diff --git a/content/.trash/Untitled 5.md b/content/.trash/Untitled 5.md new file mode 100644 index 000000000..e69de29bb diff --git a/content/.trash/series_MOC.md b/content/.trash/series_MOC.md new file mode 100644 index 000000000..0968a0600 --- /dev/null +++ b/content/.trash/series_MOC.md @@ -0,0 +1,8 @@ +--- +title: Series - MOC +tags: + - math + - basic + - series +date: 2024-05-28 +--- diff --git a/content/assets/pdf/ID.rar b/content/assets/pdf/ID.rar new file mode 100644 index 000000000..958bdcee7 Binary files /dev/null and b/content/assets/pdf/ID.rar differ diff --git a/content/computer_sci/code_frame_learn/data/streamlit/MOC.md b/content/computer_sci/code_frame_learn/data/streamlit/MOC.md index 8541efda2..783a52d12 100644 --- a/content/computer_sci/code_frame_learn/data/streamlit/MOC.md +++ b/content/computer_sci/code_frame_learn/data/streamlit/MOC.md @@ -8,4 +8,5 @@ date: 2024-05-24 --- # Reference -* https://streamlit.io/ \ No newline at end of file +* https://streamlit.io/ +* https://30days.streamlit.app/ \ No newline at end of file diff --git a/content/computer_sci/deep_learning_and_machine_learning/Trick/quantile_loss.md b/content/computer_sci/deep_learning_and_machine_learning/Trick/quantile_loss.md index d30c79396..570051f36 100644 --- a/content/computer_sci/deep_learning_and_machine_learning/Trick/quantile_loss.md +++ b/content/computer_sci/deep_learning_and_machine_learning/Trick/quantile_loss.md @@ -13,7 +13,7 @@ Quantile loss用于衡量预测分布和目标分布之间的差异，特别适 # What is quantile -[Quantile](math/Statistics/Basic/Quantile.md) +[quantile_concept](math/Statistics/basic_concepot/quantile_concept.md) # What is a prediction interval diff --git a/content/electrical_electronics/EE_MOC.md b/content/electrical_electronics/EE_MOC.md index ed2485721..3d243c3ad 100644 --- a/content/electrical_electronics/EE_MOC.md +++ b/content/electrical_electronics/EE_MOC.md @@ -16,7 +16,12 @@ date: 2024-05-21 ## Basic +### Antenna + * [Antenna](electrical_electronics/RF/antenna/antenna.md) -## SAR +* [Vivaldi Antenna](electrical_electronics/RF/antenna/vivaldi_antenna.md) + +## Algorithm +### SAR * [SAR_MOC](electrical_electronics/RF/algrothim/SAR/SAR_MOC.md) \ No newline at end of file diff --git a/content/electrical_electronics/RF/antenna/attachments/Pasted image 20240527104530.png b/content/electrical_electronics/RF/antenna/attachments/Pasted image 20240527104530.png new file mode 100644 index 000000000..6e6c9a1ab Binary files /dev/null and b/content/electrical_electronics/RF/antenna/attachments/Pasted image 20240527104530.png differ diff --git a/content/electrical_electronics/RF/antenna/attachments/Pasted image 20240527104536.png b/content/electrical_electronics/RF/antenna/attachments/Pasted image 20240527104536.png new file mode 100644 index 000000000..1adfacb6b Binary files /dev/null and b/content/electrical_electronics/RF/antenna/attachments/Pasted image 20240527104536.png differ diff --git a/content/electrical_electronics/RF/antenna/vivaldi_antenna.md b/content/electrical_electronics/RF/antenna/vivaldi_antenna.md index 0c63c9de9..542f371dd 100644 --- a/content/electrical_electronics/RF/antenna/vivaldi_antenna.md +++ b/content/electrical_electronics/RF/antenna/vivaldi_antenna.md @@ -4,5 +4,21 @@ tags: - antenna date: 2024-05-24 --- + +# Background Knowledge + +* [Maxwells Equation](physics/electromagnetism/maxwells_equation.md) + # Introduction +## History + +Vivaldi antenna, also known as a **tapered slot antenna**(TSA, 锥形槽天线)，是一种线性极化平面天线，由P.J.Gibson于 1978 年发明，他最初将其称为维瓦尔第天线。Vivaldi antenna是宽带宽traveling antennas的一员。 + +## Antenna Structure + + + +# Reference + +* https://jemengineering.com/blog-anatomy-of-a-vivaldi-antenna/ \ No newline at end of file diff --git a/content/math/MOC.md b/content/math/MOC.md index 4cb0e1536..b0b73c1c7 100644 --- a/content/math/MOC.md +++ b/content/math/MOC.md @@ -10,7 +10,7 @@ date: 2023-12-03 ## Basic Concept -* [Quantile](math/Statistics/Basic/Quantile.md) +* [quantile_concept](math/Statistics/basic_concepot/quantile_concept.md) ## Significance Test diff --git a/content/math/Statistics/basic_concepot/distribution/attachments/2bbb645362366906ace3296d35612625_720.jpg b/content/math/Statistics/basic_concepot/distribution/attachments/2bbb645362366906ace3296d35612625_720.jpg new file mode 100644 index 000000000..e606b17ec Binary files /dev/null and b/content/math/Statistics/basic_concepot/distribution/attachments/2bbb645362366906ace3296d35612625_720.jpg differ diff --git a/content/math/Statistics/basic_concepot/distribution/attachments/df15541df80b6065fb8296d80ffceac5_720.jpg b/content/math/Statistics/basic_concepot/distribution/attachments/df15541df80b6065fb8296d80ffceac5_720.jpg new file mode 100644 index 000000000..7c45179d0 Binary files /dev/null and b/content/math/Statistics/basic_concepot/distribution/attachments/df15541df80b6065fb8296d80ffceac5_720.jpg differ diff --git a/content/math/Statistics/basic_concepot/distribution/attachments/prove.jpg b/content/math/Statistics/basic_concepot/distribution/attachments/prove.jpg new file mode 100644 index 000000000..5299d940e Binary files /dev/null and b/content/math/Statistics/basic_concepot/distribution/attachments/prove.jpg differ diff --git a/content/math/Statistics/basic_concepot/distribution/beta_binomial.md b/content/math/Statistics/basic_concepot/distribution/beta_binomial.md new file mode 100644 index 000000000..1c19fd220 --- /dev/null +++ b/content/math/Statistics/basic_concepot/distribution/beta_binomial.md @@ -0,0 +1,11 @@ +--- +title: Beta-Binomial Distribution +tags: + - basic + - math + - distribution +date: 2024-05-28 +--- +# Reference + +* https://medium.com/@ro.mo.flo47/the-beta-binomial-model-an-introduction-to-bayesian-statistics-154395875f93 \ No newline at end of file diff --git a/content/math/Statistics/basic_concepot/distribution/exponential_distribution_and_poisson_distribution.md b/content/math/Statistics/basic_concepot/distribution/exponential_distribution_and_poisson_distribution.md new file mode 100644 index 000000000..8d819552f --- /dev/null +++ b/content/math/Statistics/basic_concepot/distribution/exponential_distribution_and_poisson_distribution.md @@ -0,0 +1,71 @@ +--- +title: Exponential Distribution +tags: + - basic + - math + - statistics + - distribution +date: 2024-06-03 +--- +# Background + +## Poisson Process + +日常生活中，大量的事件是有固定频率的。 + +- 某医院平均每小时出生3个婴儿 +- 某公司平均每10分钟接到1个电话 +- 某超市平均每天销售4包xx牌奶粉 +- 某网站平均每分钟有2次访问 + +$N(t)$等于t时间内发生事件的次数，在这个过程中，两个不重叠区间内所发生的事件数目是互相独立的随机变量，那么这个随机过程$N(t)$即是一维泊松过程。 + +# Poisson Distribution + +这个过程中，在区$[t, t+\tau]$内发生的事件数目的概率分布满足Poisson Distribution, +$$ +P[(N(t+\tau) - N(t)) = k] = \frac{e^{-\lambda\tau}(\lambda\tau)^k}{k!}, \quad k=0,1,\cdots +$$ + +$\lambda$是一个正数，为固定的参数，通常称为抵达率(arrival rate)或强度(intensity)。常常用事件在单位长度$\tau$内发生的平均频率表达。 + +Poisson Distribution可以将t代为0，简化为在接下来单位时间$\tau$内有k次时间发生的概率的分布： + +$P(N(t) = k) = \frac{e^{-\lambda t}(\lambda t)^k}{k!}$ + +# Exponential Distribution + +这些事件之间的时间间隔，是属于指数分布。 + +指数分布的公式可以从泊松分布推断出来。如果下一个事件发生要有间隔时间 t ，就等同于 t 之内没有任何事件发生。 + +$$ +P(X>t) = P(N(t)=0) = \frac{e^{-\lambda t}(\lambda t)^0}{0!} = e^{-\lambda t} +$$ + +so, + +$$ +P(X\leq t) = 1 - P(X>t) = 1 - e^{-\lambda t} +$$ + +那么指数分布的CDF即为$P(X\leq t)$，同时有： + +$$ +\text{CDF}(t) = \int_{-\infty}^{\infty} \text{PDF}(t) dt +$$ +则，可以推导出： + +$$ +\text{PDF}(t) = (1-e^{-\lambda t})' = \lambda e^{-\lambda t} +$$ + + +# Deduction + +![](math/Statistics/basic_concepot/distribution/attachments/2bbb645362366906ace3296d35612625_720.jpg) +# Reference + +* https://www.ruanyifeng.com/blog/2015/06/poisson-distribution.html +* https://zh.wikipedia.org/wiki/%E6%B3%8A%E6%9D%BE%E8%BF%87%E7%A8%8B +* https://www.le.ac.uk/users/dsgp1/COURSES/LEISTATS/poisson.pdf \ No newline at end of file diff --git a/content/math/Statistics/basic_concepot/distribution/gamma_distribution.md b/content/math/Statistics/basic_concepot/distribution/gamma_distribution.md new file mode 100644 index 000000000..086860235 --- /dev/null +++ b/content/math/Statistics/basic_concepot/distribution/gamma_distribution.md @@ -0,0 +1,62 @@ +--- +title: Gamma Distribution +tags: + - basic + - math + - statistics +date: 2024-06-03 +--- + +# Background + +## Gamma Function + +Factorial: + +$$ +n! = \prod_{i=1}^{n} i = 1\times2\times3\times\cdots\times n +$$ +那如何计算$\frac{3}{2}!$呢？通过对阶乘函数的插值将阶乘函数托展到non-integer value。但是插值的方法有很多，要如何选择合适的插值的方法？ + +最重要的条件是，插值后的函数要满足阶乘最重要的条件， + +$$ +n! = n\times(n-1)! +$$ +这个插值后的广义阶乘，就是**Gamma Function**： + +$$ +\Gamma(z) = \int_{0}^{\infty} x^{z-1}e^{-x}dx +$$ +可以验算，阶乘最重要的性质并没有变，不过形式有所偏移，性质如下： + +$$ +\Gamma(z+1)=z \times \Gamma(z) +$$ +证明如下： + +![](math/Statistics/basic_concepot/distribution/attachments/prove.jpg) + +同时，在integer节点，Gamma function也和阶乘对应起来，即： + +$$ +\Gamma(n+1) = n! +$$ + +证明如下： + +![](math/Statistics/basic_concepot/distribution/attachments/df15541df80b6065fb8296d80ffceac5_720.jpg) + + + +## Exponential Distribution + +Exponential Distribution指的是，probability of the waiting time between events in a Poisson Process + +Here's the exponential distribution explain: [Exponential Distribution](math/Statistics/basic_concepot/distribution/exponential_distribution_and_poisson_distribution.md) + + +# Reference + +* https://www.youtube.com/watch?v=c7_F4P71E2E +* https://www.youtube.com/watch?v=GJoZWPocAm0 \ No newline at end of file diff --git a/content/math/Statistics/Basic/Quantile.md b/content/math/Statistics/basic_concepot/quantile_concept.md similarity index 100% rename from content/math/Statistics/Basic/Quantile.md rename to content/math/Statistics/basic_concepot/quantile_concept.md diff --git a/content/math/calculus/calculus_moc.md b/content/math/calculus/calculus_moc.md index c017da425..cf42336c6 100644 --- a/content/math/calculus/calculus_moc.md +++ b/content/math/calculus/calculus_moc.md @@ -15,4 +15,8 @@ date: 2024-05-24 # Integration * [Common Integration](math/calculus/integration/common_integration.md) -* [Integration by Parts](math/calculus/integration/integration_by_parts.md) \ No newline at end of file +* [Integration by Parts](math/calculus/integration/integration_by_parts.md) + +# Series + +* \ No newline at end of file diff --git a/content/math/calculus/differential/common_differential.md b/content/math/calculus/differential/common_differential.md index 4ef6b0c07..3cd81fbf3 100644 --- a/content/math/calculus/differential/common_differential.md +++ b/content/math/calculus/differential/common_differential.md @@ -7,5 +7,6 @@ tags: - math date: 2024-05-24 --- -## cos(x) +# Reference +* https://www.youtube.com/watch?v=oBlHiX6vrQY \ No newline at end of file diff --git a/content/math/calculus/series/attachments/Pasted image 20240528113553.png b/content/math/calculus/series/attachments/Pasted image 20240528113553.png new file mode 100644 index 000000000..3daa75527 Binary files /dev/null and b/content/math/calculus/series/attachments/Pasted image 20240528113553.png differ diff --git a/content/math/calculus/series/common_series.md b/content/math/calculus/series/common_series.md new file mode 100644 index 000000000..436acb887 --- /dev/null +++ b/content/math/calculus/series/common_series.md @@ -0,0 +1,10 @@ +--- +title: Common Series +tags: + - math + - calculus + - series +date: 2024-05-28 +--- +## $\frac{1}{n!}$ + diff --git a/content/math/calculus/series/convergence_tests.md b/content/math/calculus/series/convergence_tests.md new file mode 100644 index 000000000..1a4292851 --- /dev/null +++ b/content/math/calculus/series/convergence_tests.md @@ -0,0 +1,17 @@ +--- +title: Series Convergence Tests - 级数收敛判断 +tags: + - math + - calculus + - series +date: 2024-05-28 +--- +# 无穷级数的敛散性 + +![](math/calculus/series/attachments/Pasted%20image%2020240528113553.png) + +# Reference + +* https://zh.wikipedia.org/wiki/%E7%BA%A7%E6%95%B0#%E6%97%A0%E7%A9%B7%E7%BA%A7%E6%95%B0%E7%9A%84%E6%95%9B%E6%95%A3%E6%80%A7 +* https://en.wikipedia.org/wiki/Series_(mathematics)#Calculus_and_partial_summation_as_an_operation_on_sequences +* https://zhuanlan.zhihu.com/p/416667179 \ No newline at end of file