{ "markdown": "\\nabla_{\\sigma} J(\\sigma) = \\frac{1}{m} X^T ( \\sigma(X \\sigma) - Y ) + \\frac{\\alpha}{x^2}\n\\iint_{D} k^2 \\cdot t^2 \\, dx \\, dy\n\\int_{5}^{100} \\min(j) \\, dj = n^2 \\times C\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## مبرهنة\n\\vec{F} = m\\vec{a}\n## ملاحظة\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## تعريف\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n\\mathbb{E}[\\lambda] = \\int x f_\\lambda(x) dx\n## مبرهنة\nP(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{n}{\\lambda^2}", "images": [], "tables": [], "hyperlinks": [], "header": null, "footer": null, "dimensions": { "dpi": 96, "height": 998, "width": 863 }, "confidence_scores": { "word_confidence_scores": [ { "text": "\\nabla_{\\sigma}", "confidence": 1.0, "start_index": 0 }, { "text": "J(\\sigma)", "confidence": 1.0, "start_index": 16 }, { "text": "=", "confidence": 1.0, "start_index": 26 }, { "text": "\\frac{1}{m}", "confidence": 1.0, "start_index": 28 }, { "text": "X^T", 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"\\int_{5}^{100}", "confidence": 1.0, "start_index": 126 }, { "text": "\\min(j)", "confidence": 1.0, "start_index": 141 }, { "text": "\\,", "confidence": 1.0, "start_index": 149 }, { "text": "dj", "confidence": 1.0, "start_index": 152 }, { "text": "=", "confidence": 1.0, "start_index": 155 }, { "text": "n^2", "confidence": 1.0, "start_index": 157 }, { "text": "\\times", "confidence": 1.0, "start_index": 161 }, { "text": "C", "confidence": 1.0, "start_index": 168 }, { "text": "P(A|B)", "confidence": 1.0, "start_index": 170 }, { "text": "=", "confidence": 1.0, "start_index": 177 }, { "text": "\\frac{P(A", "confidence": 1.0, "start_index": 179 }, { "text": "\\cap", "confidence": 1.0, "start_index": 189 }, { "text": "B)}{P(B)}", "confidence": 1.0, "start_index": 194 }, { "text": "##", "confidence": 1.0, "start_index": 204 }, { "text": "مبرهنة", "confidence": 1.0, "start_index": 207 }, { "text": "\\vec{F}", "confidence": 1.0, "start_index": 214 }, { "text": "=", "confidence": 1.0, "start_index": 222 }, { "text": "m\\vec{a}", "confidence": 1.0, "start_index": 224 }, { "text": "##", "confidence": 1.0, "start_index": 233 }, { "text": "ملاحظة", "confidence": 1.0, "start_index": 236 }, { "text": "P(A|B)", "confidence": 1.0, "start_index": 243 }, { "text": "=", "confidence": 1.0, "start_index": 250 }, { "text": "\\frac{P(A", "confidence": 1.0, "start_index": 252 }, { "text": "\\cap", "confidence": 1.0, "start_index": 262 }, { "text": "B)}{P(B)}", "confidence": 1.0, "start_index": 267 }, { "text": "P(A|B)", "confidence": 1.0, "start_index": 277 }, { "text": "=", "confidence": 1.0, "start_index": 284 }, { "text": "\\frac{P(A", "confidence": 1.0, "start_index": 286 }, { "text": "\\cap", "confidence": 1.0, "start_index": 296 }, { "text": "B)}{P(B)}", "confidence": 1.0, "start_index": 301 }, { "text": "##", "confidence": 1.0, "start_index": 311 }, { "text": "تعريف", "confidence": 1.0, "start_index": 314 }, { "text": "P(A|B)", "confidence": 1.0, "start_index": 320 }, { 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"confidence": 1.0, "start_index": 433 }, { "text": "+", "confidence": 1.0, "start_index": 443 }, { "text": "\\frac{n}{\\lambda^2}", "confidence": 1.0, "start_index": 445 } ], "average_page_confidence_score": 1.0, "minimum_page_confidence_score": 1.0 }, "blocks": [ { "top_left_x": 40, "top_left_y": 52, "bottom_right_x": 823, "bottom_right_y": 101, "content": "\\nabla_{\\sigma} J(\\sigma) = \\frac{1}{m} X^T ( \\sigma(X \\sigma) - Y ) + \\frac{\\alpha}{x^2}", "type": "text", "confidence_scores": null, "reading_index": 1 }, { "top_left_x": 40, "top_left_y": 113, "bottom_right_x": 823, "bottom_right_y": 169, "content": "\\iint_{D} k^2 \\cdot t^2 \\, dx \\, dy", "type": "text", "confidence_scores": null, "reading_index": 2 }, { "top_left_x": 40, "top_left_y": 175, "bottom_right_x": 823, "bottom_right_y": 235, "content": "\\int_{5}^{100} \\min(j) \\, dj = n^2 \\times C", "type": "text", "confidence_scores": null, "reading_index": 3 }, { "top_left_x": 40, "top_left_y": 241, "bottom_right_x": 823, "bottom_right_y": 306, "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", "type": "text", "confidence_scores": null, "reading_index": 4 }, { "top_left_x": 52, "top_left_y": 324, "bottom_right_x": 807, "bottom_right_y": 358, "content": "مبرهنة", "type": "title", "confidence_scores": null, "reading_index": 5 }, { "top_left_x": 52, "top_left_y": 364, "bottom_right_x": 807, "bottom_right_y": 403, "content": "\\vec{F} = m\\vec{a}", "type": "text", "confidence_scores": null, "reading_index": 6 }, { "top_left_x": 52, "top_left_y": 447, "bottom_right_x": 807, "bottom_right_y": 481, "content": "ملاحظة", "type": "title", "confidence_scores": null, "reading_index": 7 }, { "top_left_x": 52, "top_left_y": 487, "bottom_right_x": 807, "bottom_right_y": 543, "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", "type": "text", "confidence_scores": null, "reading_index": 8 }, { "top_left_x": 40, "top_left_y": 575, "bottom_right_x": 823, "bottom_right_y": 635, "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", "type": "text", "confidence_scores": null, "reading_index": 9 }, { "top_left_x": 52, "top_left_y": 653, "bottom_right_x": 807, "bottom_right_y": 687, "content": "تعريف", "type": "title", "confidence_scores": null, "reading_index": 10 }, { "top_left_x": 52, "top_left_y": 693, "bottom_right_x": 807, "bottom_right_y": 749, "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", "type": "text", "confidence_scores": null, "reading_index": 11 }, { "top_left_x": 40, "top_left_y": 781, "bottom_right_x": 823, "bottom_right_y": 839, "content": "\\mathbb{E}[\\lambda] = \\int x f_\\lambda(x) dx", "type": "text", "confidence_scores": null, "reading_index": 12 }, { "top_left_x": 52, "top_left_y": 857, "bottom_right_x": 807, "bottom_right_y": 891, "content": "مبرهنة", "type": "title", "confidence_scores": null, "reading_index": 13 }, { "top_left_x": 52, "top_left_y": 897, "bottom_right_x": 807, "bottom_right_y": 953, "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{n}{\\lambda^2}", 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