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<!doctype html><html><head><title>View article</title><meta http-equiv="Content-Type" content="text/html;charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="referrer" content="always"><meta name="viewport" content="width=device-width,initial-scale=1,minimum-scale=1,maximum-scale=2"><meta name="format-detection" content="telephone=no"><link rel="shortcut icon" href="/favicon.ico"><meta name="description" content="‪AG Abac, R Abbott, I Abouelfettouh, F Acernese, K Ackley, S Adhicary, N Adhikari, RX Adhikari, VK Adkins, D Agarwal…‬, ‪arXiv preprint arXiv:2410.09151, 2024‬"><meta property="og:description" content="‪AG Abac, R Abbott, I Abouelfettouh, F Acernese, K Ackley, S Adhicary, N Adhikari, RX Adhikari, VK Adkins, D Agarwal…‬, ‪arXiv preprint arXiv:2410.09151, 2024‬"><meta property="og:title" content="‪A search using GEO600 for gravitational waves coincident with fast radio bursts from SGR 1935+ 2154‬"><meta property="og:image" content=""><meta 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id="gsc_vcpb" data-edit-link="/citations?view_op=edit_citation&hl=en&user=2DfFr6IAAAAJ&sortby=pubdate&citation_for_view=2DfFr6IAAAAJ:uVUOdF_882EC&citation_for_view=2DfFr6IAAAAJ:uVUOdF_882EC&back_view_op=view_citation"><form method="post" id="gsc_vcpb_btns" action="/citations?view_op=view_citation&hl=en"><input type="hidden" name="xsrf" value="ADIE8skAAAAAZ0kqq5e_BQckY4IcQB_RT383Iw4"><input type="hidden" name="s" value="2DfFr6IAAAAJ:uVUOdF_882EC"><input type="hidden" name="continue" value="/citations?view_op=list_works&hl=en&hl=en&user=2DfFr6IAAAAJ&sortby=pubdate"></form><div id="gsc_oci_title_wrapper"><div id="gsc_oci_title_gg"><div class="gsc_oci_title_ggi"><a href="https://arxiv.org/pdf/2410.09151" data-clk="hl=en&sa=T&ei=K9lHZ6-mNubOy9YPicOikA8"><span class='gsc_vcd_title_ggt'>[PDF]</span> from arxiv.org</a></div></div><div id="gsc_oci_title"><a class="gsc_oci_title_link" href="https://arxiv.org/abs/2410.09151" data-clk="hl=en&sa=T&ei=K9lHZ6-mNubOy9YPicOikA8">A search using GEO600 for gravitational waves coincident with fast radio bursts from SGR 1935+ 2154</a></div></div><div id="gsc_oci_table"><div class="gs_scl"><div class="gsc_oci_field">Authors</div><div class="gsc_oci_value">AG Abac, R Abbott, I Abouelfettouh, F Acernese, K Ackley, S Adhicary, N Adhikari, RX Adhikari, VK Adkins, D Agarwal, M Agathos, M Aghaei Abchouyeh, OD Aguiar, I Aguilar, L Aiello, A Ain, P Ajith, T Akutsu, S Albanesi, RA Alfaidi, A Al-Jodah, C Alléné, A Allocca, S Al-Shammari, PA Altin, S Alvarez-Lopez, A Amato, L Amez-Droz, A Amorosi, C Amra, A Ananyeva, SB Anderson, WG Anderson, M Andia, M Ando, T Andrade, N Andres, M Andrés-Carcasona, T Andrić, J Anglin, S Ansoldi, JM Antelis, S Antier, M Aoumi, EZ Appavuravther, S Appert, SK Apple, K Arai, A Araya, MC Araya, JS Areeda, L Argianas, N Aritomi, F Armato, N Arnaud, M Arogeti, SM Aronson, G Ashton, Y Aso, M Assiduo, S Melo, SM Aston, P Astone, F Attadio, F Aubin, K AultONeal, G Avallone, D Azrad, S Babak, F Badaracco, C Badger, S Bae, S Bagnasco, E Bagui, JG Baier, L Baiotti, R Bajpai, T Baka, M Ball, G Ballardin, SW Ballmer, S Banagiri, B Banerjee, D Bankar, P Baral, JC Barayoga, BC Barish, D Barker, P Barneo, F Barone, B Barr, L Barsotti, M Barsuglia, D Barta, AM Bartoletti, MA Barton, I Bartos, S Basak, A Basalaev, R Bassiri, A Basti, DE Bates, M Bawaj, P Baxi, JC Bayley, AC Baylor, II Baynard, M Bazzan, VM Bedakihale, F Beirnaert, M Bejger, D Belardinelli, AS Bell, V Benedetto, W Benoit, JD Bentley, M Ben Yaala, S Bera, M Berbel, F Bergamin, BK Berger, S Bernuzzi, M Beroiz, D Bersanetti, A Bertolini, J Betzwieser, D Beveridge, N Bevins, R Bhandare, U Bhardwaj, R Bhatt, D Bhattacharjee, S Bhaumik, S Bhowmick, A Bianchi, IA Bilenko, G Billingsley, A Binetti, S Bini, O Birnholtz, S Biscoveanu, A Bisht, M Bitossi, M-A Bizouard, JK Blackburn, LA Blagg, CD Blair, DG Blair, F Bobba, N Bode</div></div><div class="gs_scl"><div class="gsc_oci_field">Publication date</div><div class="gsc_oci_value">2024/10/11</div></div><div class="gs_scl"><div class="gsc_oci_field">Journal</div><div class="gsc_oci_value">arXiv preprint arXiv:2410.09151</div></div><div class="gs_scl"><div class="gsc_oci_field">Description</div><div class="gsc_oci_value" id="gsc_oci_descr"><div class="gsh_small">The magnetar SGR 1935+2154 is the only known Galactic source of fast radio bursts (FRBs). FRBs from SGR 1935+2154 were first detected by CHIME/FRB and STARE2 in 2020 April, after the conclusion of the LIGO, Virgo, and KAGRA Collaborations' O3 observing run. Here we analyze four periods of gravitational wave (GW) data from the GEO600 detector coincident with four periods of FRB activity detected by CHIME/FRB, as well as X-ray glitches and X-ray bursts detected by NICER and NuSTAR close to the time of one of the FRBs. We do not detect any significant GW emission from any of the events. Instead, using a short-duration GW search (for bursts <svg class="gs_fsvg" aria-label="\leq" width="11px" height="11px" style="vertical-align:-2px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 8.90400)"><path transform="scale(0.48828, -0.48828)" d="M 209 -281 Q 192 -281 181 -268 T 170 -240 Q 170 -223 181 -211 T 209 -199 H 1384 Q 1400 -199 1410 -211 T 1421 -240 Q 1421 -255 1410 -268 T 1384 -281 H 209 Z M 190 676 Q 170 682 170 711 Q 170 737 197 748 L 1366 1300 Q 1370 1303 1380 1303 Q 1397 1303 1409 1291 T 1421 1262 Q 1421 1235 1397 1225 L 307 711 L 1403 193 Q 1421 183 1421 158 Q 1421 140 1409 128 T 1380 117 Q 1370 117 1366 121 L 190 676 Z "/></g></svg> 1 s) we derive 50\% (90\%) upper limits of <svg class="gs_fsvg" aria-label="10^{48}" width="25px" height="12px" style="vertical-align:0px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.58769)"><path transform="scale(0.48828, -0.48828)" d="M 190 0 V 72 Q 446 72 446 137 V 1212 Q 340 1161 178 1161 V 1233 Q 429 1233 557 1364 H 586 Q 593 1364 599 1358 T 606 1346 V 137 Q 606 72 862 72 V 0 H 190 Z "/><g transform="translate(500.00000, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/><g transform="translate(500.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 80 336 V 418 L 762 1346 Q 772 1360 791 1360 H 831 Q 844 1360 852 1352 T 860 1331 V 418 H 1083 V 336 H 860 V 143 Q 860 82 1081 82 V 0 H 457 V 82 Q 678 82 678 143 V 336 H 80 Z M 168 418 H 692 V 1133 L 168 418 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 398.60800, 0.00000)" d="M 111 315 Q 111 444 199 538 T 420 688 L 350 729 Q 271 776 222 851 T 174 1014 Q 174 1117 234 1196 T 388 1318 T 582 1360 Q 676 1360 770 1326 T 927 1221 T 989 1053 Q 989 947 917 870 T 735 741 L 852 672 Q 909 639 955 589 T 1027 479 T 1053 350 Q 1053 232 984 143 T 806 6 T 582 -41 Q 469 -41 361 -1 T 182 120 T 111 315 Z M 242 315 Q 242 231 291 166 T 419 67 T 582 33 Q 710 33 816 96 T 922 279 Q 922 338 884 390 T 795 471 L 496 645 Q 426 613 368 564 T 276 453 T 242 315 Z M 395 938 L 664 782 Q 754 829 813 897 T 872 1053 Q 872 1123 829 1178 T 719 1263 T 582 1292 Q 517 1292 450 1271 T 337 1205 T 291 1092 Q 291 1000 395 938 Z "/></g></g></g></svg> (<svg class="gs_fsvg" aria-label="10^{49}" width="25px" height="12px" style="vertical-align:0px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.58769)"><path transform="scale(0.48828, -0.48828)" d="M 190 0 V 72 Q 446 72 446 137 V 1212 Q 340 1161 178 1161 V 1233 Q 429 1233 557 1364 H 586 Q 593 1364 599 1358 T 606 1346 V 137 Q 606 72 862 72 V 0 H 190 Z "/><g transform="translate(500.00000, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/><g transform="translate(500.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 80 336 V 418 L 762 1346 Q 772 1360 791 1360 H 831 Q 844 1360 852 1352 T 860 1331 V 418 H 1083 V 336 H 860 V 143 Q 860 82 1081 82 V 0 H 457 V 82 Q 678 82 678 143 V 336 H 80 Z M 168 418 H 692 V 1133 L 168 418 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 398.60800, 0.00000)" d="M 285 92 Q 320 58 372 45 T 487 33 Q 557 33 618 65 T 725 150 T 799 272 Q 848 397 848 637 Q 804 551 727 498 T 557 446 Q 430 446 328 507 T 169 673 T 111 903 Q 111 1001 149 1085 T 254 1232 T 409 1327 T 594 1360 Q 845 1360 949 1151 T 1053 662 Q 1053 540 1015 415 T 903 186 T 722 20 T 487 -41 Q 354 -41 261 14 T 168 193 Q 168 237 197 266 T 270 295 Q 290 295 309 287 T 342 266 T 363 233 T 371 193 Q 371 155 347 126 T 285 92 Z M 569 512 Q 655 512 718 564 T 812 696 T 844 862 Q 844 875 843 883 T 842 901 Q 843 904 843 906 T 844 911 Q 844 1058 786 1175 T 594 1292 Q 428 1292 371 1187 T 315 903 Q 315 790 331 707 T 404 568 T 569 512 Z "/></g></g></g></svg>) erg for GWs at 300 Hz and <svg class="gs_fsvg" aria-label="10^{49}" width="25px" height="12px" style="vertical-align:0px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.58769)"><path transform="scale(0.48828, -0.48828)" d="M 190 0 V 72 Q 446 72 446 137 V 1212 Q 340 1161 178 1161 V 1233 Q 429 1233 557 1364 H 586 Q 593 1364 599 1358 T 606 1346 V 137 Q 606 72 862 72 V 0 H 190 Z "/><g transform="translate(500.00000, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/><g transform="translate(500.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 80 336 V 418 L 762 1346 Q 772 1360 791 1360 H 831 Q 844 1360 852 1352 T 860 1331 V 418 H 1083 V 336 H 860 V 143 Q 860 82 1081 82 V 0 H 457 V 82 Q 678 82 678 143 V 336 H 80 Z M 168 418 H 692 V 1133 L 168 418 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 398.60800, 0.00000)" d="M 285 92 Q 320 58 372 45 T 487 33 Q 557 33 618 65 T 725 150 T 799 272 Q 848 397 848 637 Q 804 551 727 498 T 557 446 Q 430 446 328 507 T 169 673 T 111 903 Q 111 1001 149 1085 T 254 1232 T 409 1327 T 594 1360 Q 845 1360 949 1151 T 1053 662 Q 1053 540 1015 415 T 903 186 T 722 20 T 487 -41 Q 354 -41 261 14 T 168 193 Q 168 237 197 266 T 270 295 Q 290 295 309 287 T 342 266 T 363 233 T 371 193 Q 371 155 347 126 T 285 92 Z M 569 512 Q 655 512 718 564 T 812 696 T 844 862 Q 844 875 843 883 T 842 901 Q 843 904 843 906 T 844 911 Q 844 1058 786 1175 T 594 1292 Q 428 1292 371 1187 T 315 903 Q 315 790 331 707 T 404 568 T 569 512 Z "/></g></g></g></svg> (<svg class="gs_fsvg" aria-label="10^{50}" width="25px" height="12px" style="vertical-align:0px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.58769)"><path transform="scale(0.48828, -0.48828)" d="M 190 0 V 72 Q 446 72 446 137 V 1212 Q 340 1161 178 1161 V 1233 Q 429 1233 557 1364 H 586 Q 593 1364 599 1358 T 606 1346 V 137 Q 606 72 862 72 V 0 H 190 Z "/><g transform="translate(500.00000, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/><g transform="translate(500.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 227 223 Q 267 136 354 84 T 537 33 Q 643 33 709 85 T 803 221 T 831 412 Q 831 504 815 587 T 748 731 T 606 791 Q 526 791 472 771 T 388 726 T 330 668 T 289 633 H 266 Q 245 638 240 659 V 1337 Q 240 1347 247 1353 T 264 1360 H 272 Q 356 1326 434 1310 T 594 1294 Q 675 1294 754 1310 T 915 1360 H 922 Q 932 1360 939 1353 T 946 1337 V 1317 Q 946 1309 940 1303 Q 860 1211 747 1159 T 514 1108 Q 415 1108 322 1133 V 758 Q 438 856 606 856 Q 724 856 822 794 T 977 630 T 1034 410 Q 1034 313 993 229 T 880 84 T 720 -9 T 539 -41 Q 434 -41 338 7 T 186 140 T 129 332 Q 129 376 160 407 T 236 438 Q 281 438 311 407 T 342 332 Q 342 286 311 254 T 236 223 H 227 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 398.60800, 0.00000)" d="M 582 -41 Q 396 -41 289 60 T 143 314 T 104 651 Q 104 951 208 1155 T 582 1360 Q 853 1360 956 1155 T 1059 651 Q 1059 468 1019 314 T 874 60 T 582 -41 Z M 582 25 Q 710 25 772 134 T 849 380 T 864 686 Q 864 848 849 973 T 773 1196 T 582 1294 Q 482 1294 422 1233 T 337 1081 T 305 897 T 299 686 Q 299 564 305 464 T 338 262 T 424 92 T 582 25 Z "/></g></g></g></svg>) erg at 2 kHz, and constrain the GW-to-radio energy ratio to <svg class="gs_fsvg" aria-label="\leq 10^{14} - 10^{16}" width="82px" height="14px" style="vertical-align:-2px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.58769)"><path transform="scale(0.48828, -0.48828)" d="M 209 -281 Q 192 -281 181 -268 T 170 -240 Q 170 -223 181 -211 T 209 -199 H 1384 Q 1400 -199 1410 -211 T 1421 -240 Q 1421 -255 1410 -268 T 1384 -281 H 209 Z M 190 676 Q 170 682 170 711 Q 170 737 197 748 L 1366 1300 Q 1370 1303 1380 1303 Q 1397 1303 1409 1291 T 1421 1262 Q 1421 1235 1397 1225 L 307 711 L 1403 193 Q 1421 183 1421 158 Q 1421 140 1409 128 T 1380 117 Q 1370 117 1366 121 L 190 676 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1055.55859, 0.00000)" d="M 190 0 V 72 Q 446 72 446 137 V 1212 Q 340 1161 178 1161 V 1233 Q 429 1233 557 1364 H 586 Q 593 1364 599 1358 T 606 1346 V 137 Q 606 72 862 72 V 0 H 190 Z "/><g transform="translate(1555.55859, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/><g transform="translate(500.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 233 0 V 82 Q 516 82 516 143 V 1202 Q 401 1147 219 1147 V 1229 Q 341 1229 447 1258 T 629 1360 H 666 Q 685 1355 690 1335 V 143 Q 690 82 973 82 V 0 H 233 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 398.60800, 0.00000)" d="M 80 336 V 418 L 762 1346 Q 772 1360 791 1360 H 831 Q 844 1360 852 1352 T 860 1331 V 418 H 1083 V 336 H 860 V 143 Q 860 82 1081 82 V 0 H 457 V 82 Q 678 82 678 143 V 336 H 80 Z M 168 418 H 692 V 1133 L 168 418 Z "/></g></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 3074.99756, 0.00000)" d="M 209 471 Q 192 471 181 484 T 170 512 Q 170 527 181 540 T 209 553 H 1384 Q 1400 553 1410 540 T 1421 512 Q 1421 497 1410 484 T 1384 471 H 209 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 4075.00049, 0.00000)" d="M 190 0 V 72 Q 446 72 446 137 V 1212 Q 340 1161 178 1161 V 1233 Q 429 1233 557 1364 H 586 Q 593 1364 599 1358 T 606 1346 V 137 Q 606 72 862 72 V 0 H 190 Z "/><g transform="translate(4575.00049, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/><g transform="translate(500.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 233 0 V 82 Q 516 82 516 143 V 1202 Q 401 1147 219 1147 V 1229 Q 341 1229 447 1258 T 629 1360 H 666 Q 685 1355 690 1335 V 143 Q 690 82 973 82 V 0 H 233 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 398.60800, 0.00000)" d="M 582 -41 Q 448 -41 355 22 T 209 188 T 133 414 T 111 662 Q 111 833 185 995 T 396 1259 T 709 1360 Q 829 1360 912 1302 T 995 1126 Q 995 1098 981 1075 T 944 1039 T 895 1026 Q 852 1026 822 1054 T 793 1126 Q 793 1164 819 1195 T 885 1227 Q 830 1292 709 1292 Q 617 1292 537 1244 T 408 1116 Q 353 1031 334 924 T 315 684 Q 359 770 436 822 T 606 874 Q 732 874 834 813 T 994 649 T 1053 420 Q 1053 290 989 184 T 817 19 T 582 -41 Z M 582 33 Q 692 33 751 86 T 829 223 T 848 420 Q 848 533 832 615 T 759 753 T 594 809 Q 509 809 447 757 T 353 626 T 322 463 V 422 V 410 Q 322 262 384 147 T 582 33 Z "/></g></g></g></svg>. We also derive upper limits from a long-duration search for bursts with durations between 1 and 10 s. These represent the strictest upper limits on concurrent GW emission from FRBs.</div></div></div><div class="gs_scl"><div class="gsc_oci_field">Scholar articles</div><div class="gsc_oci_value"><div class="gsc_oci_merged_snippet"><div><a href="/scholar?oi=bibs&cluster=9061563233618790801&btnI=1&hl=en">A search using GEO600 for gravitational waves coincident with fast radio bursts from SGR 1935+ 2154</a></div><div>AG Abac, R Abbott, I Abouelfettouh, F Acernese… - arXiv preprint arXiv:2410.09151, 2024</div><div><a class="gsc_oms_link" href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&q=related:kYmWMcAjwX0J:scholar.google.com/">Related articles</a> <a class="gsc_oms_link" href="https://scholar.google.co.in/scholar?oi=bibs&hl=en&cluster=9061563233618790801">All 5 versions</a> </div></div></div></div></div></div></div></div><div id="gs_ftr_sp" role="presentation"></div><div id="gs_ftr" class="gs_md_rmb" role="contentinfo"><div id="gs_ftr_rt"><a href="//www.google.co.in/intl/en/policies/privacy/">Privacy</a><a href="//www.google.co.in/intl/en/policies/terms/">Terms</a><a href="javascript:void(0)" ontouchstart="gs_evt_dsp(event)" role="button" aria-controls="gs_ftr_mnu" aria-haspopup="true" class="gs_press gs_md_tb">Help</a></div><div id="gs_ftr_mnu" class="gs_md_d gs_md_ds gs_ttzi gs_md_ulr" role="menu" tabindex="-1"><a role="menuitem" href="/intl/en/scholar/about.html" tabindex="-1" class="gs_md_li">About Scholar</a><a role="menuitem" href="//support.google.com/websearch?p=scholar_dsa&hl=en" tabindex="-1" class="gs_md_li">Search help</a></div></div></div></body></html>