Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation

Search Page

Filters

My Custom Filters

Results by year

Table representation of search results timeline featuring number of search results per year.

Year Number of Results
1964 1
1967 1
1971 1
1975 1
1981 1
1982 2
1985 1
1986 2
1987 2
1988 4
1989 3
1990 10
1991 12
1992 9
1993 13
1994 5
1995 7
1996 7
1997 9
1998 12
1999 20
2000 6
2001 14
2002 15
2003 4
2004 14
2005 6
2006 11
2007 16
2008 20
2009 24
2010 28
2011 31
2012 29
2013 27
2014 28
2015 35
2016 35
2017 39
2018 46
2019 43
2020 84
2021 73
2022 47
2023 56
2024 52
2025 33

Publication date

Text availability

Article attribute

Article type

Additional filters

Article Language

Species

Sex

Age

Other

Search Results

855 results

Results by year

Filters applied: . Clear all
Page 1
Benoit Mandelbrot (1924-2010).
Gomory R. Gomory R. Nature. 2010 Nov 18;468(7322):378. doi: 10.1038/468378a. Nature. 2010. PMID: 21085164 No abstract available.
Persistent currents and electronic properties of Mandelbrot quantum rings.
Tehrani DHT, Solaimani M. Tehrani DHT, et al. Sci Rep. 2023 Apr 7;13(1):5710. doi: 10.1038/s41598-023-32905-w. Sci Rep. 2023. PMID: 37029195 Free PMC article.
In this study, we investigate the persistent current, and electronic energy levels of Mandelbrot quantum rings. For this purpose, three types of Mandelbrot quantum rings are proposed. Furthermore, Mandelbrot equation is generalized by introducing parameter m, …
In this study, we investigate the persistent current, and electronic energy levels of Mandelbrot quantum rings. For this purpose, thr …
Zipf-Mandelbrot law, f-divergences and the Jensen-type interpolating inequalities.
Lovričević N, Pečarić Ð, Pečarić J. Lovričević N, et al. J Inequal Appl. 2018;2018(1):36. doi: 10.1186/s13660-018-1625-y. Epub 2018 Feb 8. J Inequal Appl. 2018. PMID: 29456419 Free PMC article.
Motivated by the method of interpolating inequalities that makes use of the improved Jensen-type inequalities, in this paper we integrate this approach with the well known Zipf-Mandelbrot law applied to various types of f-divergences and distances, such are Kullback-Leible …
Motivated by the method of interpolating inequalities that makes use of the improved Jensen-type inequalities, in this paper we integrate th …
A study of Mandelbrot and Julia Sets via Picard-Thakur iteration with s-convexity.
Nawaz B, Gdawiec K, Ullah K, Aphane M. Nawaz B, et al. PLoS One. 2025 Mar 21;20(3):e0315271. doi: 10.1371/journal.pone.0315271. eCollection 2025. PLoS One. 2025. PMID: 40117320 Free PMC article.
In this paper, we explore the formation of Mandelbrot and Julia sets using the Picard-Thakur iteration process, extended with s-convexity. ...Based on our proposed algorithms, we provide graphical illustrations of the Mandelbrot and Julia sets. Additionally, we exte …
In this paper, we explore the formation of Mandelbrot and Julia sets using the Picard-Thakur iteration process, extended with s-conve …
Tailoring angular momentum density via Mandelbrot fractal polarization singularities.
Wang Q, Zhao J, Li Y, Yin Z, Zeng J, Lü JQ, Xie X, Tu CH. Wang Q, et al. Opt Express. 2025 Jun 30;33(13):28189-28200. doi: 10.1364/OE.563450. Opt Express. 2025. PMID: 40798343 Free article.
Structured light with engineered polarization singularities (PSs) provides unprecedented control over spin and orbital angular momentum (SAM/OAM) densities; however, conventional PSs often exhibit limited spatial complexity for advanced light-matter interactions. We propose Ma …
Structured light with engineered polarization singularities (PSs) provides unprecedented control over spin and orbital angular momentum (SAM …
Zidovudine and breast-feeding.
Van de Perre P, Meda N, Cartoux M, Mandelbrot L, Leroy V, Dabis F, Salamon R. Van de Perre P, et al. AIDS Patient Care STDS. 1997 Feb;11(1):4-5. doi: 10.1089/apc.1997.11.4. AIDS Patient Care STDS. 1997. PMID: 11361730 No abstract available.
New Estimations for Shannon and Zipf-Mandelbrot Entropies.
Adil Khan M, Al-Sahwi ZM, Chu YM. Adil Khan M, et al. Entropy (Basel). 2018 Aug 16;20(8):608. doi: 10.3390/e20080608. Entropy (Basel). 2018. PMID: 33265697 Free PMC article.
Finally, we derive different estimations for the Zipf-Mandelbrot entropy (ZME) by using the new bounds of the Shannon entropy for the Zipf-Mandelbrot law (ZML). We also discuss particular cases and the bounds related to two different parametrics of the Zipf-Mande …
Finally, we derive different estimations for the Zipf-Mandelbrot entropy (ZME) by using the new bounds of the Shannon entropy for the …
Entropy Estimation Using a Linguistic Zipf-Mandelbrot-Li Model for Natural Sequences.
Back AD, Wiles J. Back AD, et al. Entropy (Basel). 2021 Aug 24;23(9):1100. doi: 10.3390/e23091100. Entropy (Basel). 2021. PMID: 34573725 Free PMC article.
This typically requires a large amount of data; however, we propose a new approach which is based on a new rank-based analytic Zipf-Mandelbrot-Li probabilistic model. Unlike previous approaches, which do not consider the nature of the probability distribution in relation t …
This typically requires a large amount of data; however, we propose a new approach which is based on a new rank-based analytic Zipf-Mande …
A strong construction of S-box using Mandelbrot set an image encryption scheme.
Aslam M, Beg S, Anjum A, Qadir Z, Khan S, Malik SUR, Mahmud MP. Aslam M, et al. PeerJ Comput Sci. 2022 Sep 9;8:e892. doi: 10.7717/peerj-cs.892. eCollection 2022. PeerJ Comput Sci. 2022. PMID: 36262157 Free PMC article.
A complex number-based S-box and a chaotic map diffusion are proposed to achieve high nonlinearity and low correlation. This study proposed a Mandelbrot set S-box construction based on the complex number and Chen chaotic map for resisting cryptanalytic attacks by creating …
A complex number-based S-box and a chaotic map diffusion are proposed to achieve high nonlinearity and low correlation. This study proposed …
855 results