text:
# If elements with principal quantum number n > 4 were not allowed in nature, the number of possible elements…

Q: If elements with principal quantum number n > 4 were not allowed in nature, the number of possible elements would be

(A) 60

(B) 32

(C) 4

(D) 64

Ans: (A)

Sol: The maximum number of electrons in an orbit = 2n2

If principal quantum number n > 4 were not allowed , then the number of maximum electrons that can be in first four orbits are :

$\large = 2(1)^2 + 2(2)^2 + 2(3)^2 + 2(4)^2$

= 2 + 8 + 18 + 32 = 60

The number of possible elements would be 60

format: plain


text:
Negative Pressure Test

In this document we describe the load case Negative pressure test available in the Oliasoft application.#

Negative pressure test is a collapse load case, where the unknown is the internal pressure profile of the tubing$^1$.

NOTE!
$^1$ We denote any tubular by tubing. All calculations encompass both tubings and casings.

Summary#

The pressure profile consists of the hydrostatic salt water pressure to $l$ meters below the mud line, plus an additional pressure drop, and the hydrostatic mud pressure below.

Inputs#

The following inputs define the negative pressure test load case

1. The true vertical depth (TVD) along the wellbore as a function of measured depth. Alternatively, the wellbore described by a set of survey stations, with complete information about measured depth, inclination, and azimuth.
2. The true vertical depth/TVD of
1. The rig RKB, TVD$_{RKB}$.
2. The wellhead/BOP interface, TVD$_{WH/BOP}$.
3. The TVD from rotary table to mud line, TVD$_{RT}\ to\ _{ML}$.
4. The hanger of the tubing, TVD$_{hanger}$.
5. The shoe of the tubing, TVD$_{shoe}$.
3. Length below mud line to use seawater gradient, $l_m$, default is $l_m$ = 1000ft ($\approxeq$ 300m)
4. Pressure drop, $p_n$, default to $p_n$ = 500 psi ($\approxeq$ 3.4 MPa)
5. The mud weight/density, $\rho_m$
6. The salt water density, $\rho_{sw}$

Calculation#

The internal pressure profile, parametrized by TVD, of the tubing is then given by

$p_i = \begin{cases} \rho_{sw}\, g\, \text{TVD} - p_n, \quad &\text{TVD} \leq \text{TVD}_{\text{RT to ML}} + l_m, \\ p_{\text{ml+l}_m} + \rho_m\, g\, \left(\text{TVD} - (\text{TVD}_{\text{RT to ML}} + l_m) \right), \quad &\text{else}, \end{cases}$

where $g$ is the gravitational constant, and $p_{ml+l_m}$ is the hydrostatic salt water pressure at the wellhead plus $l_m$ including the pressure drop, i.e.

$p_{\text{ml+l}_m} = \rho_{sw}\, g\, (\text{TVD}_{\text{RT to ML}} + l_m) - p_n$


text:
## Bundle Requirements - x86 VS x64

Hi! I'm in the process of testing all my bundles that I use on Windows XP Pro x86 in Windows 7 Pro x64. Usually the bundles works right away. But I'm having problems with the bundle requirements part. For example, I just created a bundle for "Adobe Acrobat Pro 10.0.1" which verify this:

Registry Keys exists - NO
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Curr entVersion\Uninstall\{AC76BA86-1033-F400-7760-000000000005}
AND
Achitecture = 32

This works great on 32 bits. But when I install this bundle on a 64 bits system, it install correctly but my bundle requirements then fail. Because now it should be something like:

Registry Keys exists - NO
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\ Windows\CurrentVersion\Uninstall\{AC76BA86-1033-F400-7760-000000000005}
AND
Achitecture = 64

So my question now his how can I set up my bundle requirements so that it can detect if I'm on a x86 or a x64 system and verify the proper registry branch? Is it even possible on 10.3.1? Right now I create 2 bundles for the same application. One for the x86 and the other for the x64!

Thanks in advance for the help!


text:
Short and Sweet Calculus

## 3.3 Graphing the Derivative

If we have the graph of $$y=f(x)$$, we can draw a sketch of the graph of $$y=f'(x)$$ by estimating the slope of the tangent to the graph of $$f$$ at each $$x$$ value. We then plot the points $$(x,f'(x))$$ in the $$xy$$-plane and connect them by a smooth curve whenever possible. This curve represents the graph of $$y=f'(x)$$.

• When you seek to graph the derivative, it is often easiest to first identify the places where the slope of the tangent line is 0. Those are the places where you can hope the sign on the derivative may change.

Example 3.4. The graph of $$y=f(x)$$ is shown below. Give a rough sketch of the graph of $$y=f'(x).$$

Solution

The tangent to the curve is horizontal at $$x=0$$ and $$x=2.$$ $\begin{cases} x<0 & \text{tangent line makes an acute angle with positive \ensuremath{x} axis}\Rightarrow f'(x)>0\\ 0<x<2 & \text{tangent line makes an obtuse angle with positive \ensuremath{x} axis}\Rightarrow f'(x)<0\\ 2<x & \text{tangent line makes an acute angle with positive \ensuremath{x} axis}\Rightarrow f'(x)>0 \end{cases}$ Specifically, the slope of the tangent line at $$x=-1$$ is $m_{\text{tan}}=\frac{3}{1}\Rightarrow f'(-1)=3.$ The slope of the tangent line at $$x=1$$ is $m_{\text{tan}}=\frac{-1}{1}\Rightarrow f'(1)=-1.$ At $$x=3$$ $m_{\text{tan}}=\frac{-3}{-1}\Rightarrow f'(3)=3.$ If we connects these points: $(-1,3),(0,0),(1,-1),(2,0),(3,3),$ we can sketch the graph of $$f’$$ (Figure 3.3).


text:
## Anyway to make nercromage misslie change as level progresses

Post here about all aspects of D2 mod making whether it's information, problems or whatever. Please specify whether your post is relating to Classic D2 or the Expansion.

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Anyway to make nercromage misslie change as level progresses

I'd like to make each necromage have their missiles change from a bolt spell to a better spell all the way to a really powerful missile but how do I go about doing this?

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Sorry, I didn't really explain what I meant. I want each mage to start with a bolt spell and as you level skeleton mastery, their missiles would improve and change to a different missile.

gogodanny
Arch-Angel
Posts: 1223
Joined: Mon Nov 06, 2006 2:14 am
Location: Graz, Austria

### Re: Anyway to make nercromage misslie change as level progre

Not sure, but I guess it's hardcoded.

Perhaps what's possible, is to change the likelyhood certain skills are used at certain levels.
Meaning: At lvl 1 Each mage has a 100% Chance to use skill 1 and 0% at 2,3,4 and those change every 2-4-6? levels?
Think of Mercenaries who use their skills at different ratios depending on their level and slvl.
Or think of Shadowmasters who can use all skills.

However what makes this so hard (if not impossible) is that mages use: Lightning/fire/Ice/Poison spells. So basically that's already 4 different skills and I don't think 16 Skills is possible on 1 monster.

I may be wrong though and have wasted 20 seconds of your life ;-)
only 2 things are infinite - the universe and human stupidity ... although i'm not sure yet about the universe (c) Albert Einstein
http://miyoshino.la.coocan.jp/eswiki/?p ... hot051.jpg (WOW)

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

It's only a single skill. Necromagemissile has a hardcoded function which makes you shoot one of four missiles depending on your S4 or S5 body appearance (in case of the necromages, the S4\S5 are reperesented by their orbs).
The only way I can think of to reach what you want is this:
- In your data\monster folder find SK. now, look for all of the "-WLHTH" dcc files. Copy them and rename them to -RNHTH (antrenamer helps a lot)
- In your data\monster folder find again SK and do the same with COF files.
- Use Animdata Editor to clone the SKWLHTH row and rename the cloned one to SKRNHTH (the new AI you're going to use runs a lot: this DCC\COF part is to avoid flickering\disappearing anims with your mages!)

- Change "inventory" column of necromages and set it to 1
- Change the Aip's of your necromages as follows:

Code: Select all

Aip1: 20/20/20
Aip2: 36/36/20 (the 20 in the aip2(H) indicates the leash distances. Should you reduce it, your mages will stick closer to you
- Delete your necromages skills from both monstats.txt and skills.txt(sumskill#). That's because the Shadow Master's AI can also use skills via items or monprop, as you're going to do
- Under one of the skill# column, insert this[1]:

Code: Select all

Skill1: Attack
Sk1Mode: NU
sk1vl: 1

- In monstats2.txt, find your necromage row and insert 999 under the MeleeRng column[1]. Also, set 1 under the "RN" column
- Clone NecromageMissile from skills.txt
- Set the AiType of both your necromage skill and the new one to 5 (ranged spells for the shadow master's ai)
- Clone Necromage1-4 from missiles.txt[2] and edit them as you like. After you've done it, you'll assign the first of the cloned missiles (ID order) to the srvmisile and cltmissile of your skill. Remember that the order to follow is this: Poison, Ice, Fire, Lightning or you might end up with lightning mages throwing fire missiles
- Clone the ring row from misc.txt and change its itemcode from "rin" to something else.Do this twice (let's call the new codes dk8 and dk9).
- In UniqueItems.txt, clone an unique ring twice, delete every magic properties it has and write 1 under "nolimit". After that, change its code once from rin to dk8 and once from rin to dk9. Add +1 to NecromageMissile for dk8, and +1 to your new skill for dk9, like this

Code: Select all

(dk8 ring skill)
prop1: oskill
par1: necromagemissile
min1\max1: 1\1

(dk9 ring skill)
prop1: oskill
par1: NEWnecromagemissile (your new skill name)
min1\max1: 1\1

- In MonEquip, create 2 new rows for your necromages and assign them your ring as follows

Code: Select all

(row1)
monster: necromage
level: 1     (level = the level of the skill that summons the monster)
item1: dk8
loc: rrin
mod1: 7 (= unique quality --> your dummy ring with the old necromagemissile)
eol: 0
(row2)
monster: necromage
level: 10  (level = the level of the skill that summons the monster)
item1: dk9
loc: rrin
mod1: 7 (= unique quality --> your dummy ring with the new skill)
eol: 0

If you want your necromages to gain skill levels as they progress, you can do this:

Code: Select all

(in skills.txt, in the Raise Skeletal Mage's row)
aurastat1: item_allskills
aurastatcalc1 : lvl (so basically they get +(skill level) to their skills

OR, in order to get closer to what you want to achieve

aurastatcalc1: (skill('Skeleton Mastery'.lvl)) --> they get bonus to all skills(i.e bonus to the skill they use) depending on your mastery level

[1] This fixes the odd behavior for which ShadowMaster using pets attack in melee even if they're supposed to be spellcasters.
viewtopic.php?f=8&t=62883

[2] In this example I made you clone the necromage1-4 missiles, but you can use the missiles you prefer, provided you follow the elemental order described above: what's relevant to the purpose of your necromages is the skill srvdofunc, as thats the one that allows the missiles to match the elemental type (i.e body part)

I hope it helps! Let me know if you still need aid

@gogodanny:
Mercenaries use their skills depending on what you specify in Hireling.txt: It controls which skill(s), which mode, which level, which bonus-per-level and which probability [However, you can also assign them the ShadowMaster's AI and have them fully customizable. Just think that they're equippable. They could also use skills from items ]
The Shadow Warrior mimics your left\right skills because the AI tells her to do so, while the Shadow Master can only use skills with an AiType set (1-13) in skills.txt . Her AI can also include, in their skill list:
- skills from monstats.txt
- skills from skills.txt (sumskill#)
- skills from items (as exemplified above)
- skills from MonProp
- skills from player himself, provided the skill you assign to the player character have an aitype (check the Assassin's vanilla skills: they're all aityped ). This is why if you're going to make a skill using pet you should avoid setting an aitype on your character class skills, unless you want it to be a replica of yourself like the Shadow Master is

EDIT: Typos

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

@Ogodei

Holy {filtered} thanks!!! I mean that will take me some time as my modifying skills are pretty basic but I shall give it a shot and let you know where I get I really appreciate the effort you put into your response

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Okay so I do have a problem before I start this whole thing. I don't seem to have a SK folder in the monsters folder.

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

Hi

Open D2Data.mpq with a MPQ editor. You'll find the SK folder in data\global\monsters

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Ahh okay thanks. Now I don't really understand how to use the Animdata editor, am I extracting it, loading the .txt file in D2Excel editor cloning it, saving it to the data file and then replacing it back with all the d2 files using MPQEditor?

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

That's not necessary: you need to place your new AnimData in your data/global folder.

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

For setting the RN to 1 I don't have just a siblge RN column, but I have a mRN and lRN do I set those to 1?

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

Yeah, sorry set mRN to 1

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Thanks ;D

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

You're welcome. Let me know if I can assist further

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Also how can I clone the NercroMage Missile skill? Cant figure out how to do it using D2Excel

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

Try using AFJ Sheet editor. That's the one I use.
While using that program, open the skill.txt file, find "Necromagemissile", left click on the row's number, right click -> row operations -> clone row: it will appear at the very end of the txt.

EDIT: AFJ's sheet editor link here:

Last edited by Ogodei on Wed Aug 23, 2017 11:46 pm, edited 2 times in total.

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Heh damn you know your stuff ;D thanks again.

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Okay so I'm at the point of clong the missle in the missile.txt but how exactly will this make it go from a spell missile, progress all th way to some strong bigger missile (i.e ice bolt-ice blast-glacial spike and finally ice orb)

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

Then you have to clone all of the necromage missiles thrice more : As described above, necromage missile uses 4 different type of missiles, one per element. Try starting with the one that comes after the Ice Bolt: Ice Blast. Change the celfile column of your cloned icebolt to "IceBlast" . After that, you need to assign the missile to a skill: In your cloned necromage skill, write the first one of the new necromage missiles

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Alright I understand. How would I be able to apply it to level though? (I.e ice bolt 1-5 ice blast 6-10 glacial 11-15 and orb 16+?)

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

You will use the custom rings as I explained above

the "level" in monequip determines the minimum level of the skill required for the ring to spawn on the necromages. Higher level rings will always overwrite the lower ones, so basically you set your spell progression in that way.

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

Ahh okay gotcha

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

okay so now where am I putting in the missile id info? Nercromissile skill for srvmisile and cltmissile

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

Yes. It's illustrated above step by step

Jaygore
Posts: 75
Joined: Fri Mar 01, 2013 4:33 am

### Re: Anyway to make nercromage misslie change as level progre

But I don't understand, am I just using one code for srvmissile and cltmissile or should I have made multiple clones of Nercromissile in skills.txt for each missile I want them to have?

Ogodei
Champion of the Light
Posts: 321
Joined: Thu Mar 10, 2016 8:31 am

### Re: Anyway to make nercromage misslie change as level progre

You need 1 skill every 4 new missiles you create.

In your new necromage skill, write the first of your new 4 missiles (name taken from missiles.txt) in both srvmissile and cltmissile (skills.txt)


text:
Regions on a sphere that avoid a fixed point set

Let $P$ be a finite set of points on a unit-radius sphere $S$ in $\mathbb{R}^3$. Treat $P$ as a fixed pattern that can be rigidly slid around $S$ as a unit (no reflection).

Let $R$ be a subset of $S$. Say that $P$ fits in $R$ if there is some placement of $P$ such that each point of $P$ is strictly in the interior of $R$. Finally, say that $R$ avoids $P$ if $P$ cannot fit in $R$.

For example, let $P$ be the $n{=}5$ points shown below; I've drawn in the convex hull (blue) and an enclosing circle (red) for perspective. A hemisphere does not avoid $P$, because $P$ easily fits in a hemisphere.

My question is:

Q. What is the largest-area region $R$ that avoids a given set $P$?

Here area is the measure of $R$.

The convex hull of $P$ avoids $P$ (above, the hull is the illustrated quadrilateral formed of (blue) geodesic arcs), because the vertices of the hull are not strictly interior to the hull. A larger region that avoids $P$ is the smallest enclosing disk, whose boundary is outlined in red above. But I believe this is not the largest $R$ that avoids this particular $P$, for a slightly larger disk with an annular hole to "capture" the interior $5$th point has larger area.

The problem feels different if (a) $P$ fits in a hemisphere, and (b) all points of $P$ lie on its convex hull.

It is likely this question has been considered before, in which case I'd appreciate a reference. The same question may be asked for spheres in $\mathbb{R}^d$ for arbitrary $d$.

Update (23Oct15). I posed this question at the Canadian Conference on Computational Geometry, and a participant, Alexandru Damian, proved that, for an $n$-point set $P$, the area of an avoiding set cannot be larger than $\frac{n-1}{n} A$, where $A$ is the area of the sphere. The argument is sketched here (PDF download). The bound is tight for $n=2$ antipodal points.

• Not sure about the general case, but something related to this came up towards the end of a recent paper "Connectivity of confined 3D networks with anisotropically radiating nodes." O. Georgiou, C. P. Dettmann and J. P. Coon, IEEE Trans. Wireless Commun. 13, 4534-4546 (2014). In order to ensure connectivity for randomly oriented transmitters in a cube domain, we needed the $P$ with the smallest number of points which avoids the sphere minus an octant. It seems the answer is $14$, arranged as a gyro-elongated hexagonal bipyramid. – user25199 Jun 2 '15 at 13:38
• It's not true in general that the convex hull of $P$ avoids $P$. If $P$ is four points at the vertices of a regular tetrahedron, then the convex hull of $P$ is the whole sphere, which obviously does not avoid $P$. This makes me suspicious about more general cases of $P$ and its convex hull. – Dylan Thurston Jun 2 '15 at 14:16
• @DylanThurston: Good point. So perhaps only if $P$ lies in a hemisphere does the hull make sense. – Joseph O'Rourke Jun 2 '15 at 15:12


text:
# Algebra and Geometry Seminar

### Info

The seminar runs on Thursdays at 2:10pm–3:00pm in Carver Hall 401 at Iowa State University. Talks are 50 minutes including questions. Themes include

• associative algebras and commutative rings,
• representation theory and Lie theory,
• connections to combinatorics, geometry and physics.

### Talks

January 30, 2020
The Hopf Algebra of Symmetric Functions
One of the most important goals in representation theory is to classify all indecomposable representations and morphisms between them. The ring Λ of symmetric functions plays an important role in the representation theory of the symmetric group and general linear groups and it has various bases whose elements are in one-to-one correspondence with Young diagrams. They very much help in classifying all indecomposable representations of representation theory of the symmetric group and general linear groups. Λ has a Hopf algebra structure designed in a very nice combinatorial approach. We will focus on the explicit combinatorial description of the structure of this Hopf algebra.
December 12, 2019
Symmetric categories in characteristic $$p$$
Shlomo Gelaki (ISU)
I will discuss new developments in the classification of symmetric tensor categories in positive characteristic.
December 5, 2019
Bases of infinite-dimensional tensor product representations of $$\mathfrak{osp}(1|2n)$$ and $$\mathfrak{gl}(2n)$$
Dwight A. Williams II (UT Arlington)
We consider the complex orthosymplectic Lie superalgebra $$\mathfrak{osp}(1|2n)$$ acting on the super vector space $$\mathbb{C}[x_1, x_2, \dots, x_n] \otimes_{\mathbb{C}} \mathbb{C}^{1|2n}$$, where $$\mathfrak{osp}(1|2n)$$ acts via differential operators on polynomials $$\mathbb{C}[x_1, x_2, \dots, x_n]$$ (Weyl representation). The resulting tensor product representation decomposes into the direct sum of two simple infinite-dimensional submodules. We provide an explicit basis for each of these modules by introducing certain operators, including a "fake Casimir". This is joint work with D. Grantcharov.
November 14, 2019
Gelfand-Zeitlin Integrable Systems:
Where linear algebra, geometry, and representation theory meet
Mark Colarusso (University of South Alabama)
In the 19th century, physicists were interested in determining the conditions under which the equations of motion for a classical mechanical system could be found by integrating a finite number of times. Such a system was said to be completely integrable. Using symplectic geometry, we can generalize the notion of an integrable system beyond the realm of physics and into Lie theory and representation theory. Such "abstract" integrable systems can be used to geometrically construct infinite dimensional representations of Lie algebras.

In this talk, I will discuss a family of integrable systems, the Gelfand-Zeitlin systems, that arise from purely linear algebraic data. For an $$n\times n$$ complex matrix $$X$$, we consider the eigenvalues of all the $$i\times i$$ submatrices in the top left hand corner of $$X$$. These are known as Ritz values and play an important role in numerical linear algebra. We will see how questions about Ritz values naturally lead to the construction of the Gelfand-Zeitlin integrable systems. I will explain results about the geometric properties of these systems and indicate how they answer questions of Parlett and Strang about Ritz values. I will also show how this research provides the foundation for the geometric construction of a category of infinite dimensional representations of certain classical Lie algberas using the theory of quantization.
November 7, 2019
Youngsu Kim (U. Arkansas)
Linkage is a classical topic in algebraic geometry and commutative algebra. Fix an affine space A. We say two subschemes X, Y of A are (directly) linked if their union is a complete intersection in A while X and Y having no common component. Two linked subschemes share several properties in common. Linkage has been studied by various people, Artin-Nagata, Peskine-Szprio, Huneke-Ulrich, to name a few. In 2014, Niu showed that if Y is a generic link of a variety X, then $$LCT (A, X) \le LCT (A, Y)$$, where LCT stands for the log canonical threshold. In this talk, we show that if Y is a generic link of a determinantal variety X, then X and Y have the same log canonical threshold. This is joint work with Lance E. Miller and Wenbo Niu.
October 31, 2019
Representation Theory of the Space of Holomorphic Polydifferentials
Let X be a smooth projective curve over an algebraically closed field and let G be a finite group acting on X. The space of holomorphic m-polydifferentials is defined to be the space of global sections of the m-fold tensor product of the sheaf of relative differentials with itself. This space provides a representation of G and a classical problem is to determine the decomposition of the space of holomorphic polydifferentials as a direct sum of indecomposable representations. We discuss work on this problem in the case when k has prime characteristic p and G has cyclic Sylow p-subgroups.
October 24, 2019
Matrix factorizations in commutative algebra and algebraic geometry
Michael Brown (University of Wisconsin)
In 1980, David Eisenbud introduced a gadget called a matrix factorization as a tool for studying the homological properties of modules over hypersurface rings (i.e. rings of the form R/(f), where R is a regular local ring and f is a nonzero element of R). Decades later, it was discovered that matrix factorizations also play a key role in algebraic geometry, for instance in homological mirror symmetry and noncommutative Hodge theory. In this talk, I will give an overview of Eisenbud's classical theory of matrix factorizations, and I will give a glimpse of some modern applications of matrix factorizations beyond commutative algebra.
October 17, 2019
Spherical degenerate double affine nil-Hecke algebras
Jonas Hartwig (ISU)
I'll explain the words in the title and their relation to representation theory of the general linear Lie algebra.
October 10, 2019
Quadratic Gorenstein rings, Lefschetz elements, and the Koszul property
Henry Schenck (ISU)
I’ll discuss some fundamental objects in commutative algebra, in particular, Gorenstein and Koszul algebras. One way to construct such objects is via idealization, but to guarantee that the idealization has the desired properties, we need certain condtions to hold. I’ll discuss how one can use the Lefschetz property to guarantee this.
October 3, 2019
Singularities and syzygies of secant varieties of curves
Wenbo Niu (U. Arkansas)
Consider a projective nonsingular algebraic curve embedded in a projective space by a very ample line bundle. The (k + 1)-secant k-plans to the curve span the k-th secant variety of the curve. There has been a great deal of work in the last three decades to understand properties of such secant varieties, including their local properties, defining equations, and syzygies. In this talk, I will present a recent study on secant varieties of curves by showing the interaction between singularities and syzygies. The main idea in the talk is that if the degree of the embedding line bundle increases, then the properties of secant varieties become better. This is a joint work with L. Ein and J. Park.
September 26, 2019
Hopf (co)quasigroups
Alex Nowak (ISU)
A Moufang loop is a set under binary multiplication which possesses a unit element and two-sided inverses; the multiplication also obeys the nearly associative" law $$(zx)(yz)=z((xy)z)$$. In the spirit of Lie theory, Klim and Majid defined Hopf quasigroups and Hopf coquasigroups --extending Moufang loops to categories of vector spaces-- in order to capture algebraic aspects of $$S^7$$, the unit octonions. We will show how to construct, out of a finite Moufang loop $$Q$$ and a subgroup $$H\leq \text{Aut}(Q)$$, a Hopf coquasigroup that is genuinely quantum" (neither commutative nor cocommutative) and genuinely quasi" (noncoassociative). Through this example, we'll illustrate some features of Hopf (co)quasigroup representation theory.
September 19, 2019
Morse theory and persistence
Michael Catanzaro (ISU)
Morse theory provides an elegant and powerful method for studying the topology and geometry or manifolds by means of smooth functions. In this talk, we’ll start from the beginnings of Morse theory and show its utility through a variety of examples. We’ll survey how Morse theory has been used in the past, and how it can be used to understand persistent homology, a new area of data science. The first half is especially intended for graduate students, and we won’t assume much beyond multivariable calculus.
September 12, 2019
Crystal Structure on Gelfand-Zeitlin-Zhelobenko Patterns
O'Neill Kingston (ISU)
In this talk, we begin by presenting the crystal structure of finite-dimensional irreducible representations of the Lie algebra $$\mathfrak{sl}_n$$ in terms of Gelfand-Zeitlin patterns. We then define a crystal structure using the set of symplectic Zhelobenko patterns, parametrizing bases for finite-dimensional irreducible representations of $$\mathfrak{sp}_4$$. This is obtained by a bijectionwith Kashiwara-Nakashima tableaux and the symplectic jeu de taquin of Sheats and Lecouvey. We offer some conjectures on the generalization of this structure to rank $$n$$.
September 12, 2019
An Alternating Analogue of $$U(\mathfrak{gl}_n)$$ and Its Representations
Erich Jauch (ISU)
The universal enveloping algebra of a Lie algebra $$\mathfrak{g}$$ is of utmost importance when studying representations of $$\mathfrak{g}$$. In 2010, V. Futorny and S. Ovsienko gave a realization of $$U(\mathfrak{gl}_n)$$ as a subalgebra of the ring of invariants of a certain noncommutative ring with respect to the action of $$S_1\times S_2\times\cdots\times S_n$$ where $$S_j$$ is the symmetric group on $$j$$ variables. With some connections to Galois Theory, an interesting question is what would a similar object be in the invariant ring with respect to a product of Alternating groups? We will discuss such an object and some results about its representations. In particular, we will focus on the case of $$n=2$$.
September 5, 2019
Bialgebra flag orders and rational Cherednik algebras
Jonas Hartwig (ISU)
Rational Cherednik algebras have a representation due to Dunkl-Opdam by differential operators making them look similar to a recently introduced class of principal flag orders due to Webster. We show that there is a common generalization using bialgebras. Via Morita equivalence this unifies the Gelfand-Tsetlin representation theory of type A enveloping algebras (and Yangians, finite W-algebras, Coulomb branches) with that of Cherednik algebras and conjecturally other Hecke algebras. We state some open problems regarding these bialgebra Galois orders.


text:
# Chung Kevin's favorite - (2)

$\begin{array}{c}(26 & = & 5+6+7+8 \\ 27 & = & 8+9+10 \\ 28 & = & 1+2+3+4+5+6+7 \\ 29 & = & 14+15 \\ 30 & = & 4+5+6+7+8 \\ 31 & = & 15+16 \end{array}$

If you see the above numbers , they can be represented as a sum of some consecutive numbers.If 32 can be expressed as $\displaystyle\sum_{i=1}^n a_i$ , where $a_1,a_2,a_3, \dots a_n$ are some consecutive positive numbers , compute $\displaystyle\prod_{i=1}^n a_i$.

Note: If you think that 32 is not lucky enough to have such representation , input the answer as 999.

×


text:
# filename (n) - Linux Man Pages

## NAME

filename - File name conventions supported by Tcl commands

## INTRODUCTION

All Tcl commands and C procedures that take file names as arguments expect the file names to be in one of three forms, depending on the current platform. On each platform, Tcl supports file names in the standard forms(s) for that platform. In addition, on all platforms, Tcl supports a Unix-like syntax intended to provide a convenient way of constructing simple file names. However, scripts that are intended to be portable should not assume a particular form for file names. Instead, portable scripts must use the file split and file join commands to manipulate file names (see the file manual entry for more details).

## PATH TYPES

File names are grouped into three general types based on the starting point for the path used to specify the file: absolute, relative, and volume-relative. Absolute names are completely qualified, giving a path to the file relative to a particular volume and the root directory on that volume. Relative names are unqualified, giving a path to the file relative to the current working directory. Volume-relative names are partially qualified, either giving the path relative to the root directory on the current volume, or relative to the current directory of the specified volume. The file pathtype command can be used to determine the type of a given path.

## PATH SYNTAX

The rules for native names depend on the value reported in the Tcl array element tcl_platform(platform):

Unix
On Unix and Apple MacOS X platforms, Tcl uses path names where the components are separated by slashes. Path names may be relative or absolute, and file names may contain any character other than slash. The file names . and .. are special and refer to the current directory and the parent of the current directory respectively. Multiple adjacent slash characters are interpreted as a single separator. Any number of trailing slash characters at the end of a path are simply ignored, so the paths foo, foo/ and foo// are all identical, and in particular foo/ does not necessarily mean a directory is being referred.

The following examples illustrate various forms of path names:

/
Absolute path to the root directory.
/etc/passwd
Absolute path to the file named passwd in the directory etc in the root directory.
.
Relative path to the current directory.
foo
Relative path to the file foo in the current directory.
foo/bar
Relative path to the file bar in the directory foo in the current directory.
../foo
Relative path to the file foo in the directory above the current directory.
Windows
On Microsoft Windows platforms, Tcl supports both drive-relative and UNC style names. Both / and \ may be used as directory separators in either type of name. Drive-relative names consist of an optional drive specifier followed by an absolute or relative path. UNC paths follow the general form \\servername\sharename\path\file, but must at the very least contain the server and share components, i.e. \\servername\sharename. In both forms, the file names . and .. are special and refer to the current directory and the parent of the current directory respectively. The following examples illustrate various forms of path names:
\\Host\share/file
Absolute UNC path to a file called file in the root directory of the export point share on the host Host. Note that repeated use of file dirname on this path will give //Host/share, and will never give just //Host.
c:foo
Volume-relative path to a file foo in the current directory on drive c.
c:/foo
Absolute path to a file foo in the root directory of drive c.
foo\bar
Relative path to a file bar in the foo directory in the current directory on the current volume.
\foo
Volume-relative path to a file foo in the root directory of the current volume.
\\foo
Volume-relative path to a file foo in the root directory of the current volume. This is not a valid UNC path, so the assumption is that the extra backslashes are superfluous.

## TILDE SUBSTITUTION

In addition to the file name rules described above, Tcl also supports csh-style tilde substitution. If a file name starts with a tilde, then the file name will be interpreted as if the first element is replaced with the location of the home directory for the given user. If the tilde is followed immediately by a separator, then the $HOME environment variable is substituted. Otherwise the characters between the tilde and the next separator are taken as a user name, which is used to retrieve the user's home directory for substitution. This works on Unix, MacOS X and Windows (except very old releases). Old Windows platforms do not support tilde substitution when a user name follows the tilde. On these platforms, attempts to use a tilde followed by a user name will generate an error that the user does not exist when Tcl attempts to interpret that part of the path or otherwise access the file. The behaviour of these paths when not trying to interpret them is the same as on Unix. File names that have a tilde without a user name will be correctly substituted using the$HOME environment variable, just like for Unix.

## PORTABILITY ISSUES

Not all file systems are case sensitive, so scripts should avoid code that depends on the case of characters in a file name. In addition, the character sets allowed on different devices may differ, so scripts should choose file names that do not contain special characters like: <>:?"/\|. The safest approach is to use names consisting of alphanumeric characters only. Care should be taken with filenames which contain spaces (common on Windows systems) and filenames where the backslash is the directory separator (Windows native path names). Also Windows 3.1 only supports file names with a root of no more than 8 characters and an extension of no more than 3 characters.

On Windows platforms there are file and path length restrictions. Complete paths or filenames longer than about 260 characters will lead to errors in most file operations.

Another Windows peculiarity is that any number of trailing dots .'' in filenames are totally ignored, so, for example, attempts to create a file or directory with a name foo.'' will result in the creation of a file/directory with name foo''. This fact is reflected in the results of file normalize. Furthermore, a file name consisting only of dots .........'' or dots with trailing characters .....abc'' is illegal.

## KEYWORDS

current directory, absolute file name, relative file name, volume-relative file name, portability


text:
# Thread: HSC 2012 Marathon :)

1. ## Re: HSC 2012 Marathon :)

Originally Posted by barbernator
~ between words
thanks bruh

3. ## Re: HSC 2012 Marathon :)

dulip, that question is more suited for an Extension 2 student under the topic "Polynomials". It is a very commonly asked question, and is essentially the 'Discriminant' of a cubic.

Here is one for the mean time:

By letting x = tan(u), evaluate the integral: (Medium/Hard)

$\int \frac{dx}{\left (1+x^2 \right )^2}$

Or:

By letting u = cos(x), show that: (Easy)

$\int \tan(x) dx = - \ln(\cos(x)) + C$

4. ## Re: HSC 2012 Marathon :)

Originally Posted by Carrotsticks
dulip, that question is more suited for an Extension 2 student under the topic "Polynomials". It is a very commonly asked question, and is essentially the 'Discriminant' of a cubic.

Here is one for the mean time:

By letting x = tan(u), evaluate the integral:

$\int \frac{dx}{\left (1+x^2 \right )^2}$
$\frac{1}{2}(tan^{-1}x + \frac{x}{1 + x^2})$

Hopefully i did it right in my head lol.

5. ## Re: HSC 2012 Marathon :)

Originally Posted by nightweaver066
$tan^{-1}x + \frac{x}{1 + x^2}$

Hopefully i did it right in my head lol.
Nope, but close.

7. ## Re: HSC 2012 Marathon :)

Correct!

I'll put up another question since you forgot to post one up yourself.

Find the condition such that the two lines:

ax+by+c=0 and dx+ey+f=0

Are:

a) Perpendicular.

b) Parallel.

8. ## Re: HSC 2012 Marathon :)

Cmon Carrot.

ax+by+c=0 => y=[-ax-c]/b has gradient -a/b
dx+ey+f=0 => y=[-dx-f]/e has gradient -d/e
a) If the two lines are parallel then their gradient are equal,
i.e. -a/b=-d/e
Hence, bd=ae
b) If the two lines are parallel then the product of their gradient is -1,
i.e. (-a/b)(-d/e)=-1

9. ## Re: HSC 2012 Marathon :)

Originally Posted by bleakarcher
Cmon Carrot.

ax+by+c=0 => y=[-ax-c]/b has gradient -a/b
dx+ey+f=0 => y=[-dx-f]/e has gradient -d/e
a) If the two lines are parallel then their gradient are equal,
i.e. -a/b=-d/e
Hence, bd=ae
b) If the two lines are parallel then the product of their gradient is -1,
i.e. (-a/b)(-d/e)=-1
For the parallel one though, you also have to put in the condition that they aren't the same line.

10. ## Re: HSC 2012 Marathon :)

Originally Posted by RealiseNothing
For the parallel one though, you also have to put in the condition that they aren't the same line.
oh right completely forgot about that one. so you just add c/b =/= f/e
so bf=/=ec

11. ## Re: HSC 2012 Marathon :)

A polynomials question.

CodeCogsEqn.gif

12. ## Re: HSC 2012 Marathon :)

^ a lot of you will probably recognise that one. If you do, please leave it for someone else lol.

13. ## Re: HSC 2012 Marathon :)

hmm, if you write the polynomial as a product of n terms then take the derivative using the special nth product rule, then use a trig sub...you will get no where
so i will leave it for the hsc kids to figure out what they are properly meant to do

14. ## Re: HSC 2012 Marathon :)

alright

anyone gonna give the question a go?

15. ## Re: HSC 2012 Marathon :)

ok ill give it a go in words.

Express z^n -1 as a procduct of its n roots in factored form, divide both sides by z-1, which is a factor of z^n-1. now the hsc kids finish it for me... i i i...forgot what to do next.

16. ## Re: HSC 2012 Marathon :)

-cotx / 2 using the chain rule twice

17. ## Re: HSC 2012 Marathon :)

You could have used log laws to simplify the expression before continuing =)

$\frac{d}{dx} \left ( \ln \left ( \frac{1}{\sqrt{\sin x}} \right ) \right ) = \frac{d}{dx} \left ( - \frac{1}{2} \ln \left ( \sin x \right )} \right ) = - \frac{1}{2} \cot x$

20. ## Re: HSC 2012 Marathon :)

Originally Posted by deswa1
This isn't the answer- maybe try again or someone else can have a go.
i am sure that is the answer

Page 3 of 24 First 1234513 ... Last

##### Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•


text:
# If the time interval remains constant, the current wil _____ when the amount of charge is increased.

## Expert Answers

Answer: If the time interval remains constant, the current will increase when the amount of charge is increased.

Explanation: The current intensity `I` of a charge `Q` that passes through a certain section of a conductor in the time `t` is by DEFINITION

`I = Q/t` .

Therefore the current is directly proportional to the charge and inversely proportional to the flow time. Increasing charge, increases the current if the time remains the same.

Observation:

From the expression above one usually further define the density of current `j` as being the current that flows through the unity surface.

`j = I/S =Q/(t*S)`

Approved by eNotes Editorial Team


text:
# LaTeX

LaTeX is a computer typesetting language for mathematical markup. It was designed and developed by Leslie Lamport[1] as an extension of TeX, an existing typesetting language developed by Donald Knuth. LaTeX is used nearly universally by mathematicians, physicists, engineers, computer scientists and other scientists in need of technical formatting in their publications.

## Examples

\documentclass[12pt]{article}        %Specifies the font size and the document style
\begin{document}                     %Begins the document
$$\sqrt{\frac{1}{4}} = \frac{1}{2}$$ %Dollar sign ($) delimits math expressions;$\$ delimits math expressions displayed centered on their own line
\end{document}                       %Document closing tag

This LaTeX code would output:

$\sqrt{\frac{1}{4}} = \frac{1}{2}$

Highly complex mathematical expressions are also possible; for example, the following code[2]:

 \operatorname{erfc}(x) =
\frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt =
\frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}

would output:

$\operatorname{erfc}(x) = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt = \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}$

The style declaration, beginning and closing end tags are omitted for brevity.

## References

1. Gratzer, G. First Steps in LaTeX. Birkhauser, Boston; p. xiv (1999) [1]
2. Mediawiki Help:Displaying a Formula


text:
# Spring Potential Energy Problem

A wedge of mass M fitted with a spring of stiffness 'k' is kept on a smooth horizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all surfaces are smooth, the potential energy stored on the spring is:

A)$\frac{mg^2tan^2\theta}{2k}$ B)$\frac{m^2gtan^2\theta}{2k}$ C)$\frac{m^2g^2tan^2\theta}{2k}$ D)$\frac{m^2g^2tan^2\theta}{k}$

Note by Shubham Srivastava
5 years, 2 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Make free body diagram of forces on both the blocks one by one. For wedge of mass M the forces acting along the floor are N sinθ (normal reaction from block of mass m) and kx. Next, make free body diagram of block of mass m. Forces acting on it perpendicular to the floor are N cosθ and mg. Solving these equations

Nsinθ = kx,

Ncosθ = mg,

We get the value of x, hence value of potential energy can be evaluated.

- 5 years, 2 months ago

c

- 5 years, 2 months ago

Solution????

- 5 years, 2 months ago

kx=mgtan@

x=mgtan@/2k

1/2 kx^2 = m^2g^2tan^2/2k

- 2 months, 3 weeks ago

Start with determining the state of spring at equilibrium. Should it be compressed or stretched to keep the system at equilibrium?

- 5 years, 2 months ago

make forces acting on M, weight of m & a force F which is acts opposite to spring force to keep system is in equilibrium. then \Tan\theta\ = F\mg. from this find out F and substituted in P.E = F*2\ 2K get the ans... (C) is correct

- 5 years, 1 month ago

My attitude towards the problem is this: The weight, mg, of the rod will have 2 components- mgsin0 and mgcos0. The component, mgcos0, can be again resolved into two vectors having a horizontal component, mgcos0sin0. For equilibrium, the spring force should be equal to horizontal force. Therefore, mgcos0sin0= kx. We can now substitute value of x from this equation in the equation for spring potential energy, i.e., 0.5kx^2.

- 5 years, 2 months ago

I fear your reasoning is not accurate. You are making components of components. This is probably wrong way and you will get the wrong answer I think.

- 5 years, 2 months ago

mgcos0 (0 to be read as theta) is not a component but the normal reaction of m on M... So there are two forces on M....one is the spring force kx which is horizontal and towards right...and the other is the normal reaction of m on M which towards left, and downwards making an angle of (ninty - theta) with the horizontal...So, on resolving mgcos0 in the horizontal left direction, we get mgcos0sin0...and for M to remain in equillibrium, kx should be equal to mgcos0sin0...

so,

mgcos0sin0 = kx

x=(mgcos0sin0)/k

the potential energy stored in spring = 1/2(k . x^2)..

solvong further will give the answer... So the explanation of Shubham S is accurate....

- 5 years ago

BY DIMENSIONAL ANALYSIS IT CAN ONLY BE C OR D MOSTLY C

- 5 years, 2 months ago

Mind keeping Caps Lock off. :P

- 5 years, 2 months ago

how can u say it is mostly c)?

- 5 years, 1 month ago