Word to describe a person who can express their thought accurately in words?
Is there a single word for “one who explains his point of view very clearly”?
How to fill gaps in SLC-Off Landsat 7 ETM+ Images with QGIS? Explanation of the problem:     On 31 May 2003 the Landsat 7 Enhanced Thematic Mapper (ETM+) sensor had a failure of the Scan Line Corrector (SLC). Since that time all Landsat ETM+ images have had wedge-shaped gaps on both sides of each scene, resulting in approximately 22% data loss. These images are available for free download from the USGS GloVis website and are found in the L7 SLC-off collection.   source:   Can I use Qgis instead of proprietary software (ENVI, Erdas....) to fill the gaps? Proof of a formula involving Euler's totient function: $\varphi (mn) = \varphi (m) \varphi (n) \cdot \frac{d}{\varphi (d)}$ First and foremost I am sorry for this; in order to make the questions clear I must first upload the lecture notes from my institution $^\zeta$ for the derivation of Hydrostatic Equilibrium:          $^\zeta$ Lecture notes courtesy of Imperial College London, Astrophysics dept, 2017-2018 edition.    Firstly, in equation $(3.1)$ why is there no negative sign for $F_g$? Last time I checked, Newton's law of gravitation told us that   $$F=-\frac{GMm}{r^2}$$  Nextly, I have a conceptual problem with equation $(3.2)$; when they use the term 'pressure' I am going to assume that they are referring to the radiation pressure that is released due to nuclear fusion reactions taking place in the sun. In that formula it must be the case that $P(r) \gt P(r+\delta r)$ if this is the case then $(3.2)$ should read $$F_p=-\left(\frac{dP}{dr}\right)\delta r\,\delta A $$   Correct me if I'm wrong but Hydrogen nuclei are fused together to generate the more stable Helium and hence lots of radiation pressure acting outwards from the centre of the star. If this is correct then $P(r+\delta r)=0$, since the outside face of that cylindrical volume element in Figure $3.1$ will not 'feel' any of this radiation pressure because this pressure only acts on the inner face. What am I not understanding here?  Moving on to equation $(3.3)$, let's suppose the sign of the gravitational force in $(3.1)$ really is neglected. Does this mean that the negative sign in $(3.3)$ is due to $P(r+\delta r) \lt P(r)$ and hence $$\frac{GM(r)\rho(r)}{r^2}=-\left(\frac{dP}{dr}\right)\,?$$ I know this is the same equation as in $(3.3)$ but I have written it with the negative sign next to the pressure differential as I would like to know where this minus sign originates from. Does anyone know?  My final concern is the sign in $(3.4)$ as last time I checked $$g=-\frac{GM}{r^2}$$ and not $$g=\frac{GM}{r^2}$$  Hence, equation $(3.4)$ should read  $$\left(\frac{dP}{dr}\right)=\rho(r)\,g\,?$$     I forgot to mention that I have done some research and  is the closest derivation I could find, which, needless to say is no less helpful than the notes I have. Using Newton's Law of Universal Gravitation to find distance, with the question not giving sufficient information to substitute into the equation. Problem:  $F = \frac{(G m_1 m_2)}{r^2}$  An object of unknown mass is placed directly between the Earth and the Moon such that the forces of gravity acting on the object are equal from both the Earth and the Moon. The distance from the Moon to the object is exactly one-tenth of the distance from the Moon to Earth. Using the above formula, determine the distance from the Moon to the Earth.  Given is:  The factor $G≈6.67∙10−11\mathbf{N(\frac{m^2}{kg^2})}$ is a universal constant.  Mass of Earth $≈5.972∙10^{24}\mathbf{kg}$   Mass of the Moon as $≈7.348∙10^{22}\mathbf{kg}$  Mass of unknown object = $m$  My solution:  $F = \frac{(6.67 *10^-11) m (7.348*10^{24})}{R^2}$  $F = \frac{(6.67 *10^-11) (5.92* 10^22) m}{10R^2}$  As gravitational force acting on the object is equal   $\frac{(5.92\cdot 10^22)}{100r^2} = \frac{(7.348*10^{24})}{r^2}$  $R = 1.24 \cdot 10^4 KM$  Is this a viable solution to the problem? Please provide feedback. Thank you! Are there other governments in The Hunger Games world? We know that Panem exists in a post-apocalyptic North America but are there other established governments on other continents? Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic I want to buy a new MacBook Pro, from Apple. However I want to run Snow Leopard instead of Lion.  I did some Google searches and found a few success stories of people who got SL to run on their early-2011 MBPs. I didn't find much of any experiences of people doing the same on a late-2011 MBP though, so I'm wondering (and really hoping!) if it's possible? When is the present perfect tense used instead of the past tense? Blender 2.78 with Windows 10 lags when interacting with the UI How do I calculate the run rate in cricket? Testing pointers for validity (C/C++) Is there any way to determine (programatically, of course) if a given pointer is "valid"? Checking for NULL is easy, but what about things like 0x00001234? When trying to dereference this kind of pointer an exception/crash occurs.  A cross-platform method is preferred, but platform-specific (for Windows and Linux) is also ok.  Update for clarification: The problem is not with stale/freed/uninitialized pointers; instead, I'm implementing an API that takes pointers from the caller (like a pointer to a string, a file handle, etc.). The caller can send (in purpose or by mistake) an invalid value as the pointer. How do I prevent a crash? Average time alloted for manuscript review across disciplines I am asking this question because I've always had the impression that manuscripts submitted to a journal in my field (theoretical linguistics) take an insanely long time to get published, and sometimes I get the impression that this is because, most of the time, nobody other than the author cares about getting things done within a reasonable amount of time. Some examples from personal experience follow.   For the last paper I submitted before getting my PhD, I had to wait nine months from the submission date to get reviews back from the referees. Last week I got a review request from a journal I had never reviewed for previously. The review deadline is March 15 (almost four months). In early October, I submitted a manuscript to a journal that I know asks reviewers to return reviews within 6 weeks. I checked the status of the manuscript online and it still says "with editor". Earlier this year, I was about to start writing a review when my wife went into labor. By the time we came back from the hospital, I had forgotten about the review, so I missed the deadline. The editor didn't contact me to ask about the review until two months after the deadline. Late in 2013, I was asked to write a survey chapter for a handbook. The expected publication date of the handbook is summer 2016.   All of this is not me being unlucky with editors and referees. In private conversations through the years, many colleagues have confirmed that it is virtually unheard of to get reviews back within 3 months of submission; 5 or 6 months seems to be a good average, but in some cases it can take longer (see my first point above). In general, everybody seems to have accepted that the submission-to-printed-journal process is going to take a bare minimum of one year, and that's assuming that the manuscript is accepted without revisions. If revisions are required, two years is not out of the question. Also, it's not like our papers are ridiculously long. I've reviewed about 100 papers so far, and the longest one was about 50 single-space pages; 30-35 single-spaced pages is closer to average.  I remember that, when I was a postdoc, my astrophysics housemate mentioned that in his field the entire submission-to-printed-journal process took only three or four months. I really can't see a good reason why theoretical linguistics shouldn't operate on similar timeframes, other than the fact that everybody seems to have grown used to things taking way longer than they really need to. What are the wait times in other fields? How do you manage to get things done quickly? I am trying to perform centrality analysis with sDNA with ArcGIS Pro (ver. 2.7.1). However, I have failed to run the Preparation &amp; Integral Analysis in sDNA with the same reason. What is the problem and What should I do? I have a question about calculating the degree of a finite field extension over $\mathbb{Q}$.  This is problem 18 in chapter 1 of Patrick Morandi's Field and Galois Theory. The problem asked to show that $$ \left[ \mathbb{Q}{ \left( \sqrt[4]{2},\sqrt{3} \right):\mathbb{Q} }\right] =8 $$ Here's my work : First, we have $$  \left[ \mathbb{Q} ( \sqrt[4]{2},\sqrt{3}):\mathbb{Q}\right] = \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] . \left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right]$$ It's easy to show that $\left[ \mathbb{Q}{(\sqrt[4]{2})}: \mathbb{Q} \right] =4 $ because the minimal polynomial of $\sqrt[4]{2}$ over $\mathbb{Q}$ is $x^4 -2$. Next, I'm going to show that  $$ \left[ \mathbb{Q}(\sqrt[4]{2},\sqrt{3}) : \mathbb{Q}({\sqrt[4]{2}}) \right] =2$$ Consider the polynomial $f(x) = x^2 -3$. It's monic and $\sqrt{3}$ is a root of $f$, but I'm stuck in proving $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ (hence $f$ is irreducible over $\mathbb{Q}(\sqrt[4]{2}))$.  My question is: Is there any proof to show that $\sqrt{3} \notin \mathbb{Q}(\sqrt[4]{2})$ or another way to caculate the degree of this field extension?  Thank you for your help. Can I charge my laptop with a charger that has different specifications? How are digital movies sent to a movie theater? For many years, movies were stored on rolls of film that were physically mailed to theaters. Now, most theaters project their movies digitally. But how are these digital movies sent to the theater?   Do they mail a hard drive to the theater? Do they give the theater a username and password to a super secret website where they can download it? How does it get there? What does $b_i\mid b_{i+1}$ mean in this context? In the computational topology literature, the reduction algorithm for computing the Smith normal form of a boundary matrix uses the notation $b_j &gt; 1 \: \text{ and }\: b_j\mid b_{j+1}$ in the context of the diagonal elements of the Smith matrix. Can anyone give me an idea for what it means? limit: $u_n=\frac{1+2^2+3^3+...+n^n}{n^n}$. Let $u_n=\dfrac{1+2^2+3^3+...+n^n}{n^n}$. Prove that : $$\lim u_n=1$$ I tried to prove that $u_n&lt; something$ have limit  is 1 ; but I can't "He is king" vs "He is a king." I'm reading a book and encountering the phrase "insert name is king" a lot. I'm wondering, what's the difference between them? When and why should I use "He is king" instead of "He is a king"?   Examples:        Tommen is king now   Yet if neither one is king, still, how could it be Lord Renly?   And he is a king, and you’re just a spy   Everyone else is a king or prince these days      Same with other words:        They elected him president.   They called him a thief. Difference between least squares and minimum norm solution Consider a linear system of equations $Ax = b$.   If the system is overdetermined, the least squares (approximate) solution minimizes $||b - Ax||^2$. Some source sources also mention $||b - Ax||$. If the system is underdetermined one can calculate the minimum norm solution. But it does also minimize  $||b - Ax||$, or am I wrong?   But if least squares is also a minimum norm, what is the difference, or the rationale of the different naming?