 𝑑 are coprime, the sums of digits of the 𝑏-ary expressions of natural numbers are uniformly distributed over arithmetic progressions with difference 𝑑. He also obtained a power estimate for the remainder term in this problem.We consider an analogue of Gelfond’s problem for Zeckendorf representations of naturals as a sum of Fibonacci numbers. It is shown that in this case we again have the uniform distribution of the sums of digits over arithmetic progressions.Moreover, in the case when the difference of the arithmetic progression 𝑑 is equal to 2, it was prev

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26

Hashemi, Mir Sajjad, Mustafa Inc, and Somayeh Hajikhah. "Generalized squared remainder minimization method for solving multi-term fractional differential equations." Nonlinear Analysis: Modelling and Control 26, no. 1 (2021): 57–71. http://dx.doi.org/10.15388/namc.2021.26.20560.

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In this paper, we introduce a generalization of the squared remainder minimization method for solving multi-term fractional differential equations. We restrict our attention to linear equations. Approximate solutions of these equations are considered in terms of linearly independent functions. We change our problem into a minimization problem. Finally, the Lagrange-multiplier method is used to minimize the resultant problem. The convergence of this approach is discussed and theoretically investigated. Some relevant examples are investigated to illustrate the accuracy of the method, and obtaine

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27

Tsang, Kai-Man. "Mean square of the remainder term in the Dirichlet divisor problem II." Acta Arithmetica 71, no. 3 (1995): 279–99. http://dx.doi.org/10.4064/aa-71-3-279-299.

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28

Englund, G. "Addendum: A Remainder Term Estimate in a Random-Sum Central Limit Theorem." Theory of Probability & Its Applications 29, no. 1 (1985): 199. http://dx.doi.org/10.1137/1129028.

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29

Tolev, D. I. "On the remainder term in the circle problem in an arithmetic progression." Proceedings of the Steklov Institute of Mathematics 276, no. 1 (2012): 261–74. http://dx.doi.org/10.1134/s0081543812010233.

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30

Morris, Charles, and Ali Taheri. "On Weyl’s Asymptotics and Remainder Term for the Orthogonal and Unitary Groups." Journal of Fourier Analysis and Applications 24, no. 1 (2017): 184–209. http://dx.doi.org/10.1007/s00041-017-9522-1.

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31

Hamamoto, Naoki, and Futoshi Takahashi. "Sharp Hardy-Leray inequality for curl-free fields with a remainder term." Journal of Functional Analysis 280, no. 1 (2021): 108790. http://dx.doi.org/10.1016/j.jfa.2020.108790.

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32

Larson, Simon. "On the remainder term of the Berezin inequality on a convex domain." Proceedings of the American Mathematical Society 145, no. 5 (2016): 2167–81. http://dx.doi.org/10.1090/proc/13386.

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33

Carlen, Eric A. "A remainder term for Hölder’s inequality for matrices and quantum entropy inequalities." Archiv der Mathematik 109, no. 4 (2017): 365–71. http://dx.doi.org/10.1007/s00013-017-1066-8.

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34

Foster, D. M. E. "Estimates for a remainder term associated with the sum of digits function." Glasgow Mathematical Journal 29, no. 1 (1987): 109–29. http://dx.doi.org/10.1017/s001708950000673x.

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If q(≥2) is a fixed integer it is well known that every positive integer k may be expressed uniquely in the formWe introduce the ‘sum of digits’ functionBoth the above sums are of course finite. Although the behaviour of α(q, k) is somewhat erratic, its average behaviour is more regular and has been widely studied.

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35

Bezrodnykh, S. I., and O. V. Dunin-Barkovskaya. "Estimation of the Remainder Term of the Lauricella Series $$F^{(N)}_D$$." Mathematical Notes 116, no. 5-6 (2024): 905–19. https://doi.org/10.1134/s0001434624110038.

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36

Bezrodnykh, S. I., and O. V. Dunin-Barkovskaya. "Estimation of the Remainder Term of the Hypergeometric Series $$G_D^{(N,j)}$$." Mathematical Notes 117, no. 3-4 (2025): 513–29. https://doi.org/10.1134/s0001434625030174.

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37

Katz, Mikhail G., and Tahl Nowik. "A systolic inequality with remainder in the real projective plane." Open Mathematics 18, no. 1 (2020): 902–6. http://dx.doi.org/10.1515/math-2020-0050.

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Abstract The first paper in systolic geometry was published by Loewner’s student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric in the real projective plane. We prove a stronger version of Pu’s systolic inequality with a remainder term.

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38

Levendorskiĭ, S. Z. "Spectral asymptotics with a remainder estimate for Schrödinger operators with slowly growing potentials." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 4 (1996): 829–36. http://dx.doi.org/10.1017/s030821050002309x.

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39

ACU, ANA MARIA, and DANIEL FLORIN SOFONEA. "Asymptotic expressions for the remainder term in the quadrature formula of Gauss-Jacobi type." Creative Mathematics and Informatics 21, no. 1 (2012): 1–11. http://dx.doi.org/10.37193/cmi.2012.01.04.

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In this paper we have considered error analysis for a quadrature formula which is obtained by integration of linear positive operator. The asymptotic expressions for remainder term of Gauss-Jacobi type quadrature formula are also given.

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40

BARBOSU, DAN, and OVIDIU T. POP. "On the generalized Boolean sum Schurer-Stancu approximation formula." Creative Mathematics and Informatics 25, no. 2 (2016): 141–50. http://dx.doi.org/10.37193/cmi.2016.02.04.

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. In this paper, the Schurer-Stancu generalized Boolean sum (GBS, for short) approximation formula is considered and it’s remainder term is expressed in terms of bivariate divided differences. When the approximated function is sufficiently smooth, an upper bound estimation for the remainder term is also established. As particular cases, GBS Schurer and respectively GBS Bernstein approximation formulas are obtained and the expressions of their remainder are explicitly given.

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41

Pintz, J. "On the mean value of the remainder term of the prime number formula." Banach Center Publications 17, no. 1 (1985): 411–17. http://dx.doi.org/10.4064/-17-1-411-417.

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42

Kaczorowski, Jerzy. "On sign-changes in the remainder-term of the prime-number formula, II." Acta Arithmetica 45, no. 1 (1985): 65–74. http://dx.doi.org/10.4064/aa-45-1-65-74.

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43

Kaczorowski, Jerzy. "On sign-changes in the remainder-term of the prime-number formula, III." Acta Arithmetica 48, no. 4 (1987): 347–71. http://dx.doi.org/10.4064/aa-48-4-347-371.

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44

Kaczorowski, Jerzy. "On sign-changes in the remainder-term of the prime-number formula, IV." Acta Arithmetica 50, no. 1 (1988): 15–21. http://dx.doi.org/10.4064/aa-50-1-15-21.

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45

Lu, Wen Chao. "On the Elementary Proof of the Prime Number Theorem with a Remainder Term." Rocky Mountain Journal of Mathematics 29, no. 3 (1999): 979–1053. http://dx.doi.org/10.1216/rmjm/1181071619.

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46

Falk, Michael. "Weak convergence of the remainder term in the Bahadur representation of extreme quantiles." Statistics & Probability Letters 9, no. 1 (1990): 47–50. http://dx.doi.org/10.1016/0167-7152(90)90094-n.

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47

MICLAUS, DAN. "On the Stancu type bivariate approximation formula." Carpathian Journal of Mathematics 32, no. 1 (2016): 103–11. http://dx.doi.org/10.37193/cjm.2016.01.11.

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In the present paper we establish the form of remainder term associated to the bivariate approximation formula for Stancu type operators, using bivariate divided differences. We also shall establish an upper bound estimation for the remainder term, in the case when approximated function fulfills some given properties.

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48

Pahirya, Mykhaylo. "Application of a continuant to the estimation of a remainder term of Thiele's interpolation continued fraction." Ukrainian Mathematical Bulletin 16, no. 4 (2019): 588–603. http://dx.doi.org/10.37069/1810-3200-2019-16-4-9.

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New properties of a continuant has been proved. Using the relationship between the continuant and the continued fraction, an estimate of the remainder term of Thiele's interpolation continued fraction is obtained.

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49

Prajanto, Wahyu Adi, Zakiyah Ramhanti Farah, and Winarno Edy. "Robust Watermarking through Dual Band IWT and Chinese Remainder Theorem." Bulletin of Electrical Engineering and Informatics 7, no. 4 (2018): 561–69. https://doi.org/10.11591/eei.v7i4.690.

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CRT was a widely used algorithm in the development of watermarking methods. The algorithm produced good image quality but it had low robustness against compression and filtering. This paper proposed a new watermarking scheme through dual band IWT to improve the robustness and preserving the image quality. The high frequency sub band was used to index the embedding location on the low frequency sub band. In robustness test, the CRT method resulted average NC value of 0.7129, 0.4846, and 0.6768 while the proposed method had higher NC value of 0.7902, 0.7473, and 0.8163 in corresponding Gaussian

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50

Mihic, Ljubica. "The remainder term of Gauss-Radau quadrature rule with single and double end point." Publications de l'Institut Math?matique (Belgrade) 102, no. 116 (2017): 73–83. http://dx.doi.org/10.2298/pim161115002m.

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The remainder term of quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours for Gauss?Radau quadrature formula with the Chebyshev weight function of the second kind with double and single end point. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where the maximum modulus of the kernel is attained.

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