Research article
|
21 May 2015
Research article |
|
21 May 2015
An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current
I. V. Shugan , H. H. Hwung , and R. Y. Yang
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Total article views: 2,225 (including HTML, PDF, and XML)
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Total
BibTeX
EndNote
1,177
890
158
2,225
170
175
HTML: 1,177
PDF: 890
XML: 158
Total: 2,225
BibTeX: 170
EndNote: 175
Views and downloads (calculated since 05 Dec 2014)
Month
HTML
PDF
XML
Total
Dec 2014
39
20
2
61
Jan 2015
18
18
3
39
Feb 2015
4
6
1
11
Mar 2015
2
1
2
5
Apr 2015
6
0
6
May 2015
30
29
2
61
Jun 2015
54
17
2
73
Jul 2015
38
18
0
56
Aug 2015
21
13
2
36
Sep 2015
18
7
2
27
Oct 2015
22
6
1
29
Nov 2015
30
13
2
45
Dec 2015
2
11
0
13
Jan 2016
22
16
0
38
Feb 2016
5
15
0
20
Mar 2016
5
6
1
12
Apr 2016
3
4
0
7
May 2016
3
6
0
9
Jun 2016
7
3
0
10
Jul 2016
5
1
2
8
Aug 2016
6
8
0
14
Sep 2016
8
4
0
12
Oct 2016
6
4
1
11
Nov 2016
4
1
0
5
Dec 2016
2
3
0
5
Jan 2017
6
1
0
7
Feb 2017
8
2
0
10
Mar 2017
16
3
0
19
Apr 2017
19
7
0
26
May 2017
21
4
0
25
Jun 2017
21
6
0
27
Jul 2017
10
5
0
15
Aug 2017
8
11
3
22
Sep 2017
9
10
1
20
Oct 2017
13
14
2
29
Nov 2017
9
8
2
19
Dec 2017
18
9
5
32
Jan 2018
20
12
11
43
Feb 2018
15
5
1
21
Mar 2018
13
8
3
24
Apr 2018
15
13
7
35
May 2018
11
6
3
20
Jun 2018
16
12
4
32
Jul 2018
17
12
7
36
Aug 2018
19
10
5
34
Sep 2018
16
9
3
28
Oct 2018
18
15
7
40
Nov 2018
14
12
3
29
Dec 2018
12
8
1
21
Jan 2019
11
9
3
23
Feb 2019
11
9
3
23
Mar 2019
8
8
3
19
Apr 2019
13
11
4
28
May 2019
10
7
2
19
Jun 2019
5
10
0
15
Jul 2019
11
7
0
18
Aug 2019
13
13
1
27
Sep 2019
9
8
0
17
Oct 2019
6
4
1
11
Nov 2019
6
6
1
13
Dec 2019
9
9
1
19
Jan 2020
17
7
3
27
Feb 2020
9
5
1
15
Mar 2020
7
10
3
20
Apr 2020
8
8
1
17
May 2020
10
6
1
17
Jun 2020
24
12
2
38
Jul 2020
24
17
10
51
Aug 2020
3
6
6
15
Sep 2020
11
5
0
16
Oct 2020
7
12
0
19
Nov 2020
2
2
0
4
Dec 2020
7
5
0
12
Jan 2021
19
10
0
29
Feb 2021
8
4
0
12
Mar 2021
2
2
0
4
Apr 2021
8
3
0
11
May 2021
4
6
0
10
Jun 2021
5
2
0
7
Jul 2021
5
7
0
12
Aug 2021
4
6
0
10
Sep 2021
9
10
3
22
Oct 2021
4
33
1
38
Nov 2021
11
25
1
37
Dec 2021
12
10
0
22
Jan 2022
5
7
0
12
Feb 2022
6
2
2
10
Mar 2022
6
7
0
13
Apr 2022
6
6
0
12
May 2022
5
5
1
11
Jun 2022
4
5
1
10
Jul 2022
5
7
0
12
Aug 2022
4
7
0
11
Sep 2022
4
4
0
8
Oct 2022
5
3
1
9
Nov 2022
8
5
0
13
Dec 2022
8
5
0
13
Jan 2023
10
6
0
16
Feb 2023
10
5
1
16
Mar 2023
6
8
0
14
Apr 2023
2
6
0
8
May 2023
2
8
1
11
Jun 2023
2
2
1
5
Jul 2023
4
6
0
10
Aug 2023
4
5
2
11
Sep 2023
2
6
0
8
Oct 2023
5
3
1
9
Nov 2023
8
1
3
12
Dec 2023
13
3
1
17
Jan 2024
3
8
1
12
Feb 2024
5
0
5
Mar 2024
4
9
0
13
Cumulative views and downloads
(calculated since 05 Dec 2014)
Month
HTML views
PDF downloads
XML downloads
Dec 2014
39
20
2
61
Jan 2015
57
38
5
100
Feb 2015
61
44
6
111
Mar 2015
63
45
8
116
Apr 2015
69
45
8
122
May 2015
99
74
10
183
Jun 2015
153
91
12
256
Jul 2015
191
109
12
312
Aug 2015
212
122
14
348
Sep 2015
230
129
16
375
Oct 2015
252
135
17
404
Nov 2015
282
148
19
449
Dec 2015
284
159
19
462
Jan 2016
306
175
19
500
Feb 2016
311
190
19
520
Mar 2016
316
196
20
532
Apr 2016
319
200
20
539
May 2016
322
206
20
548
Jun 2016
329
209
20
558
Jul 2016
334
210
22
566
Aug 2016
340
218
22
580
Sep 2016
348
222
22
592
Oct 2016
354
226
23
603
Nov 2016
358
227
23
608
Dec 2016
360
230
23
613
Jan 2017
366
231
23
620
Feb 2017
374
233
23
630
Mar 2017
390
236
23
649
Apr 2017
409
243
23
675
May 2017
430
247
23
700
Jun 2017
451
253
23
727
Jul 2017
461
258
23
742
Aug 2017
469
269
26
764
Sep 2017
478
279
27
784
Oct 2017
491
293
29
813
Nov 2017
500
301
31
832
Dec 2017
518
310
36
864
Jan 2018
538
322
47
907
Feb 2018
553
327
48
928
Mar 2018
566
335
51
952
Apr 2018
581
348
58
987
May 2018
592
354
61
1,007
Jun 2018
608
366
65
1,039
Jul 2018
625
378
72
1,075
Aug 2018
644
388
77
1,109
Sep 2018
660
397
80
1,137
Oct 2018
678
412
87
1,177
Nov 2018
692
424
90
1,206
Dec 2018
704
432
91
1,227
Jan 2019
715
441
94
1,250
Feb 2019
726
450
97
1,273
Mar 2019
734
458
100
1,292
Apr 2019
747
469
104
1,320
May 2019
757
476
106
1,339
Jun 2019
762
486
106
1,354
Jul 2019
773
493
106
1,372
Aug 2019
786
506
107
1,399
Sep 2019
795
514
107
1,416
Oct 2019
801
518
108
1,427
Nov 2019
807
524
109
1,440
Dec 2019
816
533
110
1,459
Jan 2020
833
540
113
1,486
Feb 2020
842
545
114
1,501
Mar 2020
849
555
117
1,521
Apr 2020
857
563
118
1,538
May 2020
867
569
119
1,555
Jun 2020
891
581
121
1,593
Jul 2020
915
598
131
1,644
Aug 2020
918
604
137
1,659
Sep 2020
929
609
137
1,675
Oct 2020
936
621
137
1,694
Nov 2020
938
623
137
1,698
Dec 2020
945
628
137
1,710
Jan 2021
964
638
137
1,739
Feb 2021
972
642
137
1,751
Mar 2021
974
644
137
1,755
Apr 2021
982
647
137
1,766
May 2021
986
653
137
1,776
Jun 2021
991
655
137
1,783
Jul 2021
996
662
137
1,795
Aug 2021
1,000
668
137
1,805
Sep 2021
1,009
678
140
1,827
Oct 2021
1,013
711
141
1,865
Nov 2021
1,024
736
142
1,902
Dec 2021
1,036
746
142
1,924
Jan 2022
1,041
753
142
1,936
Feb 2022
1,047
755
144
1,946
Mar 2022
1,053
762
144
1,959
Apr 2022
1,059
768
144
1,971
May 2022
1,064
773
145
1,982
Jun 2022
1,068
778
146
1,992
Jul 2022
1,073
785
146
2,004
Aug 2022
1,077
792
146
2,015
Sep 2022
1,081
796
146
2,023
Oct 2022
1,086
799
147
2,032
Nov 2022
1,094
804
147
2,045
Dec 2022
1,102
809
147
2,058
Jan 2023
1,112
815
147
2,074
Feb 2023
1,122
820
148
2,090
Mar 2023
1,128
828
148
2,104
Apr 2023
1,130
834
148
2,112
May 2023
1,132
842
149
2,123
Jun 2023
1,134
844
150
2,128
Jul 2023
1,138
850
150
2,138
Aug 2023
1,142
855
152
2,149
Sep 2023
1,144
861
152
2,157
Oct 2023
1,149
864
153
2,166
Nov 2023
1,157
865
156
2,178
Dec 2023
1,170
868
157
2,195
Jan 2024
1,173
876
158
2,207
Feb 2024
1,173
881
158
2,212
Mar 2024
1,177
890
158
2,225
Total article views: 1,773 (including HTML, PDF, and XML)
HTML
PDF
XML
Total
BibTeX
EndNote
938
698
137
1,773
157
162
HTML: 938
PDF: 698
XML: 137
Total: 1,773
BibTeX: 157
EndNote: 162
Views and downloads (calculated since 21 May 2015)
Month
HTML
PDF
XML
Total
May 2015
21
26
2
49
Jun 2015
40
14
1
55
Jul 2015
26
16
0
42
Aug 2015
16
10
0
26
Sep 2015
11
5
1
17
Oct 2015
14
3
0
17
Nov 2015
17
9
0
26
Dec 2015
2
10
0
12
Jan 2016
17
14
0
31
Feb 2016
4
9
0
13
Mar 2016
5
6
1
12
Apr 2016
3
2
0
5
May 2016
3
6
0
9
Jun 2016
4
1
0
5
Jul 2016
4
1
1
6
Aug 2016
5
7
0
12
Sep 2016
7
3
0
10
Oct 2016
5
2
1
8
Nov 2016
3
1
0
4
Dec 2016
2
2
0
4
Jan 2017
5
1
0
6
Feb 2017
7
2
0
9
Mar 2017
14
3
0
17
Apr 2017
13
6
0
19
May 2017
20
4
0
24
Jun 2017
21
6
0
27
Jul 2017
10
5
0
15
Aug 2017
6
7
3
16
Sep 2017
6
9
1
16
Oct 2017
11
11
2
24
Nov 2017
8
7
2
17
Dec 2017
14
7
5
26
Jan 2018
19
10
11
40
Feb 2018
13
5
1
19
Mar 2018
12
7
3
22
Apr 2018
12
11
7
30
May 2018
9
5
3
17
Jun 2018
13
11
4
28
Jul 2018
15
10
7
32
Aug 2018
18
8
5
31
Sep 2018
15
6
3
24
Oct 2018
17
14
7
38
Nov 2018
12
10
3
25
Dec 2018
11
7
1
19
Jan 2019
10
7
3
20
Feb 2019
10
8
3
21
Mar 2019
7
6
3
16
Apr 2019
11
8
4
23
May 2019
9
7
2
18
Jun 2019
5
10
0
15
Jul 2019
11
6
0
17
Aug 2019
11
12
1
24
Sep 2019
8
7
0
15
Oct 2019
4
3
1
8
Nov 2019
5
5
1
11
Dec 2019
5
7
1
13
Jan 2020
15
6
3
24
Feb 2020
7
3
1
11
Mar 2020
5
8
3
16
Apr 2020
7
6
1
14
May 2020
10
5
1
16
Jun 2020
20
11
2
33
Jul 2020
23
13
8
44
Aug 2020
2
4
3
9
Sep 2020
11
4
0
15
Oct 2020
5
11
0
16
Nov 2020
2
2
0
4
Dec 2020
5
2
0
7
Jan 2021
18
5
0
23
Feb 2021
6
1
0
7
Mar 2021
2
2
0
4
Apr 2021
5
1
0
6
May 2021
4
3
0
7
Jun 2021
5
2
0
7
Jul 2021
5
6
0
11
Aug 2021
4
5
0
9
Sep 2021
9
10
3
22
Oct 2021
4
33
1
38
Nov 2021
10
20
1
31
Dec 2021
12
2
0
14
Jan 2022
5
6
0
11
Feb 2022
6
2
2
10
Mar 2022
6
7
0
13
Apr 2022
5
6
0
11
May 2022
5
5
1
11
Jun 2022
4
5
1
10
Jul 2022
4
7
0
11
Aug 2022
4
6
0
10
Sep 2022
4
4
0
8
Oct 2022
5
1
1
7
Nov 2022
7
4
0
11
Dec 2022
8
5
0
13
Jan 2023
10
6
0
16
Feb 2023
9
3
1
13
Mar 2023
6
6
0
12
Apr 2023
2
6
0
8
May 2023
2
6
1
9
Jun 2023
2
2
1
5
Jul 2023
3
5
0
8
Aug 2023
4
3
2
9
Sep 2023
2
6
0
8
Oct 2023
5
3
1
9
Nov 2023
8
1
3
12
Dec 2023
13
1
1
15
Jan 2024
3
8
1
12
Feb 2024
5
0
5
Mar 2024
4
9
0
13
Cumulative views and downloads
(calculated since 21 May 2015)
Month
HTML views
PDF downloads
XML downloads
May 2015
21
26
2
Jun 2015
61
40
3
Jul 2015
87
56
3
Aug 2015
103
66
3
Sep 2015
114
71
4
Oct 2015
128
74
4
Nov 2015
145
83
4
Dec 2015
147
93
4
Jan 2016
164
107
4
Feb 2016
168
116
4
Mar 2016
173
122
5
Apr 2016
176
124
5
May 2016
179
130
5
Jun 2016
183
131
5
Jul 2016
187
132
6
Aug 2016
192
139
6
Sep 2016
199
142
6
Oct 2016
204
144
7
Nov 2016
207
145
7
Dec 2016
209
147
7
Jan 2017
214
148
7
Feb 2017
221
150
7
Mar 2017
235
153
7
Apr 2017
248
159
7
May 2017
268
163
7
Jun 2017
289
169
7
Jul 2017
299
174
7
Aug 2017
305
181
10
Sep 2017
311
190
11
Oct 2017
322
201
13
Nov 2017
330
208
15
Dec 2017
344
215
20
Jan 2018
363
225
31
Feb 2018
376
230
32
Mar 2018
388
237
35
Apr 2018
400
248
42
May 2018
409
253
45
Jun 2018
422
264
49
Jul 2018
437
274
56
Aug 2018
455
282
61
Sep 2018
470
288
64
Oct 2018
487
302
71
Nov 2018
499
312
74
Dec 2018
510
319
75
Jan 2019
520
326
78
Feb 2019
530
334
81
Mar 2019
537
340
84
Apr 2019
548
348
88
May 2019
557
355
90
Jun 2019
562
365
90
Jul 2019
573
371
90
Aug 2019
584
383
91
Sep 2019
592
390
91
Oct 2019
596
393
92
Nov 2019
601
398
93
Dec 2019
606
405
94
Jan 2020
621
411
97
Feb 2020
628
414
98
Mar 2020
633
422
101
Apr 2020
640
428
102
May 2020
650
433
103
Jun 2020
670
444
105
Jul 2020
693
457
113
Aug 2020
695
461
116
Sep 2020
706
465
116
Oct 2020
711
476
116
Nov 2020
713
478
116
Dec 2020
718
480
116
Jan 2021
736
485
116
Feb 2021
742
486
116
Mar 2021
744
488
116
Apr 2021
749
489
116
May 2021
753
492
116
Jun 2021
758
494
116
Jul 2021
763
500
116
Aug 2021
767
505
116
Sep 2021
776
515
119
Oct 2021
780
548
120
Nov 2021
790
568
121
Dec 2021
802
570
121
Jan 2022
807
576
121
Feb 2022
813
578
123
Mar 2022
819
585
123
Apr 2022
824
591
123
May 2022
829
596
124
Jun 2022
833
601
125
Jul 2022
837
608
125
Aug 2022
841
614
125
Sep 2022
845
618
125
Oct 2022
850
619
126
Nov 2022
857
623
126
Dec 2022
865
628
126
Jan 2023
875
634
126
Feb 2023
884
637
127
Mar 2023
890
643
127
Apr 2023
892
649
127
May 2023
894
655
128
Jun 2023
896
657
129
Jul 2023
899
662
129
Aug 2023
903
665
131
Sep 2023
905
671
131
Oct 2023
910
674
132
Nov 2023
918
675
135
Dec 2023
931
676
136
Jan 2024
934
684
137
Feb 2024
934
689
137
Mar 2024
938
698
137
Total article views: 452 (including HTML, PDF, and XML)
HTML
PDF
XML
Total
BibTeX
EndNote
239
192
21
452
13
13
HTML: 239
PDF: 192
XML: 21
Total: 452
BibTeX: 13
EndNote: 13
Views and downloads (calculated since 05 Dec 2014)
Month
HTML
PDF
XML
Total
Dec 2014
39
20
2
61
Jan 2015
18
18
3
39
Feb 2015
4
6
1
11
Mar 2015
2
1
2
5
Apr 2015
6
0
6
May 2015
9
3
0
12
Jun 2015
14
3
1
18
Jul 2015
12
2
0
14
Aug 2015
5
3
2
10
Sep 2015
7
2
1
10
Oct 2015
8
3
1
12
Nov 2015
13
4
2
19
Dec 2015
1
0
1
Jan 2016
5
2
0
7
Feb 2016
1
6
0
7
Mar 2016
0
Apr 2016
2
0
2
May 2016
0
Jun 2016
3
2
0
5
Jul 2016
1
1
2
Aug 2016
1
1
0
2
Sep 2016
1
1
0
2
Oct 2016
1
2
0
3
Nov 2016
1
0
1
Dec 2016
1
0
1
Jan 2017
1
0
1
Feb 2017
1
0
1
Mar 2017
2
0
2
Apr 2017
6
1
0
7
May 2017
1
0
1
Jun 2017
0
Jul 2017
0
Aug 2017
2
4
0
6
Sep 2017
3
1
0
4
Oct 2017
2
3
0
5
Nov 2017
1
1
0
2
Dec 2017
4
2
0
6
Jan 2018
1
2
0
3
Feb 2018
2
0
2
Mar 2018
1
1
0
2
Apr 2018
3
2
0
5
May 2018
2
1
0
3
Jun 2018
3
1
0
4
Jul 2018
2
2
0
4
Aug 2018
1
2
0
3
Sep 2018
1
3
0
4
Oct 2018
1
1
0
2
Nov 2018
2
2
0
4
Dec 2018
1
1
0
2
Jan 2019
1
2
0
3
Feb 2019
1
1
0
2
Mar 2019
1
2
0
3
Apr 2019
2
3
0
5
May 2019
1
0
1
Jun 2019
0
Jul 2019
1
0
1
Aug 2019
2
1
0
3
Sep 2019
1
1
0
2
Oct 2019
2
1
0
3
Nov 2019
1
1
0
2
Dec 2019
4
2
0
6
Jan 2020
2
1
0
3
Feb 2020
2
2
0
4
Mar 2020
2
2
0
4
Apr 2020
1
2
0
3
May 2020
1
0
1
Jun 2020
4
1
0
5
Jul 2020
1
4
2
7
Aug 2020
1
2
3
6
Sep 2020
1
0
1
Oct 2020
2
1
0
3
Nov 2020
0
Dec 2020
2
3
0
5
Jan 2021
1
5
0
6
Feb 2021
2
3
0
5
Mar 2021
0
Apr 2021
3
2
0
5
May 2021
3
0
3
Jun 2021
0
Jul 2021
1
0
1
Aug 2021
1
0
1
Sep 2021
0
Oct 2021
0
Nov 2021
1
5
0
6
Dec 2021
8
0
8
Jan 2022
1
0
1
Feb 2022
0
Mar 2022
0
Apr 2022
1
0
1
May 2022
0
Jun 2022
0
Jul 2022
1
0
1
Aug 2022
1
0
1
Sep 2022
0
Oct 2022
2
0
2
Nov 2022
1
1
0
2
Dec 2022
0
Jan 2023
0
Feb 2023
1
2
0
3
Mar 2023
2
0
2
Apr 2023
0
May 2023
2
0
2
Jun 2023
0
Jul 2023
1
1
0
2
Aug 2023
2
0
2
Sep 2023
0
Oct 2023
0
Nov 2023
0
Dec 2023
2
0
2
Jan 2024
0
Feb 2024
0
Mar 2024
0
Cumulative views and downloads
(calculated since 05 Dec 2014)
Month
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Dec 2014
39
20
2
Jan 2015
57
38
5
Feb 2015
61
44
6
Mar 2015
63
45
8
Apr 2015
69
45
8
May 2015
78
48
8
Jun 2015
92
51
9
Jul 2015
104
53
9
Aug 2015
109
56
11
Sep 2015
116
58
12
Oct 2015
124
61
13
Nov 2015
137
65
15
Dec 2015
137
66
15
Jan 2016
142
68
15
Feb 2016
143
74
15
Mar 2016
143
74
15
Apr 2016
143
76
15
May 2016
143
76
15
Jun 2016
146
78
15
Jul 2016
147
78
16
Aug 2016
148
79
16
Sep 2016
149
80
16
Oct 2016
150
82
16
Nov 2016
151
82
16
Dec 2016
151
83
16
Jan 2017
152
83
16
Feb 2017
153
83
16
Mar 2017
155
83
16
Apr 2017
161
84
16
May 2017
162
84
16
Jun 2017
162
84
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Jul 2017
162
84
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Aug 2017
164
88
16
Sep 2017
167
89
16
Oct 2017
169
92
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Nov 2017
170
93
16
Dec 2017
174
95
16
Jan 2018
175
97
16
Feb 2018
177
97
16
Mar 2018
178
98
16
Apr 2018
181
100
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May 2018
183
101
16
Jun 2018
186
102
16
Jul 2018
188
104
16
Aug 2018
189
106
16
Sep 2018
190
109
16
Oct 2018
191
110
16
Nov 2018
193
112
16
Dec 2018
194
113
16
Jan 2019
195
115
16
Feb 2019
196
116
16
Mar 2019
197
118
16
Apr 2019
199
121
16
May 2019
200
121
16
Jun 2019
200
121
16
Jul 2019
200
122
16
Aug 2019
202
123
16
Sep 2019
203
124
16
Oct 2019
205
125
16
Nov 2019
206
126
16
Dec 2019
210
128
16
Jan 2020
212
129
16
Feb 2020
214
131
16
Mar 2020
216
133
16
Apr 2020
217
135
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May 2020
217
136
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Jun 2020
221
137
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Jul 2020
222
141
18
Aug 2020
223
143
21
Sep 2020
223
144
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Oct 2020
225
145
21
Nov 2020
225
145
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Dec 2020
227
148
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Jan 2021
228
153
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Feb 2021
230
156
21
Mar 2021
230
156
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Apr 2021
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158
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May 2021
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Jun 2021
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Jul 2021
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Aug 2021
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Sep 2021
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Oct 2021
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Nov 2021
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168
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Dec 2021
234
176
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Jan 2022
234
177
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Feb 2022
234
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Mar 2022
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Apr 2022
235
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May 2022
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Aug 2022
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Sep 2022
236
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Oct 2022
236
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Nov 2022
237
181
21
Dec 2022
237
181
21
Jan 2023
237
181
21
Feb 2023
238
183
21
Mar 2023
238
185
21
Apr 2023
238
185
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May 2023
238
187
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Jun 2023
238
187
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Jul 2023
239
188
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Aug 2023
239
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Sep 2023
239
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Oct 2023
239
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Nov 2023
239
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Dec 2023
239
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Jan 2024
239
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Feb 2024
239
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Mar 2024
239
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21
Cited
Saved (final revised paper)
Latest update: 28 Mar 2024