The inclusive J/psi production cross-section and fraction of J/psi mesons produced in B-hadron decays are measured in proton proton collisions at root s = 7 TeV with the ATLAS detector at the LHC, as a function of the transverse momentum and rapidity of the J/psi, using 2.3 pb(-1) of integrated luminosity. The cross-section is measured from a minimum P(T) of 1 GeV to a maximum of 70 GeV and for rapidities within vertical bar y vertical bar < 2.4 giving the widest reach of any measurement of J/psi production to date. The differential production cross-sections of prompt and non-prompt J/psi are separately determined and are compared to Colour Singlet NNLO*, Colour Evaporation Model, and FONLL predictions. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved. RI Andreazza, Attilio/E-5642-2011; Jakubek, Jan/E-6530-2011; valente, paolo/A-6640-2010; Smirnov, Sergei/F-1014-2011; Fazio, Salvatore /G-5156-2010; Marti-Garcia, Salvador/F-3085-2011; Doyle, Anthony/C-5889-2009; Laycock, Paul/F-7543-2011; Conde Muino, Patricia/F-7696-2011; Stoicea, Gabriel/B-6717-2011; Robson, Aidan/G-1087-2011; Kladiva, Eduard/G-6305-2011; Losada, Marta/B-2261-2010; Bauer, Florian/G-8816-2011; Jones, Roger/H-5578-2011; Gutierrez, Phillip/C-1161-2011; Ferrando, James/A-9192-2012; collins-tooth, christopher/A-9201-2012; Perrino, Roberto/B-4633-2010; De Cecco, Sandro/B-1016-2012; branchini, paolo/A-4857-2011; Wolter, Marcin/A-7412-2012; McKee, Shawn/B-6435-2012; Rotaru, Marina/A-3097-2011; O'Shea, Val/G-1279-2010; Nemecek, Stanislav/C-3487-2012; Buttar, Craig/D-3706-2011; Takai, Helio/C-3301-2012; St.Denis, Richard/C-8997-2012; Britton, David/F-2602-2010; Pina, Joao /C-4391-2012; Li, Xuefei/C-3861-2012; Smirnova, Lidia/D-8089-2012; Gladilin, Leonid/B-5226-2011; Kramarenko, Victor/E-1781-2012; Prokoshin, Fedor/E-2795-2012; Price, Darren/E-6162-2012; Alexa, Calin/F-6345-2010; Pacheco Pages, Andres/C-5353-2011; Moorhead, Gareth/B-6634-2009; Livan, Michele/D-7531-2012; Petrucci, Fabrizio/G-8348-2012; Wemans, Andre/A-6738-2012; Fabbri, Laura/H-3442-2012; Kurashige, Hisaya/H-4916-2012; Villa, Mauro/C-9883-2009; Kuzhir, Polina/H-8653-2012; Delmastro, Marco/I-5599-2012
The inclusive J/psi production cross-section and fraction of J/psi mesons produced in B-hadron decays are measured in proton proton collisions at root s = 7 TeV with the ATLAS detector at the LHC, as a function of the transverse momentum and rapidity of the J/psi, using 2.3 pb(-1) of integrated luminosity. The cross-section is measured from a minimum P(T) of 1 GeV to a maximum of 70 GeV and for rapidities within vertical bar y vertical bar < 2.4 giving the widest reach of any measurement of J/psi production to date. The differential production cross-sections of prompt and non-prompt J/psi are separately determined and are compared to Colour Singlet NNLO*, Colour Evaporation Model, and FONLL predictions. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.
Measurement of the differential cross-sections of inclusive, prompt and non-prompt J/psi production in proton-proton collisions at root s=7 TeV
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Landon MPJ; Landsman H; Lane JL; Lange C; Lankford AJ; Lanni F; Lantzsch K; Lapin VV; Laplace S; Lapoire C; Laporte JF; Lari T; Larionov AV; Lamer A; Lasseur C; Lassnig M; Lau W; Laurelli P; Lavorato A; Lavrijsen W; Laycock P; Lazarev AB; Lazzaro A; Le Dortz O; Le Guirriec E; Le Maner C; Le Menedeu E; Leahu M; Lebedev A; Lebel C; LeCompte T; Ledroit Guillon F; Lee H; Lee JSH; Lee SC; Lee L; Lefebvre M; Legendre M; Leger A; LeGeyt BC; Legger F; Leggett C; Lehmacher M; Miotto GL; Lei X; Leite MAL; Leitner R; Lellouch D; Lellouch J; Leltchouk M; Lendermann V; Leney KJC; Lenz T; Lenzen G; Lenzi B; Leonhardt K; Leontsinis S; Leroy C; Lessard JR; Lesser J; Lester CG; Cheong ALF; Leveque J; Levin D; Levinson LJ; Levitski MS; Lewandowska M; Lewis GH; Leyton M; Li B; Li H; Li S; Li X; Liang Z; Liang Z; Liberti B; Lichard P; Lichtnecker M; Lie K; Liebig W; Lifshitz R; Lilley JN; Limbach C; Limosani A; Limper M; Lin SC; Linde F; Linnemann JT; Lipeles E; Lipinsky L; Lipniacka A; Liss TM; Lissauer D; Lister A; Litke AM; Liu C; Liu D; Liu H; Liu M; Liu S; Liu Y; Livan M; Livermore SSA; Lleres A; Lloyd SL; Lobodzinska E; Loch P; Lockman WS; Lockwitz S; Loddenkoetter T; Loebinger FK; Loginov A; Loh CW; Lohse T; Lohwasser K; Lokajicek M; Loken J; Lombardo VP; Long RE; Lopes L; Mateos DL; Losada M; Loscutoff P; Lo Sterzo F; Losty MJ; Lou X; Lounis A; Loureiro KF; Love J; Love PA; Lowe AJ; Lu F; Lu J; Lu L; Lubatti HJ; Luci C; Lucotte A; Ludwig A; Ludwig D; Ludwig I; Ludwig J; Luehring F; Luijckx G; Lumb D; Luminari L; Lund E; Lund Jensen B; Lundberg B; Lundberg J; Lundquist J; Lungwitz M; Lupi A; Lutz G; Lynn D; Lys J; Lytken E; Ma H; Ma LL; Goia JAM; Maccarrone G; Macchiolo A; Macek B; Miguens JM; Macina D; Mackeprang R; Madaras RJ; Mader WF; Maenner R; Maeno T; Mattig P; Mattig S; Martins PJM; Magnoni L; Magradze E; Magrath CA; Mahalalel Y; Mahboubi K; Mahout G; Maiani C; Maidantchik C; Maio A; Majewski S; Makida Y; Makovec N; Mal P; Malecki P; Malecki P; Maleev VP; Malek F; Mallik U; Malon D; Maltezos S; Malyshev V; Malyukov S; Mameghani R; Mamuzic J; Manabe A; Mandelli L; Mandic I; Mandrysch R; Maneira J; Mangeard PS; Manjavidze ID; Mann A; Manning PM; Manousakis Katsikakis A; Mansoulie B; Manz A; Mapelli A; Mapeill L; March L; Marchand JF; Marchese F; Marchesotti M; Marchiori G; Marcisovsky M; Marin A; Marino CP; Marroquim F; Marshall R; Marshall Z; Martens FK; Marti Garcia S; Martin AJ; Martin B; Martin B; Martin FF; Martin JP; Martin P; Martin TA; Latour BMD; Martinez M; Outschoorn VM; Martyniuk AC; Marx M; Marzano F; Marzin A; Masetti L; Mashimo T; Mashinistov R; Masik J; Maslennikov AL; Mass M; Massa I; Massaro G; Massol N; MASTROBERARDINO, Anna ;Masubuchi T; Mathes M; Matricon P; Matsumoto H; Matsunaga H; Matsushita T; Mattravers C; Maugain JM; Maxfield SJ; Maximov DA; May EN; Mayne A; Mazini R; Mazur M; Mazzanti M; Mazzoni E; Mc Kee SP; McCarn A; McCarthy RL; McCarthy TG; McCubbin NA; McFarlane KW; Mcfayden JA; McGlone H; Mchedlidze G; McLaren RA; Mclaughlan T; McMahon SJ; McPherson RA; Meade A; Mechnich J; Mechtel M; Medinnis M; Meera Lebbai R; Meguro T; Mehdiyev R; Mehlhase S; Mehta A; Meier K; Meinhardt J; Meirose B; Melachrinos C; Garcia BRM; Navas LM; Meng Z; Mengarelli A; Menke S; Menot C; Meoni E ;Mercurio KM; Mermod P; Merola L; Meroni C; Merritt FS; Messina A; Metcalfe J; Mete AS; Meuser S; Meyer C; Meyer JP; Meyer J; Meyer J; Meyer TC; Meyer WT; Miao J; Michal S; Micu L; Middleton RP; Miele P; Migas S; Mijovic L; Mikenberg G; Mikestikova M; Mikulec B; Mikuz M; Miller DW; Miller RJ; Mills WJ; Mills C; Milov A; Milstead DA; Milstein D; Minaenko AA; Minano M; Minashvili IA; Mincer AI; Mindur B; Mineev M; Ming Y; Mir LM; Mirabelli G; Verge LM; Misiejuk A; Mitrevski J; Mitrofanov GY; Mitsou VA; Mitsui S; Miyagawa PS; Miyazaki K; Mjornmark JU; Moa T; Mockett R; Moed S; Moeller V; Monig K; Moser N; Mohapatra S; Mohn B; Mohr W; Mohrdieck Mock S; Moisseev AM; Moles Valls R; Molina Perez J; Moneta L; Monk J; Monnier E; Montesano S; Monticelli F; Monzani S; Moore RW; Moorhead GF; Herrera CM; Moraes A; Morais A; Morange N; Morello G; Moreno D; Llacer MM; Morettini P; Morii M; Morin J; Morita Y; Morley AK; Mornacchi G; Morone MC; Morozov SV; Morris JD; Moser HG; Mosidze M; Moss J; Mount R; Mountricha E; Mouraviev SV; Moyse EJW; Mudrinic M; Mueller F; Mueller J; Mueller K; Muller TA; Muenstermann D; Muijs A; Muir A; Munwes Y; Murakami K; Murray WJ; Mussche J; Musto E; Myagkov AG; Myska M; Nadal J; Nagai K; Nagano K; Nagasaka Y; Nairz AM; Nakahama Y; Nakamura K; Nakano I; Nanava G; Napier A; Nash M; Nation NR; Nattermann T; Naumann T; Navarro G; Neal HA; Nebot E; Nechaeva PY; Negri A; Negri G; Nektarijevic S; Nelson A; Nelson S; Nelson TK; Nemecek S; Nemethy P; Nepomuceno AA; Nessi M; Nesterov SY; Neubauer MS; Neusiedl A; Neves RM; Nevski P; Newman PR; Nickerson RB; Nicolaidou R; Nicolas L; Nicquevert B; Niedercorn F; Nielsen J; Niinikoski T; Nikiforov A; Nikolaenko V; Nikolaev K; Nikolic Audit I; Nikolopoulos K; Nilsen H; Nilsson P; Ninomiya Y; Nisati A; Nishiyama T; Nisius R; Nodulman L; Nomachi M; Nomidis I; Nomoto H; Nordberg M; Nordkvist B; Norton PR; Novakova J; Nozaki M; Nozicka M; Nozka L; Nugent IM; Nuncio Quiroz AE; Hanninger GN; Nunnemann T; Nurse E; Nyman T; O'Brien BJ; O'Neale SW; O'Neil DC; O'Shea V; Oakham FG; Oberlack H; Ocariz J; Ochi A; Oda S; Odaka S; Odier J; Ogren H; Oh A; Oh SH; Ohm CC; Ohshima T; Ohshita H; Ohska TK; Ohsugi T; Okada S; Okawa H; Okumura Y; Okuyama T; Olcese M; Olchevski AG; Oliveira M; Damazio DO; Garcia EO; Olivito D; Olszewski A; Olszowska J; Omachi C; Onofre A; Onyisi PUE; Oram CJ; Ordonez G; Oreglia MJ; Orellana F; Oren Y; Orestano D; Orlov I; Barrera CO; Orr RS; Ortega EO; Osculati B; Ospanov R; Osuna C; Garzon GOY; Ottersbach JP; Ouchrif M; Ould Saada F; Ouraou A; Ouyang Q; Owen M; Owen S; Oyarzun A; Oye OK; Ozcan VE; Ozturk N; Pages AP; Aranda CP; Paganis E; Paige F; Pajchel K; Palestini S; Pallin D; Palma A; Palmer JD; Pan YB; Panagiotopoulou E; Panes B; Panikashvili N; Panitkin S; Pantea D; Panuskova M; Paolone V; Paoloni A; Papadelis A; Papadopoulou TD; Paramonov A; Park W; Parker MA; Parodi F; Parsons JA; Parzefall U; Pasqualucci E; Passeri A; Pastore F; Pastore F; Pasztor G; Pataraia S; Patel N; Pater JR; Patricelli S; Pauly T; Pecsy M; Morales MIP; Peleganchuk SV; Peng H; Pengo R; Penson A; Penwell J; Perantoni M; Perez K; Cavalcanti TP; Codina EP; Garcia Estan MTP; Reale VP; Peric I; Perini L; Pernegger H; Perrino R; Perrodo R; Persembe S; Peshekhonov VD; Peters O; Petersen BA; Petersen J; Petersen TC; Petit E; Petridis A; Petridou C; Petrolo E; Petrucci F; Petschull D; Petteni M; Pezoa R; Phan A; Phillips AW; Phillips PW; Piacquadio G; Piccaro E; Piccinini M; Pickford A; Piec SM; Piegaia R; Pilcher JE; Pilkington AD; Pina J; Pinamonti M; Pinder A; Pinfold JL; Ping J; Pinto B; Pirotte O; Pizio C; Placakyte R; Plamondon M; Plano WG; Pleier MA; Pleskach AV; Poblaguev A; Poddar S; Podlyski F; Poggioli L; Poghosyan T; Pohl M; Polci F; Polesello G; Policicchio A; Polini A; Poll J; Polychronakos V; Pomarede DM; Pomeroy D; Pommes K; Pontecorvo L; Pope BG; Popeneciu GA; Popovic DS; Poppleton A; Bueso XP; Porter R; Posch C; Pospelov GE; Pospisil S; Potrap IN; Potter CJ; Potter CT; Poulard G; Poveda J; Prabhu R; Pralavorio P; Prasad S; Pravahan R; Prell S; Pretzl K; Pribyl L; Price D; Price LE; Price MJ; Prichard PM; Prieur D; Primavera M; Prokofiev K; Prokoshin F; Protopopescu S; Proudfoot J; Prudent X; Przysiezniak H; Psoroulas S; Ptacek E; Purdham J; Purohit M; Puzo P; Pylypchenko Y; Qian J; Qian Z; Qin Z; Quadt A; Quarrie DR; Quayle WB; Quinonez F; Raas M; Radescu V; Radics B; Rador T; Ragusa F; Rahal G; Rahimi AM; Rahm D; Rajagopalan S; Rajek S; Rammensee M; Rammes M; Ramstedt M; Randrianarivony K; Ratoff PN; Rauscher F; Rauter E; Raymond M; Read AL; Rebuzzi DM; Redelbach A; Redlinger G; Reece R; Reeves K; Reichold A; Reinherz Aronis E; Reinsch A; Reisinger I; Reljic D; Rembser C; Ren ZL; Renaud A; Renkel P; Rensch B; Rescigno M; Resconi S; Resende B; Reznicek P; Rezvani R; Richter R; Richter Was E; Ridel M; Rieke S; Rijpstra M; Rijssenbeek M; Rimoldi A; Rinaldi L; Rios RR; Riu I; Rivoltella G; Rizatdinova F; Rizvi E; Robertson SH; Robichaud Veronneau A; Robinson D; Robinson JEM; Robinson M; Robson A; de Lima JGR; Roda C; Dos Santos DR; Rodier S; Rodriguez D; Garcia YR; Roe A; Roe S; Rohne O; Rojo V; Rolli S; Romaniouk A; Romanov VM; Romeo G; Maltrana DR; Roos L; Ros E; Rosati S; Rose M; Rosenbaum GA; Rosenberg EI; Rosendahl PL; Rosselet L; Rossetti V; Rossi E; Rossi LP; Rossi L; Rotaru M; Roth I; Rothberg J; Rottlander I; Rousseau D; Royon CR; Rozanov A; Rozen Y; Ruan X; Rubinskiy I; Ruckert B; Ruckstuhl N; Rud V; Rudolph G; Ruhr F; Ruggieri F; Ruiz Martinez A; Rulikowska Zarebska E; Rumiantsev V; Rumyantsev L; Runge K; Runolfsson O; Rurikova Z; Rusakovich NA; Rust DR; Rutherfoord JP; Ruwiedel C; Ruzicka P; Ryabov YF; Ryadovikov V; Ryan P; Rybar M; Rybkin G; Ryder NC; Rzaeva S; Saavedra AF; Sadeh I; Sadrozinslci HFW; Sadykov R; Tehrani FS; Sakamoto H; Salamanna G; Salamon A; Saleem M; Salihagic D; Salnikov A; Salt J; Ferrando BMS; Salvatore D; Salvatore F; Salvucci A; Salzburger A; Sampsonidis D; Samset BH; Sandaker H; Sander HG; Sanders MP; Sandhoff M; Sandhu P; Sandoval T; Sandstroem R; Sandvoss S; Sankey DPC; Sansoni A; Rios CS; Santoni C; Santonico R; Santos H; Saraiva JG; Sarangi T; Sarkisyan Grinbaum E; Sarri F; Sartisohn G; Sasaki O; Sasaki T; Sasao N; Satsounkevitch I; Sauvage G; Sauvan JB; Savard P; Savinov V; Savu DO; Savva P; Sawyer L; Saxon DH; Says LP; Sbarra C; Sbrizzi A; Scallon O; Scannicchio DA; Schaarschmidt J; Schacht P; Schafer U; Schaepe S; Schaetzel S; Schaffer AC; Schaile D; Schamberger RD; Schamov AG; Scharf V; Schegelsky VA; Scheirich D; Scherzer MI; Schiavi C; Schieck J; Schioppa M ;Schlenker S; Schlereth JL; Schmidt E; Schmidt MP; Schmieden K; Schmitt C; Schmitz M; Schoning A; Schott M; Schouten D; Schovancova J; Schram M; Schroeder C; Schroer N; Schuh S; Schuler G; Schultes J; Schultz Coulon HC; Schulz H; Schumacher J; Schumacher M; Schumm BA; Schune P; Schwanenberger C; Schwartzman A; Schwemling P; Schwienhorst R; Schwierz R; Schwindling J; Scott WG; Searcy J; Sedykh E; Segura E; Seidel SC; Seiden A; Seifert F; Seixas JM; Sekhniaidze G; Seliverstov DM; Sellden B; Sellers G; Seman M; Semprini Cesari N; Serfon C; Serin L; Seuster R; Severini H; Sevior ME; Sfyrla A; Shabalina E; Shamim M; Shan LY; Shank JT; Shao QT; Shapiro M; Shatalov PB; Shaver L; Shaw C; Shaw K; Sherman D; Sherwood P; Shibata A; Shimizu S; Shimojima M; Shin T; Shmeleva A; Shochet MJ; Short D; Shupe MA; Sicho P; Sidoti A; Siebel A; Siegert F; Siegrist J; Sijacki D; Silbert O; Silva J; Silver Y; Silverstein D; Silverstein SB; Simak V; Simard O; Simic LJ; Simion S; Simmons B; Simonyan M; Sinervo P; Sinev NB; Sipica V; Siragusa G; Sisakyan AN; Sivoklokov SY; Sjolin J; Sjursen TB; Skinnari LA; Skovpen K; Skubic P; Skvorodnev N; Slater M; Slavicek T; Sliwa K; Sloan TJ; Sloper J; Smakhtin V; Smirnov SY; Smirnova LN; 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2011-01-01
Abstract
The inclusive J/psi production cross-section and fraction of J/psi mesons produced in B-hadron decays are measured in proton proton collisions at root s = 7 TeV with the ATLAS detector at the LHC, as a function of the transverse momentum and rapidity of the J/psi, using 2.3 pb(-1) of integrated luminosity. The cross-section is measured from a minimum P(T) of 1 GeV to a maximum of 70 GeV and for rapidities within vertical bar y vertical bar < 2.4 giving the widest reach of any measurement of J/psi production to date. The differential production cross-sections of prompt and non-prompt J/psi are separately determined and are compared to Colour Singlet NNLO*, Colour Evaporation Model, and FONLL predictions. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.
Breve descrizione dei contenuti (Abstract)
The inclusive J/psi production cross-section and fraction of J/psi mesons produced in B-hadron decays are measured in proton proton collisions at root s = 7 TeV with the ATLAS detector at the LHC, as a function of the transverse momentum and rapidity of the J/psi, using 2.3 pb(-1) of integrated luminosity. The cross-section is measured from a minimum P(T) of 1 GeV to a maximum of 70 GeV and for rapidities within vertical bar y vertical bar < 2.4 giving the widest reach of any measurement of J/psi production to date. The differential production cross-sections of prompt and non-prompt J/psi are separately determined and are compared to Colour Singlet NNLO*, Colour Evaporation Model, and FONLL predictions. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved. RI Andreazza, Attilio/E-5642-2011; Jakubek, Jan/E-6530-2011; valente, paolo/A-6640-2010; Smirnov, Sergei/F-1014-2011; Fazio, Salvatore /G-5156-2010; Marti-Garcia, Salvador/F-3085-2011; Doyle, Anthony/C-5889-2009; Laycock, Paul/F-7543-2011; Conde Muino, Patricia/F-7696-2011; Stoicea, Gabriel/B-6717-2011; Robson, Aidan/G-1087-2011; Kladiva, Eduard/G-6305-2011; Losada, Marta/B-2261-2010; Bauer, Florian/G-8816-2011; Jones, Roger/H-5578-2011; Gutierrez, Phillip/C-1161-2011; Ferrando, James/A-9192-2012; collins-tooth, christopher/A-9201-2012; Perrino, Roberto/B-4633-2010; De Cecco, Sandro/B-1016-2012; branchini, paolo/A-4857-2011; Wolter, Marcin/A-7412-2012; McKee, Shawn/B-6435-2012; Rotaru, Marina/A-3097-2011; O'Shea, Val/G-1279-2010; Nemecek, Stanislav/C-3487-2012; Buttar, Craig/D-3706-2011; Takai, Helio/C-3301-2012; St.Denis, Richard/C-8997-2012; Britton, David/F-2602-2010; Pina, Joao /C-4391-2012; Li, Xuefei/C-3861-2012; Smirnova, Lidia/D-8089-2012; Gladilin, Leonid/B-5226-2011; Kramarenko, Victor/E-1781-2012; Prokoshin, Fedor/E-2795-2012; Price, Darren/E-6162-2012; Alexa, Calin/F-6345-2010; Pacheco Pages, Andres/C-5353-2011; Moorhead, Gareth/B-6634-2009; Livan, Michele/D-7531-2012; Petrucci, Fabrizio/G-8348-2012; Wemans, Andre/A-6738-2012; Fabbri, Laura/H-3442-2012; Kurashige, Hisaya/H-4916-2012; Villa, Mauro/C-9883-2009; Kuzhir, Polina/H-8653-2012; Delmastro, Marco/I-5599-2012
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Il report seguente simula gli indicatori relativi alla propria produzione scientifica in relazione alle soglie ASN 2023-2025 del proprio SC/SSD. Si ricorda che il superamento dei valori soglia (almeno 2 su 3) è requisito necessario ma non sufficiente al conseguimento dell'abilitazione. La simulazione si basa sui dati IRIS e sugli indicatori bibliometrici alla data indicata e non tiene conto di eventuali periodi di congedo obbligatorio, che in sede di domanda ASN danno diritto a incrementi percentuali dei valori. La simulazione può differire dall'esito di un’eventuale domanda ASN sia per errori di catalogazione e/o dati mancanti in IRIS, sia per la variabilità dei dati bibliometrici nel tempo. Si consideri che Anvur calcola i valori degli indicatori all'ultima data utile per la presentazione delle domande. La presente simulazione è stata realizzata sulla base delle specifiche raccolte sul tavolo ER del Focus Group IRIS coordinato dall’Università di Modena e Reggio Emilia e delle regole riportate nel DM 589/2018 e allegata Tabella A. Cineca, l’Università di Modena e Reggio Emilia e il Focus Group IRIS non si assumono alcuna responsabilità in merito all’uso che il diretto interessato o terzi faranno della simulazione. Si specifica inoltre che la simulazione contiene calcoli effettuati con dati e algoritmi di pubblico dominio e deve quindi essere considerata come un mero ausilio al calcolo svolgibile manualmente o con strumenti equivalenti.