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Dental Aligners in Mumbai | Clear & Invisible Aligners
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Dental Aligners in Mumbai | Clear & Invisible A...
Decoding AI's Hidden Agenda: The 5 Alignments You Need to Understand to Protect Your Interests - Part 2 of AI Alignment Series
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Decoding AI's Hidden Agenda: The 5 Alignments Y...
The Alignment Problem: Why aligning AI with human values is harder than it sounds
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The Alignment Problem: Why aligning AI with hum...
False Alignment Is Worse Than No Alignment
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False Alignment Is Worse Than No Alignment
“Don't wait for the stars to get aligned - align them by yourself”
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“Don't wait for the stars to get aligned - alig...
🧠 Memory, Context, and Alignment: Architecting Agents That Think, Reflect, and Align
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🧠 Memory, Context, and Alignment: Architecting...
Core Alignment vs. Cladding Alignment: Understanding the Difference in Fusion Splicers
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Core Alignment vs. Cladding Alignment: Understa...
Vertically Aligned? What About Horizontally Aligned?
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Bringing Alignment to Change: How Improvement Science Helps Align Teams, Leadership, and Strategy
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{\displaystyle {\begin{aligned}\mathrm {NPV} &=68,136.91-100,000\\&=-31,863.09\end{aligned}}}
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{\displaystyle {\begin{aligned}\mathrm {NPV} &=...
{\displaystyle {\begin{aligned}X_{k_{1},k_{2}}&=\sum _{n_{1}=0}^{N_{1}-1}\left(\sum _{n_{2}=0}^{N_{2}-1}x_{n_{1},n_{2}}\cos \left[{\frac {\pi }{N_{2}}}\left(n_{2}+{\frac {1}{2}}\right)k_{2}\right]\right)\cos \left[{\frac {\pi }{N_{1}}}\left(n_{1}+{\frac {1}{2}}\right)k_{1}\right]\\&=\sum _{n_{1}=0}^{N_{1}-1}\sum _{n_{2}=0}^{N_{2}-1}x_{n_{1},n_{2}}\cos \left[{\frac {\pi }{N_{1}}}\left(n_{1}+{\frac {1}{2}}\right)k_{1}\right]\cos \left[{\frac {\pi }{N_{2}}}\left(n_{2}+{\frac {1}{2}}\right)k_{2}\right].\end{aligned}}}
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{\displaystyle {\begin{aligned}X_{k_{1},k_{2}}&...
{\displaystyle {\begin{aligned}50&=2\times 5\times 5\\&=2\times 5^{2}.\end{aligned}}}
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{\displaystyle {\begin{aligned}50&=2\times 5\ti...
{\displaystyle {\begin{aligned}\mathbf {I} _{1}&={\begin{bmatrix}1\end{bmatrix}},\\[4pt]\mathbf {I} _{2}&={\begin{bmatrix}1&0\\0&1\end{bmatrix}},\\[4pt]\vdots &\\[4pt]\mathbf {I} _{n}&={\begin{bmatrix}1&0&\cdots &0\\0&1&\cdots &0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &1\end{bmatrix}}\end{aligned}}}
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{\displaystyle {\begin{aligned}\mathbf {I} _{1}...
{\displaystyle {\begin{aligned}a_{1,1}x_{1}+a_{1,2}x_{2}+&\cdots +a_{1,n}x_{n}=b_{1}\\&\ \ \vdots \\a_{m,1}x_{1}+a_{m,2}x_{2}+&\cdots +a_{m,n}x_{n}=b_{m}\end{aligned}}}
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{\displaystyle {\begin{aligned}a_{1,1}x_{1}+a_{...
{\displaystyle {\begin{aligned}{\begin{bmatrix}{\underline {2}}&{\underline {3}}&{\underline {4}}\\1&0&0\\\end{bmatrix}}{\begin{bmatrix}0&{\underline {1000}}\\1&{\underline {100}}\\0&{\underline {10}}\\\end{bmatrix}}&={\begin{bmatrix}3&{\underline {2340}}\\0&1000\\\end{bmatrix}}.\end{aligned}}}
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{\displaystyle {\begin{aligned}{\begin{bmatrix}...
{\displaystyle {\begin{aligned}({\mathbf {A}}+{\mathbf {B}})_{i,j}={\mathbf {A}}_{i,j}+{\mathbf {B}}_{i,j},\quad 1\leq i\leq m,\quad 1\leq j\leq n.\\({\mathbf {A}}-{\mathbf {B}})_{i,j}={\mathbf {A}}_{i,j}-{\mathbf {B}}_{i,j},\quad 1\leq i\leq m,\quad 1\leq j\leq n.\end{aligned}}}
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{\displaystyle {\begin{aligned}({\mathbf {A}}+{...
{\displaystyle {\begin{aligned}\operatorname {soft\_cosine} _{1}(a,b)={\frac {\sum \nolimits _{i,j}^{N}s_{ij}a_{i}b_{j}}{{\sqrt {\sum \nolimits _{i,j}^{N}s_{ij}a_{i}a_{j}}}{\sqrt {\sum \nolimits _{i,j}^{N}s_{ij}b_{i}b_{j}}}}},\end{aligned}}}
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{\displaystyle {\begin{aligned}\operatorname {s...
{\displaystyle {\begin{aligned}e_{1}&=(1,0,0,\dots )\\e_{2}&=(0,1,0,\dots )\\&\ \ \vdots \end{aligned}}}
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{\displaystyle {\begin{aligned}e_{1}&=(1,0,0,\d...
{\displaystyle {\begin{aligned}f(\mathbf {v} +\mathbf {w} )&=f(\mathbf {v} )+f(\mathbf {w} ),\\f(a\cdot \mathbf {v} )&=a\cdot f(\mathbf {v} )\end{aligned}}}
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{\displaystyle {\begin{aligned}f(\mathbf {v} +\...
{\displaystyle {\begin{aligned}(x_{1},y_{1})+(x_{2},y_{2})&=(x_{1}+x_{2},y_{1}+y_{2}),\\a(x,y)&=(ax,ay).\end{aligned}}}
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{\displaystyle {\begin{aligned}(x_{1},y_{1})+(x...