Inhomogeneous Khintchine-Groshev theorem without monotonicity

Autor: Kim, Seongmin

The Khintchine-Groshev theorem in Diophantine approximation theory says that there is a dichotomy of the Lebesgue measure of sets of $\psi$-approximable numbers, given a monotonic function $\psi$. Allen and Ram\'irez removed the monotonicity conditio

Externí odkaz: http://arxiv.org/abs/2411.07932

A quantitative Khintchine-Groshev theorem for S-arithmetic Diophantine approximation

Autor: Han, Jiyoung

In his 1960 paper, Schmidt studied a quantitative type of Khintchine-Groshev theorem for general (higher) dimensions. Recently, a new proof of the theorem was found, which made it possible to relax the dimensional constraint and more generally, to ad

Externí odkaz: http://arxiv.org/abs/2205.06425

The Khintchine-Groshev Theorem for Planar Curves

Autor: Beresnevich, V. V., Bernik, V. I., Dickinson, H., Dodson, M. M.

Publikováno v: Proceedings: Mathematical, Physical and Engineering Sciences, 1999 Aug 01. 455(1988), 3053-3063.

Externí odkaz: https://www.jstor.org/stable/53469

The Llama 3 Herd of Models

Autor: Grattafiori, Aaron, Dubey, Abhimanyu, Jauhri, Abhinav, Pandey, Abhinav, Kadian, Abhishek, Al-Dahle, Ahmad, Letman, Aiesha, Mathur, Akhil, Schelten, Alan, Vaughan, Alex, Yang, Amy, Fan, Angela, Goyal, Anirudh, Hartshorn, Anthony, Yang, Aobo, Mitra, Archi, Sravankumar, Archie, Korenev, Artem, Hinsvark, Arthur, Rao, Arun, Zhang, Aston, Rodriguez, Aurelien, Gregerson, Austen, Spataru, Ava, Roziere, Baptiste, Biron, Bethany, Tang, Binh, Chern, Bobbie, Caucheteux, Charlotte, Nayak, Chaya, Bi, Chloe, Marra, Chris, McConnell, Chris, Keller, Christian, Touret, Christophe, Wu, Chunyang, Wong, Corinne, Ferrer, Cristian Canton, Nikolaidis, Cyrus, Allonsius, Damien, Song, Daniel, Pintz, Danielle, Livshits, Danny, Wyatt, Danny, Esiobu, David, Choudhary, Dhruv, Mahajan, Dhruv, Garcia-Olano, Diego, Perino, Diego, Hupkes, Dieuwke, Lakomkin, Egor, AlBadawy, Ehab, Lobanova, Elina, Dinan, Emily, Smith, Eric Michael, Radenovic, Filip, Guzmán, Francisco, Zhang, Frank, Synnaeve, Gabriel, Lee, Gabrielle, Anderson, Georgia Lewis, Thattai, Govind, Nail, Graeme, Mialon, Gregoire, Pang, Guan, Cucurell, Guillem, Nguyen, Hailey, Korevaar, Hannah, Xu, Hu, Touvron, Hugo, Zarov, Iliyan, Ibarra, Imanol Arrieta, Kloumann, Isabel, Misra, Ishan, Evtimov, Ivan, Zhang, Jack, Copet, Jade, Lee, Jaewon, Geffert, Jan, Vranes, Jana, Park, Jason, Mahadeokar, Jay, Shah, Jeet, van der Linde, Jelmer, Billock, Jennifer, Hong, Jenny, Lee, Jenya, Fu, Jeremy, Chi, Jianfeng, Huang, Jianyu, Liu, Jiawen, Wang, Jie, Yu, Jiecao, Bitton, Joanna, Spisak, Joe, Park, Jongsoo, Rocca, Joseph, Johnstun, Joshua, Saxe, Joshua, Jia, Junteng, Alwala, Kalyan Vasuden, Prasad, Karthik, Upasani, Kartikeya, Plawiak, Kate, Li, Ke, Heafield, Kenneth, Stone, Kevin, El-Arini, Khalid, Iyer, Krithika, Malik, Kshitiz, Chiu, Kuenley, Bhalla, Kunal, Lakhotia, Kushal, Rantala-Yeary, Lauren, van der Maaten, Laurens, Chen, Lawrence, Tan, Liang, Jenkins, Liz, Martin, Louis, Madaan, Lovish, Malo, Lubo, Blecher, Lukas, Landzaat, Lukas, de Oliveira, Luke, Muzzi, Madeline, Pasupuleti, Mahesh, Singh, Mannat, Paluri, Manohar, Kardas, Marcin, Tsimpoukelli, Maria, Oldham, Mathew, Rita, Mathieu, Pavlova, Maya, Kambadur, Melanie, Lewis, Mike, Si, Min, Singh, Mitesh Kumar, Hassan, Mona, Goyal, Naman, Torabi, Narjes, Bashlykov, Nikolay, Bogoychev, Nikolay, Chatterji, Niladri, Zhang, Ning, Duchenne, Olivier, Çelebi, Onur, Alrassy, Patrick, Zhang, Pengchuan, Li, Pengwei, Vasic, Petar, Weng, Peter, Bhargava, Prajjwal, Dubal, Pratik, Krishnan, Praveen, Koura, Punit Singh, Xu, Puxin, He, Qing, Dong, Qingxiao, Srinivasan, Ragavan, Ganapathy, Raj, Calderer, Ramon, Cabral, Ricardo Silveira, Stojnic, Robert, Raileanu, Roberta, Maheswari, Rohan, Girdhar, Rohit, Patel, Rohit, Sauvestre, Romain, Polidoro, Ronnie, Sumbaly, Roshan, Taylor, Ross, Silva, Ruan, Hou, Rui, Wang, Rui, Hosseini, Saghar, Chennabasappa, Sahana, Singh, Sanjay, Bell, Sean, Kim, Seohyun Sonia, Edunov, Sergey, Nie, Shaoliang, Narang, Sharan, Raparthy, Sharath, Shen, Sheng, Wan, Shengye, Bhosale, Shruti, Zhang, Shun, Vandenhende, Simon, Batra, Soumya, Whitman, Spencer, Sootla, Sten, Collot, Stephane, Gururangan, Suchin, Borodinsky, Sydney, Herman, Tamar, Fowler, Tara, Sheasha, Tarek, Georgiou, Thomas, Scialom, Thomas, Speckbacher, Tobias, Mihaylov, Todor, Xiao, Tong, Karn, Ujjwal, Goswami, Vedanuj, Gupta, Vibhor, Ramanathan, Vignesh, Kerkez, Viktor, Gonguet, Vincent, Do, Virginie, Vogeti, Vish, Albiero, Vítor, Petrovic, Vladan, Chu, Weiwei, Xiong, Wenhan, Fu, Wenyin, Meers, Whitney, Martinet, Xavier, Wang, Xiaodong, Wang, Xiaofang, Tan, Xiaoqing Ellen, Xia, Xide, Xie, Xinfeng, Jia, Xuchao, Wang, Xuewei, Goldschlag, Yaelle, Gaur, Yashesh, Babaei, Yasmine, Wen, Yi, Song, Yiwen, Zhang, Yuchen, Li, Yue, Mao, Yuning, Coudert, Zacharie Delpierre, Yan, Zheng, Chen, Zhengxing, Papakipos, Zoe, Singh, Aaditya, Srivastava, Aayushi, Jain, Abha, Kelsey, Adam, Shajnfeld, Adam, Gangidi, Adithya, Victoria, Adolfo, Goldstand, Ahuva, Menon, Ajay, Sharma, Ajay, Boesenberg, Alex, Baevski, Alexei, Feinstein, Allie, Kallet, Amanda, Sangani, Amit, Teo, Amos, Yunus, Anam, Lupu, Andrei, Alvarado, Andres, Caples, Andrew, Gu, Andrew, Ho, Andrew, Poulton, Andrew, Ryan, Andrew, Ramchandani, Ankit, Dong, Annie, Franco, Annie, Goyal, Anuj, Saraf, Aparajita, Chowdhury, Arkabandhu, Gabriel, Ashley, Bharambe, Ashwin, Eisenman, Assaf, Yazdan, Azadeh, James, Beau, Maurer, Ben, Leonhardi, Benjamin, Huang, Bernie, Loyd, Beth, De Paola, Beto, Paranjape, Bhargavi, Liu, Bing, Wu, Bo, Ni, Boyu, Hancock, Braden, Wasti, Bram, Spence, Brandon, Stojkovic, Brani, Gamido, Brian, Montalvo, Britt, Parker, Carl, Burton, Carly, Mejia, Catalina, Liu, Ce, Wang, Changhan, Kim, Changkyu, Zhou, Chao, Hu, Chester, Chu, Ching-Hsiang, Cai, Chris, Tindal, Chris, Feichtenhofer, Christoph, Gao, Cynthia, Civin, Damon, Beaty, Dana, Kreymer, Daniel, Li, Daniel, Adkins, David, Xu, David, Testuggine, Davide, David, Delia, Parikh, Devi, Liskovich, Diana, Foss, Didem, Wang, Dingkang, Le, Duc, Holland, Dustin, Dowling, Edward, Jamil, Eissa, Montgomery, Elaine, Presani, Eleonora, Hahn, Emily, Wood, Emily, Le, Eric-Tuan, Brinkman, Erik, Arcaute, Esteban, Dunbar, Evan, Smothers, Evan, Sun, Fei, Kreuk, Felix, Tian, Feng, Kokkinos, Filippos, Ozgenel, Firat, Caggioni, Francesco, Kanayet, Frank, Seide, Frank, Florez, Gabriela Medina, Schwarz, Gabriella, Badeer, Gada, Swee, Georgia, Halpern, Gil, Herman, Grant, Sizov, Grigory, Guangyi, Zhang, Lakshminarayanan, Guna, Inan, Hakan, Shojanazeri, Hamid, Zou, Han, Wang, Hannah, Zha, Hanwen, Habeeb, Haroun, Rudolph, Harrison, Suk, Helen, Aspegren, Henry, Goldman, Hunter, Zhan, Hongyuan, Damlaj, Ibrahim, Molybog, Igor, Tufanov, Igor, Leontiadis, Ilias, Veliche, Irina-Elena, Gat, Itai, Weissman, Jake, Geboski, James, Kohli, James, Lam, Janice, Asher, Japhet, Gaya, Jean-Baptiste, Marcus, Jeff, Tang, Jeff, Chan, Jennifer, Zhen, Jenny, Reizenstein, Jeremy, Teboul, Jeremy, Zhong, Jessica, Jin, Jian, Yang, Jingyi, Cummings, Joe, Carvill, Jon, Shepard, Jon, McPhie, Jonathan, Torres, Jonathan, Ginsburg, Josh, Wang, Junjie, Wu, Kai, U, Kam Hou, Saxena, Karan, Khandelwal, Kartikay, Zand, Katayoun, Matosich, Kathy, Veeraraghavan, Kaushik, Michelena, Kelly, Li, Keqian, Jagadeesh, Kiran, Huang, Kun, Chawla, Kunal, Huang, Kyle, Chen, Lailin, Garg, Lakshya, A, Lavender, Silva, Leandro, Bell, Lee, Zhang, Lei, Guo, Liangpeng, Yu, Licheng, Moshkovich, Liron, Wehrstedt, Luca, Khabsa, Madian, Avalani, Manav, Bhatt, Manish, Mankus, Martynas, Hasson, Matan, Lennie, Matthew, Reso, Matthias, Groshev, Maxim, Naumov, Maxim, Lathi, Maya, Keneally, Meghan, Liu, Miao, Seltzer, Michael L., Valko, Michal, Restrepo, Michelle, Patel, Mihir, Vyatskov, Mik, Samvelyan, Mikayel, Clark, Mike, Macey, Mike, Wang, Mike, Hermoso, Miquel Jubert, Metanat, Mo, Rastegari, Mohammad, Bansal, Munish, Santhanam, Nandhini, Parks, Natascha, White, Natasha, Bawa, Navyata, Singhal, Nayan, Egebo, Nick, Usunier, Nicolas, Mehta, Nikhil, Laptev, Nikolay Pavlovich, Dong, Ning, Cheng, Norman, Chernoguz, Oleg, Hart, Olivia, Salpekar, Omkar, Kalinli, Ozlem, Kent, Parkin, Parekh, Parth, Saab, Paul, Balaji, Pavan, Rittner, Pedro, Bontrager, Philip, Roux, Pierre, Dollar, Piotr, Zvyagina, Polina, Ratanchandani, Prashant, Yuvraj, Pritish, Liang, Qian, Alao, Rachad, Rodriguez, Rachel, Ayub, Rafi, Murthy, Raghotham, Nayani, Raghu, Mitra, Rahul, Parthasarathy, Rangaprabhu, Li, Raymond, Hogan, Rebekkah, Battey, Robin, Wang, Rocky, Howes, Russ, Rinott, Ruty, Mehta, Sachin, Siby, Sachin, Bondu, Sai Jayesh, Datta, Samyak, Chugh, Sara, Hunt, Sara, Dhillon, Sargun, Sidorov, Sasha, Pan, Satadru, Mahajan, Saurabh, Verma, Saurabh, Yamamoto, Seiji, Ramaswamy, Sharadh, Lindsay, Shaun, Feng, Sheng, Lin, Shenghao, Zha, Shengxin Cindy, Patil, Shishir, Shankar, Shiva, Zhang, Shuqiang, Wang, Sinong, Agarwal, Sneha, Sajuyigbe, Soji, Chintala, Soumith, Max, Stephanie, Chen, Stephen, Kehoe, Steve, Satterfield, Steve, Govindaprasad, Sudarshan, Gupta, Sumit, Deng, Summer, Cho, Sungmin, Virk, Sunny, Subramanian, Suraj, Choudhury, Sy, Goldman, Sydney, Remez, Tal, Glaser, Tamar, Best, Tamara, Koehler, Thilo, Robinson, Thomas, Li, Tianhe, Zhang, Tianjun, Matthews, Tim, Chou, Timothy, Shaked, Tzook, Vontimitta, Varun, Ajayi, Victoria, Montanez, Victoria, Mohan, Vijai, Kumar, Vinay Satish, Mangla, Vishal, Ionescu, Vlad, Poenaru, Vlad, Mihailescu, Vlad Tiberiu, Ivanov, Vladimir, Li, Wei, Wang, Wenchen, Jiang, Wenwen, Bouaziz, Wes, Constable, Will, Tang, Xiaocheng, Wu, Xiaojian, Wang, Xiaolan, Wu, Xilun, Gao, Xinbo, Kleinman, Yaniv, Chen, Yanjun, Hu, Ye, Jia, Ye, Qi, Ye, Li, Yenda, Zhang, Yilin, Zhang, Ying, Adi, Yossi, Nam, Youngjin, Yu, Wang, Zhao, Yu, Hao, Yuchen, Qian, Yundi, Li, Yunlu, He, Yuzi, Rait, Zach, DeVito, Zachary, Rosnbrick, Zef, Wen, Zhaoduo, Yang, Zhenyu, Zhao, Zhiwei, Ma, Zhiyu

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage

Externí odkaz: http://arxiv.org/abs/2407.21783

Classical metric Diophantine approximation revisited: the Khintchine-Groshev theorem

Autor: Beresnevich, Victor, Velani, Sanju

Publikováno v: Int. Math. Res. Not. 2010, No. 1, 69-86 (2010)

Under the assumption that the approximating function $\psi$ is monotonic, the classical Khintchine-Groshev theorem provides an elegant probabilistic criterion for the Lebesgue measure of the set of $\psi$-approximable matrices in $\R^{mn}$. The famou

Externí odkaz: http://arxiv.org/abs/0811.0809