Comptes Rendus Mathematique最新文献_第5页

On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations 非线性漂移扩散方程的平方根近似有限体积格式

4区数学

Comptes Rendus Mathematique Pub Date : 2023-02-01 DOI: 10.5802/crmath.421

Clément Cancès, Juliette Venel

引用次数: 2

Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms 各向异性简单体和棱镜上的Brezzi-Douglas-Marini插值

4区数学

Comptes Rendus Mathematique Pub Date : 2023-01-12 DOI: 10.5802/crmath.424

Volker Kempf

引用次数: 0

Addendum to the paper: Compact embedded minimal surfaces in the Berger sphere 论文的附录:伯杰球中的致密嵌入最小表面

4区数学

Comptes Rendus Mathematique Pub Date : 2023-01-12 DOI: 10.5802/crmath.403

Heayong Shin, Young Wook Kim, Sung-Eun Koh, Hyung Yong Lee, Seong-Deog Yang

引用次数: 0

On uniform controllability of 1D transport equations in the vanishing viscosity limit 粘性消失极限下一维输运方程的均匀可控性

4区数学

Comptes Rendus Mathematique Pub Date : 2023-01-12 DOI: 10.5802/crmath.405

Camille Laurent, Matthieu Léautaud

引用次数: 5

Further Equivalent Binomial Sums 进一步等价二项式和

IF 0.8 4区数学

Comptes Rendus Mathematique Pub Date : 2021-05-27 DOI: 10.5802/CRMATH.184

M. Bai, W. Chu

{"title":"Further Equivalent Binomial Sums","authors":"M. Bai, W. Chu","doi":"10.5802/CRMATH.184","DOIUrl":"https://doi.org/10.5802/CRMATH.184","url":null,"abstract":"Five binomial sums are extended by a free parameter m, that are shown, through the generating function method, to have the same value. These sums generalize the ones by Ruehr (1980), who discovered them in the study of two unexpected equalities between definite integrals. 2020 Mathematics Subject Classification. 11B65, 05A10. Manuscript received 22nd December 2020, revised and accepted 2nd February 2021. In 1980, Kimura [14] proposed a monthly problem about two curious identities of definite integrals. If f is continuous on [− 1 2 , 3 2 ], then for δ= 0, 1, prove that ∫ 3 2 − 2 x f ( 3x −2x3)dx = 2∫ 1 0 x f ( 3x −2x3)dx. In his (trigonometric) proof, Ruehr [14] observed by linearity that to prove these identities, it is enough to verify them for monomials f (x) = xn . This led him to discover the following interesting identities An =Cn and Bn = Dn , where for a natural number n, the four binomial sums are defined by An = n ∑ j=0 3 j ( 3n − j 2n ) , Bn = n ∑ j=0 2 j ( 3n +1 2n + j +1 ) , Cn = 2n ∑ j=0 (−3) j ( 3n − j n ) , Dn = 2n ∑ j=0 (−4) j ( 3n +1 n + j +1 ) . ∗Corresponding author. ISSN (electronic) : 1778-3569 https://comptes-rendus.academie-sciences.fr/mathematique/ 422 Mei Bai and Wenchang Chu Allouche [1, 2] examined the related integrals and reviewed these identities in a more elegant manner. These identities were also reconfirmed by Meehan et al [16] who found, through the WZ-algorithm, that these four sequences satisfy also the common recurrence relation: X0 = 1 and Xn+1 = 27 4 Xn − 3 (3n+1 n ) 4(n +1) . By introducing a variable, Alzer and Prodinger [3] recently considered the polynomial analogues, that were also examined by Kilic–Arikan [13] through bijections. By applying the generating function approach to the binomial convolutions Ωn = n ∑ k=0 ( 3k k )( 3n −3k n −k ) the authors [4] not only confirmed the identities Ωn = An = Bn =Cn = Dn ; (1) but also found the two additional ones Ωn = En = Fn , (2)","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"80 1","pages":"421-425"},"PeriodicalIF":0.8,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90924742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the construction of the Śrī Yantra 关于Śrī Yantra的建设

IF 0.8 4区数学

Comptes Rendus Mathematique Pub Date : 2021-05-27 DOI: 10.5802/CRMATH.163

A. Chiodo

引用次数: 1

Linear dependence of quasi-periods over the rationals 拟周期对有理数的线性依赖

IF 0.8 4区数学

Comptes Rendus Mathematique Pub Date : 2021-05-27 DOI: 10.5802/CRMATH.171

K. S. Kumar

引用次数: 0

On a surprising instability result of Perfectly Matched Layers for Maxwell’s equations in 3D media with diagonal anisotropy 具有对角线各向异性的三维介质中麦克斯韦方程组的完美匹配层的惊人不稳定性结果