When I use $$$$ for mathematical text, there is too much vertical blank space between the mathematical text and the main text. How can I solve this problem?
How could I go about setting the 'above' and 'below' vspaces around the equation environment?  If the same could be done for the subequations or gather environments, this would be a bonus.
Issue with using ContactID as subscriber key in Marketing Cloud We have set up our Sales Cloud - Marketing Cloud integration where Contact ID is used as the subscriber key.  What we've noticed is when we have contact ID as the subscriber relationship on our sendable data extension, Marketing Cloud will reference contact ID on All Subscribers list and if data matches, it will send to the email address listed on All Subscribers and not to the one on the data extension.  This has caused us headaches for a number of reasons:   Email addresses always change so the one on All Subscribers is out-of-date. Whilst preference center can update a recipients address and write this back to All Subscribers that not how most addresses are updated by the user Email address is typically updated in Sales Cloud instance and migrated to Marketing Cloud either through imports or via synchronized data extensions.  It does not map directly to All Subscribers. Marketing Cloud users assume (and quite rightly) the address listed on the data extension is what will be used in the send. Not the one on All subscribers.   Anyone else experienced this? Any solution to resolve this issue? Does infinity exist in physical systems? Sometimes people fail at asking a question by being too broad, unclear like . So I'll take a stab at what I believe to be the same question, but more concise and clearly stated:     Does infinity exist in either terms of structure, parameters, or   measurement in any physical systems?   Can infinity have any real connection with reality?  Or is infinity purely a mathematical concept just used by physicists as a convenient way to describe the very large, an approximation?  I have heard that if you model a physical system (), and you run into infinity as a solution, then you have either made an error in your calculations or your model is wrong. Please help me prove this. I'm not sure how to apply the parallelogram law to the norm. There several types of graphics files. In no particular order .jpeg .eps .pdf .png .tif .jif (and no doubt others). Some work with latex, dvips and some work with pdflatex. How am I supposed to know which?  Just to confuse matters, metapost produces .eps but I can use these with pdflatex as long as I put in a four line incantation.  Can anyone explain this? How to fix "-5 No address associated with hostname error" while updating? Quadrilateral problem with midpoints of diagonals For an arbitrary convex quadrialteral $ABCD$:   $$AF=FC, BE=ED, GI=IH$$  Prove that points $F$, $E$ and $I$ are collinear.  I was able to solve the problem by using vectors and I think that it can be also solved analytically but I wanted some more elegant proof, more in the spirit of Euclid. This question pertains to L1 &amp; L2 regularization parameters in Light GBM. As per official documentation:  reg_alpha (float, optional (default=0.)) – L1 regularization term on weights.  reg_lambda (float, optional (default=0.)) – L2 regularization term on weights  I have seen data scientists using both of these parameters at the same time, ideally either you use L1 or L2 not both together.   While reading about tuning LGBM parameters I cam across one such case: Kaggle official GBDT Specification and Optimization Workshop in Paris where Instructors are ML experts. And these experts have used positive values of both L1 &amp; L2 params in LGBM model. Link below (Ctrl+F 'search_spaces' to directly reach parameter grid in this long kernel)      I have seen same in XGBoost implementations.  My question is why use both at the same time in LGBM/XGBoost.  Thanks. Passport validity for Canada I am traveling from Boston to Canada by cruise ship. The first port of arrival is on July 30 and the last port in Canada is on August 4. Then I'm flying on August 5 from Montreal to California. My passport is valid until August 20th. Will I have a problem? If $\cos x=\cos y$ and $\sin x=\sin y$ is $x=y$ or $x=2\pi,y=0$ or $x=0,y=2\pi$? $x,y\in[0,2\pi]$ I know that if $\sin x=\sin y$ then $x=n\pi+(-1)^ny$  and $\cos x=\cos y$ implies that $x=y+2k\pi$ or $x=-y+2l\pi$. Since the latter does not fit the form above $x=y+2k\pi$ which implies that $k=0,1,-1$. Hence, we have x=y or $x=2\pi,y=0$ or $x=0,y=2\pi$. Could Dark Matter form black hole? Some people speculate that the mysterious dark matter in the universe could be tiny black holes. But on the other side, could dark matter particles attract each other by gravity and finally form a black hole? Since dark matter is even more abundant than normal matter, the dark matter black hole should not be rare. SSH tunneling error: "channel 1: open failed: administratively prohibited: open failed" When I open this ssh tunnel:  ssh -nXNT -p 22 localhost -L 0.0.0.0:8984:remote:8983   I get this error when trying to access the HTTP server running on localhost:8984:  channel 1: open failed: administratively prohibited: open failed   What does this error mean, and on which machine can you fix the problem? What are Ctools plugin (content type, access, etc), and how does one create them? What are Ctools plugins, and how does one create them? Related to : The question specifies morphs, but I wondered if this was true for Manifest as well? As Manifest is not an ability on the card, does  prevent it from being turned face up for its mana cost? Story identification: Old man has hacker neighbor who mysteriously dies Does anyone know this story? It was a novelette published with another one (I don't remember what it was) in . The premise was that the narrator is an old man whose neighbor, a hacker, dies under mysterious circumstances. A younger woman who is an expert in computer security is hired by the police to investigate what happened, and she has a fling with the narrator. After a while she dies as well, and the narrator realizes that it is an evil force that comes through electric lines is responsible for the killings. The title has interesting formatting in that it ends with a square (much like a command prompt cursor: [_] ) "He was neither seer nor prophet" How would you explain the absence of an article? Here's a fragment from Jack London's Star Rover:     Wordsworth knew. He was neither seer nor prophet, but just ordinary man like you or any man. What he knew you know, any man knows. But he most aptly stated it in his passage that begins "Not in utter nakedness, not in entire forgetfulness.   To the best of my — admittedly sketchy — knowledge of grammar, the second sentence should read neither a seer nor (a) prophet, but just an ordinary man. Even if we accept the seer and the prophet as "poetic entities" ("father and son," "robber and robbed," "man to man," or whatever), logic would still dictate that ordinary man should be preceded by an an.  It is a well-known fact that Jack London's usage wasn't always up to par; his grammar, on the other hand, was always top-notch.  Logically, the sentence is grammatically incorrect (correct me if I'm wrong: no pun intended).  Illogically, it reads smoothly: intuitively, a native speaker understands that there's nothing wrong here.  However, those to whom English is not the first language cannot be expected to be intuitive in this case and would want an explanation. Any suggestions? Difference between pre-increment and post-increment in a loop? Is there a difference in ++i and i++ in a for loop? Is it simply a syntax thing? Hyperlinks to web sites using anchors sometimes don't work Mac OS X Darwin: how to reset admin password? Today I bought an ibook G4 from a garage sale. The people who sold it to me didn't know the password for the 2 accounts on it. Apparently it was the guys late father's laptop. Any suggestions on how to get into the laptop and set a new admin account and password? Who was/were the first Jedi? What happened to Jarvis at the end of Avengers: Age of Ultron