Add notes

content/.trash/series_MOC.md

@@ -0,0 +1,8 @@
+---
+title: Series - MOC
+tags:
+  - math
+  - basic
+  - series
+date: 2024-05-28
+---

content/computer_sci/code_frame_learn/data/streamlit/MOC.md

@@ -8,4 +8,5 @@ date: 2024-05-24
 ---
 # Reference
 
-* https://streamlit.io/
+* https://streamlit.io/
+* https://30days.streamlit.app/

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
 

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)

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/

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
 

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

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

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

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)
+* [Integration by Parts](math/calculus/integration/integration_by_parts.md)
+
+# Series
+
+* 

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

content/math/calculus/series/common_series.md

@@ -0,0 +1,10 @@
+---
+title: Common Series
+tags:
+  - math
+  - calculus
+  - series
+date: 2024-05-28
+---
+## $\frac{1}{n!}$
+

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