image imagewidth (px) 107 3.63k | text stringlengths 266 2.21k | is_augmented bool 2
classes | original_id stringlengths 8 11 ⌀ |
|---|---|---|---|
<html>
<body>
<table>
<thead>
<tr>
<th>矩阵分解方法</th>
<th>数学表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>LU分解</td>
<td>$$A = LU$$</td>
</tr>
<tr>
<td>QR分解</td>
<td>$$A = QR$$</td>
</tr>
<tr>
<td>奇异值分解 (SVD)</td>
<td>$$A = U\Sigma V^T$$</td>
</tr>
</tbody>
</table>
</body>
</html> | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>矩阵分解方法</th>
<th>数学表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>LU分解</td>
<td>$$A = LU$$</td>
</tr>
<tr>
<td>QR分解</td>
<td>$$A = QR$$</td>
</tr>
<tr>
<td>奇异值分解 (SVD)</td>
<td>$$A = U\Sigma V^T$$</td>
</tr>
</tbody>
</table>
</body>
</html> | true | 数学_00000 | |
<html>
<body>
<table>
<thead>
<tr>
<th>矩阵分解方法</th>
<th>数学表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>LU分解</td>
<td>$$A = LU$$</td>
</tr>
<tr>
<td>QR分解</td>
<td>$$A = QR$$</td>
</tr>
<tr>
<td>奇异值分解 (SVD)</td>
<td>$$A = U\Sigma V^T$$</td>
</tr>
</tbody>
</table>
</body>
</html> | true | 数学_00000 | |
<html>
<body>
<table>
<thead>
<tr>
<th colspan="2">化学键类型</th>
<th>特征</th>
<th>实例</th>
<th>形成的能量变化</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">共价键</td>
<td>单键</td>
<td>两个原子通过共享一对电子形成</td>
<td>$$H_2$$, $$Cl_2$$</td>
<td>放热过程, $$\Delta H < 0$$</td>
</tr>
<tr>
<td>双键</td>
<td>两个原子通过共享两对电子形成</td>
<td>$$O_2$$, $$C_2H_4$... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th colspan="2">化学键类型</th>
<th>特征</th>
<th>实例</th>
<th>形成的能量变化</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">共价键</td>
<td>单键</td>
<td>两个原子通过共享一对电子形成</td>
<td>$$H_2$$, $$Cl_2$$</td>
<td>放热过程, $$\Delta H < 0$$</td>
</tr>
<tr>
<td>双键</td>
<td>两个原子通过共享两对电子形成</td>
<td>$$O_2$$, $$C_2H_4$... | true | 化学_00003 | |
<html>
<body>
<table>
<thead>
<tr>
<th colspan="2">化学键类型</th>
<th>特征</th>
<th>实例</th>
<th>形成的能量变化</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">共价键</td>
<td>单键</td>
<td>两个原子通过共享一对电子形成</td>
<td>$$H_2$$, $$Cl_2$$</td>
<td>放热过程, $$\Delta H < 0$$</td>
</tr>
<tr>
<td>双键</td>
<td>两个原子通过共享两对电子形成</td>
<td>$$O_2$$, $$C_2H_4$... | true | 化学_00003 | |
<html>
<body>
<table>
<thead>
<tr>
<th>性能要求</th>
<th>适航标准</th>
<th>公式表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>起飞距离</td>
<td>CCAR-25.121</td>
<td>$$S_{TO} = \frac{1.15 \cdot V_{LOF}^2}{2 \cdot g \cdot (c_{L_{MAX}} - \mu \cdot c_{D_{LOF}})}$$</td>
</tr>
<tr>
<td>着陆距离</td>
<td>CCAR-25.125</td>
<td>$$S_{LD} = \frac{1.15 \cd... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>性能要求</th>
<th>适航标准</th>
<th>公式表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>起飞距离</td>
<td>CCAR-25.121</td>
<td>$$S_{TO} = \frac{1.15 \cdot V_{LOF}^2}{2 \cdot g \cdot (c_{L_{MAX}} - \mu \cdot c_{D_{LOF}})}$$</td>
</tr>
<tr>
<td>着陆距离</td>
<td>CCAR-25.125</td>
<td>$$S_{LD} = \frac{1.15 \cd... | true | 适航标准_00006 | |
<html>
<body>
<table>
<thead>
<tr>
<th>性能要求</th>
<th>适航标准</th>
<th>公式表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>起飞距离</td>
<td>CCAR-25.121</td>
<td>$$S_{TO} = \frac{1.15 \cdot V_{LOF}^2}{2 \cdot g \cdot (c_{L_{MAX}} - \mu \cdot c_{D_{LOF}})}$$</td>
</tr>
<tr>
<td>着陆距离</td>
<td>CCAR-25.125</td>
<td>$$S_{LD} = \frac{1.15 \cd... | true | 适航标准_00006 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">机翼部件</th>
<th colspan="2">尺寸 (单位: 米)</th>
<th rowspan="2">重量 (单位: 千克)</th>
<th colspan="2">性能参数</th>
</tr>
<tr>
<th>翼展</th>
<th>翼面积</th>
<th>升力系数 $$C_L$$</th>
<th>阻力系数 $$C_D$$</th>
</tr>
</thead>
<tbody>
<tr>
<td>主翼</td>
<td>35.8</td>
<td>112.8</td>
<td>5400</td>
<td>0... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">机翼部件</th>
<th colspan="2">尺寸 (单位: 米)</th>
<th rowspan="2">重量 (单位: 千克)</th>
<th colspan="2">性能参数</th>
</tr>
<tr>
<th>翼展</th>
<th>翼面积</th>
<th>升力系数 $$C_L$$</th>
<th>阻力系数 $$C_D$$</th>
</tr>
</thead>
<tbody>
<tr>
<td>主翼</td>
<td>35.8</td>
<td>112.8</td>
<td>5400</td>
<td>0... | true | 飞机部件_00009 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">机翼部件</th>
<th colspan="2">尺寸 (单位: 米)</th>
<th rowspan="2">重量 (单位: 千克)</th>
<th colspan="2">性能参数</th>
</tr>
<tr>
<th>翼展</th>
<th>翼面积</th>
<th>升力系数 $$C_L$$</th>
<th>阻力系数 $$C_D$$</th>
</tr>
</thead>
<tbody>
<tr>
<td>主翼</td>
<td>35.8</td>
<td>112.8</td>
<td>5400</td>
<td>0... | true | 飞机部件_00009 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">滴定类型</th>
<th colspan="2">滴定过程</th>
<th colspan="2">计算公式</th>
</tr>
<tr>
<th>滴定剂</th>
<th>被滴定物</th>
<th>滴定终点</th>
<th>浓度计算</th>
</tr>
</thead>
<tbody>
<tr>
<td>酸碱滴定</td>
<td>NaOH</td>
<td>HCl</td>
<td>pH = 7</td>
<td>$$C_1V_1 = C_2V_2$$</td>
</tr>
<tr>
<td>氧化还原滴定</td>
... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">滴定类型</th>
<th colspan="2">滴定过程</th>
<th colspan="2">计算公式</th>
</tr>
<tr>
<th>滴定剂</th>
<th>被滴定物</th>
<th>滴定终点</th>
<th>浓度计算</th>
</tr>
</thead>
<tbody>
<tr>
<td>酸碱滴定</td>
<td>NaOH</td>
<td>HCl</td>
<td>pH = 7</td>
<td>$$C_1V_1 = C_2V_2$$</td>
</tr>
<tr>
<td>氧化还原滴定</td>
... | true | 化学_00012 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">滴定类型</th>
<th colspan="2">滴定过程</th>
<th colspan="2">计算公式</th>
</tr>
<tr>
<th>滴定剂</th>
<th>被滴定物</th>
<th>滴定终点</th>
<th>浓度计算</th>
</tr>
</thead>
<tbody>
<tr>
<td>酸碱滴定</td>
<td>NaOH</td>
<td>HCl</td>
<td>pH = 7</td>
<td>$$C_1V_1 = C_2V_2$$</td>
</tr>
<tr>
<td>氧化还原滴定</td>
... | true | 化学_00012 | |
<html>
<body>
<table>
<thead>
<tr>
<th>试验项目</th>
<th>试验参数</th>
<th>试验方法</th>
<th>结果评估</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">静载试验</td>
<td>最大载荷 $$P_{max}$$</td>
<td>逐步增加载荷至最大值，记录变形量</td>
<td>变形量不超过设计值</td>
</tr>
<tr>
<td>变形量 $$\Delta$$</td>
<td>使用位移传感器测量变形量</td>
<td>变形量与载荷成线性关系</td>
</tr>
<tr>
<td>动载试验</td>
<... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>试验项目</th>
<th>试验参数</th>
<th>试验方法</th>
<th>结果评估</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">静载试验</td>
<td>最大载荷 $$P_{max}$$</td>
<td>逐步增加载荷至最大值，记录变形量</td>
<td>变形量不超过设计值</td>
</tr>
<tr>
<td>变形量 $$\Delta$$</td>
<td>使用位移传感器测量变形量</td>
<td>变形量与载荷成线性关系</td>
</tr>
<tr>
<td>动载试验</td>
<... | true | 试验方法_00015 | |
<html>
<body>
<table>
<thead>
<tr>
<th>试验项目</th>
<th>试验参数</th>
<th>试验方法</th>
<th>结果评估</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">静载试验</td>
<td>最大载荷 $$P_{max}$$</td>
<td>逐步增加载荷至最大值，记录变形量</td>
<td>变形量不超过设计值</td>
</tr>
<tr>
<td>变形量 $$\Delta$$</td>
<td>使用位移传感器测量变形量</td>
<td>变形量与载荷成线性关系</td>
</tr>
<tr>
<td>动载试验</td>
<... | true | 试验方法_00015 | |
<html>
<body>
<table>
<thead>
<tr>
<th colspan="2">高分子化学基础</th>
<th>化学式</th>
<th>反应条件</th>
<th>应用领域</th>
</tr>
<tr>
<th>单体</th>
<th>聚合类型</th>
<th></th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>乙烯</td>
<td>自由基聚合</td>
<td>$$C_2H_4$$</td>
<td>高温、高压</td>
<td>塑料制品</td>
</tr>
<tr>
<td rowspan="2">苯乙烯</td>
<td>阴离子聚... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th colspan="2">高分子化学基础</th>
<th>化学式</th>
<th>反应条件</th>
<th>应用领域</th>
</tr>
<tr>
<th>单体</th>
<th>聚合类型</th>
<th></th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>乙烯</td>
<td>自由基聚合</td>
<td>$$C_2H_4$$</td>
<td>高温、高压</td>
<td>塑料制品</td>
</tr>
<tr>
<td rowspan="2">苯乙烯</td>
<td>阴离子聚... | true | 化学_00018 | |
<html>
<body>
<table>
<thead>
<tr>
<th colspan="2">高分子化学基础</th>
<th>化学式</th>
<th>反应条件</th>
<th>应用领域</th>
</tr>
<tr>
<th>单体</th>
<th>聚合类型</th>
<th></th>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>乙烯</td>
<td>自由基聚合</td>
<td>$$C_2H_4$$</td>
<td>高温、高压</td>
<td>塑料制品</td>
</tr>
<tr>
<td rowspan="2">苯乙烯</td>
<td>阴离子聚... | true | 化学_00018 | |
<html>
<body>
<table>
<thead>
<tr>
<th>参数</th>
<th>公式</th>
<th>单位</th>
</tr>
</thead>
<tbody>
<tr>
<td>最大起飞重量</td>
<td>$$MTOW = W_{empty} + W_{fuel} + W_{payload}$$</td>
<td>kg</td>
</tr>
<tr>
<td>翼展</td>
<td>$$B = 2 \times \sqrt{\frac{A \cdot S}{\pi}}$$</td>
<td>m</td>
</tr>
<tr>
<td>升力系数</td>
<td>$$C_L = \frac{2 \cdo... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>参数</th>
<th>公式</th>
<th>单位</th>
</tr>
</thead>
<tbody>
<tr>
<td>最大起飞重量</td>
<td>$$MTOW = W_{empty} + W_{fuel} + W_{payload}$$</td>
<td>kg</td>
</tr>
<tr>
<td>翼展</td>
<td>$$B = 2 \times \sqrt{\frac{A \cdot S}{\pi}}$$</td>
<td>m</td>
</tr>
<tr>
<td>升力系数</td>
<td>$$C_L = \frac{2 \cdo... | true | 航空设计_00021 | |
<html>
<body>
<table>
<thead>
<tr>
<th>参数</th>
<th>公式</th>
<th>单位</th>
</tr>
</thead>
<tbody>
<tr>
<td>最大起飞重量</td>
<td>$$MTOW = W_{empty} + W_{fuel} + W_{payload}$$</td>
<td>kg</td>
</tr>
<tr>
<td>翼展</td>
<td>$$B = 2 \times \sqrt{\frac{A \cdot S}{\pi}}$$</td>
<td>m</td>
</tr>
<tr>
<td>升力系数</td>
<td>$$C_L = \frac{2 \cdo... | true | 航空设计_00021 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">材料类型</th>
<th colspan="2">成分（%）</th>
<th rowspan="2">屈服强度 $$\sigma_y$$ (MPa)</th>
<th rowspan="2">抗拉强度 $$\sigma_t$$ (MPa)</th>
<th rowspan="2">延伸率 $$\delta$$ (%)</th>
</tr>
<tr>
<th>碳 (C)</th>
<th>合金元素</th>
</tr>
</thead>
<tbody>
<tr>
<td>低合金钢</td>
<td>0.15</td>
<td>Mn... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">材料类型</th>
<th colspan="2">成分（%）</th>
<th rowspan="2">屈服强度 $$\sigma_y$$ (MPa)</th>
<th rowspan="2">抗拉强度 $$\sigma_t$$ (MPa)</th>
<th rowspan="2">延伸率 $$\delta$$ (%)</th>
</tr>
<tr>
<th>碳 (C)</th>
<th>合金元素</th>
</tr>
</thead>
<tbody>
<tr>
<td>低合金钢</td>
<td>0.15</td>
<td>Mn... | true | 航空材料_00024 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">材料类型</th>
<th colspan="2">成分（%）</th>
<th rowspan="2">屈服强度 $$\sigma_y$$ (MPa)</th>
<th rowspan="2">抗拉强度 $$\sigma_t$$ (MPa)</th>
<th rowspan="2">延伸率 $$\delta$$ (%)</th>
</tr>
<tr>
<th>碳 (C)</th>
<th>合金元素</th>
</tr>
</thead>
<tbody>
<tr>
<td>低合金钢</td>
<td>0.15</td>
<td>Mn... | true | 航空材料_00024 | |
<html>
<body>
<table>
<thead>
<tr>
<th>项</th>
<th>描述</th>
<th colspan="2">公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">卷积运算</td>
<td>定义</td>
<td colspan="2">$$ (f * g)(t) = \int_{-\infty}^{\infty} f(\tau)g(t-\tau)d\tau $$</td>
</tr>
<tr>
<td>图像处理中的卷积</td>
<td>$$ I(x, y) * K(x, y) = \sum_{i=-a}^{a} \sum_{j=-b}^{b... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>项</th>
<th>描述</th>
<th colspan="2">公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">卷积运算</td>
<td>定义</td>
<td colspan="2">$$ (f * g)(t) = \int_{-\infty}^{\infty} f(\tau)g(t-\tau)d\tau $$</td>
</tr>
<tr>
<td>图像处理中的卷积</td>
<td>$$ I(x, y) * K(x, y) = \sum_{i=-a}^{a} \sum_{j=-b}^{b... | true | 信号处理_00027 | |
<html>
<body>
<table>
<thead>
<tr>
<th>项</th>
<th>描述</th>
<th colspan="2">公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">卷积运算</td>
<td>定义</td>
<td colspan="2">$$ (f * g)(t) = \int_{-\infty}^{\infty} f(\tau)g(t-\tau)d\tau $$</td>
</tr>
<tr>
<td>图像处理中的卷积</td>
<td>$$ I(x, y) * K(x, y) = \sum_{i=-a}^{a} \sum_{j=-b}^{b... | true | 信号处理_00027 | |
<html>
<body>
<table>
<thead>
<tr>
<th>工程优化类型</th>
<th>数学模型</th>
</tr>
</thead>
<tbody>
<tr>
<td>线性规划</td>
<td>$$\min \{ c^T x \mid Ax \leq b, x \geq 0 \}$$</td>
</tr>
<tr>
<td>非线性规划</td>
<td>$$\min \{ f(x) \mid g_i(x) \leq 0, h_j(x) = 0 \}$$</td>
</tr>
<tr>
<td>整数规划</td>
<td>$$\min \{ c^T x \mid Ax \leq b, x \in \math... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>工程优化类型</th>
<th>数学模型</th>
</tr>
</thead>
<tbody>
<tr>
<td>线性规划</td>
<td>$$\min \{ c^T x \mid Ax \leq b, x \geq 0 \}$$</td>
</tr>
<tr>
<td>非线性规划</td>
<td>$$\min \{ f(x) \mid g_i(x) \leq 0, h_j(x) = 0 \}$$</td>
</tr>
<tr>
<td>整数规划</td>
<td>$$\min \{ c^T x \mid Ax \leq b, x \in \math... | true | 工程_00030 | |
<html>
<body>
<table>
<thead>
<tr>
<th>工程优化类型</th>
<th>数学模型</th>
</tr>
</thead>
<tbody>
<tr>
<td>线性规划</td>
<td>$$\min \{ c^T x \mid Ax \leq b, x \geq 0 \}$$</td>
</tr>
<tr>
<td>非线性规划</td>
<td>$$\min \{ f(x) \mid g_i(x) \leq 0, h_j(x) = 0 \}$$</td>
</tr>
<tr>
<td>整数规划</td>
<td>$$\min \{ c^T x \mid Ax \leq b, x \in \math... | true | 工程_00030 | |
<html>
<body>
<table>
<thead>
<tr>
<th>航空安全指标</th>
<th>定义</th>
<th>计算公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">事故率</td>
<td>每百万飞行小时的事故数量</td>
<td>$$\frac{事故数量}{飞行小时数} \times 10^6$$</td>
</tr>
<tr>
<td>反映航空公司的安全管理效率</td>
<td></td>
</tr>
<tr>
<td>严重事故率</td>
<td>每百万飞行小时的严重事故数量</td>
<td>$$\frac{严重事故数量}{飞行小时数} \ti... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>航空安全指标</th>
<th>定义</th>
<th>计算公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">事故率</td>
<td>每百万飞行小时的事故数量</td>
<td>$$\frac{事故数量}{飞行小时数} \times 10^6$$</td>
</tr>
<tr>
<td>反映航空公司的安全管理效率</td>
<td></td>
</tr>
<tr>
<td>严重事故率</td>
<td>每百万飞行小时的严重事故数量</td>
<td>$$\frac{严重事故数量}{飞行小时数} \ti... | true | 航空_00033 | |
<html>
<body>
<table>
<thead>
<tr>
<th>航空安全指标</th>
<th>定义</th>
<th>计算公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">事故率</td>
<td>每百万飞行小时的事故数量</td>
<td>$$\frac{事故数量}{飞行小时数} \times 10^6$$</td>
</tr>
<tr>
<td>反映航空公司的安全管理效率</td>
<td></td>
</tr>
<tr>
<td>严重事故率</td>
<td>每百万飞行小时的严重事故数量</td>
<td>$$\frac{严重事故数量}{飞行小时数} \ti... | true | 航空_00033 | |
<html>
<body>
<table>
<thead>
<tr>
<th>机翼部件</th>
<th>功能描述</th>
<th>材料</th>
<th colspan="2">设计参数</th>
</tr>
</thead>
<tbody>
<tr>
<td>翼梁</td>
<td>支撑机翼结构，传递载荷</td>
<td>铝合金、复合材料</td>
<td>截面形状</td>
<td>I型、C型</td>
</tr>
<tr>
<td>蒙皮</td>
<td>形成气动外形，保护内部结构</td>
<td>铝合金、钛合金</td>
<td>厚度</td>
<td>0.5-2.0 mm</td>
</tr>
<tr>
<td>翼... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>机翼部件</th>
<th>功能描述</th>
<th>材料</th>
<th colspan="2">设计参数</th>
</tr>
</thead>
<tbody>
<tr>
<td>翼梁</td>
<td>支撑机翼结构，传递载荷</td>
<td>铝合金、复合材料</td>
<td>截面形状</td>
<td>I型、C型</td>
</tr>
<tr>
<td>蒙皮</td>
<td>形成气动外形，保护内部结构</td>
<td>铝合金、钛合金</td>
<td>厚度</td>
<td>0.5-2.0 mm</td>
</tr>
<tr>
<td>翼... | true | 飞机部件_00036 | |
<html>
<body>
<table>
<thead>
<tr>
<th>机翼部件</th>
<th>功能描述</th>
<th>材料</th>
<th colspan="2">设计参数</th>
</tr>
</thead>
<tbody>
<tr>
<td>翼梁</td>
<td>支撑机翼结构，传递载荷</td>
<td>铝合金、复合材料</td>
<td>截面形状</td>
<td>I型、C型</td>
</tr>
<tr>
<td>蒙皮</td>
<td>形成气动外形，保护内部结构</td>
<td>铝合金、钛合金</td>
<td>厚度</td>
<td>0.5-2.0 mm</td>
</tr>
<tr>
<td>翼... | true | 飞机部件_00036 | |
<html>
<body>
<table>
<thead>
<tr>
<th>序号</th>
<th>试验项目</th>
<th>试验方法</th>
<th>评判标准</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>材料强度测试</td>
<td>拉伸试验</td>
<td>$$\sigma = \frac{F}{A}$$</td>
</tr>
<tr>
<td>2</td>
<td>耐久性测试</td>
<td>循环加载</td>
<td>$$N > 10^6$$</td>
</tr>
<tr>
<td>3</td>
<td>热稳定性测试</td>
<td>温度循环</td>
<td... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>序号</th>
<th>试验项目</th>
<th>试验方法</th>
<th>评判标准</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>材料强度测试</td>
<td>拉伸试验</td>
<td>$$\sigma = \frac{F}{A}$$</td>
</tr>
<tr>
<td>2</td>
<td>耐久性测试</td>
<td>循环加载</td>
<td>$$N > 10^6$$</td>
</tr>
<tr>
<td>3</td>
<td>热稳定性测试</td>
<td>温度循环</td>
<td... | true | 标准规范_00039 | |
<html>
<body>
<table>
<thead>
<tr>
<th>序号</th>
<th>试验项目</th>
<th>试验方法</th>
<th>评判标准</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>材料强度测试</td>
<td>拉伸试验</td>
<td>$$\sigma = \frac{F}{A}$$</td>
</tr>
<tr>
<td>2</td>
<td>耐久性测试</td>
<td>循环加载</td>
<td>$$N > 10^6$$</td>
</tr>
<tr>
<td>3</td>
<td>热稳定性测试</td>
<td>温度循环</td>
<td... | true | 标准规范_00039 | |
<html>
<body>
<table>
<thead>
<tr>
<th>生物数学-神经元网络模型</th>
<th>模型描述</th>
<th>数学公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">Hodgkin-Huxley 模型</td>
<td>描述动作电位产生和传播的详细机制</td>
<td>$$\begin{aligned} C_m \frac{dV}{dt} &= I - \bar{g}_{Na}m^3h(V - E_{Na}) - \bar{g}_K n^4(V - E_K) - \bar{g}_L(V - E_L) \\ \frac{dm}{dt} &= ... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>生物数学-神经元网络模型</th>
<th>模型描述</th>
<th>数学公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">Hodgkin-Huxley 模型</td>
<td>描述动作电位产生和传播的详细机制</td>
<td>$$\begin{aligned} C_m \frac{dV}{dt} &= I - \bar{g}_{Na}m^3h(V - E_{Na}) - \bar{g}_K n^4(V - E_K) - \bar{g}_L(V - E_L) \\ \frac{dm}{dt} &= ... | true | 生物数学_00042 | |
<html>
<body>
<table>
<thead>
<tr>
<th>生物数学-神经元网络模型</th>
<th>模型描述</th>
<th>数学公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">Hodgkin-Huxley 模型</td>
<td>描述动作电位产生和传播的详细机制</td>
<td>$$\begin{aligned} C_m \frac{dV}{dt} &= I - \bar{g}_{Na}m^3h(V - E_{Na}) - \bar{g}_K n^4(V - E_K) - \bar{g}_L(V - E_L) \\ \frac{dm}{dt} &= ... | true | 生物数学_00042 | |
<html>
<body>
<table>
<thead>
<tr>
<th>非线性控制概念</th>
<th>数学表达</th>
</tr>
</thead>
<tbody>
<tr>
<td>非线性系统</td>
<td>$$\dot{x} = f(x, u)$$</td>
</tr>
<tr>
<td>李雅普诺夫稳定性</td>
<td>$$V(x) > 0, \forall x \neq 0; V(0) = 0$$</td>
</tr>
<tr>
<td>反馈线性化</td>
<td>$$\dot{x} = A(x)u + B(x)$$</td>
</tr>
</tbody>
</table>
</body>
</html> | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>非线性控制概念</th>
<th>数学表达</th>
</tr>
</thead>
<tbody>
<tr>
<td>非线性系统</td>
<td>$$\dot{x} = f(x, u)$$</td>
</tr>
<tr>
<td>李雅普诺夫稳定性</td>
<td>$$V(x) > 0, \forall x \neq 0; V(0) = 0$$</td>
</tr>
<tr>
<td>反馈线性化</td>
<td>$$\dot{x} = A(x)u + B(x)$$</td>
</tr>
</tbody>
</table>
</body>
</html> | true | 控制理论_00045 | |
<html>
<body>
<table>
<thead>
<tr>
<th>非线性控制概念</th>
<th>数学表达</th>
</tr>
</thead>
<tbody>
<tr>
<td>非线性系统</td>
<td>$$\dot{x} = f(x, u)$$</td>
</tr>
<tr>
<td>李雅普诺夫稳定性</td>
<td>$$V(x) > 0, \forall x \neq 0; V(0) = 0$$</td>
</tr>
<tr>
<td>反馈线性化</td>
<td>$$\dot{x} = A(x)u + B(x)$$</td>
</tr>
</tbody>
</table>
</body>
</html> | true | 控制理论_00045 | |
<html>
<body>
<table>
<thead>
<tr>
<th>状态</th>
<th>转移概率</th>
<th>$$P_{ij}$$</th>
<th>稳态概率</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">状态1</td>
<td>$$P_{11}$$</td>
<td>$$P_{12}$$</td>
<td>$$\pi_1$$</td>
</tr>
<tr>
<td>$$P_{21}$$</td>
<td>$$P_{22}$$</td>
<td>$$\pi_2$$</td>
</tr>
<tr>
<td>状态2</td>
<td colspan="2">$$P... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>状态</th>
<th>转移概率</th>
<th>$$P_{ij}$$</th>
<th>稳态概率</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">状态1</td>
<td>$$P_{11}$$</td>
<td>$$P_{12}$$</td>
<td>$$\pi_1$$</td>
</tr>
<tr>
<td>$$P_{21}$$</td>
<td>$$P_{22}$$</td>
<td>$$\pi_2$$</td>
</tr>
<tr>
<td>状态2</td>
<td colspan="2">$$P... | true | 数学_00048 | |
<html>
<body>
<table>
<thead>
<tr>
<th>状态</th>
<th>转移概率</th>
<th>$$P_{ij}$$</th>
<th>稳态概率</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">状态1</td>
<td>$$P_{11}$$</td>
<td>$$P_{12}$$</td>
<td>$$\pi_1$$</td>
</tr>
<tr>
<td>$$P_{21}$$</td>
<td>$$P_{22}$$</td>
<td>$$\pi_2$$</td>
</tr>
<tr>
<td>状态2</td>
<td colspan="2">$$P... | true | 数学_00048 | |
<html>
<body>
<table>
<thead>
<tr>
<th>利率模型</th>
<th>数学表达式</th>
<th>应用场景</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">Vasicek模型</td>
<td>$$dr_t = a(b-r_t)dt + \sigma dW_t$$</td>
<td>短期利率动态模拟</td>
</tr>
<tr>
<td>$$P(t,T) = A(t,T)e^{-B(t,T)r_t}$$</td>
<td>债券定价</td>
</tr>
<tr>
<td>Cox-Ingersoll-Ross (CIR) 模型</td>
<td>... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>利率模型</th>
<th>数学表达式</th>
<th>应用场景</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">Vasicek模型</td>
<td>$$dr_t = a(b-r_t)dt + \sigma dW_t$$</td>
<td>短期利率动态模拟</td>
</tr>
<tr>
<td>$$P(t,T) = A(t,T)e^{-B(t,T)r_t}$$</td>
<td>债券定价</td>
</tr>
<tr>
<td>Cox-Ingersoll-Ross (CIR) 模型</td>
<td>... | true | 金融数学_00051 | |
<html>
<body>
<table>
<thead>
<tr>
<th>利率模型</th>
<th>数学表达式</th>
<th>应用场景</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">Vasicek模型</td>
<td>$$dr_t = a(b-r_t)dt + \sigma dW_t$$</td>
<td>短期利率动态模拟</td>
</tr>
<tr>
<td>$$P(t,T) = A(t,T)e^{-B(t,T)r_t}$$</td>
<td>债券定价</td>
</tr>
<tr>
<td>Cox-Ingersoll-Ross (CIR) 模型</td>
<td>... | true | 金融数学_00051 | |
<html>
<body>
<table>
<thead>
<tr>
<th>控制理论概念</th>
<th>卡尔曼滤波公式</th>
</tr>
</thead>
<tbody>
<tr>
<td>状态预测方程</td>
<td>$$\hat{x}_{k|k-1} = A\hat{x}_{k-1|k-1} + Bu_k$$</td>
</tr>
<tr>
<td>预测误差协方差</td>
<td>$$P_{k|k-1} = AP_{k-1|k-1}A^T + Q$$</td>
</tr>
<tr>
<td>卡尔曼增益</td>
<td>$$K_k = P_{k|k-1}H^T(HP_{k|k-1}H^T + R)^{-1}$$</... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>控制理论概念</th>
<th>卡尔曼滤波公式</th>
</tr>
</thead>
<tbody>
<tr>
<td>状态预测方程</td>
<td>$$\hat{x}_{k|k-1} = A\hat{x}_{k-1|k-1} + Bu_k$$</td>
</tr>
<tr>
<td>预测误差协方差</td>
<td>$$P_{k|k-1} = AP_{k-1|k-1}A^T + Q$$</td>
</tr>
<tr>
<td>卡尔曼增益</td>
<td>$$K_k = P_{k|k-1}H^T(HP_{k|k-1}H^T + R)^{-1}$$</... | true | 控制理论_00054 | |
<html>
<body>
<table>
<thead>
<tr>
<th>控制理论概念</th>
<th>卡尔曼滤波公式</th>
</tr>
</thead>
<tbody>
<tr>
<td>状态预测方程</td>
<td>$$\hat{x}_{k|k-1} = A\hat{x}_{k-1|k-1} + Bu_k$$</td>
</tr>
<tr>
<td>预测误差协方差</td>
<td>$$P_{k|k-1} = AP_{k-1|k-1}A^T + Q$$</td>
</tr>
<tr>
<td>卡尔曼增益</td>
<td>$$K_k = P_{k|k-1}H^T(HP_{k|k-1}H^T + R)^{-1}$$</... | true | 控制理论_00054 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">飞行器模型</th>
<th colspan="2">测试参数</th>
<th colspan="2">测试结果</th>
</tr>
<tr>
<th>最大速度 (m/s)</th>
<th>续航时间 (h)</th>
<th>$$\Delta V$$ (m/s)</th>
<th>燃料效率 (km/kg)</th>
</tr>
</thead>
<tbody>
<tr>
<td>模型A</td>
<td>340</td>
<td>8.5</td>
<td>$$\frac{2 \times 340}{8.5}$$</td>
<t... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">飞行器模型</th>
<th colspan="2">测试参数</th>
<th colspan="2">测试结果</th>
</tr>
<tr>
<th>最大速度 (m/s)</th>
<th>续航时间 (h)</th>
<th>$$\Delta V$$ (m/s)</th>
<th>燃料效率 (km/kg)</th>
</tr>
</thead>
<tbody>
<tr>
<td>模型A</td>
<td>340</td>
<td>8.5</td>
<td>$$\frac{2 \times 340}{8.5}$$</td>
<t... | true | 飞行器_00057 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">飞行器模型</th>
<th colspan="2">测试参数</th>
<th colspan="2">测试结果</th>
</tr>
<tr>
<th>最大速度 (m/s)</th>
<th>续航时间 (h)</th>
<th>$$\Delta V$$ (m/s)</th>
<th>燃料效率 (km/kg)</th>
</tr>
</thead>
<tbody>
<tr>
<td>模型A</td>
<td>340</td>
<td>8.5</td>
<td>$$\frac{2 \times 340}{8.5}$$</td>
<t... | true | 飞行器_00057 | |
<html>
<body>
<table>
<thead>
<tr>
<th>小波变换类型</th>
<th>数学表达式</th>
</tr>
</thead>
<tbody>
<tr>
<td>连续小波变换 (CWT)</td>
<td>$$CWT_{f}(a, b) = \frac{1}{\sqrt{a}} \int_{-\infty}^{\infty} f(t) \overline{\psi\left(\frac{t-b}{a}\right)} dt$$</td>
</tr>
<tr>
<td>离散小波变换 (DWT)</td>
<td>$$DWT_{f}(j, k) = \frac{1}{\sqrt{2^j}} \sum_{... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>小波变换类型</th>
<th>数学表达式</th>
</tr>
</thead>
<tbody>
<tr>
<td>连续小波变换 (CWT)</td>
<td>$$CWT_{f}(a, b) = \frac{1}{\sqrt{a}} \int_{-\infty}^{\infty} f(t) \overline{\psi\left(\frac{t-b}{a}\right)} dt$$</td>
</tr>
<tr>
<td>离散小波变换 (DWT)</td>
<td>$$DWT_{f}(j, k) = \frac{1}{\sqrt{2^j}} \sum_{... | true | 信号处理_00060 | |
<html>
<body>
<table>
<thead>
<tr>
<th>小波变换类型</th>
<th>数学表达式</th>
</tr>
</thead>
<tbody>
<tr>
<td>连续小波变换 (CWT)</td>
<td>$$CWT_{f}(a, b) = \frac{1}{\sqrt{a}} \int_{-\infty}^{\infty} f(t) \overline{\psi\left(\frac{t-b}{a}\right)} dt$$</td>
</tr>
<tr>
<td>离散小波变换 (DWT)</td>
<td>$$DWT_{f}(j, k) = \frac{1}{\sqrt{2^j}} \sum_{... | true | 信号处理_00060 | |
<html>
<body>
<table>
<thead>
<tr>
<th>测量项目</th>
<th>公差范围</th>
<th>公式</th>
</tr>
</thead>
<tbody>
<tr>
<td>翼展</td>
<td>±0.5 cm</td>
<td>$$\Delta L = L_{max} - L_{min}$$</td>
</tr>
<tr>
<td>机身长度</td>
<td>±1.0 cm</td>
<td>$$\Delta L = L_{max} - L_{min}$$</td>
</tr>
<tr>
<td>发动机间距</td>
<td>±0.2 cm</td>
<td>$$\Delta D = D_... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>测量项目</th>
<th>公差范围</th>
<th>公式</th>
</tr>
</thead>
<tbody>
<tr>
<td>翼展</td>
<td>±0.5 cm</td>
<td>$$\Delta L = L_{max} - L_{min}$$</td>
</tr>
<tr>
<td>机身长度</td>
<td>±1.0 cm</td>
<td>$$\Delta L = L_{max} - L_{min}$$</td>
</tr>
<tr>
<td>发动机间距</td>
<td>±0.2 cm</td>
<td>$$\Delta D = D_... | true | 飞机测量_00063 | |
<html>
<body>
<table>
<thead>
<tr>
<th>测量项目</th>
<th>公差范围</th>
<th>公式</th>
</tr>
</thead>
<tbody>
<tr>
<td>翼展</td>
<td>±0.5 cm</td>
<td>$$\Delta L = L_{max} - L_{min}$$</td>
</tr>
<tr>
<td>机身长度</td>
<td>±1.0 cm</td>
<td>$$\Delta L = L_{max} - L_{min}$$</td>
</tr>
<tr>
<td>发动机间距</td>
<td>±0.2 cm</td>
<td>$$\Delta D = D_... | true | 飞机测量_00063 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">标准规范</th>
<th colspan="2">符号缩略语</th>
<th colspan="2">定义</th>
</tr>
<tr>
<th>中文</th>
<th>英文</th>
<th>数学表示</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">国际单位制</td>
<td>米</td>
<td>m</td>
<td>$$1 m = 100 cm$$</td>
<td>长度单位</td>
</tr>
<tr>
<td>千克</td>
<td>kg<... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">标准规范</th>
<th colspan="2">符号缩略语</th>
<th colspan="2">定义</th>
</tr>
<tr>
<th>中文</th>
<th>英文</th>
<th>数学表示</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">国际单位制</td>
<td>米</td>
<td>m</td>
<td>$$1 m = 100 cm$$</td>
<td>长度单位</td>
</tr>
<tr>
<td>千克</td>
<td>kg<... | true | 标准规范_00066 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">标准规范</th>
<th colspan="2">符号缩略语</th>
<th colspan="2">定义</th>
</tr>
<tr>
<th>中文</th>
<th>英文</th>
<th>数学表示</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">国际单位制</td>
<td>米</td>
<td>m</td>
<td>$$1 m = 100 cm$$</td>
<td>长度单位</td>
</tr>
<tr>
<td>千克</td>
<td>kg<... | true | 标准规范_00066 | |
<html>
<body>
<table>
<thead>
<tr>
<th>飞机型号</th>
<th>最大起飞重量 (MTOW)</th>
<th>航程 (Range)</th>
<th>燃油效率 $$\left(\frac{km}{kg}\right)$$</th>
</tr>
</thead>
<tbody>
<tr>
<td>A320neo</td>
<td>79,000 kg</td>
<td>6,000 km</td>
<td>$$0.32$$</td>
</tr>
<tr>
<td>B737 MAX 8</td>
<td>79,000 kg</td>
<td>6,570 km</td>
<td>$$0.34$$</t... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>飞机型号</th>
<th>最大起飞重量 (MTOW)</th>
<th>航程 (Range)</th>
<th>燃油效率 $$\left(\frac{km}{kg}\right)$$</th>
</tr>
</thead>
<tbody>
<tr>
<td>A320neo</td>
<td>79,000 kg</td>
<td>6,000 km</td>
<td>$$0.32$$</td>
</tr>
<tr>
<td>B737 MAX 8</td>
<td>79,000 kg</td>
<td>6,570 km</td>
<td>$$0.34$$</t... | true | 航空设计_00069 | |
<html>
<body>
<table>
<thead>
<tr>
<th>飞机型号</th>
<th>最大起飞重量 (MTOW)</th>
<th>航程 (Range)</th>
<th>燃油效率 $$\left(\frac{km}{kg}\right)$$</th>
</tr>
</thead>
<tbody>
<tr>
<td>A320neo</td>
<td>79,000 kg</td>
<td>6,000 km</td>
<td>$$0.32$$</td>
</tr>
<tr>
<td>B737 MAX 8</td>
<td>79,000 kg</td>
<td>6,570 km</td>
<td>$$0.34$$</t... | true | 航空设计_00069 | |
<html>
<body>
<table>
<thead>
<tr>
<th>反应类型</th>
<th>反应机理</th>
</tr>
</thead>
<tbody>
<tr>
<td>亲电加成反应</td>
<td>$$\text{R-CH=CH}_2 + \text{H}^+ \rightarrow \text{R-CH}^+\text{-CH}_3$$</td>
</tr>
<tr>
<td>亲核取代反应 (SN2)</td>
<td>$$\text{R-X} + \text{Nu}^- \rightarrow \text{R-Nu} + \text{X}^-$$</td>
</tr>
<tr>
<td>消除反应 (E2)... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>反应类型</th>
<th>反应机理</th>
</tr>
</thead>
<tbody>
<tr>
<td>亲电加成反应</td>
<td>$$\text{R-CH=CH}_2 + \text{H}^+ \rightarrow \text{R-CH}^+\text{-CH}_3$$</td>
</tr>
<tr>
<td>亲核取代反应 (SN2)</td>
<td>$$\text{R-X} + \text{Nu}^- \rightarrow \text{R-Nu} + \text{X}^-$$</td>
</tr>
<tr>
<td>消除反应 (E2)... | true | 化学_00072 | |
<html>
<body>
<table>
<thead>
<tr>
<th>反应类型</th>
<th>反应机理</th>
</tr>
</thead>
<tbody>
<tr>
<td>亲电加成反应</td>
<td>$$\text{R-CH=CH}_2 + \text{H}^+ \rightarrow \text{R-CH}^+\text{-CH}_3$$</td>
</tr>
<tr>
<td>亲核取代反应 (SN2)</td>
<td>$$\text{R-X} + \text{Nu}^- \rightarrow \text{R-Nu} + \text{X}^-$$</td>
</tr>
<tr>
<td>消除反应 (E2)... | true | 化学_00072 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">类别</th>
<th colspan="3">符号缩略语</th>
<th rowspan="2">描述</th>
</tr>
<tr>
<th>缩写</th>
<th>全称</th>
<th>数学表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>通用</td>
<td>AI</td>
<td>Artificial Intelligence</td>
<td>$$\text{AI} = \frac{\text{Machine Learning}}{\text{Data}}$$</td>
<td>人工智... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">类别</th>
<th colspan="3">符号缩略语</th>
<th rowspan="2">描述</th>
</tr>
<tr>
<th>缩写</th>
<th>全称</th>
<th>数学表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>通用</td>
<td>AI</td>
<td>Artificial Intelligence</td>
<td>$$\text{AI} = \frac{\text{Machine Learning}}{\text{Data}}$$</td>
<td>人工智... | true | 标准规范_00075 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">类别</th>
<th colspan="3">符号缩略语</th>
<th rowspan="2">描述</th>
</tr>
<tr>
<th>缩写</th>
<th>全称</th>
<th>数学表示</th>
</tr>
</thead>
<tbody>
<tr>
<td>通用</td>
<td>AI</td>
<td>Artificial Intelligence</td>
<td>$$\text{AI} = \frac{\text{Machine Learning}}{\text{Data}}$$</td>
<td>人工智... | true | 标准规范_00075 | |
<html>
<body>
<table>
<thead>
<tr>
<th>试验项目</th>
<th>试验条件</th>
<th>试验方法</th>
<th>试验结果评估</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">强度试验</td>
<td>温度: 20°C ± 5°C, 湿度: 60% ± 10%</td>
<td>加载至材料极限强度的70%，保持时间: $$t = 30 \, \text{min}$$</td>
<td>无裂纹或永久变形</td>
</tr>
<tr>
<td>加载速率: 10 mm/min</td>
<td colspan="2">记录最大承载力 $$... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>试验项目</th>
<th>试验条件</th>
<th>试验方法</th>
<th>试验结果评估</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">强度试验</td>
<td>温度: 20°C ± 5°C, 湿度: 60% ± 10%</td>
<td>加载至材料极限强度的70%，保持时间: $$t = 30 \, \text{min}$$</td>
<td>无裂纹或永久变形</td>
</tr>
<tr>
<td>加载速率: 10 mm/min</td>
<td colspan="2">记录最大承载力 $$... | true | 标准规范_00078 | |
<html>
<body>
<table>
<thead>
<tr>
<th>试验项目</th>
<th>试验条件</th>
<th>试验方法</th>
<th>试验结果评估</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">强度试验</td>
<td>温度: 20°C ± 5°C, 湿度: 60% ± 10%</td>
<td>加载至材料极限强度的70%，保持时间: $$t = 30 \, \text{min}$$</td>
<td>无裂纹或永久变形</td>
</tr>
<tr>
<td>加载速率: 10 mm/min</td>
<td colspan="2">记录最大承载力 $$... | true | 标准规范_00078 | |
<html>
<body>
<table>
<thead>
<tr>
<th>概念</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td>布朗运动</td>
<td>一种随机过程，用于模拟金融市场的价格变动。</td>
</tr>
<tr>
<td>数学表示</td>
<td>$$W_t$$ 表示在时间 $$t$$ 的布朗运动值。</td>
</tr>
<tr>
<td>性质</td>
<td>布朗运动具有独立增量和正态分布的性质。</td>
</tr>
</tbody>
</table>
</body>
</html> | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>概念</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td>布朗运动</td>
<td>一种随机过程，用于模拟金融市场的价格变动。</td>
</tr>
<tr>
<td>数学表示</td>
<td>$$W_t$$ 表示在时间 $$t$$ 的布朗运动值。</td>
</tr>
<tr>
<td>性质</td>
<td>布朗运动具有独立增量和正态分布的性质。</td>
</tr>
</tbody>
</table>
</body>
</html> | true | 金融数学_00081 | |
<html>
<body>
<table>
<thead>
<tr>
<th>概念</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td>布朗运动</td>
<td>一种随机过程，用于模拟金融市场的价格变动。</td>
</tr>
<tr>
<td>数学表示</td>
<td>$$W_t$$ 表示在时间 $$t$$ 的布朗运动值。</td>
</tr>
<tr>
<td>性质</td>
<td>布朗运动具有独立增量和正态分布的性质。</td>
</tr>
</tbody>
</table>
</body>
</html> | true | 金融数学_00081 | |
<html>
<body>
<table>
<thead>
<tr>
<th>参数</th>
<th>公式</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">总重量 (G)</td>
<td>$$G = W + F$$</td>
<td>飞行器的总重量等于空机重量(W)加上燃料重量(F)</td>
</tr>
<tr>
<td>$$G = \sum m_i$$</td>
<td>总重量也可以通过计算各部分质量之和得到</td>
</tr>
<tr>
<td>重心位置 (CG)</td>
<td>$$CG = \frac{\sum (m_i \times d_i)... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>参数</th>
<th>公式</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">总重量 (G)</td>
<td>$$G = W + F$$</td>
<td>飞行器的总重量等于空机重量(W)加上燃料重量(F)</td>
</tr>
<tr>
<td>$$G = \sum m_i$$</td>
<td>总重量也可以通过计算各部分质量之和得到</td>
</tr>
<tr>
<td>重心位置 (CG)</td>
<td>$$CG = \frac{\sum (m_i \times d_i)... | true | 飞行器_00084 | |
<html>
<body>
<table>
<thead>
<tr>
<th>参数</th>
<th>公式</th>
<th>描述</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">总重量 (G)</td>
<td>$$G = W + F$$</td>
<td>飞行器的总重量等于空机重量(W)加上燃料重量(F)</td>
</tr>
<tr>
<td>$$G = \sum m_i$$</td>
<td>总重量也可以通过计算各部分质量之和得到</td>
</tr>
<tr>
<td>重心位置 (CG)</td>
<td>$$CG = \frac{\sum (m_i \times d_i)... | true | 飞行器_00084 | |
<html>
<body>
<table>
<thead>
<tr>
<th>力学概念</th>
<th>数学表达</th>
<th>应用实例</th>
<th rowspan="2">相关领域</th>
</tr>
</thead>
<tbody>
<tr>
<td>应力 $$\sigma$$</td>
<td>$$\sigma = \frac{F}{A}$$</td>
<td>桥梁设计</td>
</tr>
<tr>
<td>应变 $$\epsilon$$</td>
<td>$$\epsilon = \frac{\Delta L}{L_0}$$</td>
<td>材料测试</td>
</tr>
<tr>
<td>胡克定律</td... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>力学概念</th>
<th>数学表达</th>
<th>应用实例</th>
<th rowspan="2">相关领域</th>
</tr>
</thead>
<tbody>
<tr>
<td>应力 $$\sigma$$</td>
<td>$$\sigma = \frac{F}{A}$$</td>
<td>桥梁设计</td>
</tr>
<tr>
<td>应变 $$\epsilon$$</td>
<td>$$\epsilon = \frac{\Delta L}{L_0}$$</td>
<td>材料测试</td>
</tr>
<tr>
<td>胡克定律</td... | true | 工程_00087 | |
<html>
<body>
<table>
<thead>
<tr>
<th>力学概念</th>
<th>数学表达</th>
<th>应用实例</th>
<th rowspan="2">相关领域</th>
</tr>
</thead>
<tbody>
<tr>
<td>应力 $$\sigma$$</td>
<td>$$\sigma = \frac{F}{A}$$</td>
<td>桥梁设计</td>
</tr>
<tr>
<td>应变 $$\epsilon$$</td>
<td>$$\epsilon = \frac{\Delta L}{L_0}$$</td>
<td>材料测试</td>
</tr>
<tr>
<td>胡克定律</td... | true | 工程_00087 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">控制理论基础</th>
<th colspan="2">模型预测控制 (MPC)</th>
<th rowspan="2">应用场景</th>
<th rowspan="2">优势与挑战</th>
</tr>
<tr>
<th>基本原理</th>
<th>数学模型</th>
</tr>
</thead>
<tbody>
<tr>
<td>反馈控制</td>
<td>预测未来系统状态</td>
<td>$$\min_{u_k} \sum_{t=k}^{k+N} \left( x_t - r_t \right)^T Q \left( x... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">控制理论基础</th>
<th colspan="2">模型预测控制 (MPC)</th>
<th rowspan="2">应用场景</th>
<th rowspan="2">优势与挑战</th>
</tr>
<tr>
<th>基本原理</th>
<th>数学模型</th>
</tr>
</thead>
<tbody>
<tr>
<td>反馈控制</td>
<td>预测未来系统状态</td>
<td>$$\min_{u_k} \sum_{t=k}^{k+N} \left( x_t - r_t \right)^T Q \left( x... | true | 控制理论_00090 | |
<html>
<body>
<table>
<thead>
<tr>
<th rowspan="2">控制理论基础</th>
<th colspan="2">模型预测控制 (MPC)</th>
<th rowspan="2">应用场景</th>
<th rowspan="2">优势与挑战</th>
</tr>
<tr>
<th>基本原理</th>
<th>数学模型</th>
</tr>
</thead>
<tbody>
<tr>
<td>反馈控制</td>
<td>预测未来系统状态</td>
<td>$$\min_{u_k} \sum_{t=k}^{k+N} \left( x_t - r_t \right)^T Q \left( x... | true | 控制理论_00090 | |
<html>
<body>
<table>
<thead>
<tr>
<th>项目</th>
<th>描述</th>
<th>公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">安装角定义</td>
<td>安装角是指机翼或尾翼与飞机纵轴的夹角。</td>
<td>$$\theta_i = \arctan\left(\frac{dy}{dx}\right)$$</td>
</tr>
<tr>
<td>测量方法包括使用角度测量仪或激光水平仪。</td>
<td>$$\Delta \theta = \theta_{\text{实际}} - \theta_{\text{设计}}$$</t... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>项目</th>
<th>描述</th>
<th>公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">安装角定义</td>
<td>安装角是指机翼或尾翼与飞机纵轴的夹角。</td>
<td>$$\theta_i = \arctan\left(\frac{dy}{dx}\right)$$</td>
</tr>
<tr>
<td>测量方法包括使用角度测量仪或激光水平仪。</td>
<td>$$\Delta \theta = \theta_{\text{实际}} - \theta_{\text{设计}}$$</t... | true | 飞机测量_00093 | |
<html>
<body>
<table>
<thead>
<tr>
<th>项目</th>
<th>描述</th>
<th>公式</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">安装角定义</td>
<td>安装角是指机翼或尾翼与飞机纵轴的夹角。</td>
<td>$$\theta_i = \arctan\left(\frac{dy}{dx}\right)$$</td>
</tr>
<tr>
<td>测量方法包括使用角度测量仪或激光水平仪。</td>
<td>$$\Delta \theta = \theta_{\text{实际}} - \theta_{\text{设计}}$$</t... | true | 飞机测量_00093 | |
<html>
<body>
<table>
<thead>
<tr>
<th>结构类型</th>
<th>数学模型</th>
<th>关键公式</th>
<th>应用场景</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">梁结构</td>
<td>一维模型</td>
<td>$$\frac{d^2w}{dx^2} = -\frac{M(x)}{EI}$$</td>
<td>建筑物、桥梁</td>
</tr>
<tr>
<td>边界条件</td>
<td>$$w(0) = 0, \quad w(L) = 0$$</td>
<td>固定端、自由端</td>
</tr>
<tr>
<td>拱... | false | null | |
<html>
<body>
<table>
<thead>
<tr>
<th>结构类型</th>
<th>数学模型</th>
<th>关键公式</th>
<th>应用场景</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">梁结构</td>
<td>一维模型</td>
<td>$$\frac{d^2w}{dx^2} = -\frac{M(x)}{EI}$$</td>
<td>建筑物、桥梁</td>
</tr>
<tr>
<td>边界条件</td>
<td>$$w(0) = 0, \quad w(L) = 0$$</td>
<td>固定端、自由端</td>
</tr>
<tr>
<td>拱... | true | 工程数学_00096 | |
<html>
<body>
<table>
<thead>
<tr>
<th>结构类型</th>
<th>数学模型</th>
<th>关键公式</th>
<th>应用场景</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="2">梁结构</td>
<td>一维模型</td>
<td>$$\frac{d^2w}{dx^2} = -\frac{M(x)}{EI}$$</td>
<td>建筑物、桥梁</td>
</tr>
<tr>
<td>边界条件</td>
<td>$$w(0) = 0, \quad w(L) = 0$$</td>
<td>固定端、自由端</td>
</tr>
<tr>
<td>拱... | true | 工程数学_00096 | |
<html>
<body>
<table>
<thead>
<tr>
<th>频率 (Hz)</th>
<th>幅度 (dB)</th>
<th>相位 (度)</th>
<th>信号公式</th>
</tr>
</thead>
<tbody>
<tr>
<td>100</td>
<td>20</td>
<td>30</td>
<td>$$x(t) = A \cos(2\pi f t + \phi)$$</td>
</tr>
<tr>
<td>500</td>
<td>30</td>
<td>45</td>
<td>$$x(t) = A \cos(2\pi f t + \phi)$$</td>
</tr>
<tr>
<td>1000<... | false | null |
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