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pro vyhledávání: '"Carlen P"'
Autor:
Zhang, Teng
In this paper, we give two new generalizations of Clarkson-McCarthy with several operators, which depends on the unitary orbit technique developed by Bourin, Hadamard Three-lines Theorem and the duality argument developed by Ball, Carlen and Lieb. Mo
Externí odkaz:
http://arxiv.org/abs/2410.12244
Autor:
Zhang, Haonan
In this paper we study the joint convexity/concavity of the trace functions \[ \Psi_{p,q,s}(A,B)=\text{Tr}(B^{\frac{q}{2}}K^*A^{p}KB^{\frac{q}{2}})^s,~~p,q,s\in \mathbb{R}, \] where $A$ and $B$ are positive definite matrices and $K$ is any fixed inve
Externí odkaz:
http://arxiv.org/abs/1811.01205
Akademický článek
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The Lane-Emden inequality controls $\iint_{\mathbb{R}^{2d}}\rho(x)\rho(y)|x-y|^{-\lambda}\,dx\,dy$ in terms of the $L^1$ and $L^p$ norms of $\rho$. We provide a remainder estimate for this inequality in terms of a suitable distance of $\rho$ to the m
Externí odkaz:
http://arxiv.org/abs/2410.20113
We study finite-dimensional open quantum systems whose density matrix evolves via a Lindbladian, $\dot{\rho}=-i[H,\rho]+{\mathcal D}\rho$. Here $H$ is the Hamiltonian of the isolated system and ${\mathcal D}$ is the dissipator. We consider the case w
Externí odkaz:
http://arxiv.org/abs/2408.06887
Akademický článek
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Autor:
Carlen, Eric A., Loss, Michael P.
We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the non Neumann entropy.
Comment: This version corrects several typos, includes a short discussion of cases of equality, and corrects a small
Comment: This version corrects several typos, includes a short discussion of cases of equality, and corrects a small
Externí odkaz:
http://arxiv.org/abs/2402.15920
In modeling phase transitions, it is useful to be able to connect diffuse interface descriptions of the dynamics with corresponding limiting sharp interface motions. In the case of the deep quench obstacle problem (DQOP) and surface diffusion (SD), w
Externí odkaz:
http://arxiv.org/abs/2312.11098
Autor:
Gemini Team, Anil, Rohan, Borgeaud, Sebastian, Alayrac, Jean-Baptiste, Yu, Jiahui, Soricut, Radu, Schalkwyk, Johan, Dai, Andrew M., Hauth, Anja, Millican, Katie, Silver, David, Johnson, Melvin, Antonoglou, Ioannis, Schrittwieser, Julian, Glaese, Amelia, Chen, Jilin, Pitler, Emily, Lillicrap, Timothy, Lazaridou, Angeliki, Firat, Orhan, Molloy, James, Isard, Michael, Barham, Paul R., Hennigan, Tom, Lee, Benjamin, Viola, Fabio, Reynolds, Malcolm, Xu, Yuanzhong, Doherty, Ryan, Collins, Eli, Meyer, Clemens, Rutherford, Eliza, Moreira, Erica, Ayoub, Kareem, Goel, Megha, Krawczyk, Jack, Du, Cosmo, Chi, Ed, Cheng, Heng-Tze, Ni, Eric, Shah, Purvi, Kane, Patrick, Chan, Betty, Faruqui, Manaal, Severyn, Aliaksei, Lin, Hanzhao, Li, YaGuang, Cheng, Yong, Ittycheriah, Abe, Mahdieh, Mahdis, Chen, Mia, Sun, Pei, Tran, Dustin, Bagri, Sumit, Lakshminarayanan, Balaji, Liu, Jeremiah, Orban, Andras, Güra, Fabian, Zhou, Hao, Song, Xinying, Boffy, Aurelien, Ganapathy, Harish, Zheng, Steven, Choe, HyunJeong, Weisz, Ágoston, Zhu, Tao, Lu, Yifeng, Gopal, Siddharth, Kahn, Jarrod, Kula, Maciej, Pitman, Jeff, Shah, Rushin, Taropa, Emanuel, Merey, Majd Al, Baeuml, Martin, Chen, Zhifeng, Shafey, Laurent El, Zhang, Yujing, Sercinoglu, Olcan, Tucker, George, Piqueras, Enrique, Krikun, Maxim, Barr, Iain, Savinov, Nikolay, Danihelka, Ivo, Roelofs, Becca, White, Anaïs, Andreassen, Anders, von Glehn, Tamara, Yagati, Lakshman, Kazemi, Mehran, Gonzalez, Lucas, Khalman, Misha, Sygnowski, Jakub, Frechette, Alexandre, Smith, Charlotte, Culp, Laura, Proleev, Lev, Luan, Yi, Chen, Xi, Lottes, James, Schucher, Nathan, Lebron, Federico, Rrustemi, Alban, Clay, Natalie, Crone, Phil, Kocisky, Tomas, Zhao, Jeffrey, Perz, Bartek, Yu, Dian, Howard, Heidi, Bloniarz, Adam, Rae, Jack W., Lu, Han, Sifre, Laurent, Maggioni, Marcello, Alcober, Fred, Garrette, Dan, Barnes, Megan, Thakoor, Shantanu, Austin, Jacob, Barth-Maron, Gabriel, Wong, William, Joshi, Rishabh, Chaabouni, Rahma, Fatiha, Deeni, Ahuja, Arun, Tomar, Gaurav Singh, Senter, Evan, Chadwick, Martin, Kornakov, Ilya, Attaluri, Nithya, Iturrate, Iñaki, Liu, Ruibo, Li, Yunxuan, Cogan, Sarah, Chen, Jeremy, Jia, Chao, Gu, Chenjie, Zhang, Qiao, Grimstad, Jordan, Hartman, Ale Jakse, Garcia, Xavier, Pillai, Thanumalayan Sankaranarayana, Devlin, Jacob, Laskin, Michael, Casas, Diego de Las, Valter, Dasha, Tao, Connie, Blanco, Lorenzo, Badia, Adrià Puigdomènech, Reitter, David, Chen, Mianna, Brennan, Jenny, Rivera, Clara, Brin, Sergey, Iqbal, Shariq, Surita, Gabriela, Labanowski, Jane, Rao, Abhi, Winkler, Stephanie, Parisotto, Emilio, Gu, Yiming, Olszewska, Kate, Addanki, Ravi, Miech, Antoine, Louis, Annie, Teplyashin, Denis, Brown, Geoff, Catt, Elliot, Balaguer, Jan, Xiang, Jackie, Wang, Pidong, Ashwood, Zoe, Briukhov, Anton, Webson, Albert, Ganapathy, Sanjay, Sanghavi, Smit, Kannan, Ajay, Chang, Ming-Wei, Stjerngren, Axel, Djolonga, Josip, Sun, Yuting, Bapna, Ankur, Aitchison, Matthew, Pejman, Pedram, Michalewski, Henryk, Yu, Tianhe, Wang, Cindy, Love, Juliette, Ahn, Junwhan, Bloxwich, Dawn, Han, Kehang, Humphreys, Peter, Sellam, Thibault, Bradbury, James, Godbole, Varun, Samangooei, Sina, Damoc, Bogdan, Kaskasoli, Alex, Arnold, Sébastien M. 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This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging fro
Externí odkaz:
http://arxiv.org/abs/2312.11805
Autor:
Carlen, Eric A.
We apply a duality method to prove an optimal stability theorem for the logarithmic Hardy-Littlewood-Sobolev inequality, and we apply it to the estimation of the rate of approach to equilibrium for the critical mass Keller-Segel system.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2312.00614