See how on the image the positioning isn't correct. I'm talking about the white pieces see how far they are from those movers with arrows that means If I move I would have to move an extra. It also makes it impossible for me to rotate them to the exact way I want without spending 2 hours.
How can I change the local origin of an object, without changing the object location in the world space.  This is the object located at position (0,0,0) in the world space    This is the same object located at position (0,1,0) in the world space, but with its local origin offset so that the object is in the same place    Is there a way to do this in a single step?
Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$ I know that $\mathbb Z[\sqrt{7}]$ is a UFD, and I can write the equation $(2 + \sqrt{7})(3 - 2\sqrt{7}) = (5 - 2\sqrt{7})(18 + 7\sqrt{7}) $. So clearly these are not all irreducibles. How do I determine which of these aren't irreducible? How do I factor those into irreducibles?  It seems difficult when dealing with $\mathbb Z [\sqrt{d}] $ with $d$ positive, since the norm map isn't as nice (it's not always positive).  Thanks Prove the inequality $\,\frac{1}{\sqrt{1}+ \sqrt{3}} +\frac{1}{\sqrt{5}+ \sqrt{7} }+\ldots+\frac{1}{\sqrt{9997}+\sqrt{9999}}\gt 24$ Prove the inequality $$\frac{1}{\sqrt{1}+ \sqrt{3}}  +\frac{1}{\sqrt{5}+ \sqrt{7} }+......... +\frac{1}{\sqrt{9997}+\sqrt{9999}} &gt; 24$$   My work:   Rationalizing the denominator gives   $$\frac{\sqrt{3}-1}{2}  +\frac{\sqrt{7}-\sqrt{5}}{2}+......+\frac{\sqrt{9999}-\sqrt{9997}}{2} .$$  Now by taking two as common and separating the positive and negative terms gives  $$\frac{1}{2} [ \{\sqrt{3} +\sqrt{7}+\dots +\sqrt{9999}\} - \{1+\sqrt{5} +\dots+\sqrt{9997}\}].$$  Can we do like this please suggest. Thanks. Workflow email with link to document in library Where do I place my own .sty or .cls files, to make them available to all my .tex files? Should you use a plural verb if you refer to a fraction?     Nine tenths of the pillar have rotted away.   I think has should be used here, but I'm not sure. What is the weight equation through general relativity? Does a passive Perception (Wisdom) check add WIS mod + Perception skill? I'm new to D&amp;D. There seems to be a discrepancy between the 5e Starter Set Rulebook and the associated character sheets. The Rulebook says that a passive wisdom (percep) score is "10 + the creature's wisdom modifier, as well as any bonuses."  In the example they have a 1st-level character (with a proficiency bonus of +2) Wisdom of 15 (+2) and a  proficiency in Perception, he or she has a passive Wisdom (Perception) of 14 (10+2+2).  But the Human Fighter Folk hero character has a WIS mod of +1, and a +3 written beside perception, and a passive Wis percep of 13 (not 14?).  The Dwarven Cleric has Wis mod of +3 and a +3 written beside perception, and only a 13 passive wisdom.  I guess this has to do with proficiency in the skill, but I'm confused. Can someone explain these instances and maybe also when proficiency is used, vs when just the modifier or just the skill without proficiency? I have an expression for a covariance matrix $C$ in terms of the indices $i$ and $j$.  In this way I can analytically calculate the elements of my covariance matrix, however when I try to invert $C$ matlab gives a warning about the matrix being close to singular.  The inversion therefore doesn't work, by which I mean the multiplying $C$ by the inverse given i do not get the identity.  I have tried calculating the pseudo inverse but this also does not work.  I have also tried adding a small constant along the diagonal but again the results do not work.  In general I'm working with matrices of dimension 1200 but I will give low dimensional example matrix that has the same properties, i.e. the matrices are symmetric about the diagonal and the anti-diagonal     19.9939  19.9954  19.9958  19.9951  19.9933  19.9905  19.9865    19.9954  19.9973  19.9981  19.9978  19.9965  19.9940  19.9905    19.9958  19.9981  19.9993  19.9995  19.9985  19.9965  19.9933    19.9951  19.9978  19.9995  20.0000  19.9995  19.9978  19.9951    19.9933  19.9965  19.9985  19.9995  19.9993  19.9981  19.9958    19.9905  19.9940  19.9965  19.9978  19.9981  19.9973  19.9954    19.9865  19.9905  19.9933  19.9951  19.9958  19.9954  19.9939   As mentioned in the title the matrix isn't positive, however the the negative eigenvalues are very small suggesting that the matrix is not positive only due to machine precision.  The negative eigenvalues are $-1.4048e-14$ and $-2.4571e-15$.  How can I go about inverting these matrices? In a theoretical physics homework problem, I have to show the following: $$\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$$  Where $T$ is the Energy-Momentum-Tensor, $j$ the generalized current and $F$ the Field-Tensor. We use the $g$ for the metric tensor, I think in English the $\eta$ is more common.  I know the following relationships:   Current and magnetic potential with Lorenz gauge condition: $$\mathop\Box A^\mu = \mu_0 j^\mu$$ Energy-Momentum-Tensor: $$T^{\mu\nu} = \frac1{\mu_0} g^{\mu\alpha} F_{\alpha\beta} F^{\beta\nu} + \frac1{4\mu_0} g^{\mu\nu} F_{\kappa\lambda} F^{\kappa\lambda}$$ Field-Tensor: $$F^{\mu\nu} = 2 \partial^{[\mu} A^{\nu]} = \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}$$ d'Alembert operator: $$\mathop\Box = \partial_\mu \partial^\mu$$ Bianchi identity: $$\partial^{[\mu} F^{\nu\alpha]} = 0$$   So far I have set all the definitions into the formula I have to show, but I only end up a lot of terms from antisymmetrisation and product rule. I also drew all what I have in , but I still cannot see how to tackle this problem.  Could somebody please give me a hint into the right direction? How can I install Visual Studio? How can I install Visual Studio?    I'd prefer to use it in Wine or PlayOnLinux if possible. How do I prove $F(a)=F(a^2)?$ Let $E$ be an extension field of $F$. If $a \in E$ has a minimal polynomial of odd degree over $F$, show that $F(a)=F(a^2)$.  let $n$ be the degree of the minimal polynomial $p(x)$ of $a$ over $F$ and $k$ be the degree of the minimal polynomial $q(x)$ of $a^2$ over $F$.   Since $a^2 \in F(a)$, We have $F(a^2) \subset F(a)$, then $k\le n$  In order to prove the converse:  $q(a^2)=b_0+b_1a^2+b_2(a^2)^2\ldots+b_k(a^2)^k=0$   implies   $q(a)=b_0+b_1a^2+b_2a^4\ldots+b_ka^{2k}=0$ Then   $p(x)|q(x)$, because $p(x)$ is the minimal polynomial of $a$ over $F$.  If I prove that $n|2k$ we done, since $k$ is odd, we have $n|k$ and $n\le k$ and finally $n=k$.  So I almost finished the question I only need to know how to prove that $n|2k$ It should be only a detail, but I can't see, someone can help me please?  Thanks What is a word for deliberate dismissal of some facts? Some people (me) would prefer the straight GNOME experience as opposed to the Unity style desktop offered in Ubuntu 17.10.  How can I get the standard GNOME desktop and interface? "Calling dibs" - what does it imply? The term "to have dibs on something" or "to call dibs on something" plays a recurring role in American film and television (e.g. ), so it gets exported a lot.   describes "dibs" as     [...] a common, "informal" convention to reserve or declare full or partial ownership of a community resource, such as a chair [...]   From the usages in the media I have seen, this convention also seems to contain some moral concept which is not described in dictionaries. For me, it looks like by calling dibs (or ), the caller actually receives the (implicit, moral) right to that resource, and this typically goes undisputed by their rivals.  Can you confirm the existence of this concept? Is this something that varies between groups of people (or maybe between regions), or is there a concensus on how to respond to this? For distinct prime numbers $p_1,...,p_n$, what is the Galois group of $(x^2-p_1)\cdots(x^2-p_n)$ over $\mathbb{Q}$?     This problem appears to be quite common, however my understanding of Galois theory is quite poor, and I have no idea how to do this problem. How to pick one number from each sorted list so that the difference between the minimum and maximum is as small as possible? Consider the vectorspace of all real $m \times n$ vectors and define an    inner product $\langle A,B\rangle = \operatorname{tr}(B^T   A)$.    "tr" stands for "trace"        which is the sum of the diagonal entries of a matrix.   How do you prove that $\operatorname{tr}(B^T   A)$ is indeed a inner product?  Kind regards Some text lines are italicized with no spaces between words Are repository updates secure?  As a bear of little brain from the developer side, I cannot understand why the repository list is http://security.ubuntu.com and the other http(unsecured) sites listed in /etc/apt/sources.list.  Without a certificate chain match this appears as "ask any responder for a list of packages to update" instead of "ask the ubuntu.com site..."  Can any network choose to spoof the update sites, and is this a common practice to provide a locally cached and vetted copy? Fontconfig warning: "/etc/fonts/conf.d/90-fonts-unfonts-core.conf" I am getting the following error frequently. (Example: when running zenity,firefox etc. commands / applications.)  Fontconfig warning: "/etc/fonts/conf.d/90-fonts-unfonts-core.conf", line 11: Having multiple values in &lt;test&gt; isn't supported and may not work as expected   Here is contents of file /etc/fonts/conf.d/90-fonts-unfonts-core.conf:  &lt;?xml version="1.0"?&gt; &lt;!DOCTYPE fontconfig SYSTEM "fonts.dtd"&gt; &lt;fontconfig&gt;     &lt;match target="font"&gt;         &lt;test name="family" qual="any"&gt;             &lt;string&gt;은 바탕&lt;/string&gt;&lt;string&gt;UnBatang&lt;/string&gt;                 &lt;string&gt;은 돋움&lt;/string&gt;&lt;string&gt;UnDotum&lt;/string&gt;                 &lt;string&gt;은 궁서&lt;/string&gt;&lt;string&gt;UnGungseo&lt;/string&gt;                 &lt;string&gt;은 필기&lt;/string&gt;&lt;string&gt;UnPilgi&lt;/string&gt;                 &lt;string&gt;은 그래픽&lt;/string&gt;&lt;string&gt;UnGraphic&lt;/string&gt;         &lt;/test&gt;          &lt;edit name="antialias" mode="assign" binding="strong"&gt;&lt;bool&gt;true&lt;/bool&gt;&lt;/edit&gt;         &lt;edit name="hinting"   mode="assign" binding="strong"&gt;&lt;bool&gt;false&lt;/bool&gt;&lt;/edit&gt;         &lt;edit name="autohint"  mode="assign" binding="strong"&gt;&lt;bool&gt;true&lt;/bool&gt;&lt;/edit&gt;         &lt;edit name="hintstyle" mode="assign" binding="strong"&gt;&lt;const&gt;hintslight&lt;/const&gt;&lt;/edit&gt;     &lt;/match&gt; &lt;/fontconfig&gt;   How to solve it?