I need to prove that continuously differentiable functions on $\,\left[a,b\right]\,$ are a subset of Hölder space of order $1$ and that the Hölder space of order $1$ is a subset of the Hölder space of order $\mu$, $\;0 &lt; \mu &lt; 1,\,$ i.e.  $\,C^1 \subset H_1 \subset H_\mu$.  Can anyone point me in the direction of a book or a theorem that proves this?
I have a question on Holder space.Is the space $C^2(\mathbb{R}^n)$ embedded in $C^{1,\alpha}(\mathbb{R}^n)$? I think in the bounded domain case, this should be true. But what if in the case where the domain is not bounded? Thanks for any hint!
iMac only show flashing folder with question mark after formatting OS X partition drive Today i format my "OS X El capitan" partition for installing "Yosemite". But due an error in bootable yosemite usb it didn't install on this partition. After some hours when i turned on iMac and hold down "option" key for boot into usb but just blank screen and mouse show. And every time when i turend on iMac it only show flashing folder with question mark. I've tried to resolve it by reseting "NVRAM". But after restarting problem still same.  Also I've tried many "Startup key combinations for Mac" but didn't work any combination on startup.  Also i have important data in my other one partition. Please can anyone tell me what i do for resolving that issue Without loosing my data? How can I extract text from images?  I am not talking about scanned files, but garden variety images, such as when you take a high-def picture of a blackboard at class, and it is nicely handwritten; or when you photograph a page from a recipe book and want the recipe in text format.  Any free and open software for that?  I tried tesseract, and the results were awful. Does ReLU layer work well for a shallow network? Creating account didn't log me in / didn't create an account find an approximate solution, up to the order of epsilon The question is to find an approximate solution, up to the order of epsilon of following problem.  $$y'' + y+\epsilon y^3 = 0$$ $$y(0) = a$$ $$y'(0) = 0$$  I tried to solve the given problem using perturbation theory.  $$y(t) = y_0(t) + \epsilon y_1(t) + \epsilon^2 y_2(t) + \cdots$$ $$t = w(\epsilon)t = (1 + \epsilon w_1 + \epsilon^2 w_2 + \cdots )t$$  However, i failed to find an appropriate approximate solution... help me!! What IDE to use for Python? What IDEs ("GUIs/editors") do others use for Python coding? prominently sports purple hair.    Is this her natural hair color?  Natural extensions in the answer depending on the correct answer: Is she wholly human and humans in the Galaxy Far Far Away can have this hair color?   Or is she partly human or not human?   Or does she dye her hair?   Or is there another hair color changing technology? Response.Redirect to new window I want to do a Response.Redirect("MyPage.aspx") but have it open in a new browser window. I've done this before without using the JavaScript register script method. I just can't remember how? Appending the same string to a list of strings in Python Can't find wifi drivers for 0bda:f179 Realtek Semiconductor Corp How to get rid of OTA software update notification? I upgraded my Nexus 4 to Lollipop a few days ago but I don't like it. I'll leave out my reasons because they're not relevant here. I wiped my phone and installed a clean stock 4.2.2 version instead. I'm happy with this.  Not long after, Android automatically downloaded the 4.3 upgrade and notifies me with the choices "Later" and "Install". I don't want to do this upgrade.  How do I:   get rid of the notification, and  remove the downloaded update (to free up precious storage space).     I have already tried choosing "Later" but the same notification immediately reappears.    Based on Google search results, I also tried going to Settings &gt; Apps &gt; All &gt; Google Services Framework and unticked "show notifications" but it still appears. Force stop or disable also doesn't seem to help, so I've re-enabled the service including notifications. I didn't see any other apps in this list that sounded relevant - did I just not see it? Looking to achieve frame effect with shadows at corners scanf() misbehaving I have just booted my clean Ubuntu 18.04 LTS VM and tried to install some application with sudo apt install.  But got error message:     E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable)       E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend), is another process using it?   What process created the /var/lib/dpkg/lock-frontend file in Ubuntu? How to gently stop it and take manual control on APT? "'void' type not allowed here" error (Java) How do I find out which DOM element has the focus? sudo on Windows 10 Linux subsystem cannot resolve local machine name I installed Windows 10 Anniversary update and the Linux subsystem. When running anything with sudo it takes ages and then I get this error message:     sudo: unable to resolve host MYMACHINE   How to get rid of this and make sudo fast? I cast  on my opponent, whose hand has two Mountain cards. Wistful Thinking resolves and my opponent draws a  and another Mountain.  Can my opponent cast Shock before discarding it? I am working on refactoring some old code and have found few structs containing zero length arrays (below). Warnings depressed by pragma, of course, but I've failed to create by "new" structures containing such structures (error 2233). Array 'byData' used as pointer, but why not to use pointer instead? or array of length 1? And of course, no comments were added to make me enjoy the process...  Any causes to use such thing? Any advice in refactoring those?  struct someData {    int nData;    BYTE byData[0]; }   NB It's C++, Windows XP, VS 2003 Prove or give a counterexample:  $$(A ∪ B = A ∪ C) \land (A ∩ B = A ∩ C) \implies B = C.$$  I think this is true, but I am not sure how to show it. I don't know if there are any manipulations with unions and intersections that allows me to move things around. Thanks in advance for any hints.