I apologize if this is a duplicate but I can't find a good answer or area to know where to find the correct answer.  I am looking for the technology or hardware around wearables or similar technology that can detect movement or at least log location within about a 2 foot area.  I have looked around at it looks like the most common devices use triangulation but aren't more accurate than around 400 feet.  Is there any tech that is more specific than a two foot radius?  I am not trying to waste anyone's time but I can't find a better place to get an answer....
I am looking for a device that can track my location (lat,long) and speed all day long. Perhaps, I need GPS and accelerometer data bundled together.  What I want to do is to log my daily activities. I spend time walking, running, driving, taking a bus, staying in a building, etc., just like any normal human-being :) I am willing to carry the device with me at all times and would like to see every place I go into and my speed at certain positions.  My requirements are that the location and speed data should be recorded at least every ~20 seconds. I would also like the device to timestamp (date+time) each record. It would be enough if timestamp is precise to nearest minute and the location can go off about a maximum of 10-15m. (30-50ft.)  What I want is a portable device so I can carry all day long for about 2-3 months. I will only use it during casual, daily activities.  I don't want real-time tracking. I can collect the data from a storage later on.
tense and time and composite sentence If the eating meal starts at 7:00 AM and finishes at 8:00 AM. the drinking liquor starts at 7:00 AM and finishes at 7:50 AM.  can I say that :   I drank the liquor when I ate the meal. I ate the meal when I drank the liquor.   Is I need to use progressive tense ? Reverse Cauchy Schwarz for integrals Let $f,g$ be two continuous positive functions over $[a,b]$ Let $m_1$ and $M_1$ be the minimum and maximum of $f$ Let $m_2$ and $M_2$ be the minimum and maximum of $g$ Prove that $$\sqrt{\int_a^bf^2 \int_a^b g^2}\leq \frac{1}{2}\left(\sqrt{\frac{M_1M_2}{m_1m_2}}+\sqrt{\frac{m_1m_2}{M_1M_2}}\right)\int_a^bfg$$  I can't make any significant progress on this one... Thanks for any hint. Indefinite integral of secant cubed I need to calculate the following indefinite integral:  $$I=\int \frac{1}{\cos^3(x)}dx$$  I know what the result is (from Mathematica):  $$I=\tanh^{-1}(\tan(x/2))+(1/2)\sec(x)\tan(x)$$  but I don't know how to integrate it myself. I have been trying some substitutions to no avail.   Equivalently, I need to know how to compute:  $$I=\int \sqrt{1+z^2}dz$$  which follows after making the change of variables $z=\tan x$. Why the Principle of Least Action? I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$.  Okay, fine.  You write down the action functional, require that it be a minimum (or maximum), and arrive at the Euler-Lagrange equations.  Great.  But now you want these Euler-Lagrange equations to not just be derivable from the Principle of Least Action, but you want it to be equivalent to the Principle of Least Action.  After thinking about it for awhile, you realize that this implies that the Principle of Least Action isn't really the Principle of Least Action at all:  it's the "Principle of Stationary Action".  Maybe this is just me, but as generous as I may be, I will not grant you that it is "natural" to assume that nature tends to choose the path that is stationary point of the action functional.  Not to mention, it isn't even obvious that there is such a path, or if there is one, that it is unique.  But the problems don't stop there.  Even if you grant the "Principle of Stationary Action" as fundamentally and universally true, you realize that not all the equations of motions that you would like to have are derivable from this if you restrict yourself to a Lagrangian of the form $T-V$.  As far as I can tell, from here it's a matter of playing around until you get a Lagrangian that produces the equations of motion you want.  From my (perhaps naive point of view), there is nothing at all particularly natural (although I will admit, it is quite useful) about the formulation of classical mechanics this way.  Of course, this wouldn't be such a big deal if these classical ideas stayed with the classical physics, but these ideas are absolutely fundamental to how we think about things as modern as quantum field theory.  Could someone please convince me that there is something natural about the choice of the Lagrangian formulation of classical mechanics (I don't mean in comparison with the Hamiltonian formulation; I mean period), and in fact, that it is so natural that we would not even dare abandon these ideas? My Logitech G5 Laser mouse has 9 buttons but it's SetPoint software only allows 5 of them to be used as "mouse buttons" and the remaining 4 can only be assigned special windows functions (Forward, Back, Cruise Up, etc) or Keystroke Assignments.  Many of the games I play will take up to 10 "MOUSE BUTTON" inputs for in-game actions but wont recognize the remaining 4 buttons even when assigned keystroke assignments.  Is there a way to make these last 4 buttons "Generic Buttons" as well as buttons 3,4,and 5? (1 is left click and 2 is right click).  My other question is if the above is not possible, maybe I can use AutoHotkey to remap keystrokes as assigned by my SetPoint software to mouse button commands?  If so how? Why can't I buy the Windhelm house (Hjerim)? I've finished the Stormcloak storyline, and now cannot become a Thane of Windhelm without buying Hjerim. The Steward keeps saying something has happened and he can't sell it right now.  What the heck am I missing? I've been doing every random little quest from people in town I can find, hoping to unlock the house. I'm well over the 5/5 requirement of helping people.  Any ideas? Implementing a PIVOT query How can I pivot the following SELECT statement:           SELECT sc.CID,                 sc.CodeName     as OverviewText,                 scRAG.CodeName  as RAGStatusText             FROM StatusCode      sc LEFT OUTER JOIN ProjectOverview po               ON sc.CID          = po.ProjectOverviewCID              AND po.ProjectId    = 180 LEFT OUTER JOIN StatusCode      scRAG               ON po.RAGStatusCID = scRAG.CID           WHERE sc.SCID         = 18   Such statement yields the result set that follows:  CID OverviewText    RAGStatusText --- ------------    ------------- 153 Cost            Green 154 Requirements    Yellow 155 Schedule        NULL 156 Technical       NULL 157 Testing         NULL   But, I want it to return one single row with 10 values, as shown bellow:   ----------------------------------------------------------------------------------------------  | Cost | Green | Requirements | Yellow | Schedule | NULL | Technical | NULL | Testing | NULL |  ----------------------------------------------------------------------------------------------   Can I pivot on CID? ls command operating differently depending on recipient Chatroom owners can star their own messages I was able to star my own message by pinning it and unpinning it.  Pinning a message adds a star, even to your own messages, but when the pin is removed, the star remains. Why are objects at rest in motion through spacetime at the speed of light? I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward.  What troubles me here, is the fact that it is traveling through space-time at the speed of light. Why is it at the speed of light? I am trying to prove the following.  Proposition Let $g$ be a Lie algebra such that the first derived algebra $Dg$ is a proper ideal of $g$. Consider the quotient $g/D^1 g$, and show that the preimage of any codimension 1 subspace is   an ideal, and has codimension 1.   I could show that the preimage is indeed an ideal, but I need some help with the part about the dimensions:  So suppose that $\phi: x \mapsto [x]$ is the quotient projection. And write $[h] + Dg$  for a codimension 1 subspace of $g$ (here $h\subset g$). Then the preimage of this subspace is just the linear span $h+Dg\leq g$. Let $y+z \in h+Dg$ with $y\in h$ and $z\in Dg$. Let $x\in g$. We want to show that $[x, y+z]\in h$, ie that $h + Dg \lhd g$. We can write $x$ as $x_0+x_1$ for $x_0 \in Dg$, $x_1\not\in Dg$. Then  $$[x,y+z] = [x_0, y+z] + [x_1, y] + [x_1,z] \in h + Dg$$  The inclusion follows since $Dg$ is an ideal so the first and third terms belong $Dg$; and $[x_1, y] \in D_g$, as $g/Dg$ is abelian. In .NET, the  is used in a lot of places throughout the .NET base class libraries. Implementing it properly is especially important to find items quickly in a collection or when determining equality.  Is there a standard algorithm or best practice on how to implement GetHashCode for my custom classes so I don't degrade performance? Title bar settings missing in GNOME Tweaks on Ubuntu 20.04 I tried to move my "close, minimise and maximise" to the right + add the macOS theme to it. However, I have not been able to find any settings for that. In GNOME Tweaks > Windows the settings to put the buttons to the right are missing completely. It is a common practice to apply PCA (principal component analysis) before a clustering algorithm (such as k-means). It is believed that it improves the clustering results in practice (noise reduction).   However I am interested in a comparative and in-depth study of the relationship between PCA and k-means. For example, Chris Ding and Xiaofeng He, 2004,  showed that "principal components are the continuous solutions to the discrete cluster membership indicators for K-means clustering". However, I have hard time understanding this paper, and Wikipedia actually .  Also, the results of the two methods are somewhat different in the sense that PCA helps to reduce the number of "features" while preserving the variance, whereas clustering reduces the number of "data-points" by summarizing several points by their expectations/means (in the case of k-means). So if the dataset consists in $N$ points with $T$ features each, PCA aims at compressing the $T$ features whereas clustering aims at compressing the $N$ data-points.  I am looking for a layman explanation of the relations between these two techniques + some more technical papers relating the two techniques. How to prove or disprove statements about sets Prove or disprove:  The set: $\{ \emptyset\}^{\Bbb N}$ has only one element.  The set $\emptyset^{\Bbb N}$ is empty.    I'm pretty sure both are true, for 1. all the natural numbers go to the empty set and that is the only element. Where as 2. all the natural numbers go to nothing so that's why it's empty. (Same as $ {\Bbb N}^{\emptyset} $ nothing goes to something is nothing (I think)). The problem is I have no idea how to show this so advice would be appreciated.  Edit: My defintion of a function is: $f:B\to A$ if  $(a_1,b),(a_2,b)\in f \ \Rightarrow \ a_1=a_2$ So for 2. I can simply say that: $(1,\emptyset),(2,\emptyset)\in f \Rightarrow a_1\neq a_2$  ? Do harmonic numbers have a “closed-form” expression? How can I connect a texture node to a material with Python? I have a file, which was encrypted with AES-128 in ECB mode. I know the format of the original file and know that all files in this format have the same headers. So, I have an encrypted block and the original block.  Can I get the encryption key, using this information? Difference between systemctl and service commands systemd gives us the systemctl commands suite which is mostly used to enable services to start at boot time. We can also start, stop, reload, restart and check status of services with the help of systemctl.  We can do, for example, sudo systemctl enable service_name, and service_name will automatically start at boot time. We can also disable services not to start at boot time.  Is the only difference between the service and systemctl commands that systemctl can be used to enable the start of services at run time? Can we use systemctl on any service? What other significant differences are there? This formula provides the $n$th term in the Fibonacci Sequence, and is defined using the recurrence formula: $u_n = u_{n − 1} + u_{n − 2}$, for $n &gt; 1$,  where $u_0 = 0$ and $u_1 = 1$.   Show that     $$u_n = \frac{(1 + \sqrt{5})^n - (1 - \sqrt{5})^n}{2^n \sqrt{5}}.$$    Please help me with its proof. Thank you.