Technical note
|
27 Aug 2025
Technical note |
|
27 Aug 2025
Technical note: General formulation for the distribution problem – prognostic assumed probability density function (PDF) approach based on the maximum-entropy principle and the Liouville equation
Jun-Ichi Yano , Vincent E. Larson , and Vaughan T. J. Phillips
Viewed
Total article views: 7,081 (including HTML, PDF, and XML)
HTML
PDF
XML
Total
BibTeX
EndNote
6,153
783
145
7,081
166
273
HTML: 6,153
PDF: 783
XML: 145
Total: 7,081
BibTeX: 166
EndNote: 273
Views and downloads (calculated since 23 Jan 2024)
Month
HTML
PDF
XML
Total
Jan 2024
74
22
2
98
Feb 2024
51
11
6
68
Mar 2024
29
6
3
38
Apr 2024
28
9
7
44
May 2024
44
14
5
63
Jun 2024
19
12
5
36
Jul 2024
44
14
4
62
Aug 2024
28
4
0
32
Sep 2024
36
18
2
56
Oct 2024
16
14
0
30
Nov 2024
24
2
0
26
Dec 2024
12
12
2
26
Jan 2025
20
12
2
34
Feb 2025
28
20
0
48
Mar 2025
22
20
2
44
Apr 2025
20
22
0
42
May 2025
10
16
2
28
Jun 2025
42
26
0
68
Jul 2025
14
34
0
48
Aug 2025
943
47
3
993
Sep 2025
2,948
57
10
3,015
Oct 2025
217
53
4
274
Nov 2025
259
31
10
300
Dec 2025
176
62
13
251
Jan 2026
286
46
25
357
Feb 2026
469
46
12
527
Mar 2026
106
81
12
199
Apr 2026
93
37
8
138
May 2026
95
35
6
136
Cumulative views and downloads
(calculated since 23 Jan 2024)
Month
HTML views
PDF downloads
XML downloads
Jan 2024
74
22
2
98
Feb 2024
125
33
8
166
Mar 2024
154
39
11
204
Apr 2024
182
48
18
248
May 2024
226
62
23
311
Jun 2024
245
74
28
347
Jul 2024
289
88
32
409
Aug 2024
317
92
32
441
Sep 2024
353
110
34
497
Oct 2024
369
124
34
527
Nov 2024
393
126
34
553
Dec 2024
405
138
36
579
Jan 2025
425
150
38
613
Feb 2025
453
170
38
661
Mar 2025
475
190
40
705
Apr 2025
495
212
40
747
May 2025
505
228
42
775
Jun 2025
547
254
42
843
Jul 2025
561
288
42
891
Aug 2025
1,504
335
45
1,884
Sep 2025
4,452
392
55
4,899
Oct 2025
4,669
445
59
5,173
Nov 2025
4,928
476
69
5,473
Dec 2025
5,104
538
82
5,724
Jan 2026
5,390
584
107
6,081
Feb 2026
5,859
630
119
6,608
Mar 2026
5,965
711
131
6,807
Apr 2026
6,058
748
139
6,945
May 2026
6,153
783
145
7,081
Total article views: 4,988 (including HTML, PDF, and XML)
HTML
PDF
XML
Total
BibTeX
EndNote
4,690
238
60
4,988
75
115
HTML: 4,690
PDF: 238
XML: 60
Total: 4,988
BibTeX: 75
EndNote: 115
Views and downloads (calculated since 27 Aug 2025)
Month
HTML
PDF
XML
Total
Aug 2025
777
11
3
791
Sep 2025
2,644
17
6
2,667
Oct 2025
149
17
2
168
Nov 2025
149
13
4
166
Dec 2025
136
42
7
185
Jan 2026
226
30
15
271
Feb 2026
407
28
4
439
Mar 2026
58
39
6
103
Apr 2026
73
21
8
102
May 2026
71
20
5
96
Cumulative views and downloads
(calculated since 27 Aug 2025)
Month
HTML views
PDF downloads
XML downloads
Aug 2025
777
11
3
Sep 2025
3,421
28
9
Oct 2025
3,570
45
11
Nov 2025
3,719
58
15
Dec 2025
3,855
100
22
Jan 2026
4,081
130
37
Mar 2026
4,488
158
41
Mar 2026
4,546
197
47
Apr 2026
4,619
218
55
May 2026
4,690
238
60
Total article views: 2,093 (including HTML, PDF, and XML)
HTML
PDF
XML
Total
BibTeX
EndNote
1,463
545
85
2,093
91
158
HTML: 1,463
PDF: 545
XML: 85
Total: 2,093
BibTeX: 91
EndNote: 158
Views and downloads (calculated since 23 Jan 2024)
Month
HTML
PDF
XML
Total
Jan 2024
74
22
2
98
Feb 2024
51
11
6
68
Mar 2024
29
6
3
38
Apr 2024
28
9
7
44
May 2024
44
14
5
63
Jun 2024
19
12
5
36
Jul 2024
44
14
4
62
Aug 2024
28
4
0
32
Sep 2024
36
18
2
56
Oct 2024
16
14
0
30
Nov 2024
24
2
0
26
Dec 2024
12
12
2
26
Jan 2025
20
12
2
34
Feb 2025
28
20
0
48
Mar 2025
22
20
2
44
Apr 2025
20
22
0
42
May 2025
10
16
2
28
Jun 2025
42
26
0
68
Jul 2025
14
34
0
48
Aug 2025
166
36
0
202
Sep 2025
304
40
4
348
Oct 2025
68
36
2
106
Nov 2025
110
18
6
134
Dec 2025
40
20
6
66
Jan 2026
60
16
10
86
Feb 2026
62
18
8
88
Mar 2026
48
42
6
96
Apr 2026
20
16
0
36
May 2026
24
15
1
40
Cumulative views and downloads
(calculated since 23 Jan 2024)
Month
HTML views
PDF downloads
XML downloads
Jan 2024
74
22
2
Mar 2024
125
33
8
Mar 2024
154
39
11
Apr 2024
182
48
18
May 2024
226
62
23
Jun 2024
245
74
28
Jul 2024
289
88
32
Aug 2024
317
92
32
Sep 2024
353
110
34
Oct 2024
369
124
34
Nov 2024
393
126
34
Dec 2024
405
138
36
Jan 2025
425
150
38
Mar 2025
453
170
38
Mar 2025
475
190
40
Apr 2025
495
212
40
May 2025
505
228
42
Jun 2025
547
254
42
Jul 2025
561
288
42
Aug 2025
727
324
42
Sep 2025
1,031
364
46
Oct 2025
1,099
400
48
Nov 2025
1,209
418
54
Dec 2025
1,249
438
60
Jan 2026
1,309
454
70
Mar 2026
1,371
472
78
Mar 2026
1,419
514
84
Apr 2026
1,439
530
84
May 2026
1,463
545
85
Viewed (geographical distribution)
Total article views: 7,081 (including HTML, PDF, and XML)
Thereof 7,054 with geography defined
and 27 with unknown origin.
Total article views: 4,988 (including HTML, PDF, and XML)
Thereof 4,965 with geography defined
and 23 with unknown origin.
Total article views: 2,093 (including HTML, PDF, and XML)
Thereof 2,089 with geography defined
and 4 with unknown origin.
Total:
0
HTML:
0
PDF:
0
XML:
0
Total:
0
HTML:
0
PDF:
0
XML:
0
Total:
0
HTML:
0
PDF:
0
XML:
0
Latest update: 30 May 2026