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Exactly solvable piecewise analytic double well potential $V_{D}(x)=min[(x+d)^2,(x-d)^2]$ and its dual single well potential $V_{S}(x)=max[(x+d)^2,(x-d)^2]$

Autor: Sasaki, Ryu

Publikováno v: Journal of Mathematical Physics 64 (2023) 022102

By putting two harmonic oscillator potential $x^2$ side by side with a separation $2d$, two exactly solvable piecewise analytic quantum systems with a free parameter $d>0$ are obtained. Due to the mirror symmetry, their eigenvalues $E$ for the even a

Externí odkaz: http://arxiv.org/abs/2209.09445

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ON THE INTEGRAL EQUATION $\mathrm{f}\left(\mathrm{x}\right)-(\mathrm{c}/\mathrm{L}(\mathrm{x}\left)\right){\int }_{0}^{\mathrm{L}\left(\mathrm{x}\right)}\mathrm{f}\left(\mathrm{y}\right)\mathrm{d}\mathrm{y}=\mathrm{g}\left(\mathrm{x}\right)$ WHERE L(x)=min{ax, 1}, a>1

Autor: PIILA, JYRKI, PITKÄRANTA, JUHANI

Publikováno v: The Journal of Integral Equations and Applications, 1996 Jul 01. 8(3), 363-378.

Externí odkaz: https://www.jstor.org/stable/26163175

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Exactly solvable piecewise analytic double well potential VD(x) = min[(x + d)², (x − d)²] and its dual single well potential VS(x) = max[(x + d)², (x − d)²].

Autor: Sasaki, Ryu¹ (AUTHOR) ryu@yukawa.kyoto-u.ac.jp

Publikováno v: Journal of Mathematical Physics. Feb2023, Vol. 64 Issue 2, p1-11. 11p.

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Erratum: Zhao, H.; Zhang, H.; Miao, C.; Ye, X.; Min, M. Linking Heat Source–Sink Landscape Patterns with Analysis of Urban Heat Islands: Study on the Fast-Growing Zhengzhou City in Central China. Remote Sens. 2018, 10, 1268

Autor: Hongbo Zhao, Hao Zhang, Changhong Miao, Xinyue Ye, Min Min

Publikováno v: Remote Sensing, Vol 12, Iss 18, p 2965 (2020)

The authors wish to make the following corrections to this paper [...]

Externí odkaz: https://doaj.org/article/f40b58c20fbb43518b622f360d450c7f

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Exactly solvable piecewise analytic double well potential VD(x) = min[(x + d)2, (x − d)2] and its dual single well potential VS(x) = max[(x + d)2, (x − d)2]

Autor: Ryu Sasaki

Publikováno v: Journal of Mathematical Physics. 64:022102

By putting two harmonic oscillator potentials x2 side by side with a separation 2 d, two exactly solvable piecewise analytic quantum systems with a free parameter d > 0 are obtained. Due to the mirror symmetry, their eigenvalues { E} for the even and

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::33f6058d5a488da006cee62e711e729a
https://doi.org/10.1063/5.0127371

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Erratum for the Research Article: "Long-acting MIC-1/GDF15 molecules to treat obesity: Evidence from mice to monkeys" by Y. Xiong, K. Walker, X. Min, C. Hale, T. Tran, R. Komorowski, J. Yang, J. Davda, N. Nuanmanee, D. Kemp, X. Wang, H. Liu, S. Miller, K. J. Lee, Z. Wang, M. M. Véniant.

Publikováno v: Science translational medicine [Sci Transl Med] 2018 Aug 29; Vol. 10 (456).

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City composition and accessibility statistics in and around Paris

Autor: Marie-Olive Thaury, Simon Genet, Léopold Maurice, Paola Tubaro, Sarah J. Berkemer

Publikováno v: Frontiers in Big Data, Vol 7 (2024)

IntroductionIs Paris a 15-min city, where inhabitants can access essential amenities such as schools and shops with a 15-min walk or bike ride? The concept of a 15-min (more generally, X-minute) city was launched in the French capital and was part of

Externí odkaz: https://doaj.org/article/ebdcd19238984b6392e8612a7658f389

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