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+ "text": "ุชุฃุชูŠู†ูŠ\".",
372
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373
+ "start_index": 353
374
+ },
375
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376
+ "text": "\"ุงุจู†",
377
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379
+ },
380
+ {
381
+ "text": "ุณุนุฏ\".",
382
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384
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385
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386
+ "text": "ุฃู†",
387
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389
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391
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394
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399
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401
+ "text": "ู‡ุฐุง",
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+ "confidence": 1.0,
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+ "start_index": 386
404
+ },
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+ {
406
+ "text": "ุจู‚ูˆู„ู‡",
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+ "start_index": 390
409
+ },
410
+ {
411
+ "text": "ููŠ",
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416
+ "text": "ู„ูŠู„ุฉ",
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+ "start_index": 399
419
+ },
420
+ {
421
+ "text": "ุงู„ุตู‘ูŠุงู…:",
422
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+ "start_index": 404
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+ },
425
+ {
426
+ "text": "{ุฃูŽูŠู‘ุงู…ุงู‹",
427
+ "confidence": 1.0,
428
+ "start_index": 413
429
+ },
430
+ {
431
+ "text": "ู…ูŽุนู’ุฏููˆุฏุงุชู}",
432
+ "confidence": 1.0,
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+ "start_index": 423
434
+ },
435
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436
+ "text": "ุฃุฑุงุฏ",
437
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438
+ "start_index": 436
439
+ },
440
+ {
441
+ "text": "ุจู‡ุง",
442
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+ "start_index": 441
444
+ },
445
+ {
446
+ "text": "ุงู„ุดู‡ุฑ",
447
+ "confidence": 1.0,
448
+ "start_index": 445
449
+ },
450
+ {
451
+ "text": "ูƒู„ู‘ู‡ุ›",
452
+ "confidence": 1.0,
453
+ "start_index": 451
454
+ },
455
+ {
456
+ "text": "ู„ุฃู†ู‡",
457
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458
+ "start_index": 457
459
+ },
460
+ {
461
+ "text": "ุธุงู‡ุฑ",
462
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464
+ },
465
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466
+ "text": "ู„ูุธ",
467
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468
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469
+ },
470
+ {
471
+ "text": "ุงู„ุฃูŠู‘ุงู…",
472
+ "confidence": 1.0,
473
+ "start_index": 471
474
+ },
475
+ {
476
+ "text": "ู…ู†",
477
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479
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480
+ {
481
+ "text": "ุงู„ุซู„ุงุซุฉ",
482
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483
+ "start_index": 482
484
+ },
485
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486
+ "text": "ุฅู„ู‰",
487
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489
+ },
490
+ {
491
+ "text": "ุงู„ุนุดุฑุฉ.",
492
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493
+ "start_index": 494
494
+ },
495
+ {
496
+ "text": "ุฅู„ุงู‘",
497
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499
+ },
500
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501
+ "text": "ุฃู†ู‡",
502
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504
+ },
505
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506
+ "text": "ู‚ุฏ",
507
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508
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509
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510
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511
+ "text": "ูŠุฐูƒุฑ",
512
+ "confidence": 1.0,
513
+ "start_index": 514
514
+ },
515
+ {
516
+ "text": "ูˆูŠุฑุงุฏ",
517
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518
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519
+ },
520
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521
+ "text": "ุจู‡",
522
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523
+ "start_index": 525
524
+ },
525
+ {
526
+ "text": "ุงู„ุฒูŠุงุฏุฉุŒ",
527
+ "confidence": 1.0,
528
+ "start_index": 528
529
+ },
530
+ {
531
+ "text": "ูˆู‚ุฏ",
532
+ "confidence": 1.0,
533
+ "start_index": 537
534
+ },
535
+ {
536
+ "text": "ูุณู‘ุฑ",
537
+ "confidence": 1.0,
538
+ "start_index": 541
539
+ },
540
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541
+ "text": "ุงู„ู„ู‡",
542
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+ "start_index": 546
544
+ },
545
+ {
546
+ "text": "ุชุนุงู„ู‰",
547
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549
+ },
550
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551
+ "text": "ุฃูŠุงู…",
552
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554
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555
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556
+ "text": "ุงู„ุตูˆู…",
557
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559
+ },
560
+ {
561
+ "text": "ุจุงู„ุดู‘ู‡ุฑุŒ",
562
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563
+ "start_index": 568
564
+ },
565
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566
+ "text": "ูุงู†ุนู‚ุฏ",
567
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568
+ "start_index": 577
569
+ },
570
+ {
571
+ "text": "ุจุฐู„ูƒ",
572
+ "confidence": 1.0,
573
+ "start_index": 584
574
+ },
575
+ {
576
+ "text": "ุงู„ุชูุณูŠุฑ.",
577
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+ "start_index": 589
579
+ },
580
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581
+ "text": "ูˆุฃู…ุง",
582
+ "confidence": 1.0,
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+ "start_index": 598
584
+ },
585
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586
+ "text": "ุฃูŠุงู…",
587
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589
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590
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591
+ "text": "ุงู„ุญูŠุถ",
592
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+ "start_index": 608
594
+ },
595
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596
+ "text": "ูู…ุจู‡ู…ุฉุ›",
597
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599
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600
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601
+ "text": "ูู„ุง",
602
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604
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605
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606
+ "text": "ุจุฏู‘",
607
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609
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610
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611
+ "text": "ุฃู†",
612
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614
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615
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616
+ "text": "ุชูƒูˆู†",
617
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618
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619
+ },
620
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621
+ "text": "ู…ุญุตูˆุฑุฉุ›",
622
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623
+ "start_index": 638
624
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625
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626
+ "text": "ู„ุฃู†",
627
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628
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629
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630
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631
+ "text": "ุงู„ุฃุญูƒุงู…",
632
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633
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634
+ },
635
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636
+ "text": "ุชุฎุชู„ู",
637
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639
+ },
640
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641
+ "text": "ุจุญุงู„",
642
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644
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645
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646
+ "text": "ุงู„ุญูŠุถ",
647
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649
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650
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651
+ "text": "ูˆุงู„ุทู‘ู‡ุฑุŒ",
652
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653
+ "start_index": 675
654
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655
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656
+ "text": "ููƒุงู†",
657
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658
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659
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660
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661
+ "text": "ุญู…ู„",
662
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664
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665
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666
+ "text": "ุงู„ู„ูุธ",
667
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669
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670
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671
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672
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674
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675
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676
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677
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679
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680
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681
+ "text": "ูˆุญู‚ูŠู‚ุชู‡",
682
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684
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685
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689
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690
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691
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696
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697
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+ "text": "ู†ุญู†",
702
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704
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705
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706
+ "text": "ู‚ูˆู…",
707
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709
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710
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711
+ "text": "ู„ุง",
712
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714
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715
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716
+ "text": "ุชูˆุณุท",
717
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719
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720
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721
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722
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724
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725
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726
+ "text": "ุฅุฐุง",
727
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728
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729
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730
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731
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732
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735
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736
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737
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741
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742
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756
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757
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761
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762
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766
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781
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787
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791
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795
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796
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802
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807
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811
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+ "markdown": "ุนู„ู… ุงู„ู†ูุณ ุงู„ุชุฑุจูˆูŠ ูˆุชุทุจูŠู‚ุงุชู‡ ุงู„ุญุฏูŠุซุฉ\nุงู„ู…ู„ุฎุต: ุนู„ูŠูƒ ุญู‚ู‘ู‹ุงุŒ ูˆุฅู†ูƒ ุนุณู‰ ุฃู† ูŠุทูˆู„ ุจูƒ ุนู…ุฑุŒ ูˆุฅู† ู…ู† ุญุณุจูƒ ุฃู† ุชุตูˆู… ู…ู† ูƒู„ ุดู‡ุฑ ุซู„ุงุซุฉ ุฃูŠุงู…ุŒ ูุฅู† ุจูƒู„ ุญุณู†ุฉ ุนุดุฑูŽ ุฃู…ุซุงู„ู‡ุงุŒ ูุฐู„ูƒ ุงู„ุฏู‡ุฑ ูƒู„ู‡\"ุŒ ู‚ุงู„: ูุดูŽุฏู‘ูŽุฏุชุŒ ูุดูุฏู‘ูุฏ ุนู„ูŠู‘ุŒ ูู‚ู„ุช: ูุฅู†ูŠ ุฃุทูŠู‚ ุบูŠุฑ ุฐู„ูƒุŒ ู‚ุงู„: \"ูุตูู…ู’ ู…ู† ูƒู„ ุฌู…ุนุฉ ุซู„ุงุซุฉ ุฃูŠุงู…\"ุŒ ู‚ุงู„: ูุดูŽุฏู‘ูŽุฏุช ูุดูุฏู‘ูุฏ ุนู„ูŠู‘ุŒ ู‚ู„ุช:\n\\mathbb{E}[\\theta] = \\int x f_\\theta(x) dx\nุตูˆุฑุฉ ุชูุตูŠู„ูŠุฉ ู„ู…ูƒูˆู†ุงุช ู…ุดูƒู„ุฉ ุงู„ุจุญุซ ูˆุงู„ุชุณุงุคู„ุงุช ุงู„ุฑุฆูŠุณูŠุฉ\nู‚ุงุฆู…ุฉ ุงู„ู…ุฑุงุฌุน ูˆุงู„ู…ุตุงุฏุฑ ุงู„ุชูˆุซูŠู‚ูŠุฉ\nุฅู„ู‰ ุงู„ุฅู…ุงู… ู…ุณู„ู… ุจู† ุงู„ุญุฌุงุฌ ุฑุญู…ู‡ ุงู„ู„ู‡ ุงู„ู…ุฐูƒูˆุฑ ุฃูˆู„ูŽ ุงู„ูƒุชุงุจ ู‚ุงู„: [2732] ( โ€ฆ ) - (ุญูŽุฏู‘ูŽุซูŽู†ููŠ ุงู„ู’ู‚ูŽุงุณูู…ู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽุŒ ุญูŽุฏู‘ูŽุซูŽู†ูŽุง ุนูุจูŽูŠู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ู…ููˆุณูŽู‰ุŒ ุนูŽู†ู’ ุดูŽูŠู’ุจูŽุงู†ูŽุŒ ุนูŽู†ู’ ูŠูŽุญู’ูŠูŽู‰ุŒ ุนูŽู†ู’ ู…ูุญูŽู…ู‘ูŽุฏู ุจู’ู†ู ุนูŽุจู’ุฏู ุงู„ุฑู‘ูŽุญู’ู…ูŽู†ู ู…ูŽูˆู’ู„ูŽู‰ ุจูŽู†ููŠ ุฒูู‡ู’ุฑูŽุฉูŽุŒ ุนูŽู†ู’ ุฃุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ู‚ูŽุงู„ูŽ: ูˆูŽุฃูŽุญู’ุณูŽุจูู†ููŠ ู‚ูŽุฏู’ ุณูŽู…ูุนู’ุชูู‡ู ุฃู†ูŽุง ู…ูู†ู’ ุฃูŽุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ุนูŽู†ู’ ุนูŽุจู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ุนูŽู…ู’ุฑููˆ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡ู…ุง ู‚ูŽุงู„ูŽ: ู‚ูŽุงู„ูŽ ู„ููŠ ุฑูŽุณููˆู„ู ุงู„ู„ู‡ู ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู…: \"ุงู‚ู’ุฑูŽุฃ ุงู„ู’ู‚ูุฑู’ุขู†ูŽ ูููŠ ูƒูู„ู‘ู ุดูŽู‡ู’ุฑู\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ู ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุนูุดู’ุฑููŠู†ูŽ ู„ูŽูŠู’ู„ูŽุฉู‹\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ููŠ ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุณูŽุจู’ุนูุŒ ูˆูŽู„ูŽุง ู†ูŽุฒูุฏู’ ุนูŽู„ูŽู‰ ุฐูŽู„ููƒูŽ\"). ุฑุฌุงู„ ู‡ุฐุง ุงู„ุฅุณู†ุงุฏ: ุณุชุฉ: 1 - (ุงู„ู’ู‚ูŽุงุณูู…ู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽ\" ุงู„ู‚ุฑุดูŠู‘ุŒ ุฃุจูˆ ู…ุญู…ุฏ ุงู„ุทุญู‘ุงู† ุงู„ูƒูˆููŠู‘ุŒ ุซู‚ุฉูŒ [11] ู…ุงุช ููŠ ุญุฏูˆุฏ (250) (ู… ุช ุณ ู‚) ุชู‚ุฏู… ููŠ \"ุงู„ุฅูŠู…ุงู†\" 4/ 118. 2 - (ุนูุจูŽูŠู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ู…ููˆุณูŽู‰) ุจู† ุฃุจูŠ ุงู„ู…ุฎุชุงุฑ ุงู„ู’ุนูŽุจุณูŠู‘ุŒ ุชู‚ุฏู‘ู… ู‚ุฑูŠุจุงู‹. 3 - (ุดูŽูŠู’ุจูŽุงู†ู) ุจู† ุนุจุฏ ุงู„ุฑุญู…ู† ุงู„ู†ุญูˆูŠู‘ุŒ ุฃุจูˆ ู…ุนุงูˆูŠุฉ\n\n![image](img-0)\n\nุตูˆุฑุฉ ุชูˆุถูŠุญูŠุฉ ู„ุนู…ู„ูŠุฉ ู‚ุงุฆู…ุฉ ุงู„ู…ุฑุงุฌุน ูˆุงู„ู…ุตุงุฏุฑ ุงู„ุชูˆุซูŠู‚ูŠุฉ\n\\frac{\\partial k}{\\partial \\lambda} = \\lim_{h \\to 0} \\frac{\\min(\\lambda + h) - \\min(\\lambda)}{h} + \\frac{\\theta}{i^2}\n\\mu_{n+1} = \\mu_n - \\alpha \\nabla f(\\mu_n)\nุงู„ู…ู†ุธูˆุฑ ุงู„ู…ู‚ุงุฑู† ูˆุฃูุถู„ ุงู„ู…ู…ุงุฑุณุงุช\nู…ุณู„ู… ุจู† ุงู„ุญุฌุงุฌ ุฑุญู…ู‡ ุงู„ู„ู‡ ุงู„ู…ุฐูƒูˆุฑ ุฃูˆู„ูŽ ุงู„ูƒุชุงุจ ู‚ุงู„: [2732] ( โ€ฆ ) - (ุญูŽุฏู‘ูŽุซูŽู†ููŠ ุงู„ู’ู‚ูŽุงุณูู…ู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽุŒ ุญูŽุฏู‘ูŽุซูŽู†ูŽุง ุนูุจูŽูŠู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ู…ููˆุณูŽู‰ุŒ ุนูŽู†ู’ ุดูŽูŠู’ุจูŽุงู†ูŽุŒ ุนูŽู†ู’ ูŠูŽุญู’ูŠูŽู‰ุŒ ุนูŽู†ู’ ู…ูุญูŽู…ู‘ูŽุฏู ุจู’ู†ู ุนูŽุจู’ุฏู ุงู„ุฑู‘ูŽุญู’ู…ูŽู†ู ู…ูŽูˆู’ู„ูŽู‰ ุจูŽู†ููŠ ุฒูู‡ู’ุฑูŽุฉูŽุŒ ุนูŽู†ู’ ุฃุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ู‚ูŽุงู„ูŽ: ูˆูŽุฃูŽุญู’ุณูŽุจูู†ููŠ ู‚ูŽุฏู’ ุณูŽู…ูุนู’ุชูู‡ู ุฃู†ูŽุง ู…ูู†ู’ ุฃูŽุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ุนูŽู†ู’ ุนูŽุจู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู\nุงู„ู…ู„ุงุญู‚ ูˆุงู„ุฌุฏุงูˆู„ ุงู„ุฅุญุตุงุฆูŠุฉ\nุนูŽู…ู’ุฑููˆ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡ู…ุง ู‚ูŽุงู„ูŽ: ู‚ูŽุงู„ูŽ ู„ููŠ ุฑูŽุณููˆู„ู ุงู„ู„ู‡ู ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู…: \"ุงู‚ู’ุฑูŽุฃ ุงู„ู’ู‚ูุฑู’ุขู†ูŽ ูููŠ ูƒูู„ู‘ู ุดูŽู‡ู’ุฑู\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ู ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุนูุดู’ุฑููŠู†ูŽ ู„ูŽูŠู’ู„ูŽุฉู‹\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ููŠ ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุณูŽุจู’ุนูุŒ ูˆูŽู„ูŽุง ู†ูŽุฒูุฏู’ ุนูŽู„ูŽู‰ ุฐูŽู„ููƒูŽ\"). ุฑุฌุงู„ ู‡ุฐุง ุงู„ุฅุณู†ุงุฏ: ุณุชุฉ: 1 - (ุงู„ู’ู‚ูŽุงุณูู…ู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽ\" ุงู„ู‚ุฑุดูŠู‘ุŒ ุฃุจูˆ ู…ุญู…ุฏ ุงู„ุทุญู‘ุงู† ุงู„ูƒูˆููŠู‘ุŒ ุซู‚ุฉูŒ [11] ู…ุงุช ููŠ ุญุฏูˆุฏ (250) (ู… ุช ุณ ู‚) ุชู‚ุฏู… ููŠ \"ุงู„ุฅูŠู…ุงู†\" 4/ 118. 2\n## ุจุฑู‡ุงู†\n\\iint_{D} i^2 - \\mu^2 \\, dx \\, dy\n\n![image](img-1)\n\nุงู„ุดูƒู„ (2): ู‡ูŠูƒู„ ู‚ุงุฆู…ุฉ ุงู„ู…ุฑุงุฌุน ูˆุงู„ู…ุตุงุฏุฑ ุงู„ุชูˆุซูŠู‚ูŠุฉ ุงู„ุชู†ุธูŠู…ูŠ\n## ู…ู„ุงุญุธุฉ\n\\frac{\\partial z}{\\partial z} = \\lim_{h \\to 0} \\frac{\\sin(z + h) - \\sin(z)}{h}\nู…ู†ู‡ุฌูŠุฉ ุงู„ุจุญุซ ูˆุฃุฏูˆุงุช ุฌู…ุน ุงู„ุจูŠุงู†ุงุช\nุงู„ุฑุญู…ู† ู…ูˆู„ู‰\n\\nabla_{z} J(z) = \\frac{1}{m} X^T ( \\sigma(X z) - Y )\nุงู„ุตูุญุฉ 59",
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+ "header": null,
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+ "footer": "ุงู„ุตูุญุฉ 59",
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+ {
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+ "text": "ุนู„ู…",
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+ {
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+ "text": "ุงู„ู†ูุณ",
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+ },
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+ {
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+ "text": "ุงู„ุชุฑุจูˆูŠ",
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+ },
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+ {
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+ "text": "ูˆุชุทุจูŠู‚ุงุชู‡",
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+ },
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+ {
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+ "text": "ุงู„ุญุฏูŠุซุฉ",
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+ "text": "ุงู„ู…ู„ุฎุต:",
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+ {
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+ "text": "ุนู„ูŠูƒ",
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+ "text": "ุญู‚ู‘ู‹ุงุŒ",
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+ "start_index": 49
71
+ },
72
+ {
73
+ "text": "ูˆุฅู†ูƒ",
74
+ "confidence": 1.0,
75
+ "start_index": 56
76
+ },
77
+ {
78
+ "text": "ุนุณู‰",
79
+ "confidence": 1.0,
80
+ "start_index": 61
81
+ },
82
+ {
83
+ "text": "ุฃู†",
84
+ "confidence": 1.0,
85
+ "start_index": 65
86
+ },
87
+ {
88
+ "text": "ูŠุทูˆู„",
89
+ "confidence": 1.0,
90
+ "start_index": 68
91
+ },
92
+ {
93
+ "text": "ุจูƒ",
94
+ "confidence": 1.0,
95
+ "start_index": 73
96
+ },
97
+ {
98
+ "text": "ุนู…ุฑุŒ",
99
+ "confidence": 1.0,
100
+ "start_index": 76
101
+ },
102
+ {
103
+ "text": "ูˆุฅู†",
104
+ "confidence": 1.0,
105
+ "start_index": 81
106
+ },
107
+ {
108
+ "text": "ู…ู†",
109
+ "confidence": 1.0,
110
+ "start_index": 85
111
+ },
112
+ {
113
+ "text": "ุญุณุจูƒ",
114
+ "confidence": 1.0,
115
+ "start_index": 88
116
+ },
117
+ {
118
+ "text": "ุฃู†",
119
+ "confidence": 1.0,
120
+ "start_index": 93
121
+ },
122
+ {
123
+ "text": "ุชุตูˆู…",
124
+ "confidence": 1.0,
125
+ "start_index": 96
126
+ },
127
+ {
128
+ "text": "ู…ู†",
129
+ "confidence": 1.0,
130
+ "start_index": 101
131
+ },
132
+ {
133
+ "text": "ูƒู„",
134
+ "confidence": 1.0,
135
+ "start_index": 104
136
+ },
137
+ {
138
+ "text": "ุดู‡ุฑ",
139
+ "confidence": 1.0,
140
+ "start_index": 107
141
+ },
142
+ {
143
+ "text": "ุซู„ุงุซุฉ",
144
+ "confidence": 1.0,
145
+ "start_index": 111
146
+ },
147
+ {
148
+ "text": "ุฃูŠุงู…ุŒ",
149
+ "confidence": 1.0,
150
+ "start_index": 117
151
+ },
152
+ {
153
+ "text": "ูุฅู†",
154
+ "confidence": 1.0,
155
+ "start_index": 123
156
+ },
157
+ {
158
+ "text": "ุจูƒู„",
159
+ "confidence": 1.0,
160
+ "start_index": 127
161
+ },
162
+ {
163
+ "text": "ุญุณู†ุฉ",
164
+ "confidence": 1.0,
165
+ "start_index": 131
166
+ },
167
+ {
168
+ "text": "ุนุดุฑูŽ",
169
+ "confidence": 1.0,
170
+ "start_index": 136
171
+ },
172
+ {
173
+ "text": "ุฃู…ุซุงู„ู‡ุงุŒ",
174
+ "confidence": 1.0,
175
+ "start_index": 141
176
+ },
177
+ {
178
+ "text": "ูุฐู„ูƒ",
179
+ "confidence": 1.0,
180
+ "start_index": 150
181
+ },
182
+ {
183
+ "text": "ุงู„ุฏู‡ุฑ",
184
+ "confidence": 1.0,
185
+ "start_index": 155
186
+ },
187
+ {
188
+ "text": "ูƒู„ู‡\"ุŒ",
189
+ "confidence": 1.0,
190
+ "start_index": 161
191
+ },
192
+ {
193
+ "text": "ู‚ุงู„:",
194
+ "confidence": 1.0,
195
+ "start_index": 167
196
+ },
197
+ {
198
+ "text": "ูุดูŽุฏู‘ูŽุฏุชุŒ",
199
+ "confidence": 1.0,
200
+ "start_index": 172
201
+ },
202
+ {
203
+ "text": "ูุดูุฏู‘ูุฏ",
204
+ "confidence": 1.0,
205
+ "start_index": 182
206
+ },
207
+ {
208
+ "text": "ุนู„ูŠู‘ุŒ",
209
+ "confidence": 1.0,
210
+ "start_index": 190
211
+ },
212
+ {
213
+ "text": "ูู‚ู„ุช:",
214
+ "confidence": 1.0,
215
+ "start_index": 196
216
+ },
217
+ {
218
+ "text": "ูุฅู†ูŠ",
219
+ "confidence": 1.0,
220
+ "start_index": 202
221
+ },
222
+ {
223
+ "text": "ุฃุทูŠู‚",
224
+ "confidence": 1.0,
225
+ "start_index": 207
226
+ },
227
+ {
228
+ "text": "ุบูŠุฑ",
229
+ "confidence": 1.0,
230
+ "start_index": 212
231
+ },
232
+ {
233
+ "text": "ุฐู„ูƒุŒ",
234
+ "confidence": 1.0,
235
+ "start_index": 216
236
+ },
237
+ {
238
+ "text": "ู‚ุงู„:",
239
+ "confidence": 1.0,
240
+ "start_index": 221
241
+ },
242
+ {
243
+ "text": "\"ูุตูู…ู’",
244
+ "confidence": 1.0,
245
+ "start_index": 226
246
+ },
247
+ {
248
+ "text": "ู…ู†",
249
+ "confidence": 1.0,
250
+ "start_index": 233
251
+ },
252
+ {
253
+ "text": "ูƒู„",
254
+ "confidence": 1.0,
255
+ "start_index": 236
256
+ },
257
+ {
258
+ "text": "ุฌู…ุนุฉ",
259
+ "confidence": 1.0,
260
+ "start_index": 239
261
+ },
262
+ {
263
+ "text": "ุซู„ุงุซุฉ",
264
+ "confidence": 1.0,
265
+ "start_index": 244
266
+ },
267
+ {
268
+ "text": "ุฃูŠุงู…\"ุŒ",
269
+ "confidence": 1.0,
270
+ "start_index": 250
271
+ },
272
+ {
273
+ "text": "ู‚ุงู„:",
274
+ "confidence": 1.0,
275
+ "start_index": 257
276
+ },
277
+ {
278
+ "text": "ูุดูŽุฏู‘ูŽุฏุช",
279
+ "confidence": 1.0,
280
+ "start_index": 262
281
+ },
282
+ {
283
+ "text": "ูุดูุฏู‘ูุฏ",
284
+ "confidence": 1.0,
285
+ "start_index": 271
286
+ },
287
+ {
288
+ "text": "ุนู„ูŠู‘ุŒ",
289
+ "confidence": 1.0,
290
+ "start_index": 279
291
+ },
292
+ {
293
+ "text": "ู‚ู„ุช:",
294
+ "confidence": 1.0,
295
+ "start_index": 285
296
+ },
297
+ {
298
+ "text": "\\mathbb{E}[\\theta]",
299
+ "confidence": 1.0,
300
+ "start_index": 290
301
+ },
302
+ {
303
+ "text": "=",
304
+ "confidence": 1.0,
305
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306
+ },
307
+ {
308
+ "text": "\\int",
309
+ "confidence": 1.0,
310
+ "start_index": 311
311
+ },
312
+ {
313
+ "text": "x",
314
+ "confidence": 1.0,
315
+ "start_index": 316
316
+ },
317
+ {
318
+ "text": "f_\\theta(x)",
319
+ "confidence": 1.0,
320
+ "start_index": 318
321
+ },
322
+ {
323
+ "text": "dx",
324
+ "confidence": 1.0,
325
+ "start_index": 330
326
+ },
327
+ {
328
+ "text": "ุตูˆุฑุฉ",
329
+ "confidence": 1.0,
330
+ "start_index": 333
331
+ },
332
+ {
333
+ "text": "ุชูุตูŠู„ูŠุฉ",
334
+ "confidence": 1.0,
335
+ "start_index": 338
336
+ },
337
+ {
338
+ "text": "ู„ู…ูƒูˆู†ุงุช",
339
+ "confidence": 1.0,
340
+ "start_index": 346
341
+ },
342
+ {
343
+ "text": "ู…ุดูƒู„ุฉ",
344
+ "confidence": 1.0,
345
+ "start_index": 354
346
+ },
347
+ {
348
+ "text": "ุงู„ุจุญุซ",
349
+ "confidence": 1.0,
350
+ "start_index": 360
351
+ },
352
+ {
353
+ "text": "ูˆุงู„ุชุณุงุคู„ุงุช",
354
+ "confidence": 1.0,
355
+ "start_index": 366
356
+ },
357
+ {
358
+ "text": "ุงู„ุฑุฆูŠุณูŠุฉ",
359
+ "confidence": 1.0,
360
+ "start_index": 377
361
+ },
362
+ {
363
+ "text": "ู‚ุงุฆู…ุฉ",
364
+ "confidence": 1.0,
365
+ "start_index": 386
366
+ },
367
+ {
368
+ "text": "ุงู„ู…ุฑุงุฌุน",
369
+ "confidence": 1.0,
370
+ "start_index": 392
371
+ },
372
+ {
373
+ "text": "ูˆุงู„ู…ุตุงุฏุฑ",
374
+ "confidence": 1.0,
375
+ "start_index": 400
376
+ },
377
+ {
378
+ "text": "ุงู„ุชูˆุซูŠู‚ูŠุฉ",
379
+ "confidence": 1.0,
380
+ "start_index": 409
381
+ },
382
+ {
383
+ "text": "ุฅู„ู‰",
384
+ "confidence": 1.0,
385
+ "start_index": 419
386
+ },
387
+ {
388
+ "text": "ุงู„ุฅู…ุงู…",
389
+ "confidence": 1.0,
390
+ "start_index": 423
391
+ },
392
+ {
393
+ "text": "ู…ุณู„ู…",
394
+ "confidence": 1.0,
395
+ "start_index": 430
396
+ },
397
+ {
398
+ "text": "ุจู†",
399
+ "confidence": 1.0,
400
+ "start_index": 435
401
+ },
402
+ {
403
+ "text": "ุงู„ุญุฌุงุฌ",
404
+ "confidence": 1.0,
405
+ "start_index": 438
406
+ },
407
+ {
408
+ "text": "ุฑุญู…ู‡",
409
+ "confidence": 1.0,
410
+ "start_index": 445
411
+ },
412
+ {
413
+ "text": "ุงู„ู„ู‡",
414
+ "confidence": 1.0,
415
+ "start_index": 450
416
+ },
417
+ {
418
+ "text": "ุงู„ู…ุฐูƒูˆุฑ",
419
+ "confidence": 1.0,
420
+ "start_index": 455
421
+ },
422
+ {
423
+ "text": "ุฃูˆู„ูŽ",
424
+ "confidence": 1.0,
425
+ "start_index": 463
426
+ },
427
+ {
428
+ "text": "ุงู„ูƒุชุงุจ",
429
+ "confidence": 1.0,
430
+ "start_index": 468
431
+ },
432
+ {
433
+ "text": "ู‚ุงู„:",
434
+ "confidence": 1.0,
435
+ "start_index": 475
436
+ },
437
+ {
438
+ "text": "[2732]",
439
+ "confidence": 1.0,
440
+ "start_index": 480
441
+ },
442
+ {
443
+ "text": "(",
444
+ "confidence": 1.0,
445
+ "start_index": 487
446
+ },
447
+ {
448
+ "text": "โ€ฆ",
449
+ "confidence": 1.0,
450
+ "start_index": 489
451
+ },
452
+ {
453
+ "text": ")",
454
+ "confidence": 1.0,
455
+ "start_index": 491
456
+ },
457
+ {
458
+ "text": "-",
459
+ "confidence": 1.0,
460
+ "start_index": 493
461
+ },
462
+ {
463
+ "text": "(ุญูŽุฏู‘ูŽุซูŽู†ููŠ",
464
+ "confidence": 1.0,
465
+ "start_index": 495
466
+ },
467
+ {
468
+ "text": "ุงู„ู’ู‚ูŽุงุณูู…ู",
469
+ "confidence": 1.0,
470
+ "start_index": 507
471
+ },
472
+ {
473
+ "text": "ุจู’ู†ู",
474
+ "confidence": 1.0,
475
+ "start_index": 518
476
+ },
477
+ {
478
+ "text": "ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽุŒ",
479
+ "confidence": 1.0,
480
+ "start_index": 523
481
+ },
482
+ {
483
+ "text": "ุญูŽุฏู‘ูŽุซูŽู†ูŽุง",
484
+ "confidence": 1.0,
485
+ "start_index": 537
486
+ },
487
+ {
488
+ "text": "ุนูุจูŽูŠู’ุฏู",
489
+ "confidence": 1.0,
490
+ "start_index": 548
491
+ },
492
+ {
493
+ "text": "ุงู„ู„ู‡ู",
494
+ "confidence": 1.0,
495
+ "start_index": 557
496
+ },
497
+ {
498
+ "text": "ุจู’ู†ู",
499
+ "confidence": 1.0,
500
+ "start_index": 563
501
+ },
502
+ {
503
+ "text": "ู…ููˆุณูŽู‰ุŒ",
504
+ "confidence": 1.0,
505
+ "start_index": 568
506
+ },
507
+ {
508
+ "text": "ุนูŽู†ู’",
509
+ "confidence": 1.0,
510
+ "start_index": 576
511
+ },
512
+ {
513
+ "text": "ุดูŽูŠู’ุจูŽุงู†ูŽุŒ",
514
+ "confidence": 1.0,
515
+ "start_index": 581
516
+ },
517
+ {
518
+ "text": "ุนูŽู†ู’",
519
+ "confidence": 1.0,
520
+ "start_index": 592
521
+ },
522
+ {
523
+ "text": "ูŠูŽุญู’ูŠูŽู‰ุŒ",
524
+ "confidence": 1.0,
525
+ "start_index": 597
526
+ },
527
+ {
528
+ "text": "ุนูŽู†ู’",
529
+ "confidence": 1.0,
530
+ "start_index": 606
531
+ },
532
+ {
533
+ "text": "ู…ูุญูŽู…ู‘ูŽุฏู",
534
+ "confidence": 1.0,
535
+ "start_index": 611
536
+ },
537
+ {
538
+ "text": "ุจู’ู†ู",
539
+ "confidence": 1.0,
540
+ "start_index": 621
541
+ },
542
+ {
543
+ "text": "ุนูŽ๏ฟฝ๏ฟฝู’ุฏู",
544
+ "confidence": 1.0,
545
+ "start_index": 626
546
+ },
547
+ {
548
+ "text": "ุงู„ุฑู‘ูŽุญู’ู…ูŽู†ู",
549
+ "confidence": 1.0,
550
+ "start_index": 633
551
+ },
552
+ {
553
+ "text": "ู…ูŽูˆู’ู„ูŽู‰",
554
+ "confidence": 1.0,
555
+ "start_index": 645
556
+ },
557
+ {
558
+ "text": "ุจูŽู†ููŠ",
559
+ "confidence": 1.0,
560
+ "start_index": 653
561
+ },
562
+ {
563
+ "text": "ุฒูู‡ู’ุฑูŽุฉูŽุŒ",
564
+ "confidence": 1.0,
565
+ "start_index": 659
566
+ },
567
+ {
568
+ "text": "ุนูŽู†ู’",
569
+ "confidence": 1.0,
570
+ "start_index": 669
571
+ },
572
+ {
573
+ "text": "ุฃุจููŠ",
574
+ "confidence": 1.0,
575
+ "start_index": 674
576
+ },
577
+ {
578
+ "text": "ุณูŽู„ูŽู…ูŽุฉูŽุŒ",
579
+ "confidence": 1.0,
580
+ "start_index": 679
581
+ },
582
+ {
583
+ "text": "ู‚ูŽุงู„ูŽ:",
584
+ "confidence": 1.0,
585
+ "start_index": 689
586
+ },
587
+ {
588
+ "text": "ูˆูŽุฃูŽุญู’ุณูŽุจูู†ููŠ",
589
+ "confidence": 1.0,
590
+ "start_index": 696
591
+ },
592
+ {
593
+ "text": "ู‚ูŽุฏู’",
594
+ "confidence": 1.0,
595
+ "start_index": 710
596
+ },
597
+ {
598
+ "text": "ุณูŽู…ูุนู’ุชูู‡ู",
599
+ "confidence": 1.0,
600
+ "start_index": 715
601
+ },
602
+ {
603
+ "text": "ุฃู†ูŽุง",
604
+ "confidence": 1.0,
605
+ "start_index": 726
606
+ },
607
+ {
608
+ "text": "ู…ูู†ู’",
609
+ "confidence": 1.0,
610
+ "start_index": 731
611
+ },
612
+ {
613
+ "text": "ุฃูŽุจููŠ",
614
+ "confidence": 1.0,
615
+ "start_index": 736
616
+ },
617
+ {
618
+ "text": "ุณูŽู„ูŽู…ูŽุฉูŽุŒ",
619
+ "confidence": 1.0,
620
+ "start_index": 742
621
+ },
622
+ {
623
+ "text": "ุนูŽู†ู’",
624
+ "confidence": 1.0,
625
+ "start_index": 752
626
+ },
627
+ {
628
+ "text": "ุนูŽุจู’ุฏู",
629
+ "confidence": 1.0,
630
+ "start_index": 757
631
+ },
632
+ {
633
+ "text": "ุงู„ู„ู‡ู",
634
+ "confidence": 1.0,
635
+ "start_index": 764
636
+ },
637
+ {
638
+ "text": "ุจู’ู†ู",
639
+ "confidence": 1.0,
640
+ "start_index": 770
641
+ },
642
+ {
643
+ "text": "ุนูŽู…ู’ุฑููˆ",
644
+ "confidence": 1.0,
645
+ "start_index": 775
646
+ },
647
+ {
648
+ "text": "ุฑุถูŠ",
649
+ "confidence": 1.0,
650
+ "start_index": 783
651
+ },
652
+ {
653
+ "text": "ุงู„ู„ู‡",
654
+ "confidence": 1.0,
655
+ "start_index": 787
656
+ },
657
+ {
658
+ "text": "ุนู†ู‡ู…ุง",
659
+ "confidence": 1.0,
660
+ "start_index": 792
661
+ },
662
+ {
663
+ "text": "ู‚ูŽุงู„ูŽ:",
664
+ "confidence": 1.0,
665
+ "start_index": 798
666
+ },
667
+ {
668
+ "text": "ู‚ูŽุงู„ูŽ",
669
+ "confidence": 1.0,
670
+ "start_index": 805
671
+ },
672
+ {
673
+ "text": "ู„ููŠ",
674
+ "confidence": 1.0,
675
+ "start_index": 811
676
+ },
677
+ {
678
+ "text": "ุฑูŽุณููˆู„ู",
679
+ "confidence": 1.0,
680
+ "start_index": 815
681
+ },
682
+ {
683
+ "text": "ุงู„ู„ู‡ู",
684
+ "confidence": 1.0,
685
+ "start_index": 823
686
+ },
687
+ {
688
+ "text": "ุตู„ู‰",
689
+ "confidence": 1.0,
690
+ "start_index": 829
691
+ },
692
+ {
693
+ "text": "ุงู„ู„ู‡",
694
+ "confidence": 1.0,
695
+ "start_index": 833
696
+ },
697
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698
+ "text": "ุนู„ูŠู‡",
699
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700
+ "start_index": 838
701
+ },
702
+ {
703
+ "text": "ูˆุณู„ู…:",
704
+ "confidence": 1.0,
705
+ "start_index": 843
706
+ },
707
+ {
708
+ "text": "\"ุงู‚ู’ุฑูŽุฃ",
709
+ "confidence": 1.0,
710
+ "start_index": 849
711
+ },
712
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713
+ "text": "ุงู„ู’ู‚ูุฑู’ุขู†ูŽ",
714
+ "confidence": 1.0,
715
+ "start_index": 857
716
+ },
717
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718
+ "text": "ูููŠ",
719
+ "confidence": 1.0,
720
+ "start_index": 868
721
+ },
722
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723
+ "text": "ูƒูู„ู‘ู",
724
+ "confidence": 1.0,
725
+ "start_index": 872
726
+ },
727
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728
+ "text": "ุดูŽู‡ู’ุฑู\"ุŒ",
729
+ "confidence": 1.0,
730
+ "start_index": 878
731
+ },
732
+ {
733
+ "text": "ู‚ูŽุงู„ูŽ:",
734
+ "confidence": 1.0,
735
+ "start_index": 887
736
+ },
737
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738
+ "text": "ู‚ูู„ู’ุชู:",
739
+ "confidence": 1.0,
740
+ "start_index": 894
741
+ },
742
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743
+ "text": "ุฅูู†ู‘ู",
744
+ "confidence": 1.0,
745
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746
+ },
747
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748
+ "text": "ุฃูŽุฌูุฏู",
749
+ "confidence": 1.0,
750
+ "start_index": 908
751
+ },
752
+ {
753
+ "text": "ู‚ููˆู‘ูŽุฉู‹ุŒ",
754
+ "confidence": 1.0,
755
+ "start_index": 915
756
+ },
757
+ {
758
+ "text": "ู‚ูŽุงู„ูŽ:",
759
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760
+ "start_index": 924
761
+ },
762
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763
+ "text": "\"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู",
764
+ "confidence": 1.0,
765
+ "start_index": 931
766
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767
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768
+ "text": "ูููŠ",
769
+ "confidence": 1.0,
770
+ "start_index": 944
771
+ },
772
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773
+ "text": "ุนูุดู’ุฑููŠู†ูŽ",
774
+ "confidence": 1.0,
775
+ "start_index": 948
776
+ },
777
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778
+ "text": "ู„ูŽูŠู’ู„ูŽุฉู‹\"ุŒ",
779
+ "confidence": 1.0,
780
+ "start_index": 958
781
+ },
782
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783
+ "text": "ู‚ูŽุงู„ูŽ:",
784
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785
+ "start_index": 969
786
+ },
787
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788
+ "text": "ู‚ูู„ู’ุชู:",
789
+ "confidence": 1.0,
790
+ "start_index": 976
791
+ },
792
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793
+ "text": "ุฅูู†ู‘ููŠ",
794
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795
+ "start_index": 984
796
+ },
797
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798
+ "text": "ุฃูŽุฌูุฏู",
799
+ "confidence": 1.0,
800
+ "start_index": 991
801
+ },
802
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803
+ "text": "ู‚ููˆู‘ูŽุฉู‹ุŒ",
804
+ "confidence": 1.0,
805
+ "start_index": 998
806
+ },
807
+ {
808
+ "text": "ู‚ูŽุงู„ูŽ:",
809
+ "confidence": 1.0,
810
+ "start_index": 1007
811
+ },
812
+ {
813
+ "text": "\"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู",
814
+ "confidence": 1.0,
815
+ "start_index": 1014
816
+ },
817
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818
+ "text": "ูููŠ",
819
+ "confidence": 1.0,
820
+ "start_index": 1027
821
+ },
822
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823
+ "text": "ุณูŽุจู’ุนูุŒ",
824
+ "confidence": 1.0,
825
+ "start_index": 1031
826
+ },
827
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828
+ "text": "ูˆูŽู„ูŽุง",
829
+ "confidence": 1.0,
830
+ "start_index": 1039
831
+ },
832
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833
+ "text": "ู†ูŽุฒูุฏู’",
834
+ "confidence": 1.0,
835
+ "start_index": 1045
836
+ },
837
+ {
838
+ "text": "ุนูŽู„ูŽู‰",
839
+ "confidence": 1.0,
840
+ "start_index": 1052
841
+ },
842
+ {
843
+ "text": "ุฐูŽู„ููƒูŽ\").",
844
+ "confidence": 1.0,
845
+ "start_index": 1058
846
+ },
847
+ {
848
+ "text": "ุฑุฌุงู„",
849
+ "confidence": 1.0,
850
+ "start_index": 1068
851
+ },
852
+ {
853
+ "text": "ู‡ุฐุง",
854
+ "confidence": 1.0,
855
+ "start_index": 1073
856
+ },
857
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858
+ "text": "ุงู„ุฅุณู†ุงุฏ:",
859
+ "confidence": 1.0,
860
+ "start_index": 1077
861
+ },
862
+ {
863
+ "text": "ุณุชุฉ:",
864
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865
+ "start_index": 1086
866
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867
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868
+ "text": "1",
869
+ "confidence": 1.0,
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871
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872
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873
+ "text": "-",
874
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+ "start_index": 1093
876
+ },
877
+ {
878
+ "text": "(ุงู„ู’ู‚ูŽุงุณูู…ู",
879
+ "confidence": 1.0,
880
+ "start_index": 1095
881
+ },
882
+ {
883
+ "text": "ุจู’ู†ู",
884
+ "confidence": 1.0,
885
+ "start_index": 1107
886
+ },
887
+ {
888
+ "text": "ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽ\"",
889
+ "confidence": 1.0,
890
+ "start_index": 1112
891
+ },
892
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893
+ "text": "ุงู„ู‚ุฑุดูŠู‘ุŒ",
894
+ "confidence": 1.0,
895
+ "start_index": 1126
896
+ },
897
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898
+ "text": "ุฃุจูˆ",
899
+ "confidence": 1.0,
900
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901
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902
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903
+ "text": "ู…ุญู…ุฏ",
904
+ "confidence": 1.0,
905
+ "start_index": 1139
906
+ },
907
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908
+ "text": "ุงู„ุทุญู‘ุงู†",
909
+ "confidence": 1.0,
910
+ "start_index": 1144
911
+ },
912
+ {
913
+ "text": "ุงู„ูƒูˆููŠู‘ุŒ",
914
+ "confidence": 1.0,
915
+ "start_index": 1152
916
+ },
917
+ {
918
+ "text": "ุซู‚ุฉูŒ",
919
+ "confidence": 1.0,
920
+ "start_index": 1161
921
+ },
922
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923
+ "text": "[11]",
924
+ "confidence": 1.0,
925
+ "start_index": 1166
926
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927
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928
+ "text": "ู…ุงุช",
929
+ "confidence": 1.0,
930
+ "start_index": 1171
931
+ },
932
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933
+ "text": "ููŠ",
934
+ "confidence": 1.0,
935
+ "start_index": 1175
936
+ },
937
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938
+ "text": "ุญุฏูˆุฏ",
939
+ "confidence": 1.0,
940
+ "start_index": 1178
941
+ },
942
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943
+ "text": "(250)",
944
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946
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947
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948
+ "text": "(ู…",
949
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950
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951
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952
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953
+ "text": "ุช",
954
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956
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957
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958
+ "text": "ุณ",
959
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961
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962
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963
+ "text": "ู‚)",
964
+ "confidence": 1.0,
965
+ "start_index": 1196
966
+ },
967
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968
+ "text": "ุชู‚ุฏู…",
969
+ "confidence": 1.0,
970
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971
+ },
972
+ {
973
+ "text": "ููŠ",
974
+ "confidence": 1.0,
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+ "start_index": 1204
976
+ },
977
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978
+ "text": "\"ุงู„ุฅูŠู…ุงู†\"",
979
+ "confidence": 1.0,
980
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981
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983
+ "text": "4/",
984
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986
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987
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988
+ "text": "118.",
989
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991
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993
+ "text": "2",
994
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996
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998
+ "text": "-",
999
+ "confidence": 1.0,
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+ "start_index": 1227
1001
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1002
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1003
+ "text": "(ุนูุจูŽูŠู’ุฏู",
1004
+ "confidence": 1.0,
1005
+ "start_index": 1229
1006
+ },
1007
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1008
+ "text": "ุงู„ู„ู‡ู",
1009
+ "confidence": 1.0,
1010
+ "start_index": 1239
1011
+ },
1012
+ {
1013
+ "text": "ุจู’ู†ู",
1014
+ "confidence": 1.0,
1015
+ "start_index": 1245
1016
+ },
1017
+ {
1018
+ "text": "ู…ููˆุณูŽู‰)",
1019
+ "confidence": 1.0,
1020
+ "start_index": 1250
1021
+ },
1022
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1023
+ "text": "ุจู†",
1024
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1025
+ "start_index": 1258
1026
+ },
1027
+ {
1028
+ "text": "ุฃุจูŠ",
1029
+ "confidence": 1.0,
1030
+ "start_index": 1261
1031
+ },
1032
+ {
1033
+ "text": "ุงู„ู…ุฎุชุงุฑ",
1034
+ "confidence": 1.0,
1035
+ "start_index": 1265
1036
+ },
1037
+ {
1038
+ "text": "ุงู„ู’ุนูŽุจุณูŠู‘ุŒ",
1039
+ "confidence": 1.0,
1040
+ "start_index": 1273
1041
+ },
1042
+ {
1043
+ "text": "ุชู‚ุฏู‘ู…",
1044
+ "confidence": 1.0,
1045
+ "start_index": 1284
1046
+ },
1047
+ {
1048
+ "text": "ู‚ุฑูŠุจุงู‹.",
1049
+ "confidence": 1.0,
1050
+ "start_index": 1290
1051
+ },
1052
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1053
+ "text": "3",
1054
+ "confidence": 1.0,
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1058
+ "text": "-",
1059
+ "confidence": 1.0,
1060
+ "start_index": 1300
1061
+ },
1062
+ {
1063
+ "text": "(ุดูŽูŠู’ุจูŽุงู†ู)",
1064
+ "confidence": 1.0,
1065
+ "start_index": 1302
1066
+ },
1067
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1068
+ "text": "ุจู†",
1069
+ "confidence": 1.0,
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+ "start_index": 1314
1071
+ },
1072
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1073
+ "text": "ุนุจุฏ",
1074
+ "confidence": 1.0,
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+ "start_index": 1317
1076
+ },
1077
+ {
1078
+ "text": "ุงู„ุฑุญู…ู†",
1079
+ "confidence": 1.0,
1080
+ "start_index": 1321
1081
+ },
1082
+ {
1083
+ "text": "ุงู„ู†ุญูˆูŠู‘ุŒ",
1084
+ "confidence": 1.0,
1085
+ "start_index": 1328
1086
+ },
1087
+ {
1088
+ "text": "ุฃุจูˆ",
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+ "confidence": 1.0,
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+ "start_index": 1337
1091
+ },
1092
+ {
1093
+ "text": "ู…ุนุงูˆูŠุฉ",
1094
+ "confidence": 1.0,
1095
+ "start_index": 1341
1096
+ },
1097
+ {
1098
+ "text": "![image](img-0)",
1099
+ "confidence": 1.0,
1100
+ "start_index": 1349
1101
+ },
1102
+ {
1103
+ "text": "ุตูˆุฑุฉ",
1104
+ "confidence": 1.0,
1105
+ "start_index": 1366
1106
+ },
1107
+ {
1108
+ "text": "ุชูˆุถูŠุญูŠุฉ",
1109
+ "confidence": 1.0,
1110
+ "start_index": 1371
1111
+ },
1112
+ {
1113
+ "text": "ู„ุนู…ู„ูŠุฉ",
1114
+ "confidence": 1.0,
1115
+ "start_index": 1379
1116
+ },
1117
+ {
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+ "text": "ู‚ุงุฆู…ุฉ",
1119
+ "confidence": 1.0,
1120
+ "start_index": 1386
1121
+ },
1122
+ {
1123
+ "text": "ุงู„ู…ุฑุงุฌุน",
1124
+ "confidence": 1.0,
1125
+ "start_index": 1392
1126
+ },
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+ {
1128
+ "text": "ูˆุงู„ู…ุตุงุฏุฑ",
1129
+ "confidence": 1.0,
1130
+ "start_index": 1400
1131
+ },
1132
+ {
1133
+ "text": "ุงู„ุชูˆุซูŠู‚ูŠุฉ",
1134
+ "confidence": 1.0,
1135
+ "start_index": 1409
1136
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+ {
1138
+ "text": "\\frac{\\partial",
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+ "confidence": 1.0,
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1143
+ "text": "k}{\\partial",
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1148
+ "text": "\\lambda}",
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1153
+ "text": "=",
1154
+ "confidence": 1.0,
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+ {
1158
+ "text": "\\lim_{h",
1159
+ "confidence": 1.0,
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1161
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1162
+ {
1163
+ "text": "\\to",
1164
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1168
+ "text": "0}",
1169
+ "confidence": 1.0,
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1173
+ "text": "\\frac{\\min(\\lambda",
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+ "confidence": 1.0,
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+ "start_index": 1472
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+ },
1177
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1178
+ "text": "+",
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+ "confidence": 1.0,
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+ "start_index": 1491
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1183
+ "text": "h)",
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+ "text": "-",
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+ "confidence": 1.0,
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+ "start_index": 1496
1191
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1193
+ "text": "\\min(\\lambda)}{h}",
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+ "text": "+",
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+ "confidence": 1.0,
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1203
+ "text": "\\frac{\\theta}{i^2}",
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+ "confidence": 1.0,
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+ "start_index": 1518
1206
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1208
+ "text": "\\mu_{n+1}",
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+ "confidence": 1.0,
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1213
+ "text": "=",
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+ "confidence": 1.0,
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1218
+ "text": "\\mu_n",
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+ "confidence": 1.0,
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1221
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1223
+ "text": "-",
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+ "text": "\\alpha",
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+ "confidence": 1.0,
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1233
+ "text": "\\nabla",
1234
+ "confidence": 1.0,
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+ "start_index": 1564
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1238
+ "text": "f(\\mu_n)",
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+ "confidence": 1.0,
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+ "start_index": 1571
1241
+ },
1242
+ {
1243
+ "text": "ุงู„ู…ู†ุธูˆุฑ",
1244
+ "confidence": 1.0,
1245
+ "start_index": 1580
1246
+ },
1247
+ {
1248
+ "text": "ุงู„ู…ู‚ุงุฑู†",
1249
+ "confidence": 1.0,
1250
+ "start_index": 1588
1251
+ },
1252
+ {
1253
+ "text": "ูˆุฃูุถู„",
1254
+ "confidence": 1.0,
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+ "start_index": 1596
1256
+ },
1257
+ {
1258
+ "text": "ุงู„ู…ู…ุงุฑุณุงุช",
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+ "confidence": 1.0,
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+ "start_index": 1602
1261
+ },
1262
+ {
1263
+ "text": "ู…ุณู„ู…",
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+ "confidence": 1.0,
1265
+ "start_index": 1612
1266
+ },
1267
+ {
1268
+ "text": "ุจู†",
1269
+ "confidence": 1.0,
1270
+ "start_index": 1617
1271
+ },
1272
+ {
1273
+ "text": "ุงู„ุญุฌุงุฌ",
1274
+ "confidence": 1.0,
1275
+ "start_index": 1620
1276
+ },
1277
+ {
1278
+ "text": "ุฑุญู…ู‡",
1279
+ "confidence": 1.0,
1280
+ "start_index": 1627
1281
+ },
1282
+ {
1283
+ "text": "ุงู„ู„ู‡",
1284
+ "confidence": 1.0,
1285
+ "start_index": 1632
1286
+ },
1287
+ {
1288
+ "text": "ุงู„ู…ุฐูƒูˆุฑ",
1289
+ "confidence": 1.0,
1290
+ "start_index": 1637
1291
+ },
1292
+ {
1293
+ "text": "ุฃูˆู„ูŽ",
1294
+ "confidence": 1.0,
1295
+ "start_index": 1645
1296
+ },
1297
+ {
1298
+ "text": "ุงู„ูƒุชุงุจ",
1299
+ "confidence": 1.0,
1300
+ "start_index": 1650
1301
+ },
1302
+ {
1303
+ "text": "ู‚ุงู„:",
1304
+ "confidence": 1.0,
1305
+ "start_index": 1657
1306
+ },
1307
+ {
1308
+ "text": "[2732]",
1309
+ "confidence": 1.0,
1310
+ "start_index": 1662
1311
+ },
1312
+ {
1313
+ "text": "(",
1314
+ "confidence": 1.0,
1315
+ "start_index": 1669
1316
+ },
1317
+ {
1318
+ "text": "โ€ฆ",
1319
+ "confidence": 1.0,
1320
+ "start_index": 1671
1321
+ },
1322
+ {
1323
+ "text": ")",
1324
+ "confidence": 1.0,
1325
+ "start_index": 1673
1326
+ },
1327
+ {
1328
+ "text": "-",
1329
+ "confidence": 1.0,
1330
+ "start_index": 1675
1331
+ },
1332
+ {
1333
+ "text": "(ุญูŽุฏู‘ูŽุซูŽู†ููŠ",
1334
+ "confidence": 1.0,
1335
+ "start_index": 1677
1336
+ },
1337
+ {
1338
+ "text": "ุงู„ู’ู‚ูŽุงุณูู…ู",
1339
+ "confidence": 1.0,
1340
+ "start_index": 1689
1341
+ },
1342
+ {
1343
+ "text": "ุจู’ู†ู",
1344
+ "confidence": 1.0,
1345
+ "start_index": 1700
1346
+ },
1347
+ {
1348
+ "text": "ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽุŒ",
1349
+ "confidence": 1.0,
1350
+ "start_index": 1705
1351
+ },
1352
+ {
1353
+ "text": "ุญูŽุฏู‘ูŽุซูŽู†ูŽุง",
1354
+ "confidence": 1.0,
1355
+ "start_index": 1719
1356
+ },
1357
+ {
1358
+ "text": "ุนูุจูŽูŠู’ุฏู",
1359
+ "confidence": 1.0,
1360
+ "start_index": 1730
1361
+ },
1362
+ {
1363
+ "text": "ุงู„ู„ู‡ู",
1364
+ "confidence": 1.0,
1365
+ "start_index": 1739
1366
+ },
1367
+ {
1368
+ "text": "ุจู’ู†ู",
1369
+ "confidence": 1.0,
1370
+ "start_index": 1745
1371
+ },
1372
+ {
1373
+ "text": "ู…ููˆุณูŽู‰ุŒ",
1374
+ "confidence": 1.0,
1375
+ "start_index": 1750
1376
+ },
1377
+ {
1378
+ "text": "ุนูŽู†ู’",
1379
+ "confidence": 1.0,
1380
+ "start_index": 1758
1381
+ },
1382
+ {
1383
+ "text": "ุดูŽูŠู’ุจูŽุงู†ูŽุŒ",
1384
+ "confidence": 1.0,
1385
+ "start_index": 1763
1386
+ },
1387
+ {
1388
+ "text": "ุนูŽู†ู’",
1389
+ "confidence": 1.0,
1390
+ "start_index": 1774
1391
+ },
1392
+ {
1393
+ "text": "ูŠูŽุญู’ูŠูŽู‰ุŒ",
1394
+ "confidence": 1.0,
1395
+ "start_index": 1779
1396
+ },
1397
+ {
1398
+ "text": "ุนูŽู†ู’",
1399
+ "confidence": 1.0,
1400
+ "start_index": 1788
1401
+ },
1402
+ {
1403
+ "text": "ู…ูุญูŽู…ู‘ูŽุฏู",
1404
+ "confidence": 1.0,
1405
+ "start_index": 1793
1406
+ },
1407
+ {
1408
+ "text": "ุจู’ู†ู",
1409
+ "confidence": 1.0,
1410
+ "start_index": 1803
1411
+ },
1412
+ {
1413
+ "text": "ุนูŽุจู’ุฏู",
1414
+ "confidence": 1.0,
1415
+ "start_index": 1808
1416
+ },
1417
+ {
1418
+ "text": "ุงู„ุฑู‘ูŽุญู’ู…ูŽู†ู",
1419
+ "confidence": 1.0,
1420
+ "start_index": 1815
1421
+ },
1422
+ {
1423
+ "text": "ู…ูŽูˆู’ู„ูŽู‰",
1424
+ "confidence": 1.0,
1425
+ "start_index": 1827
1426
+ },
1427
+ {
1428
+ "text": "ุจูŽู†ููŠ",
1429
+ "confidence": 1.0,
1430
+ "start_index": 1835
1431
+ },
1432
+ {
1433
+ "text": "ุฒูู‡ู’ุฑูŽุฉูŽุŒ",
1434
+ "confidence": 1.0,
1435
+ "start_index": 1841
1436
+ },
1437
+ {
1438
+ "text": "ุนูŽู†ู’",
1439
+ "confidence": 1.0,
1440
+ "start_index": 1851
1441
+ },
1442
+ {
1443
+ "text": "ุฃุจููŠ",
1444
+ "confidence": 1.0,
1445
+ "start_index": 1856
1446
+ },
1447
+ {
1448
+ "text": "ุณูŽู„ูŽู…ูŽุฉูŽุŒ",
1449
+ "confidence": 1.0,
1450
+ "start_index": 1861
1451
+ },
1452
+ {
1453
+ "text": "ู‚ูŽุงู„ูŽ:",
1454
+ "confidence": 1.0,
1455
+ "start_index": 1871
1456
+ },
1457
+ {
1458
+ "text": "ูˆูŽุฃูŽุญู’ุณูŽุจูู†ููŠ",
1459
+ "confidence": 1.0,
1460
+ "start_index": 1878
1461
+ },
1462
+ {
1463
+ "text": "ู‚ูŽุฏู’",
1464
+ "confidence": 1.0,
1465
+ "start_index": 1892
1466
+ },
1467
+ {
1468
+ "text": "ุณูŽู…ูุนู’ุชูู‡ู",
1469
+ "confidence": 1.0,
1470
+ "start_index": 1897
1471
+ },
1472
+ {
1473
+ "text": "ุฃู†ูŽุง",
1474
+ "confidence": 1.0,
1475
+ "start_index": 1908
1476
+ },
1477
+ {
1478
+ "text": "ู…ูู†ู’",
1479
+ "confidence": 1.0,
1480
+ "start_index": 1913
1481
+ },
1482
+ {
1483
+ "text": "ุฃูŽุจููŠ",
1484
+ "confidence": 1.0,
1485
+ "start_index": 1918
1486
+ },
1487
+ {
1488
+ "text": "ุณูŽู„ูŽู…ูŽุฉูŽุŒ",
1489
+ "confidence": 1.0,
1490
+ "start_index": 1924
1491
+ },
1492
+ {
1493
+ "text": "ุนูŽู†ู’",
1494
+ "confidence": 1.0,
1495
+ "start_index": 1934
1496
+ },
1497
+ {
1498
+ "text": "ุนูŽุจู’ุฏู",
1499
+ "confidence": 1.0,
1500
+ "start_index": 1939
1501
+ },
1502
+ {
1503
+ "text": "ุงู„ู„ู‡ู",
1504
+ "confidence": 1.0,
1505
+ "start_index": 1946
1506
+ },
1507
+ {
1508
+ "text": "ุจู’ู†ู",
1509
+ "confidence": 1.0,
1510
+ "start_index": 1952
1511
+ },
1512
+ {
1513
+ "text": "ุงู„ู…ู„ุงุญู‚",
1514
+ "confidence": 1.0,
1515
+ "start_index": 1957
1516
+ },
1517
+ {
1518
+ "text": "ูˆุงู„ุฌุฏุงูˆู„",
1519
+ "confidence": 1.0,
1520
+ "start_index": 1965
1521
+ },
1522
+ {
1523
+ "text": "ุงู„ุฅุญุตุงุฆูŠุฉ",
1524
+ "confidence": 1.0,
1525
+ "start_index": 1974
1526
+ },
1527
+ {
1528
+ "text": "ุนูŽู…ู’ุฑููˆ",
1529
+ "confidence": 1.0,
1530
+ "start_index": 1984
1531
+ },
1532
+ {
1533
+ "text": "ุฑุถูŠ",
1534
+ "confidence": 1.0,
1535
+ "start_index": 1992
1536
+ },
1537
+ {
1538
+ "text": "ุงู„ู„ู‡",
1539
+ "confidence": 1.0,
1540
+ "start_index": 1996
1541
+ },
1542
+ {
1543
+ "text": "ุนู†ู‡ู…ุง",
1544
+ "confidence": 1.0,
1545
+ "start_index": 2001
1546
+ },
1547
+ {
1548
+ "text": "ู‚ูŽุงู„ูŽ:",
1549
+ "confidence": 1.0,
1550
+ "start_index": 2007
1551
+ },
1552
+ {
1553
+ "text": "ู‚ูŽุงู„ูŽ",
1554
+ "confidence": 1.0,
1555
+ "start_index": 2014
1556
+ },
1557
+ {
1558
+ "text": "ู„ููŠ",
1559
+ "confidence": 1.0,
1560
+ "start_index": 2020
1561
+ },
1562
+ {
1563
+ "text": "ุฑูŽุณููˆู„ู",
1564
+ "confidence": 1.0,
1565
+ "start_index": 2024
1566
+ },
1567
+ {
1568
+ "text": "ุงู„ู„ู‡ู",
1569
+ "confidence": 1.0,
1570
+ "start_index": 2032
1571
+ },
1572
+ {
1573
+ "text": "ุตู„ู‰",
1574
+ "confidence": 1.0,
1575
+ "start_index": 2038
1576
+ },
1577
+ {
1578
+ "text": "ุงู„ู„ู‡",
1579
+ "confidence": 1.0,
1580
+ "start_index": 2042
1581
+ },
1582
+ {
1583
+ "text": "ุนู„ูŠู‡",
1584
+ "confidence": 1.0,
1585
+ "start_index": 2047
1586
+ },
1587
+ {
1588
+ "text": "ูˆุณู„ู…:",
1589
+ "confidence": 1.0,
1590
+ "start_index": 2052
1591
+ },
1592
+ {
1593
+ "text": "\"ุงู‚ู’ุฑูŽุฃ",
1594
+ "confidence": 1.0,
1595
+ "start_index": 2058
1596
+ },
1597
+ {
1598
+ "text": "ุงู„ู’ู‚ูุฑู’ุขู†ูŽ",
1599
+ "confidence": 1.0,
1600
+ "start_index": 2066
1601
+ },
1602
+ {
1603
+ "text": "ูููŠ",
1604
+ "confidence": 1.0,
1605
+ "start_index": 2077
1606
+ },
1607
+ {
1608
+ "text": "ูƒูู„ู‘ู",
1609
+ "confidence": 1.0,
1610
+ "start_index": 2081
1611
+ },
1612
+ {
1613
+ "text": "ุดูŽู‡ู’ุฑู\"ุŒ",
1614
+ "confidence": 1.0,
1615
+ "start_index": 2087
1616
+ },
1617
+ {
1618
+ "text": "ู‚ูŽุงู„ูŽ:",
1619
+ "confidence": 1.0,
1620
+ "start_index": 2096
1621
+ },
1622
+ {
1623
+ "text": "ู‚ูู„ู’ุชู:",
1624
+ "confidence": 1.0,
1625
+ "start_index": 2103
1626
+ },
1627
+ {
1628
+ "text": "ุฅูู†ู‘ู",
1629
+ "confidence": 1.0,
1630
+ "start_index": 2111
1631
+ },
1632
+ {
1633
+ "text": "ุฃูŽุฌูุฏู",
1634
+ "confidence": 1.0,
1635
+ "start_index": 2117
1636
+ },
1637
+ {
1638
+ "text": "ู‚ููˆู‘ูŽุฉู‹ุŒ",
1639
+ "confidence": 1.0,
1640
+ "start_index": 2124
1641
+ },
1642
+ {
1643
+ "text": "ู‚ูŽุงู„ูŽ:",
1644
+ "confidence": 1.0,
1645
+ "start_index": 2133
1646
+ },
1647
+ {
1648
+ "text": "\"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู",
1649
+ "confidence": 1.0,
1650
+ "start_index": 2140
1651
+ },
1652
+ {
1653
+ "text": "ูููŠ",
1654
+ "confidence": 1.0,
1655
+ "start_index": 2153
1656
+ },
1657
+ {
1658
+ "text": "ุนูุดู’ุฑููŠู†ูŽ",
1659
+ "confidence": 1.0,
1660
+ "start_index": 2157
1661
+ },
1662
+ {
1663
+ "text": "ู„ูŽูŠู’ู„ูŽุฉู‹\"ุŒ",
1664
+ "confidence": 1.0,
1665
+ "start_index": 2167
1666
+ },
1667
+ {
1668
+ "text": "ู‚ูŽุงู„ูŽ:",
1669
+ "confidence": 1.0,
1670
+ "start_index": 2178
1671
+ },
1672
+ {
1673
+ "text": "ู‚ูู„ู’ุชู:",
1674
+ "confidence": 1.0,
1675
+ "start_index": 2185
1676
+ },
1677
+ {
1678
+ "text": "ุฅูู†ู‘ููŠ",
1679
+ "confidence": 1.0,
1680
+ "start_index": 2193
1681
+ },
1682
+ {
1683
+ "text": "ุฃูŽุฌูุฏู",
1684
+ "confidence": 1.0,
1685
+ "start_index": 2200
1686
+ },
1687
+ {
1688
+ "text": "ู‚ููˆู‘ูŽุฉู‹ุŒ",
1689
+ "confidence": 1.0,
1690
+ "start_index": 2207
1691
+ },
1692
+ {
1693
+ "text": "ู‚ูŽุงู„ูŽ:",
1694
+ "confidence": 1.0,
1695
+ "start_index": 2216
1696
+ },
1697
+ {
1698
+ "text": "\"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู",
1699
+ "confidence": 1.0,
1700
+ "start_index": 2223
1701
+ },
1702
+ {
1703
+ "text": "ูููŠ",
1704
+ "confidence": 1.0,
1705
+ "start_index": 2236
1706
+ },
1707
+ {
1708
+ "text": "ุณูŽุจู’ุนูุŒ",
1709
+ "confidence": 1.0,
1710
+ "start_index": 2240
1711
+ },
1712
+ {
1713
+ "text": "ูˆูŽู„ูŽุง",
1714
+ "confidence": 1.0,
1715
+ "start_index": 2248
1716
+ },
1717
+ {
1718
+ "text": "ู†ูŽุฒูุฏู’",
1719
+ "confidence": 1.0,
1720
+ "start_index": 2254
1721
+ },
1722
+ {
1723
+ "text": "ุนูŽู„ูŽู‰",
1724
+ "confidence": 1.0,
1725
+ "start_index": 2261
1726
+ },
1727
+ {
1728
+ "text": "ุฐูŽู„ููƒูŽ\").",
1729
+ "confidence": 1.0,
1730
+ "start_index": 2267
1731
+ },
1732
+ {
1733
+ "text": "ุฑุฌุงู„",
1734
+ "confidence": 1.0,
1735
+ "start_index": 2277
1736
+ },
1737
+ {
1738
+ "text": "ู‡ุฐุง",
1739
+ "confidence": 1.0,
1740
+ "start_index": 2282
1741
+ },
1742
+ {
1743
+ "text": "ุงู„ุฅุณู†ุงุฏ:",
1744
+ "confidence": 1.0,
1745
+ "start_index": 2286
1746
+ },
1747
+ {
1748
+ "text": "ุณุชุฉ:",
1749
+ "confidence": 1.0,
1750
+ "start_index": 2295
1751
+ },
1752
+ {
1753
+ "text": "1",
1754
+ "confidence": 1.0,
1755
+ "start_index": 2300
1756
+ },
1757
+ {
1758
+ "text": "-",
1759
+ "confidence": 1.0,
1760
+ "start_index": 2302
1761
+ },
1762
+ {
1763
+ "text": "(ุงู„ู’ู‚ูŽุงุณูู…ู",
1764
+ "confidence": 1.0,
1765
+ "start_index": 2304
1766
+ },
1767
+ {
1768
+ "text": "ุจู’ู†ู",
1769
+ "confidence": 1.0,
1770
+ "start_index": 2316
1771
+ },
1772
+ {
1773
+ "text": "ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽ\"",
1774
+ "confidence": 1.0,
1775
+ "start_index": 2321
1776
+ },
1777
+ {
1778
+ "text": "ุงู„ู‚ุฑุดูŠู‘ุŒ",
1779
+ "confidence": 1.0,
1780
+ "start_index": 2335
1781
+ },
1782
+ {
1783
+ "text": "ุฃุจูˆ",
1784
+ "confidence": 1.0,
1785
+ "start_index": 2344
1786
+ },
1787
+ {
1788
+ "text": "ู…ุญู…ุฏ",
1789
+ "confidence": 1.0,
1790
+ "start_index": 2348
1791
+ },
1792
+ {
1793
+ "text": "ุงู„ุทุญู‘ุงู†",
1794
+ "confidence": 1.0,
1795
+ "start_index": 2353
1796
+ },
1797
+ {
1798
+ "text": "ุงู„ูƒูˆููŠู‘ุŒ",
1799
+ "confidence": 1.0,
1800
+ "start_index": 2361
1801
+ },
1802
+ {
1803
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1808
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1813
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1814
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1815
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1816
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1818
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1819
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1820
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1821
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1823
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1824
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1825
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1826
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1827
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1828
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1829
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1832
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1833
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1834
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1835
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1838
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1839
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1840
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1842
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1843
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1844
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1848
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1849
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1851
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1852
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1853
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1854
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1855
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1856
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1857
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1858
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1859
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1860
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1861
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1862
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1863
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1864
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1865
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1866
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1867
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1868
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1869
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1870
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1871
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1872
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1873
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1874
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1875
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1876
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1877
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1878
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1879
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1883
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1884
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1885
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1886
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1887
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1888
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1889
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1890
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1891
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1892
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1893
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1894
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1895
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1896
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1897
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1898
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1903
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1905
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1907
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1908
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1912
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1913
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1916
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1917
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1918
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1919
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1922
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1923
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1924
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1926
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1927
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1928
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1932
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1933
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1937
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1938
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1941
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1942
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1943
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1947
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1948
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1949
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1951
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1952
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1953
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1954
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1955
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1956
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1957
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1958
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1959
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1960
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1961
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1962
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1963
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1964
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1965
+ "start_index": 2527
1966
+ },
1967
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1968
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1969
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1970
+ "start_index": 2536
1971
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1972
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1973
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1974
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1975
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1976
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1977
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1978
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1979
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1980
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1981
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1982
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1983
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1984
+ "confidence": 1.0,
1985
+ "start_index": 2558
1986
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1987
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1988
+ "text": "\\frac{\\partial",
1989
+ "confidence": 1.0,
1990
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1991
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1992
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1993
+ "text": "z}{\\partial",
1994
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1995
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1996
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1997
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1998
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1999
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2001
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2002
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2003
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2004
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2006
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2007
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2008
+ "text": "\\lim_{h",
2009
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2011
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2012
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2013
+ "text": "\\to",
2014
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2015
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2016
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2017
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2018
+ "text": "0}",
2019
+ "confidence": 1.0,
2020
+ "start_index": 2609
2021
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2022
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2023
+ "text": "\\frac{\\sin(z",
2024
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2025
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2026
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2027
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2028
+ "text": "+",
2029
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2031
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2032
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2033
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2034
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2036
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2037
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2038
+ "text": "-",
2039
+ "confidence": 1.0,
2040
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2041
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2042
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2043
+ "text": "\\sin(z)}{h}",
2044
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2045
+ "start_index": 2632
2046
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2047
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2048
+ "text": "ู…ู†ู‡ุฌูŠุฉ",
2049
+ "confidence": 1.0,
2050
+ "start_index": 2644
2051
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2052
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2053
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2054
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2055
+ "start_index": 2651
2056
+ },
2057
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2058
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2059
+ "confidence": 1.0,
2060
+ "start_index": 2657
2061
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2062
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2063
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2064
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2065
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2066
+ },
2067
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2068
+ "text": "ุงู„ุจูŠุงู†ุงุช",
2069
+ "confidence": 1.0,
2070
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2071
+ },
2072
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2073
+ "text": "ุงู„ุฑุญู…ู†",
2074
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2075
+ "start_index": 2677
2076
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2077
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2078
+ "text": "ู…ูˆู„ู‰",
2079
+ "confidence": 1.0,
2080
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2081
+ },
2082
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2083
+ "text": "\\nabla_{z}",
2084
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2085
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2086
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2087
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2088
+ "text": "J(z)",
2089
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2091
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2092
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2093
+ "text": "=",
2094
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2096
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2097
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2098
+ "text": "\\frac{1}{m}",
2099
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2100
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2101
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2102
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2103
+ "text": "X^T",
2104
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2105
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2106
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2107
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2108
+ "text": "(",
2109
+ "confidence": 1.0,
2110
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2111
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2112
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2113
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2114
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2115
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2116
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2117
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2118
+ "text": "z)",
2119
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2123
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2124
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2125
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2126
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2127
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2128
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2129
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2132
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2133
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2134
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2136
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2137
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2138
+ "text": "ุงู„ุตูุญุฉ",
2139
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2140
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2141
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2142
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2143
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+ "content": "ุฅู„ู‰ ุงู„ุฅู…ุงู… ู…ุณู„ู… ุจู† ุงู„ุญุฌุงุฌ ุฑุญู…ู‡ ุงู„ู„ู‡ ุงู„ู…ุฐูƒูˆุฑ ุฃูˆู„ูŽ ุงู„ูƒุชุงุจ ู‚ุงู„: [2732] ( โ€ฆ ) - (ุญูŽุฏู‘ูŽุซูŽู†ููŠ ุงู„ู’ู‚ูŽุงุณูู…ู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽุŒ ุญูŽุฏู‘ูŽุซูŽู†ูŽุง ุนูุจูŽูŠู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ู…ููˆุณูŽู‰ุŒ ุนูŽู†ู’ ุดูŽูŠู’ุจูŽุงู†ูŽุŒ ุนูŽู†ู’ ูŠูŽุญู’ูŠูŽู‰ุŒ ุนูŽู†ู’ ู…ูุญูŽู…ู‘ูŽุฏู ุจู’ู†ู ุนูŽุจู’ุฏู ุงู„ุฑู‘ูŽุญู’ู…ูŽู†ู ู…ูŽูˆู’ู„ูŽู‰ ุจูŽู†ููŠ ุฒูู‡ู’ุฑูŽุฉูŽุŒ ุนูŽู†ู’ ุฃุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ู‚ูŽุงู„ูŽ: ูˆูŽุฃูŽุญู’ุณูŽุจูู†ููŠ ู‚ูŽุฏู’ ุณูŽู…ูุนู’ุชูู‡ู ุฃู†ูŽุง ู…ูู†ู’ ุฃูŽุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ุนูŽู†ู’ ุนูŽุจู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ุนูŽู…ู’ุฑููˆ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡ู…ุง ู‚ูŽุงู„ูŽ: ู‚ูŽุงู„ูŽ ู„ููŠ ุฑูŽุณููˆู„ู ุงู„ู„ู‡ู ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู…: \"ุงู‚ู’ุฑูŽุฃ ุงู„ู’ู‚ูุฑู’ุขู†ูŽ ูููŠ ูƒูู„ู‘ู ุดูŽู‡ู’ุฑู\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ู ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุนูุดู’ุฑููŠู†ูŽ ู„ูŽูŠู’ู„ูŽุฉู‹\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ููŠ ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุณูŽุจู’ุนูุŒ ูˆูŽู„ูŽุง ู†ูŽุฒูุฏู’ ุนูŽู„ูŽู‰ ุฐูŽู„ููƒูŽ\"). ุฑุฌุงู„ ู‡ุฐุง ุงู„ุฅุณู†ุงุฏ: ุณุชุฉ: 1 - (ุงู„ู’ู‚ูŽุงุณู๏ฟฝ๏ฟฝู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽ\" ุงู„ู‚ุฑุดูŠู‘ุŒ ุฃุจูˆ ู…ุญู…ุฏ ุงู„ุทุญู‘ุงู† ุงู„ูƒูˆููŠู‘ุŒ ุซู‚ุฉูŒ [11] ู…ุงุช ููŠ ุญุฏูˆุฏ (250) (ู… ุช ุณ ู‚) ุชู‚ุฏู… ููŠ \"ุงู„ุฅูŠู…ุงู†\" 4/ 118. 2 - (ุนูุจูŽูŠู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ู…ููˆุณูŽู‰) ุจู† ุฃุจูŠ ุงู„ู…ุฎุชุงุฑ ุงู„ู’ุนูŽุจุณูŠู‘ุŒ ุชู‚ุฏู‘ู… ู‚ุฑูŠุจุงู‹. 3 - (ุดูŽูŠู’ุจูŽุงู†ู) ุจู† ุนุจุฏ ุงู„ุฑุญู…ู† ุงู„ู†ุญูˆูŠู‘ุŒ ุฃุจูˆ ู…ุนุงูˆูŠุฉ",
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2218
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2227
+ "content": "ุตูˆุฑุฉ ุชูˆุถูŠุญูŠุฉ ู„ุนู…ู„ูŠุฉ ู‚ุงุฆู…ุฉ ุงู„ู…ุฑุงุฌุน ูˆุงู„ู…ุตุงุฏุฑ ุงู„ุชูˆุซูŠู‚ูŠุฉ",
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2237
+ "content": "\\frac{\\partial k}{\\partial \\lambda} = \\lim_{h \\to 0} \\frac{\\min(\\lambda + h) - \\min(\\lambda)}{h} + \\frac{\\theta}{i^2}",
2238
+ "type": "text",
2239
+ "confidence_scores": null,
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2242
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2243
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+ "content": "\\mu_{n+1} = \\mu_n - \\alpha \\nabla f(\\mu_n)",
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2249
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2257
+ "content": "ุงู„ู…ู†ุธูˆุฑ ุงู„ู…ู‚ุงุฑู† ูˆุฃูุถู„ ุงู„ู…ู…ุงุฑุณุงุช",
2258
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+ "content": "ู…ุณู„ู… ุจู† ุงู„ุญุฌุงุฌ ุฑุญู…ู‡ ุงู„ู„ู‡ ุงู„ู…ุฐูƒูˆุฑ ุฃูˆู„ูŽ ุงู„ูƒุชุงุจ ู‚ุงู„: [2732] ( โ€ฆ ) - (ุญูŽุฏู‘ูŽุซูŽู†ููŠ ุงู„ู’ู‚ูŽุงุณูู…ู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽุŒ ุญูŽุฏู‘ูŽุซูŽู†ูŽุง ุนูุจูŽูŠู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู ู…ููˆุณูŽู‰ุŒ ุนูŽู†ู’ ุดูŽูŠู’ุจูŽุงู†ูŽุŒ ุนูŽู†ู’ ูŠูŽุญู’ูŠูŽู‰ุŒ ุนูŽู†ู’ ู…ูุญูŽู…ู‘ูŽุฏู ุจู’ู†ู ุนูŽุจู’ุฏู ุงู„ุฑู‘ูŽุญู’ู…ูŽู†ู ู…ูŽูˆู’ู„ูŽู‰ ุจูŽู†ููŠ ุฒูู‡ู’ุฑูŽุฉูŽุŒ ุนูŽู†ู’ ุฃุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ู‚ูŽุงู„ูŽ: ูˆูŽุฃูŽุญู’ุณูŽุจูู†ููŠ ู‚ูŽุฏู’ ุณูŽู…ูุนู’ุชูู‡ู ุฃู†ูŽุง ู…ูู†ู’ ุฃูŽุจููŠ ุณูŽู„ูŽู…ูŽุฉูŽุŒ ุนูŽู†ู’ ุนูŽุจู’ุฏู ุงู„ู„ู‡ู ุจู’ู†ู",
2268
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2272
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2273
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2274
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2275
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2276
+ "bottom_right_y": 359,
2277
+ "content": "ุงู„ู…ู„ุงุญู‚ ูˆุงู„ุฌุฏุงูˆู„ ุงู„ุฅุญุตุงุฆูŠุฉ",
2278
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2282
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2283
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2285
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2286
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2287
+ "content": "ุนูŽู…ู’ุฑููˆ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡ู…ุง ู‚ูŽุงู„ูŽ: ู‚ูŽุงู„ูŽ ู„ููŠ ุฑูŽุณููˆู„ู ุงู„ู„ู‡ู ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู…: \"ุงู‚ู’ุฑูŽุฃ ุงู„ู’ู‚ูุฑู’ุขู†ูŽ ูููŠ ูƒูู„ู‘ู ุดูŽู‡ู’ุฑู\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ู ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุนูุดู’ุฑููŠู†ูŽ ู„ูŽูŠู’ู„ูŽุฉู‹\"ุŒ ู‚ูŽุงู„ูŽ: ู‚ูู„ู’ุชู: ุฅูู†ู‘ููŠ ุฃูŽุฌูุฏู ู‚ููˆู‘ูŽุฉู‹ุŒ ู‚ูŽุงู„ูŽ: \"ููŽุงู‚ู’ุฑูŽุฃู’ู‡ู ูููŠ ุณูŽุจู’ุนูุŒ ูˆูŽู„ูŽุง ู†ูŽุฒูุฏู’ ุนูŽู„ูŽู‰ ุฐูŽู„ููƒูŽ\"). ุฑุฌุงู„ ู‡ุฐุง ุงู„ุฅุณู†ุงุฏ: ุณุชุฉ: 1 - (ุงู„ู’ู‚ูŽุงุณูู…ู ุจู’ู†ู ุฒูŽูƒูŽุฑููŠู‘ูŽุงุกูŽ\" ุงู„ู‚ุฑุดูŠู‘ุŒ ุฃุจูˆ ู…ุญู…ุฏ ุงู„ุทุญู‘ุงู† ุงู„ูƒูˆููŠู‘ุŒ ุซู‚ุฉูŒ [11] ู…ุงุช ููŠ ุญุฏูˆุฏ (250) (ู… ุช ุณ ู‚) ุชู‚ุฏู… ููŠ \"ุงู„ุฅูŠู…ุงู†\" 4/ 118. 2",
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2292
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2293
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+ "bottom_right_y": 565,
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+ "content": "ุจุฑู‡ุงู†",
2298
+ "type": "title",
2299
+ "confidence_scores": null,
2300
+ "reading_index": 15
2301
+ },
2302
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2304
+ "top_left_y": 571,
2305
+ "bottom_right_x": 372,
2306
+ "bottom_right_y": 625,
2307
+ "content": "\\iint_{D} i^2 - \\mu^2 \\, dx \\, dy",
2308
+ "type": "text",
2309
+ "confidence_scores": null,
2310
+ "reading_index": 16
2311
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2312
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2316
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2317
+ "content": "![image](img-1)",
2318
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2319
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+ "reading_index": 17
2321
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2322
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2323
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2324
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2325
+ "bottom_right_x": 388,
2326
+ "bottom_right_y": 919,
2327
+ "content": "ุงู„ุดูƒู„ (2): ู‡ูŠูƒู„ ู‚ุงุฆู…ุฉ ุงู„ู…ุฑุงุฌุน ูˆุงู„ู…ุตุงุฏุฑ ุงู„ุชูˆุซูŠู‚ูŠุฉ ุงู„ุชู†ุธูŠู…ูŠ",
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+ "bottom_right_y": 976,
2337
+ "content": "ู…ู„ุงุญุธุฉ",
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+ "type": "title",
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+ "confidence_scores": null,
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+ "bottom_right_x": 372,
2346
+ "bottom_right_y": 1035,
2347
+ "content": "\\frac{\\partial z}{\\partial z} = \\lim_{h \\to 0} \\frac{\\sin(z + h) - \\sin(z)}{h}",
2348
+ "type": "text",
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+ "confidence_scores": null,
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+ "bottom_right_y": 1081,
2357
+ "content": "ู…ู†ู‡ุฌูŠุฉ ุงู„ุจุญุซ ูˆุฃุฏูˆุงุช ุฌู…ุน ุงู„ุจูŠุงู†ุงุช",
2358
+ "type": "text",
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2366
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2367
+ "content": "ุงู„ุฑุญู…ู† ู…ูˆู„ู‰",
2368
+ "type": "text",
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+ "text": "\"ุงู„ูุชุญ\":",
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+ "text": "ุงู„ู…ุณุงูˆุงุฉ",
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+ "text": "ู‚ูˆู„ู‡",
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+ "text": "ุงู„ุฑูˆุงูŠุฉ",
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+ "text": "ุงู„ุจุฎุงุฑูŠู‘:",
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+ "text": "ุงู„ุตูŠุงู…",
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+ "text": "ุตูŠุงู…",
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633
+ "text": "ูŠู‚ุชุถูŠ",
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636
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638
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+ "text": "ุงู„ุฃูุถู„ูŠุฉ",
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+ "text": "ู…ุณู„ู…",
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661
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663
+ "text": "ูˆุงู„ุชุฑู…ุฐูŠู‘",
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666
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668
+ "text": "ุจู„ูุธ:",
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673
+ "text": "\"ุฃูุถู„",
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+ "text": "ุงู„ุตูŠุงู…",
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686
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688
+ "text": "ุฏุงูˆุฏ\"ุŒ",
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+ "start_index": 383
691
+ },
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+ "text": "ูˆู…ู‚ุชุถุงู‡",
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696
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+ "text": "ุฃู†",
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703
+ "text": "ุชูƒูˆู†",
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706
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708
+ "text": "ุงู„ุฒูŠุงุฏุฉ",
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711
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713
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716
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718
+ "text": "ุฐู„ูƒ",
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721
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723
+ "text": "ู…ู†",
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726
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728
+ "text": "ุงู„ุตูˆู…",
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+ "confidence": 1.0,
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+ "start_index": 425
731
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732
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733
+ "text": "ู…ูุถูˆู„ุฉ.",
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+ "start_index": 431
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+ },
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738
+ "text": "ุงู†ุชู‡ู‰",
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+ "confidence": 1.0,
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+ "start_index": 439
741
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743
+ "text": "ุจุชุตุฑู‘ู",
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746
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748
+ "text": "(2)",
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753
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+ "text": "ุงู„ุฌุงู…ุน",
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+ "start_index": 462
766
+ },
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768
+ "text": "ุนูุง",
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+ "confidence": 1.0,
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+ "start_index": 469
771
+ },
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773
+ "text": "ุงู„ู„ู‡",
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+ "start_index": 473
776
+ },
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778
+ "text": "ุนู†ู‡:",
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781
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783
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