{ "markdown": "z_{n+1} = z_n - \\alpha \\nabla f(z_n)\n\\iint_{D} t^2 \\geq k^2 \\, dx \\, dy\n## ملاحظة\n(1) ، انظروا أزال الرسول صلى الله عليه وسلم كل\n\\mu_{n+1} = \\mu_n - \\alpha \\nabla f(\\mu_n)\n\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y ) + \\frac{i}{\\lambda^2}", "images": [], "tables": [], "hyperlinks": [], "header": null, "footer": null, "dimensions": { "dpi": 96, "height": 368, "width": 677 }, "confidence_scores": { "word_confidence_scores": [ { "text": "z_{n+1}", "confidence": 1.0, "start_index": 0 }, { "text": "=", "confidence": 1.0, "start_index": 8 }, { "text": "z_n", "confidence": 1.0, "start_index": 10 }, { "text": "-", "confidence": 1.0, "start_index": 14 }, { "text": "\\alpha", "confidence": 1.0, "start_index": 16 }, { "text": "\\nabla", "confidence": 1.0, "start_index": 23 }, { "text": "f(z_n)", "confidence": 1.0, "start_index": 30 }, { "text": "\\iint_{D}", "confidence": 1.0, "start_index": 37 }, { "text": "t^2", "confidence": 1.0, "start_index": 47 }, { "text": "\\geq", "confidence": 1.0, "start_index": 51 }, { "text": "k^2", "confidence": 1.0, "start_index": 56 }, { "text": "\\,", "confidence": 1.0, "start_index": 60 }, { "text": "dx", "confidence": 1.0, "start_index": 63 }, { "text": "\\,", "confidence": 1.0, "start_index": 66 }, { "text": "dy", "confidence": 1.0, "start_index": 69 }, { "text": "##", "confidence": 1.0, "start_index": 72 }, { "text": "ملاحظة", "confidence": 1.0, "start_index": 75 }, { "text": "(1)", "confidence": 1.0, "start_index": 82 }, { "text": "،", "confidence": 1.0, "start_index": 86 }, { "text": "انظروا", "confidence": 1.0, "start_index": 88 }, { "text": "أزال", "confidence": 1.0, "start_index": 95 }, { "text": "الرسول", "confidence": 1.0, "start_index": 100 }, { "text": "صلى", "confidence": 1.0, "start_index": 107 }, { "text": "الله", "confidence": 1.0, "start_index": 111 }, { "text": "عليه", "confidence": 1.0, "start_index": 116 }, { "text": "وسلم", "confidence": 1.0, "start_index": 121 }, { "text": "كل", "confidence": 1.0, "start_index": 126 }, { "text": "\\mu_{n+1}", "confidence": 1.0, "start_index": 129 }, { "text": "=", "confidence": 1.0, "start_index": 139 }, { "text": "\\mu_n", "confidence": 1.0, "start_index": 141 }, { "text": "-", "confidence": 1.0, "start_index": 147 }, { "text": "\\alpha", "confidence": 1.0, "start_index": 149 }, { "text": "\\nabla", "confidence": 1.0, "start_index": 156 }, { "text": "f(\\mu_n)", "confidence": 1.0, "start_index": 163 }, { "text": "\\nabla_{\\mu}", "confidence": 1.0, "start_index": 172 }, { "text": "J(\\mu)", "confidence": 1.0, "start_index": 185 }, { "text": "=", "confidence": 1.0, "start_index": 192 }, { "text": "\\frac{1}{m}", "confidence": 1.0, "start_index": 194 }, { "text": "X^T", "confidence": 1.0, "start_index": 206 }, { "text": "(", "confidence": 1.0, "start_index": 210 }, { "text": "\\sigma(X", "confidence": 1.0, "start_index": 212 }, { "text": "\\mu)", "confidence": 1.0, "start_index": 221 }, { "text": "-", "confidence": 1.0, "start_index": 226 }, { "text": "Y", "confidence": 1.0, "start_index": 228 }, { "text": ")", "confidence": 1.0, "start_index": 230 }, { "text": "+", "confidence": 1.0, "start_index": 232 }, { "text": "\\frac{i}{\\lambda^2}", "confidence": 1.0, "start_index": 234 } ], "average_page_confidence_score": 1.0, "minimum_page_confidence_score": 1.0 }, "blocks": [ { "top_left_x": 20, "top_left_y": 26, "bottom_right_x": 657, "bottom_right_y": 69, "content": "z_{n+1} = z_n - \\alpha \\nabla f(z_n)", "type": "text", "confidence_scores": null, "reading_index": 1 }, { "top_left_x": 20, "top_left_y": 75, "bottom_right_x": 657, "bottom_right_y": 130, "content": "\\iint_{D} t^2 \\geq k^2 \\, dx \\, dy", "type": "text", "confidence_scores": null, "reading_index": 2 }, { "top_left_x": 32, "top_left_y": 148, "bottom_right_x": 641, "bottom_right_y": 170, "content": "ملاحظة", "type": "title", "confidence_scores": null, "reading_index": 3 }, { "top_left_x": 32, "top_left_y": 175, "bottom_right_x": 641, "bottom_right_y": 197, "content": "(1) ، انظروا أزال الرسول صلى الله عليه وسلم كل", "type": "text", "confidence_scores": null, "reading_index": 4 }, { "top_left_x": 32, "top_left_y": 203, "bottom_right_x": 641, "bottom_right_y": 241, "content": "\\mu_{n+1} = \\mu_n - \\alpha \\nabla f(\\mu_n)", "type": "text", "confidence_scores": null, "reading_index": 5 }, { "top_left_x": 20, "top_left_y": 273, "bottom_right_x": 657, "bottom_right_y": 321, "content": "\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y ) + \\frac{i}{\\lambda^2}", "type": "text", "confidence_scores": null, "reading_index": 6 } ], "meta": { "template": "math_proof", "hybrid": null, "page_font": "mcs-jeddah-s-u-normal.ttf", "title_font": "mcs-jeddah-s-u-normal.ttf", "language": "ar", "script": "arabic", "direction": "rtl", "augmentation": null } }