Connecting Mac Book Pro 2017 to 2 Projectors via USB C

Just wondering can i connect my 13″ mac book pro to 2 hdmi projectors? I would like to extend the displays ( 3 display, 1 laptop screen and 2 projector screen) instead of duplicating if that is possible.

I have purchased one of USB-C Digital AV Multiport Adapter from apple, and if it can connect up to 2 additional extended dispalys, i will go for another one.

Thank you very much

Cheers!

Which book or books are being used in these lectures on Distributed Systems?

Kindly take a look at these lecture materials.

The instructor is suggesting to study books of Tanenbaum along with his supplied reading list. But, I am not finding any similarity of the content between the lectures slides and Tanenbaum‘s books and other reading materials.

Take for example the following slides from Lecture#2:

Where are these images sourced from?

Kindly, provide me some suggestions regarding any book or additional reading material.

Can I use Qantas Frequent Flier points to book flights with British Airways?

Qantas and British Airways are part of the OneWorld alliance; so air-miles/points, from British Airways get added to my Qantas frequent flier card.

I am looking to do a short haul flight from the UK to Ireland. I have a fair few Qantas frequent flier points. But Qantas does not offer any flights from the UK to Ireland. British Airways does.

So I am wondering if I am able to spend my Quantas points to book a British Airways flight? Since flights from UK to Ireland are pretty cheap, I suspect I have enough to just cover the flight entirely, if that were an option.

In Kurt Strebel’s book “Quadratic Differentials”, in Chapter 2, $$\S4$$, he begins by saying:

“Every analytic function $$\varphi$$ is a domain $$G$$ of the $$z$$-plane defines, in a natural way, a field of line elements $$dz$$, namely by the requirement that $$\varphi(z)dz^2$$ is real and positive. This means of course that $$\text{arg }dz = -\frac{1}{2}\text{arg }\varphi(z)\mod \pi$$, and thus $$dz$$ is determined, up to sign, for every $$z$$, where $$\varphi(z)\ne 0,\infty$$. One may then ask for the integral curves of this field of line elements.”

I am having some trouble with the language used here.

Note that I am not a differential geometer by training. My background in differential geometry mostly comes from Voisin’s first book on Hodge theory, Bott-Tu’s “Differential forms in Algebraic Topology”, and a bit of Kobayashi-Nomizu and a few snippets from elsewhere.

This book began its first chapter on background material on Riemann surfaces, and the point of the book seems to be to study the differential geometry of Riemann surfaces. Thus, I’m sure $$G$$ must be a domain in $$\mathbb{C}$$, $$z$$ is a holomorphic coordinate, and “analytic” probably means “complex analytic”.

Now, normally, for me, a line element should be a differential 1-form. Though, for him, since he says “field of line elements”, I’m assuming he uses “line element” to refer to a cotangent vector at a point, and thus his “field of line elements” should be taken to be a differential 1-form.

Okay, fine, but what would it mean for $$\varphi(z)dz^2$$ to be real and positive? In all analogous texts, $$dz^2$$ is really short for $$dz\otimes dz$$, ie a holomorphic section of the tensor square of the complex-valued cotangent bundle, but presumably for him he really means $$\varphi(z_0)(dz|_{z_0}\otimes dz|_{z_0})$$ as an element of the tensor square of the complex-valued cotangent space at $$z_0\in G$$? In this case, if we view $$dz = dx + idy$$ as a complex-valued differential 1-form, one might interpret his requirement as saying that $$\varphi(z_0)(dz|_{z_0}\otimes dz|_{z_0})(X\otimes X) := \varphi(z_0)\cdot dz(X)\cdot dz(X)\in\mathbb{R}_{>0}\qquad\text{for all X\in T_{G,z_0} }$$ where $$T_{G,z_0}$$ is the (real) tangent space at $$z_0$$, but then this condition will never be satisfied since if it holds for $$X$$, then it will fail for $$iX$$, where $$i$$ is the complex involution on $$T_{G,z_0}$$.

But maybe there is hope, as he explains that this means $$\text{arg }dz = -\frac{1}{2}\text{arg }\varphi(z)\mod \pi$$. However, this only confuses me more. For a complex number $$z_0 = r\cdot e^{i\theta}$$ with $$r\in\mathbb{R}_{>0},\theta\in\mathbb{R}$$, $$\text{arg }(z_0) := \theta\mod 2\pi$$. But what do they mean by the argument of a differential/cotangent vector? The best I can think of is: Identify $$T_{G,z_0}$$ with $$\mathbb{C}$$ via $$\frac{\partial }{\partial x}\mapsto 1$$ and $$\frac{\partial}{\partial y}\mapsto i$$, and then $$\text{arg }dz$$ is how much the $$\mathbb{C}$$-linear map $$dz|_{z_0} : T_{G,z_0} = \mathbb{C}\rightarrow\mathbb{C}$$ “rotates” the tangent vector (viewed as an element in $$\mathbb{C}$$). However, this still does not resolve the previous issue with $$\varphi(z)dz^2$$ being “real and positive”.

Lastly, what are “the integral curves of this field of line elements”? Usually one takes integral curves of a vector field. Are the $$dz$$‘s really tangent vectors?

If a warlock loses their Book of Shadows, are others able to use it before the warlock restores it? [on hold]

If someone loses their Book of Shadows at any level, can someone who finds it (or maybe who had stolen it) make use of the spells before the warlock can restore it during a rest?

Difficulty understanding the solution of heap problem in CLRS book?

I am reading the solution of this problem in CLRS:

Show that there are at most $$\lceil {n/2^{n+1}} \rceil$$ nodes of height $$h$$ in any $$n$$-element heap.

But I don’t understand the how to come up with the fact that $$(k-1)2^h + k(2^{h-1} + 1)$$ is less than the number of leaves. Thank you very much.

Authoring software used to create illustrated Pen&Paper book

At the risk of being somewhat off-topic (sorry but couldn’t find any conclusive info on this) …

What authoring software is recommended to create rich, illustrated books in a similar style as many of the Pen&Paper supplements published by companies like Wizards of the Coast? I’m looking for a software to create layout and design in a similar style, incl. illustrations, tables, quotes, info boxes, etc.

Before you now point me at the usual suspects such as Adobe InDesign, I’m asking this question exactly to find out whether any of the big publishing tools fit the requirement better than others.

Understanding the book “The Schrödinger Equation, Berezin,Schubin”

I’m trying to understand the book “The Schrödinger Equation” whose authors are Berezin & Schubin, but I’m not a matematician, so i would like to know which books i must read before to reach a comprenhension of chapter 2 of Berezin’s book as minimun, please if someone can help, i would be very thankfully, grettings from México.

by: Dotson
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Category: eBook
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The must-read User Interface Book? [closed]

I’m looking for the Book that explains the essentials of user interface and user experience design.

I read Beautiful Visualization and Designing Interfaces from O’Reilly. I think they are very good but, I’m still looking for the one.

Please provide your recommendation and why it stands as the essential reference.