Sharp and improved regularity estimates for weighted quasilinear elliptic equations of $p-$Laplacian type and applications

Autor: da Silva, João Vitor, Prazeres, Disson dos, Ricarte, Gleydson, Sá, Ginaldo

In this manuscript, we obtain sharp and improved regularity estimates for weak solutions of weighted quasilinear elliptic models of Hardy-H\'{e}non-type, featuring an explicit regularity exponent depending only on universal parameters. Our approach i

Externí odkaz: http://arxiv.org/abs/2410.14862

A quantitative Gidas-Ni-Nirenberg-type result for the $p$-Laplacian via integral identities

Autor: Dipierro, Serena, da Silva, João Gonçalves, Poggesi, Giorgio, Valdinoci, Enrico

We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the $p$-Laplacian. Quantitative stability is achieved here via integral identities based on the proof of rigidity established by J. Serra in 2013, which extended t

Externí odkaz: http://arxiv.org/abs/2408.03522

The enigma of Li-rich giants and its relation with temporal variations observed in radial velocity and stellar activity signals

Autor: Rolo, Inês, Mena, Elisa Delgado, Tsantaki, Maria, da Silva, João Gomes

Publikováno v: A&A 688, A68 (2024)

Despite the large number of studies focused on the characterisation of Li-rich stars and understanding the mechanisms leading to such enrichment, their origin remains a mystery. Magnetic activity, particularly the phenomena usually associated with it

Externí odkaz: http://arxiv.org/abs/2406.12711

The PLATO Mission

Autor: Rauer, Heike, Aerts, Conny, Cabrera, Juan, Deleuil, Magali, Erikson, Anders, Gizon, Laurent, Goupil, Mariejo, Heras, Ana, Lorenzo-Alvarez, Jose, Marliani, Filippo, Martin-Garcia, César, Mas-Hesse, J. Miguel, O'Rourke, Laurence, Osborn, Hugh, Pagano, Isabella, Piotto, Giampaolo, Pollacco, Don, Ragazzoni, Roberto, Ramsay, Gavin, Udry, Stéphane, Appourchaux, Thierry, Benz, Willy, Brandeker, Alexis, Güdel, Manuel, Janot-Pacheco, Eduardo, Kabath, Petr, Kjeldsen, Hans, Min, Michiel, Santos, Nuno, Smith, Alan, Suarez, Juan-Carlos, Werner, Stephanie C., Aboudan, Alessio, Abreu, Manuel, a, Lorena Acu, Adams, Moritz, Adibekyan, Vardan, Affer, Laura, Agneray, François, Agnor, Craig, Børsen-Koch, Victor Aguirre, Ahmed, Saad, Aigrain, Suzanne, Al-Bahlawan, Ashraf, Gil, M de los Angeles Alcacera, Alei, Eleonora, Alencar, Silvia, Alexander, Richard, Alfonso-Garzón, Julia, Alibert, Yann, Prieto, Carlos Allende, Almeida, Leonardo, Sobrino, Roi Alonso, Altavilla, Giuseppe, Althaus, Christian, Trujillo, Luis Alonso Alvarez, Amarsi, Anish, Eiff, Matthias Ammler-von, Amôres, Eduardo, Andrade, Laerte, Antoniadis-Karnavas, Alexandros, António, Carlos, del Moral, Beatriz Aparicio, Appolloni, Matteo, Arena, Claudio, Armstrong, David, Aliaga, Jose Aroca, Asplund, Martin, Audenaert, Jeroen, Auricchio, Natalia, Avelino, Pedro, Baeke, Ann, Baillié, Kevin, Balado, Ana, Balagueró, Pau Ballber, Balestra, Andrea, Ball, Warrick, Ballans, Herve, Ballot, Jerome, Barban, Caroline, Barbary, Gaële, Barbieri, Mauro, Forteza, Sebasti Barceló, Barker, Adrian, Barklem, Paul, Barnes, Sydney, Navascues, David Barrado, Barragan, Oscar, Baruteau, Clément, Basu, Sarbani, Baudin, Frederic, Baumeister, Philipp, Bayliss, Daniel, Bazot, Michael, Beck, Paul G., Bedding, Tim, Belkacem, Kevin, Bellinger, Earl, Benatti, Serena, Benomar, Othman, Bérard, Diane, Bergemann, Maria, Bergomi, Maria, Bernardo, Pierre, Biazzo, Katia, Bignamini, Andrea, Bigot, Lionel, Billot, Nicolas, Binet, Martin, Biondi, David, Biondi, Federico, Birch, Aaron C., Bitsch, Bertram, Ceballos, Paz Victoria Bluhm, Bódi, Attila, Bognár, Zsófia, Boisse, Isabelle, Bolmont, Emeline, Bonanno, Alfio, Bonavita, Mariangela, Bonfanti, Andrea, Bonfils, Xavier, Bonito, Rosaria, Bonomo, Aldo Stefano, Börner, Anko, Saikia, Sudeshna Boro, Martín, Elisa Borreguero, Borsa, Francesco, Borsato, Luca, Bossini, Diego, Bouchy, Francois, Boué, Gwenaël, Boufleur, Rodrigo, Boumier, Patrick, Bourrier, Vincent, Bowman, Dominic M., Bozzo, Enrico, Bradley, Louisa, Bray, John, Bressan, Alessandro, Breton, Sylvain, Brienza, Daniele, Brito, Ana, Brogi, Matteo, Brown, Beverly, Brown, David J. A., Brun, Allan Sacha, Bruno, Giovanni, Bruns, Michael, Buchhave, Lars A., Bugnet, Lisa, Buldgen, Gaël, Burgess, Patrick, Busatta, Andrea, Busso, Giorgia, Buzasi, Derek, Caballero, José A., Cabral, Alexandre, Gomez, Juan-Francisco Cabrero, Calderone, Flavia, Cameron, Robert, Cameron, Andrew, Campante, Tiago, Gestal, Néstor Campos, Martins, Bruno Leonardo Canto, Cara, Christophe, Carone, Ludmila, Carrasco, Josep Manel, Casagrande, Luca, Casewell, Sarah L., Cassisi, Santi, Castellani, Marco, Castro, Matthieu, Catala, Claude, Fernández, Irene Catalán, Catelan, Márcio, Cegla, Heather, Cerruti, Chiara, Cessa, Virginie, Chadid, Merieme, Chaplin, William, Charpinet, Stephane, Chiappini, Cristina, Chiarucci, Simone, Chiavassa, Andrea, Chinellato, Simonetta, Chirulli, Giovanni, Christensen-Dalsgaard, Jørgen, Church, Ross, Claret, Antonio, Clarke, Cathie, Claudi, Riccardo, Clermont, Lionel, Coelho, Hugo, Coelho, Joao, Cogato, Fabrizio, Colomé, Josep, Condamin, Mathieu, García, Fernando Conde, Conseil, Simon, Corbard, Thierry, Correia, Alexandre C. M., Corsaro, Enrico, Cosentino, Rosario, Costes, Jean, Cottinelli, Andrea, Covone, Giovanni, Creevey, Orlagh L., Crida, Aurelien, Csizmadia, Szilard, Cunha, Margarida, Curry, Patrick, da Costa, Jefferson, da Silva, Francys, Dalal, Shweta, Damasso, Mario, Damiani, Cilia, Damiani, Francesco, Chagas, Maria Liduina das, Davies, Melvyn, Davies, Guy, Davies, Ben, Davison, Gary, de Almeida, Leandro, de Angeli, Francesca, de Barros, Susana Cristina Cabral, Leão, Izan de Castro, de Freitas, Daniel Brito, de Freitas, Marcia Cristina, De Martino, Domitilla, de Medeiros, José Renan, de Paula, Luiz Alberto, Gómez, Álvaro de Pedraza, de Plaa, Jelle, De Ridder, Joris, Deal, Morgan, Decin, Leen, Deeg, Hans, Innocenti, Scilla Degl, Deheuvels, Sebastien, del Burgo, Carlos, Del Sordo, Fabio, Delgado-Mena, Elisa, Demangeon, Olivier, Denk, Tilmann, Derekas, Aliz, Desert, Jean-Michel, Desidera, Silvano, Dexet, Marc, Di Criscienzo, Marcella, Di Giorgio, Anna Maria, Di Mauro, Maria Pia, Rial, Federico Jose Diaz, Díaz-García, José-Javier, Dima, Marco, Dinuzzi, Giacomo, Dionatos, Odysseas, Distefano, Elisa, Nascimento Jr., Jose-Dias do, Domingo, Albert, D'Orazi, Valentina, Dorn, Caroline, Doyle, Lauren, Duarte, Elena, Ducellier, Florent, Dumaye, Luc, Dumusque, Xavier, Dupret, Marc-Antoine, Eggenberger, Patrick, Ehrenreich, David, Eigmüller, Philipp, Eising, Johannes, Emilio, Marcelo, Eriksson, Kjell, Ermocida, Marco, Giribaldi, Riano Isidoro Escate, Eschen, Yoshi, ez, Lucía Espinosa Yá, Estrela, In s, Evans, Dafydd Wyn, Fabbian, Damian, Fabrizio, Michele, Faria, João Pedro, Farina, Maria, Farinato, Jacopo, Feliz, Dax, Feltzing, Sofia, Fenouillet, Thomas, Fernández, Miguel, Ferrari, Lorenza, Ferraz-Mello, Sylvio, Fialho, Fabio, Fienga, Agnes, Figueira, Pedro, Fiori, Laura, Flaccomio, Ettore, Focardi, Mauro, Foley, Steve, Fontignie, Jean, Ford, Dominic, Fornazier, Karin, Forveille, Thierry, Fossati, Luca, Franca, Rodrigo de Marca, da Silva, Lucas Franco, Frasca, Antonio, Fridlund, Malcolm, Furlan, Marco, Gabler, Sarah-Maria, Gaido, Marco, Gallagher, Andrew, Sempere, Paloma I. Gallego, Galli, Emanuele, García, Rafael A., Hernández, Antonio García, Munoz, Antonio Garcia, García-Vázquez, Hugo, Haba, Rafael Garrido, Gaulme, Patrick, Gauthier, Nicolas, Gehan, Charlotte, Gent, Matthew, Georgieva, Iskra, Ghigo, Mauro, Giana, Edoardo, Gill, Samuel, Girardi, Leo, Winter, Silvia Giuliatti, Giusi, Giovanni, da Silva, João Gomes, Zazo, Luis Jorge Gómez, Gomez-Lopez, Juan Manuel, Hernández, Jonay Isai González, Murillo, Kevin Gonzalez, Melchor, Alejandro Gonzalo, Gorius, Nicolas, Gouel, Pierre-Vincent, Goulty, Duncan, Granata, Valentina, Grenfell, John Lee, bach, Denis Grie, Grolleau, Emmanuel, Grouffal, Salomé, Grziwa, Sascha, Guarcello, Mario Giuseppe, Gueguen, Lo c, Guenther, Eike Wolf, Guilhem, Terrasa, Guillerot, Lucas, Guillot, Tristan, Guiot, Pierre, Guterman, Pascal, Gutiérrez, Antonio, Gutiérrez-Canales, Fernando, Hagelberg, Janis, Haldemann, Jonas, Hall, Cassandra, Handberg, Rasmus, Harrison, Ian, Harrison, Diana L., Hasiba, Johann, Haswell, Carole A., Hatalova, Petra, Hatzes, Artie, Haywood, Raphaelle, Hébrard, Guillaume, Heckes, Frank, Heiter, Ulrike, Hekker, Saskia, Heller, René, Helling, Christiane, Helminiak, Krzysztof, Hemsley, Simon, Heng, Kevin, Herbst, Konstantin, Hermans, Aline, Hermes, JJ, Torres, Nadia Hidalgo, Hinkel, Natalie, Hobbs, David, Hodgkin, Simon, Hofmann, Karl, Hojjatpanah, Saeed, Houdek, Günter, Huber, Daniel, Huesler, Joseph, Hui-Bon-Hoa, Alain, Huygen, Rik, Huynh, Duc-Dat, Iro, Nicolas, Irwin, Jonathan, Irwin, Mike, Izidoro, André, Jacquinod, Sophie, Jannsen, Nicholas Emborg, Janson, Markus, Jeszenszky, Harald, Jiang, Chen, Mancebo, Antonio José Jimenez, Jofre, Paula, Johansen, Anders, Johnston, Cole, Jones, Geraint, Kallinger, Thomas, Kálmán, Szilárd, Kanitz, Thomas, Karjalainen, Marie, Karjalainen, Raine, Karoff, Christoffer, Kawaler, Steven, Kawata, Daisuke, Keereman, Arnoud, Keiderling, David, Kennedy, Tom, Kenworthy, Matthew, Kerschbaum, Franz, Kidger, Mark, Kiefer, Flavien, Kintziger, Christian, Kislyakova, Kristina, Kiss, László, Klagyivik, Peter, Klahr, Hubert, Klevas, Jonas, Kochukhov, Oleg, Köhler, Ulrich, Kolb, Ulrich, Koncz, Alexander, Korth, Judith, Kostogryz, Nadiia, Kovács, Gábor, Kovács, József, Kozhura, Oleg, Krivova, Natalie, Kucinskas, Arunas, Kuhlemann, Ilyas, Kupka, Friedrich, Laauwen, Wouter, Labiano, Alvaro, Lagarde, Nadege, Laget, Philippe, Laky, Gunter, Lam, Kristine Wai Fun, Lambrechts, Michiel, Lammer, Helmut, Lanza, Antonino Francesco, Lanzafame, Alessandro, Martiz, Mariel Lares, Laskar, Jacques, Latter, Henrik, Lavanant, Tony, Lawrenson, Alastair, Lazzoni, Cecilia, Lebre, Agnes, Lebreton, Yveline, Etangs, Alain Lecavelier des, Lee, Katherine, Leinhardt, Zoe, Leleu, Adrien, Lendl, Monika, Leto, Giuseppe, Levillain, Yves, Libert, Anne-Sophie, Lichtenberg, Tim, Ligi, Roxanne, Lignieres, Francois, Lillo-Box, Jorge, Linsky, Jeffrey, Liu, John Scige, Loidolt, Dominik, Longval, Yuying, Lopes, Ilídio, Lorenzani, Andrea, Ludwig, Hans-Guenter, Lund, Mikkel, Lundkvist, Mia Sloth, Luri, Xavier, Maceroni, Carla, Madden, Sean, Madhusudhan, Nikku, Maggio, Antonio, Magliano, Christian, Magrin, Demetrio, Mahy, Laurent, Maibaum, Olaf, Malac-Allain, LeeRoy, Malapert, Jean-Christophe, Malavolta, Luca, Maldonado, Jesus, Mamonova, Elena, Manchon, Louis, Manjón, Andres, Mann, Andrew, Mantovan, Giacomo, Marafatto, Luca, Marconi, Marcella, Mardling, Rosemary, Marigo, Paola, Marinoni, Silvia, Marques, rico, Marques, Joao Pedro, Marrese, Paola Maria, Marshall, Douglas, Perales, Silvia Martínez, Mary, David, Marzari, Francesco, Masana, Eduard, Mascher, Andrina, Mathis, Stéphane, Mathur, Savita, Vodopivec, Iris Martín, Figueiredo, Ana Carolina Mattiuci, Maxted, Pierre F. L., Mazeh, Tsevi, Mazevet, Stephane, Mazzei, Francesco, McCormac, James, McMillan, Paul, Menou, Lucas, Merle, Thibault, Meru, Farzana, Mesa, Dino, Messina, Sergio, Mészáros, Szabolcs, Meunier, Nadége, Meunier, Jean-Charles, Micela, Giuseppina, Michaelis, Harald, Michel, Eric, Michielsen, Mathias, Michtchenko, Tatiana, Miglio, Andrea, Miguel, Yamila, Milligan, David, Mirouh, Giovanni, Mitchell, Morgan, Moedas, Nuno, Molendini, Francesca, Molnár, László, Mombarg, Joey, Montalban, Josefina, Montalto, Marco, Monteiro, Mário J. P. F. G., Sánchez, Francisco Montoro, Morales, Juan Carlos, Morales-Calderon, Maria, Morbidelli, Alessandro, Mordasini, Christoph, Moreau, Chrystel, Morel, Thierry, Morello, Guiseppe, Morin, Julien, Mortier, Annelies, Mosser, Beno t, Mourard, Denis, Mousis, Olivier, Moutou, Claire, Mowlavi, Nami, Moya, Andrés, Muehlmann, Prisca, Muirhead, Philip, Munari, Matteo, Musella, Ilaria, Mustill, Alexander James, Nardetto, Nicolas, Nardiello, Domenico, Narita, Norio, Nascimbeni, Valerio, Nash, Anna, Neiner, Coralie, Nelson, Richard P., Nettelmann, Nadine, Nicolini, Gianalfredo, Nielsen, Martin, Niemi, Sami-Matias, Noack, Lena, Noels-Grotsch, Arlette, Noll, Anthony, Norazman, Azib, Norton, Andrew J., Nsamba, Benard, Ofir, Aviv, Ogilvie, Gordon, Olander, Terese, Olivetto, Christian, Olofsson, Göran, Ong, Joel, Ortolani, Sergio, Oshagh, Mahmoudreza, Ottacher, Harald, Ottensamer, Roland, Ouazzani, Rhita-Maria, Paardekooper, Sijme-Jan, Pace, Emanuele, Pajas, Miriam, Palacios, Ana, Palandri, Gaelle, Palle, Enric, Paproth, Carsten, Parro, Vanderlei, Parviainen, Hannu, Granado, Javier Pascual, Passegger, Vera Maria, Pastor-Morales, Carmen, Pätzold, Martin, Pedersen, May Gade, Hidalgo, David Pena, Pepe, Francesco, Pereira, Filipe, Persson, Carina M., Pertenais, Martin, Peter, Gisbert, Petit, Antoine C., Petit, Pascal, Pezzuto, Stefania, Pichierri, Gabriele, Pietrinferni, Adriano, Pinheiro, Fernando, Pinsonneault, Marc, Plachy, Emese, Plasson, Philippe, Plez, Bertrand, Poppenhaeger, Katja, Poretti, Ennio, Portaluri, Elisa, Portell, Jordi, de Mello, Gustavo Frederico Porto, Poyatos, Julien, Pozuelos, Francisco J., Moroni, Pier Giorgio Prada, Pricopi, Dumitru, Prisinzano, Loredana, Quade, Matthias, Quirrenbach, Andreas, Reina, Julio Arturo Rabanal, Soares, Maria Cristina Rabello, Raimondo, Gabriella, Rainer, Monica, Rodón, Jose Ramón, Ramón-Ballesta, Alejandro, Zapata, Gonzalo Ramos, Rätz, Stefanie, Rauterberg, Christoph, Redman, Bob, Redmer, Ronald, Reese, Daniel, Regibo, Sara, Reiners, Ansgar, Reinhold, Timo, Renie, Christian, Ribas, Ignasi, Ribeiro, Sergio, Ricciardi, Thiago Pereira, Rice, Ken, Richard, Olivier, Riello, Marco, Rieutord, Michel, Ripepi, Vincenzo, Rixon, Guy, Rockstein, Steve, Ortiz, José Ramón Rodón, Rodríguez, María Teresa Rodrigo, Amor, Alberto Rodríguez, Díaz, Luisa Fernanda Rodríguez, Garcia, Juan Pablo Rodriguez, Rodriguez-Gomez, Julio, Roehlly, Yannick, Roig, Fernando, Rojas-Ayala, Bárbara, Rolf, Tobias, Rørsted, Jakob Lysgaard, Rosado, Hugo, Rosotti, Giovanni, Roth, Olivier, Roth, Markus, Rousseau, Alex, Roxburgh, Ian, Roy, Fabrice, Royer, Pierre, Ruane, Kirk, Mastropasqua, Sergio Rufini, de Galarreta, Claudia Ruiz, Russi, Andrea, Saar, Steven, Saillenfest, Melaine, Salaris, Maurizio, Salmon, Sebastien, Saltas, Ippocratis, Samadi, Réza, Samadi, Aunia, Samra, Dominic, da Silva, Tiago Sanches, Carrasco, Miguel Andrés Sánchez, Santerne, Alexandre, Pé, Amaia Santiago, Santoli, Francesco, Santos, ngela R. G., Mesa, Rosario Sanz, Sarro, Luis Manuel, Scandariato, Gaetano, Schäfer, Martin, Schlafly, Edward, Schmider, François-Xavier, Schneider, Jean, Schou, Jesper, Schunker, Hannah, Schwarzkopf, Gabriel Jörg, Serenelli, Aldo, Seynaeve, Dries, Shan, Yutong, Shapiro, Alexander, Shipman, Russel, Sicilia, Daniela, sanmartin, Maria Angeles Sierra, Sigot, Axelle, Silliman, Kyle, Silvotti, Roberto, Simon, Attila E., Napoli, Ricardo Simoyama, Skarka, Marek, Smalley, Barry, Smiljanic, Rodolfo, Smit, Samuel, Smith, Alexis, Smith, Leigh, Snellen, Ignas, Sódor, Ádám, Sohl, Frank, Solanki, Sami K., Sortino, Francesca, Sousa, Sérgio, Southworth, John, Souto, Diogo, Sozzetti, Alessandro, Stamatellos, Dimitris, Stassun, Keivan, Steller, Manfred, Stello, Dennis, Stelzer, Beate, Stiebeler, Ulrike, Stokholm, Amalie, Storelvmo, Trude, Strassmeier, Klaus, Strøm, Paul Anthony, Strugarek, Antoine, Sulis, Sophia, vanda, Michal, Szabados, László, Szabó, Róbert, Szabó, Gyula M., Szuszkiewicz, Ewa, Talens, Geert Jan, Teti, Daniele, Theisen, Tom, Thévenin, Frédéric, Thoul, Anne, Tiphene, Didier, Titz-Weider, Ruth, Tkachenko, Andrew, Tomecki, Daniel, Tonfat, Jorge, Tosi, Nicola, Trampedach, Regner, Traven, Gregor, Triaud, Amaury, Trønnes, Reidar, Tsantaki, Maria, Tschentscher, Matthias, Turin, Arnaud, Tvaruzka, Adam, Ulmer, Bernd, Ulmer-Moll, Solène, Ulusoy, Ceren, Umbriaco, Gabriele, Valencia, Diana, Valentini, Marica, Valio, Adriana, Guijarro, Ángel Luis Valverde, Van Eylen, Vincent, Van Grootel, Valerie, van Kempen, Tim A., Van Reeth, Timothy, Van Zelst, Iris, Vandenbussche, Bart, Vasiliou, Konstantinos, Vasilyev, Valeriy, de Mascarenhas, David Vaz, Vazan, Allona, Nunez, Marina Vela, Velloso, Eduardo Nunes, Ventura, Rita, Ventura, Paolo, Venturini, Julia, Trallero, Isabel Vera, Veras, Dimitri, Verdugo, Eva, Verma, Kuldeep, Vibert, Didier, Martinez, Tobias Vicanek, Vida, Krisztián, Vigan, Arthur, Villacorta, Antonio, Villaver, Eva, Aparicio, Marcos Villaverde, Viotto, Valentina, Vorobyov, Eduard, Vorontsov, Sergey, Wagner, Frank W., Walloschek, Thomas, Walton, Nicholas, Walton, Dave, Wang, Haiyang, Waters, Rens, Watson, Christopher, Wedemeyer, Sven, Weeks, Angharad, Weingrill, Jörg, Weiss, Annita, Wendler, Belinda, West, Richard, Westerdorff, Karsten, Westphal, Pierre-Amaury, Wheatley, Peter, White, Tim, Whittaker, Amadou, Wickhusen, Kai, Wilson, Thomas, Windsor, James, Winter, Othon, Winther, Mark Lykke, Winton, Alistair, Witteck, Ulrike, Witzke, Veronika, Woitke, Peter, Wolter, David, Wuchterl, Günther, Wyatt, Mark, Yang, Dan, Yu, Jie, Sanchez, Ricardo Zanmar, Osorio, María Rosa Zapatero, Zechmeister, Mathias, Zhou, Yixiao, Ziemke, Claas, Zwintz, Konstanze

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) ar

Externí odkaz: http://arxiv.org/abs/2406.05447

Universal regularity estimates for solutions to fully nonlinear elliptic equations with oblique boundary data

Autor: Bessa, Junior da S., da Silva, João Vitor, Ricarte, Gleydson C.

In this work, we establish universal moduli of continuity for viscosity solutions to fully nonlinear elliptic equations with oblique boundary conditions, whose general model is given by $$ \left\{ \begin{array}{rcl} F(D^2u,x) &=& f(x) \quad \mbox{in}

Externí odkaz: http://arxiv.org/abs/2402.17899