Under the fastboot, Oneplus 6T cannot be recognized by the Windows 10 even with official driver installed. The solution is simple: after connecting the phone that is in the fastboot with PC, open Windows Update and click view all optional updates. There’s a driver called Google, Inc. – Other hardware – Android Bootloader Interface. Installing this driver solves the problem.
[MAST10005] 1. The Language of Mathematics
This is a note collection for MAST10005 (Calculus 1) from the University of Melbourne.
1.1 Mathematical Statements
- Mathematical Statement: a sentence or expression that is unambiguously true of false.
- e.g. let p be the statement1+1=3, p is an valid statement. p is false.
- counter case: f(x) is continuous is not a M.S. without further information.
- Conjunction: true for p and q. (let p and q be M.S.) Denoted as p \wedge q
- Disjunction: true for p or q. (let p and q be M.S.) Denoted as p \vee q
- Negation: true for not p. (let p be M.S.) Denoted as ~ p
- Condition: let D be a set. Condition is a statement that is true or false depending on the choice of x \in D. Denoted with notation p(x).
- e.g. Consider x \in N. Let p(x) be the condition “x is even”
- Existential Quantifier: Let D be a set and p(x) be a condition over D. When at least onex \in D such that p(x) is true we say “there exists x \in D such that p(x)”. Denoted as \exists x \in D \; p(x)
- Universal Quantifier: Let D be a set and p(x) be a condition over D. When p(x) is true for every x \in D we say “for all x \in D p(x)”. Denoted as \forall x \in D \; p(x)
- Set of Numbers:
- \mathbb{N} set of natural numbers. {1, 2, 3, 4, …}
- \mathbb{Z} set of integers.
- \mathbb{Q} set of rational numbers
- \mathbb{R} set of real numbers
- Set: A collection of unique objects.
- e.g. {0, 0, 0, 1, 2, 7, 9} = {0, 1, 2, 7, 9}
- Let A and B be sets. A and B are equal when every element of A is an element of B and every element of B is an element of A. Denoted A = B
- Expressing Sets: Let D be set and let p(x) be a condition over D. The set of elements of D for which p(x) is true is denoted {x \in D | p(x)} (set-builder notation)
- Subset: Let A and B be sets. When every element of A is an element of B, A is a subset of B. Denoted A \sqsubseteq B
- Union: Let A and B be subsets of a set U. Union of A and B is the set of elements that are in at least one of A and B. Denoted A \cup B. That is: x \in A \cup B \; if \; and \; only \; if \; x \in A \; or \; x \in B
- Intersection: Let A and B be subsets of a set U. Intersection of A and B is the set of elements that are both in A and B. Denoted A \cap B. That is: A \cap B = \{x \in A \cup B | x \in A \; and \; x \in B\}
- Empty Set: \emptyset = \{\}
- Cartesian Product: Let A and B be sets. Cartesian product of A and B is the set of all poosible ordered pairs we can build using elements of A as the first element and elements of B as the second element. Denoted as A \times B = \{(a, b)|a \in A, b \in B\}
- e.g. \{0,1\} \times \{u,v,w\} = \{(0,u),(0,v),(0,w),(1,u),(1,v),(1,w)\}
- Function: A function f consists of:
- A nonempty set A called the domain of f;
- A nonempty set B called the codomain of f;
- A subset of AxB such that each element of A appears as the first element in exactly one ordered pair.
- f with domain A and codomain B is denoted as f:A \longrightarrow B
- The image of a under f is given by the notation f(a)
- Range: Let A and B be sets and let f:A \longrightarrow B. The range of f is the set of values the function takes. Formally:
- range(f) = \{b \in B \; | \; there \; exists \; a \in B \; such \; that \; f(a) = b\}
- range(f) = \{f(a) \; | \; a \in A\}
- Image: Let A and B be sets and let f:A \longrightarrow B. Let S be a subset of A. Image of S under f is the set
- f(S) = \{ b \in B \; | \; there \; exists \; s \in S \; such \; that \; f(s) = b \}
- f(S) = \{ f(s) \; | \; s \in S \}
- Image is generalisation of range.
- Function: Let A be a subset of R. Letf : A \longrightarrow \mathbb{R} and g : A \longrightarrow \mathbb{R}. Define following functions with codomain equal to R:
- (f+g)(x)=f(x)+g(x)
- (f-g)(x)=f(x)-g(x)
- (fg)(x)=f(x)*g(x)
- (f/g)(x)=f(x)/g(x)
- Domain for f+g, f-g and fg is set A. Domain for f/g is set \{ a \in A \; | \; g(a) \neq 0 \}
为”不兼容”的设备安装Windows Subsystem for Android
最近微软正式推出了Android的子系统,尝试在自己的6代i3机器上安装却被告知不兼容。一番搜寻后寻找出如下解决方案。
首先去这个网站
输入WSA的商店地址,https://www.microsoft.com/en-us/p/windows-subsystem-for-android-with-amazon-appstore/9p3395vx91nr
并选择Slow(如图)
![](https://www.zhoushangren.com/wp-content/uploads/2022/02/image.png)
进入后下载Microsoft.UI.Xaml和WSA本体。其中Xaml视自己的架构下载:
![](https://www.zhoushangren.com/wp-content/uploads/2022/02/image-1.png)
最后下载页面内最大的文件:WSA本体
![](https://www.zhoushangren.com/wp-content/uploads/2022/02/image-2.png)
下载完成后先去Microsoft Store更新电脑安装的所有应用,完成后双击安装Microsoft.UI.Xaml。
最后以管理员运行终端,输入 Add-AppxPackage WSA文件路径
,回车即可安装。WSA文件路径为以msixbundle结尾的WSA安装文件
Zuk Z2 Plus 退出FFBM模式
今天不小心使手中的Zuk z2进入了FFBM模式,怎样操作都无法退出。搜寻一番后找到如下解决方案:
- 同时按住音量+/音量-/电源键
- 待手机震动后松开电源键
- 继续按住两个音量键,直到菜单出现
- 选择进入bootloader,然后选择重启
记一次显卡黑屏排查及解决过程
去年在闲鱼收了一块980ti打算换掉原来的RX470,当时买回来就有个奇怪的问题:只插一张980ti电脑点不亮,必须同时插470(甚至无需通电)才能正常开机。因为不是太影响使用,就也没太在意。
最近显卡涨价打算把980ti卖掉,突然想起还有这问题。出于销售的角度考虑,再次复现了只插一张卡的场景,问题依旧。
太奇怪了,为何一定要多插一张不通电的卡才能工作…尝试了彻底卸载AMD显卡驱动、重置主板,均无效。
最后尝试把980ti插到第二条pcie x16槽(速度是x8的)上,问题解决,可以正常开机了。
这下真相大白,原来这980ti只能运行在pcie x8的速度下…那为什么之前多插一张470就能运行了呢?查阅主板参数后发现,当x8的槽插入东西时,x16的槽自动降速为x8,所以980ti才能正常工作…
![](https://www.zhoushangren.com/wp-content/uploads/2021/04/图片-1024x183.png)
解决Windows 10卡任务栏小图标/窗口控件
最近电脑遇到很奇怪的问题:每次开机几分钟后便会出现各种操作问题:很多窗口的控件无法点击/点击后需要十几秒才有反应(包括任务管理器)、任务栏的更多图标全部变为空白。
一番折腾后找到如下解决方案:
打开任务管理器,结束桌面窗口管理器。
此时便会恢复正常,但考虑到可能有系统文件损坏。修复损坏文件:以管理员运行Powershell后输入 Sfc /scannow
即可。
![](https://www.zhoushangren.com/wp-content/uploads/2020/12/image.png)
尝试在Windows 10下使用SkyAR更换天空
最近了解到这个有趣的项目,遂尝试自己部署并记录下其中遇到的一些坑。
项目地址:https://github.com/jiupinjia/SkyAR
训练模型:https://drive.google.com/file/d/1COMROzwR4R_7mym6DL9LXhHQlJmJaV0J/view?usp=sharing
首先clone项目到本地,并下载模型文件。将模型带目录解压到项目目录内。
安装Python3, Anaconda:https://www.anaconda.com/products/individual#windows
安装项目目录内Requirements.txt内的依赖,但有几个需要注意/单独安装:
- pytorch 使用conda安装,11.0是cuda的版本:
conda install pytorch torchvision torchaudio cudatoolkit=11.0 -c pytorch
- numpy 只能安装1.19.3,否则会报错:
pip3 install numpy==1.19.3
- 不装opencv-python,只装opencv-contrib-python:
pip3 install opencv-contrib-python
安装完成后执行 python .\skymagic.py --path .\config\config-canyon-district9ship.json
即可看到效果。
附一个自己拍的视频,效果貌似不是很好…?
解决一加9008救砖连接电脑后提示未知USB设备
近日不慎将自己的一加6T刷砖,尝试使用9008救砖。
无奈在打好驱动的情况下,连接电脑总是提示”未知USB设备 (设备描述符请求失败)”,同时救砖工具内也没有任何设备显示。
一番搜索后得知可能是数据线的问题,更换原装数据线后解决。
Ubuntu 20.04编译安装Deepin深度显卡驱动管理器
获取源码:https://github.com/linuxdeepin/deepin-graphics-driver-manager
安装依赖:
sudo apt install cmake qttools5-dev-tools qtbase5-dev freeglut3-dev libdtkwidget-dev libpci-dev
编译:
cmake -DCMAKE_INSTALL_PREFIX:PATH=/usr .. # Install to /usr
make # Add -jx for parallel
安装:
sudo make install
sudo systemctl daemon-reload # refresh systemd
sudo systemctl enable driver-installer.service # enable installer service
sudo systemctl start driver-installer.service # start installer service
使用:
sudo deepin-graphics-driver-manager
OpenWRT小米路由器Mini – 不支持所上传的文件格式请确认选择的文件无误
今天尝试给小米路由器mini(MT7620a)上的自编译openwrt刷入原版镜像,后台升级出现上述错误。
遂尝试sysupgrade,依然无法刷入:
Device xiaomi,miwifi-mini not supported by this image
Supported devices: miwifi-mini
Image check ‘fwtool_check_image’ failed.
解决方案也很简单。编辑/lib/upgrade/fwtool.sh
将46行的device="$(cat /tmp/sysinfo/board_name)"
修改为device="miwifi-mini"
即可。