I hope I am in the right place. I have a 2019 macbook pro, 13-inch, 2019, Two Thunderbolt 3 ports, 1.4 GHz Quad-Core Intel Core i5, 8 GB 2133 MHz LPDDR3, Intel Iris Plus Graphics 645 1536 MB I have been researching online the next step of optimizing my performance in Blender, but everything I'm finding is conflicting and outdated. Do I need an eGPU? What is the best option for a macbook with my specs?
I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap
Does anyone know how to find the radius of convergence of the series $\sum\ z^{n!}$, where $z$ is a complex number?  I tried to use the definition: $$\frac{1}{R}=\limsup\left|\frac{a_{n+1}}{a_{n}}\right|$$ but I wasn't successful. Let's say that there is a question asked in a bad manner, in a way that the question is missing. For example the user shows the code and doesn't explain very well which is the problem.    Usually someone starts digging in the OP mind posting comments and asking him for details. It may happen that the question gets edited and the OP edits it to a valid question.    Do you usually give the OP time to edit the question or you immediately vote to close it? When is Gauss' law not applicable? Why does the (relativistic) mass of an object increase when its speed approaches that of light? I'm reading Nano: The Essentials by T. Pradeep and I came upon this statement in the section explaining the basics of scanning electron microscopy.     However, the equation breaks down when the electron velocity approaches the speed of light as mass increases. At such velocities, one needs to do relativistic correction to the mass so that it becomes[...]   We all know about the famous theory of relativity, but I couldn't quite grasp the "why" of its concepts yet. This might shed new light on what I already know about time slowing down for me if I move faster.  Why does the (relativistic) mass of an object increase when its speed approaches that of light? 3rd iterate of a continuous function equals identity function Where can I find Obsidian in the Pocket Edition? I have looked everywhere for lava or obsidian in 0.7.1. I've looked all the way from top to bottom and all around, in about a 100 block diameter, but I can't find any. Where can I get some? Gray cone obscuring/clipping the 3D Viewport When looking at my objects in 3d view I'm seeing a gray cone that seems to be hiding other objects.   Can anyone help me turn this off and explain what it is please.  Screenshots attached. Most efficient way to check for DBNull and then assign to a variable? This question comes up occasionally, but I haven't seen a satisfactory answer.  A typical pattern is (row is a DataRow):   if (row["value"] != DBNull.Value)  {       someObject.Member = row["value"];  }   My first question is which is more efficient (I've flipped the condition):    row["value"] == DBNull.Value; // Or   row["value"] is DBNull; // Or   row["value"].GetType() == typeof(DBNull) // Or... any suggestions?    indicates that .GetType() should be faster, but maybe the compiler knows a few tricks I don't?  Second question, is it worth caching the value of row["value"] or does the compiler optimize the indexer away anyway?  For example:    object valueHolder;   if (DBNull.Value == (valueHolder = row["value"])) {}   Notes:   row["value"] exists. I don't know the column index of the column (hence the column name lookup). I'm asking specifically about checking for DBNull and then assignment (not about premature optimization, etc.).   I benchmarked a few scenarios (time in seconds, 10,000,000 trials):  row["value"] == DBNull.Value: 00:00:01.5478995 row["value"] is DBNull: 00:00:01.6306578 row["value"].GetType() == typeof(DBNull): 00:00:02.0138757   Object.ReferenceEquals has the same performance as "=="  The most interesting result? If you mismatch the name of the column by case (for example, "Value" instead of "value", it takes roughly ten times longer (for a string):  row["Value"] == DBNull.Value: 00:00:12.2792374   The moral of the story seems to be that if you can't look up a column by its index, then ensure that the column name you feed to the indexer matches the DataColumn's name exactly.  Caching the value also appears to be nearly twice as fast:  No Caching: 00:00:03.0996622 With Caching: 00:00:01.5659920   So the most efficient method seems to be:   object temp;  string variable;  if (DBNull.Value != (temp = row["value"]))  {       variable = temp.ToString();  } How to integrate Tikz code in SW? I'd like to know how to insert Tikz code in Scientific Workplace tex file. Since SW doesn't support Tikz directly, now I just create Tikz code in another tex editor and export as pdf. Then I convert pdf to images, and import images into SW. Multiple "order by" in LINQ How do I find out the user name and password for an existing account? How does the unit circle work for trigonometric ratios of obtuse angles? I know that the x coordinate is $cos (\theta )$ and the y coordinate is $sin (\theta )$. But I understand these in context of only acute angles? I don't understand why the unit circle definition works for other than acute angles? Somebody please provide me some good intuition. I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm interested in - I want to go deeper than that. We know that the real speed of light is actually not changing, the decrease in speed is just apparent. Material is mostly empty, the light will still travel with $c$ in the spacing. The rare atoms will disturb the light in some way. So I am interested in how the atoms affect the light. Photon absorption-emission theory Some textbooks that I read explain it in a way kind of like this: In a material the photons are absorbed by atom and then re-emitted a short time later, then they travel a short distance to the next atom and get absorbed&amp;emitted again and so on. How quickly the atoms in a material can absorb and re-emit the photon and how dense the atoms decides the apparent speed of light in that material. So the light appears slower because it has a smaller “drift speed”. Interference theory But recently I realize an alternative explanation: Atoms respond to the light by radiating electromagnetic wave. This “new light” interferes with the “old light” in some way that results in delayed light (advanced in phase), this can easily be shown by using simple phasor diagram. Consequently effectively the light covers a smaller phase each second, which gives the impression of a lower phase velocity. However the group velocity is changing in a complicated way. I think that the first explanation does not explain the change in phase velocity of light. if we consider light travelling into a slab of negative refractive index non-dispersive material, let’s say the light is directed perpendicular to the slab. The phase velocity’s direction will be flipped, but group velocity’s direction in the material will not change. Only the second explanation can explain the flipped phase velocity direction. I guess that the velocity that we get in the first explanation is actually belongs to the group velocity. It makes sense to me that the front most of the photon stream determines the first information that the light delivers. So the question is What really cause the phase velocity of light to be decreased?  &quot;drift velocity&quot; of photons (they aren't the same photons, they are re-emitted all the time) phase difference between absorbed and emitted light something else  And also, I still don't really understand detailed explanation of the absorption-emission process for small light's wavelength (for large lambda compare to the atoms spacing, the photons will be absorbed by the phonons). The dispersion relation that we know is continuous and also some material is non-dispersive, therefore the absorption process must occur in all frequency for a certain range. So definitely it doesn't involve the atomic transition, otherwise it will be quantized. My guess is that the relevant absorption process gets smooth out by the dipole moment. What makes the spectrum continuous? EDIT: link for dispersion relation: Rendered image doesn't show what Rendered Viewport shows... (pictures below) How do I refresh the package list? How to download/read only the first 80KB of a file? Stretch and scale CSS background Is there a way to get a background in CSS to stretch or scale to fill its container? I was doing some practice problems that my professor had sent us and I have not been able to figure out one of them. The given equation is:  $-y^2dx +x^2dy = 0$  He then asks us to verify that:  $ u(x, y) = \frac{1}{(x-y)^2}$  is an integrating factor.   I multiplied through to get:  $\frac{-y^2}{(x-y)^2}dx + \frac{x^2}{(x-y)^2}dy = 0$   However, the partial derivatives of these do not equal each other so I am a bit confused... "Pandora's Box" metaphors The majority of definitions give the same meaning - "Pandora's box" is a synonym for "a source of extensive but unforeseen troubles or problems."  Are there any other metaphors with the same meaning? Why don't players get extra xp for large encounters? Based on the table Encounter XP Multipliers from the Basic Rules' DM section, Page 57, when you're building encounters in 5E, you include an XP modifier depending on the number of creatures your PCs will be fighting: 1.5x for a pair, 2x for 3-6 and so on. However, the PCs only get the base XP as a reward.     This doesn't change the actual xp reward ... just your calculations of how difficult the encounter is.   Why is this? After acknowledging that battles vs multiple opponents are more difficult, why not reward them as such?