text:
## Cassiterite Value, Price, and Jewelry Information ...

2018-7-2 · Most cassiterite crystals have opaque, dark colors, usually black or brown. Lighter-colored, facetable crystals are much rarer and usually occur in small fragments.

## Cassiterite 'Tin Stone' - Crystal Classics

A weighty example of Cassiterite tin ore from the world famous Levant Mine, Trewellard, Cornwall. The 'Tin Stone' is a deep browny-green Chlorite heavily embedded with Cassiterite. There are lots of small cavities lined with sparkling micro-crystals of Cassiterite.

## Cassiterite: Meanings, Properties and Powers - The ...

2021-8-19 · Cassiterite is a primary of tin. It’s a tin oxide, and its name Cassiterite came from the Greek word ‘kassiteros’, which means tin. It’s commonly known as the Tin Stone as well. It’s abundant in its rough mineral form, but the transparent gemstone quality material is quite rare.

2021-8-13 · The meaning of the Cassiterite is from the Greek word “tin.” This stone comes in different colors such as white, grey, yellow, red, colorless, and black. It also comes in tinstone which is where the name came from. This stone is found in China, Australia, Brazil, Malaysia, United Kingdom, Mexico, Bolivia, and the United States of America.

## Cassiterite Meanings Properties & Uses: Healing Crystals ...

This stone is a type of tin oxide, and the most common colors found are black, brown and red-brown stones. It can also be colorless, white, yellow-grey, yellow and red. This crystal is also known as tinstone, and the meaning of the name Cassiterite comes from the Greek word meaning 'tin'.

## Where to Buy Cassiterite - Meaning of Healing Stones

Buy Cassiterite Stones. The primary ore of tin, Cassiterite is a tin oxide mineral that most often occurs in hydrothermal veins & pegmatites, typically associated with granite intrusions. A durable mineral, it is also often found in alluvial placer deposits & igneous rocks. Its color can be black, yellow, brown, red or white.

2014-8-24 · cassiterite, tin stone, tin oxid(e), SnO 2 [Tetragonal; usually black in colo(u)r; Moh’s hardness, 6 to 7; streak pink-white; specific gravity, 6.9. When pure contains 78.6 per cent tin, but is usually adulterated by other metals] Kassiterit m, Zinnstein m, Cassiterit, Zinnerz n, Zwitter m

## Cassiterite (Tin ore) stone isolated on white - Stock ...

Cassiterite (Tin ore) stone isolated on white - Stock Photo(No.40975759). Find images exactly you are looking for from more than 64,200,000 of royalty-free stock photos, illustrations, and vectors. Download and enjoy fresh & incredible images added every day.

## Tin processing | Britannica

2020-8-17 · Tin processing, preparation of the ore for use in various products. Tin (Sn) is a relatively soft and ductile metal with a silvery white colour. It has a density of 7.29 grams per cubic centimetre, a low melting point of 231.88 °C (449.38 °F), and a high boiling point of 2,625 °C (4,757 °F). Tin is

## ISMC

2020-7-20 · ISMC ... CN

2021-8-13 · The meaning of the Cassiterite is from the Greek word “tin.” This stone comes in different colors such as white, grey, yellow, red, colorless, and black. It also comes in tinstone which is where the name came from. This stone is found in China, Australia, Brazil, Malaysia, United Kingdom, Mexico, Bolivia, and the United States of America.

## Facts About Cassiterite: Meanings, Properties, and ...

2019-4-12 · Cassiterite is a tin oxide whose name is derived from the Greek word “kassiteros” that means tin. This stone, on the other hand, is commonly called the Tin Stone. Cassiterite is rich in its rough metal variety, however, the transparent stone quality materials are rare. Moreover, it’s known as the stone

## Cassiterite Tin – Gisande

Tin Stone, also known as the collector’s stone because of its rarity, is a transparent gemstone quality material that is an economically important mineral, being the prime ore of the metal tin that is highly desired. At Gisande Trading we process and add value up to quality ratings of 65-70% of cassiterite-tin.

## CASSITERITE - Russian Mineralogical Society

Especially beautiful is red cassiterite – ruby tin. Zonal-concentric texture of cryptocrystalline woody tin (holzzinnerz, Germ.) resembles timber. It is well polished, that’s why it can be used as an ornamental stone – toad’s-eye. When admixture of quartz presents in woody tin, it is called silesite.

## Cassiterite Meaning and Spiritual Properties

Alternate name Tin Stone. It is tin oxide, and the name Cassiterite comes from the Greek word Kassiteros, which means tin. Rarity, Value & Variations: Found in short prismatic crystals and masses. It is abundant in its rough mineral form, but the transparent Cassiterite gemstone is quite rare. It is considered a collectors stone because of its ...

## Cassiterite Tin Crystals Tin Stone Pendant Elsmore NSW |

Australian Cassiterite, I love using raw Stone in my designs. This grounding stone has been set into Glass Resin with a 925 Sterling Silver bale on a Stainless Steel Chain. I am very happy with how this piece turned out. Location of find the New England area, NSW. Australian designer and created. I

## Cassiterite is concentrated by: - Tardigrade

Cassiterite or tin stone $(Sn{{O}_{2}})$ is a heavy ore of tin, which contains wolframite $(FeW{{O}_{4}}\cdot MnW{{O}_{4}})$ as a magnetic impurity and some other impurities of non-metals (S etc.). Hence, it is concentrated by all the 3 methods given.

## From peaks to ports: Insights into tin provenance ...

If cassiterite had been smelted and/or tin ingots cast in the lead-silver workshops at Bolkardağ, they would undoubtedly have been contaminated by local lead, and a Bolkardağ LI signature would have been imparted onto the tin ingots. With the exception of the most Pb-rich Uluburun tin ingots, it is unlikely that the Pb addition was intentional.

## ISMC

2020-7-20 · ISMC ... CN

## Tin Ore - Final Fantasy XIV: A Realm Reborn (FFXIV) Wiki

2021-8-22 · Tin Ore is a stone. 1 Source 1.1 Drops 1.2 Gathering 1.3 Vendors 2 Uses 2.1 Armorer 2.2 Blacksmith 3 Patches 4 External links Tin Ore can be obtained as a drop, gathered, or purchased from vendors. Tin Ore can be obtained as a drop from the following mobs: Silver Coblyn -

## Cassiterite - Encyclopedia

2021-7-3 · CASSITERITE (from the Gr. Kaaaimpos, tin), the mineralogical name for tin-stone, the common ore of tin. It consists of tin dioxide, or stannic oxide (Sn02), and crystallizes in the tetragonal system. The crystals are usually 4-sided or 8-sided prisms, striated vertically, and terminated by

## Cassiterite Gems - GemSelect

2021-8-11 · Cassiterite is composed of tin oxide and is the primary ore for tin. In fact, it is also known as 'the tin stone'. In addition to its important industrial use, it has some interesting properties that make high-quality crystals valuable gemstones.

## Where to Buy Cassiterite - Meaning of Healing Stones

Buy Cassiterite Stones. The primary ore of tin, Cassiterite is a tin oxide mineral that most often occurs in hydrothermal veins & pegmatites, typically associated with granite intrusions. A durable mineral, it is also often found in alluvial placer deposits & igneous

## Cassiterite | Buy British Cassiterite specimens online ...

Cassiterite has a long, storied, and sometimes bloodied history. To understand it, we must understand Tin. Tin is a metallic chemical element with the symbol Sn. It is a silvery-grey metal that is soft, ductile, and has a low melting point to boot. Tin is the metal that brought about the Bronze age – Bronze is an alloy of Copper and Tin.

## Cassiterite – The Rose Quartz Stand

Casserite ( Tin Source) from Namibia. Lower chakras- Solar Plexus, Sacral, Root. In the “Book of Stones” by Robert Simmons, he calls Cassiterite, “ The Stone of Initiation “ and an ideal stone for those who work in “ the other world” ( Shamans, Mediums, Channelers,etc.) A stone that

## Cassiterite Tin Crystals Tin Stone Pendant Elsmore NSW |

Australian Cassiterite, I love using raw Stone in my designs. This grounding stone has been set into Glass Resin with a 925 Sterling Silver bale on a Stainless Steel Chain. I am very happy with how this piece turned out. Location of find the New England area, NSW. Australian designer and created. I

## Tin Ore Extraction - Mineral Processing & Metallurgy

2016-5-24 · The flowsheet below Explains the Extraction of Tin Ore as shown by a study adapted to the concentration of a lode tin deposit.Cassiterite (SnO2) is very friable and special considerations to crushing and grinding of the ore are necessary to avoid an excessive production of fines. The Mineral Jig is an important feature of this flowsheet to recover the coarse free tin

## From peaks to ports: Insights into tin provenance ...

If cassiterite had been smelted and/or tin ingots cast in the lead-silver workshops at Bolkardağ, they would undoubtedly have been contaminated by local lead, and a Bolkardağ LI signature would have been imparted onto the tin ingots. With the exception of the most Pb-rich Uluburun tin ingots, it is unlikely that the Pb addition was intentional.

## The Properties, Production, and Applications of Tin

2020-8-21 · Production of Tin. Tin is most often produced from the mineral cassiterite, which is made up of about 80% tin. Most tin is found in alluvial deposits, riverbeds, and former riverbeds, as a result of erosion of ore bodies containing the metal. China and Indonesia are currently the world's largest producers. Tin

## 欧尼酱 - Little Stone

2021-7-12 · 欧尼酱 - Little Stone 鸽子博主 驾校一点通 - 理论考试爬虫 July 12, 2021 • 默认分类 不支持M.2接口的旧主板使用M.2 SSD作为开机启动盘的三种方法 June 18, 2021 • 默认分类 ...


text:
Frederick - that's a nice solution to Puzzle 62. Note also that \$$\mathbb{R}^+\$$ with \$$\le\$$ as partial order, \$$\cdot\$$ as monoidal operation and \$$1\$$ as unit is _isomorphic_ as a monoidal poset to \$$\mathbb{R}\$$ with \$$\le\$$ as partial order, \$$+\$$ as monoidal operation and \$$0\$$ as unit. An isomorphism is

$\ln : \mathbb{R}^+ \to \mathbb{R}$

with inverse

$\exp: \mathbb{R} \to \mathbb{R}^+ .$

Another cute thing: you didn't need to throw out zero! There's another nice monoidal poset: \$$[0,\infty) \$$ with \$$\le\$$ as partial order, \$$\cdot\$$ as monoidal operation and \$$1\$$ as unit. This is isomorphic as a monoidal poset to \$$[-\infty, 0) \$$ with \$$\le\$$ as partial order, \$$+\$$ as monoidal operation and \$$0\$$ as unit.

format: plain


text:
# Math Help - [SOLVED] Matlab plotting help:peicewise with loops

1. ## [SOLVED] Matlab plotting help:peicewise with loops

so i've tried to plot this funtion multiple times using every trick i can come up with and the loop still only goes through the first ifelse statement in the function file. here is a copy of my function file:

Code:
function y=f(x)
if x<=-1;
y=15;
elseif -1<=x<=1;
y=-5.*x+10;
elseif 1<=x<=3;
y=-10.*x.^2+35.*x-20;
elseif 3<=x<=4;
y=-5.*x+10;
elseif 4<=x<=5 ;
y=-10;
end
end
using this file I try to plot in my main file which is:

Code:
delete g228x07.txt; diary g228x07.txt
clear; clc; close all; echo on
% Gilat 228/7
x=[-2:.01:5];
n=length(x);
for i=1:n;
y(i)=f(x(i));

end
plot(x,y);
grid on

echo off; diary off
the first three lines are just a reference header and do not impact the problem. I don't know if the loop fails in the for loop or in the ifelse on the function file.

2. The problem is here:

Code:
-1<=x<=1
when x=2 that condition is still returning true. The way I usually write these expressions is shown below (im sure there is probably a better way). Try paste this code inside a file called "mhfFoo.m" and run is. It work OK on my computer.

Code:
function mhfFoo
x=[-2:0.1:5];
n=length(x);
for i=1:n;
y(i)=f(x(i));
end
plot(x,y);
grid on
end
function y=f(x)
if x<=-1;
y=15;
elseif x>=-1 && x<=1;
y=-5.*x+10;
elseif x>=1 && x<=3;
y=-10.*x.^2+35.*x-20;
elseif x>=3 && x<=4;
y=-5.*x+10;
elseif x>=4 && x<=5 ;
y=-10;
end
end
Regards Elbarto

3. thanks a lot. Its wierd that the code has to be like that but it worked.

4. Originally Posted by apocolypto
so i've tried to plot this funtion multiple times using every trick i can come up with and the loop still only goes through the first ifelse statement in the function file. here is a copy of my function file:

Code:
function y=f(x)
if x<=-1;
y=15;
elseif -1<=x<=1;
y=-5.*x+10;
elseif 1<=x<=3;
y=-10.*x.^2+35.*x-20;
elseif 3<=x<=4;
y=-5.*x+10;
elseif 4<=x<=5 ;
y=-10;
end
end
using this file I try to plot in my main file which is:

Code:
delete g228x07.txt; diary g228x07.txt
clear; clc; close all; echo on
% Gilat 228/7
x=[-2:.01:5];
n=length(x);
for i=1:n;
y(i)=f(x(i));

end
plot(x,y);
grid on

echo off; diary off
the first three lines are just a reference header and do not impact the problem. I don't know if the loop fails in the for loop or in the ifelse on the function file.
multiple condition ifs should be of the form

Code:
if 0<x & x<1
#if body
elseif
:
:
end
[/code]

5. No problem apocolypto.

Further the CB's reply, MATLAB has support for short circuiting behavior when evaluating statements so writing the expression as follows is better for evaluating logical scalar values (at least that seems to be the convention mathworks is using).

Code:
if 0<x && x<1% Note the "&&" vs "&"
#if body
elseif
:
:
end
It is my understand that this means if "0<x" is false, then the whole statement will be false so "x<1" does not need to be evaluated. This is probably pretty trivial but thought I would mention it as it is starting become more frequent in recent code and it is something that confused me when I was starting out.

Regards Elbarto


text:
B. Marcin and Training Camp
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Marcin is a coach in his university. There are $n$ students who want to attend a training camp. Marcin is a smart coach, so he wants to send only the students that can work calmly with each other.

Let's focus on the students. They are indexed with integers from $1$ to $n$. Each of them can be described with two integers $a_i$ and $b_i$; $b_i$ is equal to the skill level of the $i$-th student (the higher, the better). Also, there are $60$ known algorithms, which are numbered with integers from $0$ to $59$. If the $i$-th student knows the $j$-th algorithm, then the $j$-th bit ($2^j$) is set in the binary representation of $a_i$. Otherwise, this bit is not set.

Student $x$ thinks that he is better than student $y$ if and only if $x$ knows some algorithm which $y$ doesn't know. Note that two students can think that they are better than each other. A group of students can work together calmly if no student in this group thinks that he is better than everyone else in this group.

Marcin wants to send a group of at least two students which will work together calmly and will have the maximum possible sum of the skill levels. What is this sum?

Input

The first line contains one integer $n$ ($1 \leq n \leq 7000$) — the number of students interested in the camp.

The second line contains $n$ integers. The $i$-th of them is $a_i$ ($0 \leq a_i < 2^{60}$).

The third line contains $n$ integers. The $i$-th of them is $b_i$ ($1 \leq b_i \leq 10^9$).

Output

Output one integer which denotes the maximum sum of $b_i$ over the students in a group of students which can work together calmly. If no group of at least two students can work together calmly, print 0.

Examples
Input
4
3 2 3 6
2 8 5 10

Output
15

Input
3
1 2 3
1 2 3

Output
0

Input
1
0
1

Output
0

Note

In the first sample test, it's optimal to send the first, the second and the third student to the camp. It's also possible to send only the first and the third student, but they'd have a lower sum of $b_i$.

In the second test, in each group of at least two students someone will always think that he is better than everyone else in the subset.


text:
# Unsupervised minimization with SGD

Hello everyone, I am trying to implement a minimization problem using SGD.
In particular, I have an objective function (or loss) that looks like this:

where q_theta is parametrized by a fully connected NN and has the form:

``````def objective(p, output):
x,y = p
a = minA
b = minB
r = 0.1

XA = 1/2 -1/2 * torch.tanh(100*((x - a[0])**2 + (y - a[1])**2 - (r + 0.02)**2))
XB = 1/2 -1/2 * torch.tanh(100*((x - b[0])**2 + (y - b[1])**2 - (r + 0.02)**2))
q = (1-XA)*((1-XB)* output - (XB))
return q
``````

“output” is the output of the NN, namely the only part of this function that is parametrized.

Now, my training function looks like this:

``````optimizer = optim.SGD(model.parameters(), lr=learning_rate)

for e in range(epochs) :
for configuration in total:
# for each point in the array of independently sampled points

#output is q~
output = model(configuration)

#loss is the objective function we defined
#in the paper, objective function is 18

loss = objective(configuration, output).backward()
optimizer.step()
``````

Where my model is a simple two-layer fully connected NN, with an input layer equal to 2 (x,y) and one output node corresponding to the parametrized part of the function.
Note that each “configuration” is a point in a 2D space, which is sampled independently from a distribution to perform the sample average, which approximates the expectation in (18).

However, the resulting minimized function does not make any sense. In particular, I am not sure I am handling the objective function correctly. Is .backward() substituting the gradient in (18) or should I compute the gradient with autograd?


text:
## Quantitative concentration inequalities for empirical measures on non-compact spaces.(English)Zbl 1113.60093

Quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances, are established. Typical estimates are of the form $P\left[\sup_{\| \varphi\| _{\text{Lip}}\leq 1} \left( N^{-1} \sum_{i=1}^N \varphi(X_t^i)- \int \varphi \,d\mu_t \right) > \varepsilon \right] \leq C e^{-\lambda N \varepsilon^2},$ where $$\| \varphi\| _{\text{Lip}}=\sup_{x \neq y} | \varphi(x)-\varphi(y)| d^{-1}(x,y)$$ and $$d(\cdot)$$ stands for the distance in phase space (say Euclidean norm in $$\mathbb{R}^d$$). The core of estimates is based on variants of Sanov’s theorem.
These results are applied to provide some error bounds for particle simulations in a simple mean-field kinetic model for granular media. A system of interacting particles is governed by the system of coupled stochastic differential equations. The tools include coupling arguments, as well as regularity and moment estimates for solutions of differential equations.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60H15 Stochastic partial differential equations (aspects of stochastic analysis)

### Keywords:

transport inequalities; Sanov Theorem
Full Text:

### References:

 [1] Araujo, A.; Giné, E., The central limit theorem for real and Banach valued random variables (1980), New York: Wiley, New York · Zbl 0457.60001 [2] Benachour, S.; Roynette, B.; Talay, D.; Vallois, P., Nonlinear self-stabilizing processes. I. Existence, invariant probability, propagation of chaos, Stoch Process Appl, 75, 2, 173-201 (1998) · Zbl 0932.60063 [3] Benachour, S.; Roynette, B.; Vallois, P., Nonlinear self-stabilizing processes. II. Convergence to invariant probability, Stoch Process Appl, 75, 2, 203-224 (1998) · Zbl 0932.60064 [4] Benedetto, D.; Caglioti, E.; Carrillo, J. A.; Pulvirenti, M., A non-Maxwellian steady distribution for one-dimensional granular media, J Stat Phys, 91, 5-6, 979-990 (1998) · Zbl 0921.60057 [5] Bobkov, S.; Gentil, I.; Ledoux, M., Hypercontractivity of Hamilton-Jacobi equations, J Math Pures Appl, 80, 7, 669-696 (2001) · Zbl 1038.35020 [6] Bobkov, S.; Götze, F., Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J Funct Anal, 163, 1-28 (1999) · Zbl 0924.46027 [7] Bolley, F.: Quantitative concentration inequalities on sample path space for mean field interaction. Preprint (2005) available online via http://www.lsp.ups-tlse. fr/Fp/Bolley · Zbl 1208.82038 [8] Bolley, F.; Villani, C., Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities, Ann Fac Sci Toulouse, 14, 3, 331-352 (2005) · Zbl 1087.60008 [9] Carrillo, J. A.; McCann, R. J.; Villani, C., Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Rev Mat Iberoamericana, 19, 3, 971-1018 (2003) · Zbl 1073.35127 [10] Carrillo, J. A.; McCann, R. J.; Villani, C., Contractions in the 2-Wasserstein length space and thermalization of granular media, Arch Rational Mech. Anal, 179, 217-263 (2006) · Zbl 1082.76105 [11] Cattiaux, P., Guillin, A.: Talagrand’s like quadratic transportation cost inequalities.Preprint (2004), available online via http://www.ceremade.dauphine.fr/  guillin/index3.html · Zbl 1118.58017 [12] Dembo, A.; Zeitouni, O., Large deviations techniques and applications (1998), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0896.60013 [13] Desvillettes, L.; Villani, C., On the spatially homogeneous Landau equation for hard potentials. I. Existence, uniqueness and smoothness, Comm Partial Differential Equations, 25, 1-2, 179-259 (2000) · Zbl 0946.35109 [14] Djellout, H.; Guillin, A.; Wu, L., Transportation cost-information inequalities and applications to random dynamical systems and diffusions, Ann Probab, 32, 3, 2702-2732 (2004) · Zbl 1061.60011 [15] Gao, F., Moderate deviations and large deviations for kernel density estimators, J Theor Prob, 16, 401-418 (2003) · Zbl 1041.62025 [16] Giné, E.; Zinn, J., Empirical processes indexed by Lipschitz functions, Ann Probab, 14, 4, 1329-1338 (1986) · Zbl 0611.60029 [17] Ledoux, M.: The concentration of measure phenomenon. In: Mathematical surveys and monographs, vol 89. Providence: American Mathematical Society, 2001 · Zbl 0995.60002 [18] Ledoux, M.; Talagrand, M., Probability in Banach spaces (1991), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0748.60004 [19] Malrieu, F., Logarithmic Sobolev inequalities for some nonlinear PDE’s, Stoch Process Appl, 95, 1, 109-132 (2001) · Zbl 1059.60084 [20] Malrieu, F., Convergence to equilibrium for granular media equations and their Euler schemes, Ann Appl Probab, 13, 2, 540-560 (2003) · Zbl 1031.60085 [21] Marchioro, C.; Pulvirenti, M., Mathematical theory of incompressible nonviscuous fluids (1994), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York [22] Massart, P.: Saint-Flour Lecture Notes. Available at http://www.math.u-psud. fr/  massart 2003 [23] Otto, F.; Villani, C., Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality, J Funct Anal, 173, 361-400 (2000) · Zbl 0985.58019 [24] Petrov, V. V., Limit theorems of probability theory (1995), New York: The Clarendon Press, Oxford University Press, New York · Zbl 0826.60001 [25] Schochet, S., The point-vortex method for periodic weak solutions of the 2-D Euler equations, Comm Pure Appl Math, 49, 9, 911-965 (1996) · Zbl 0862.35092 [26] Sion, M., On general minimax theorems, Pac J Math, 8, 171-176 (1958) · Zbl 0081.11502 [27] Sznitman, A.-S.: Topics in propagation of chaos. In: École d’Été de Probabilités de Saint-Flour XIX—1989 Lecture Notes in Mathematics.vol. 1464. Berlin Heidelberg New York: Springer, 1991 [28] Villani, C.: Topics in optimal transportation. In: Graduate studies in mathematics (58). Providence: American Mathematical Society, 2003 · Zbl 1106.90001 [29] Wang, F.-Y., Probability distance inequalities on Riemannian manifolds and path spaces, J Funct Anal, 206, 1, 167-190 (2004) · Zbl 1048.58013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# Homework Help: Finding minimum velocity.

1. Oct 30, 2011

### Miike012

What is the minimum speed the rock must have, when it leaves the sling to travel exactly 400 m?

The only equation I can think of using is...

y = (tan(theta initial))x - (g/(2Vx0^2)x^2

y = 0
x = 400
However I have to many unknowns... I need to solve for V but I dont know Vx0 or Vy0 or the initial angle...

Help would be appreciated... thank you.

2. Oct 30, 2011

### sandy.bridge

You should post the entire question as it is relatively difficult to help with what you have given.

3. Oct 30, 2011

### sandy.bridge

If that is all you are given, note that
$$v_{min}$$ will occur when $$\theta =\frac{\pi}{4}$$

4. Oct 30, 2011

### Miike012

That was all I was given

5. Oct 30, 2011

### Miike012

Why will this be a 45 deg angle?

6. Oct 30, 2011

### Miike012

Ok I got the answer correct.. but can some one please tell me why initial theta is 45 deg?

7. Oct 30, 2011

### sandy.bridge

Proof:
Use the range equation,
$$R = \frac{V_{i}^2 sin 2\theta}{g}$$
Solve this equation for the initial velocity. Then treat it like a max/min problem and differentiate the equation, set equal to zero and solve. You will determine that the minimum occurs at 45 degrees.

8. Oct 30, 2011

### Miike012

interesting... I probably dont know that because I am not in a calc based phy

9. Oct 30, 2011

### Miike012

is that the only way to determine the 45 deg angle by differentiating?

10. Oct 30, 2011

### Miike012

and how can the range equation be used for this type of problem? The range equation I thought only deals with situations when a projectile travels some horizontal distance before falling to its original position... but in the case of the problem I posted the object would have fallen to its original position, that being the ground at y = 0.

11. Oct 30, 2011

### sandy.bridge

I merely presented the range equation as a method for proving that the minimum occurs at 45 degrees. Moreover, now that you know the angle is 45 degrees, you can plug and chug into any equations that apply for this problem.

12. Oct 30, 2011

### Miike012

do i differentiate Initial V with respect to initial theta and keep R constant?

13. Oct 30, 2011

### sandy.bridge

Yes, dv/dθ

14. Oct 31, 2011

### Redbelly98

Staff Emeritus
No, it's not the only way. You (should) know that sin(anything) has a maximum value of 1, which happens when "anything" is equal to ____?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook


text:
# Panel data regression with individual fixed effects: reason to include “untreated” individuals?

I am struggling with basic intuition about individual fixed effects. I have panel data with a binary treatment $D_{it}$, where some individuals never receive the treatment. I am running a regression with individual fixed effects and time dummies: $$y_{it} = \alpha_{i}+\lambda_{t}+\beta D_{it} + \epsilon_{it}$$ My understanding is that with individual fixed effects, $\beta$ is basically determined as a differences in the within-individual means when $D_{it}=1$ and $D_{it}=0$. Does this mean that I don't need to include the observations for which $D_{it}=0$ for all $t$?


text:
Making sense of phase portrait of simple mass-spring oscillator

I'm new to physics, and I'm having trouble making sense of phase portrait of the following system,

$$m \ddot{x} + k x = 0$$

whose phase portrait is in here.

Since

$$x(t) = \sqrt{\frac{2E}{k}} \cos\left(\omega t + \phi \right)$$

where $$\omega := \sqrt{\frac{k}{m}}$$, once we are given $$k$$ and $$m$$, we are completely sure about $$x(t)$$ as a function of $$t$$, except for $$E$$. I think this $$E$$ should be related to how strong we pull or push the spring in the first time.

Can we visualize a movement of $$(x(t), v(t))$$ on the $$x-v$$ plane as a function of time $$t$$, given initial $$E$$?

Can somebody tell how can I visualize the movement? (e.g. website, MATLAB code, etc)

• $E$ is fixed by the initial conditions $x(0)$ and $\dot{x}(0)$. Every different initial condition will give you a different red curve in the figure you linked – pp.ch.te Mar 29 '19 at 8:10
• via Wolfram. For matlab you should probably try the parametric plot function. – denklo Mar 29 '19 at 9:09

The total energy of the system $$E = \frac12mv^2 + \frac 12m\omega^2x^2$$

So the graph of $$v$$ against $$x$$ will be an ellipse with $$-A\le x\le +A$$ and $$-\omega A\le v \le +\omega A$$ with $$E=\frac 12 m\omega^2 A^2$$ where $$A$$ is the amplitude of the motion.

So the graphs in your diagram are a series of ellipses with different total energies of the system and amplitudes.

You can think of a point on the graph moving along the graph with the passage of time.
For the system to move from $$(+A,0)$$ to $$(0,+\omega A)$$ with take a quarter of a period.

Here is a still from an animation using Geogebra

The total energy is fixed by your initial conditions, so each combination of $$x(0)$$ and $$\dot{x}(0)$$ will produce a specific ellipse in the phase diagram. In my opinion, phase diagrams are easier to grok in the Hamiltonian context. The Hamoltonian for simple harmonic motion is given by $$H = \frac{p^2}{2m} + \frac{1}{2}m\omega^2q^2$$

where $$p$$ is the generalized momentum conjugate to $$q$$. For our purposes, it suffices to say $$q=x$$ and $$p$$ is what we normally think of as momentum. Hamilton's euqations then give us a pair of couple differential equations that we can solve for the position and momentum at a given time, which we may then plot to get an ellipse like above. To be explicit, we get $$\dot{p} = -m\omega^2x \text{ and } \dot{q}=p/m$$

To get the phase diagram shown in your link, we may solve these two equations over many small timesteps and plot the result.

The trajectory in the top plot is parameterized by $$t$$, and the yellow dot shows the motion of the simple harmonic motion through phase space. The bottom plot is a quick schematic showing the corresponding location in real space.

The code used to generate this animation can be found here.


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Find f(x) andf(x), where f(x) =

Question:

Find $\lim _{x \rightarrow 0} f(x)$ and $\lim _{x \rightarrow 1} f(x)$, where $f(x)= \begin{cases}2 x+3, & x \leq 0 \\ 3(x+1), & x>0\end{cases}$

Solution:

The given function is

$f(x)= \begin{cases}2 x+3, & x \leq 0 \\ 3(x+1), & x>0\end{cases}$

$\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0}[2 x+3]=2(0)+3=3$

$\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0} 3(x+1)=3(0+1)=3$

$\therefore \lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0} f(x)=3$

$\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1} 3(x+1)=3(1+1)=6$

$\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1} 3(x+1)=3(1+1)=6$

$\therefore \lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}} f(x)=\lim _{x \rightarrow 1} f(x)=6$


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# Dividing by Multiples of Powers of Ten (C)

In this powers of ten worksheet, students divide six to nine-digit numbers by multiples of powers of ten. This two-page worksheet contains approximately 50 problems, with answers.

Concepts

Resource Details


text:
# Improper even integral

I have this improper integral:

$$I = \int_{-\infty}^{\infty} x^4 e^{\frac{-x^2}{2t}} \ dx$$

I used a substitution to get ($$u=\frac{x^2}{2t}$$):

$$I = \int_{-\infty}^{\infty} u^{\frac{3}{2}} e^{-u} \ du$$

(note I have taken the t's and the 2's to the front and left them out for now as they are constants)

However I am having trouble solving it. Ideally I was thinking of using the gamma integral however the limits are not correct. I need them to be between $$0$$ and $$\infty$$, I was thinking of doing this by trying to make the function even so I can change the limits. I think this should be right as this would yield $$2*\Gamma(\frac{5}{2})$$ which is the answer I wanted. However the function above is not even to my knowledge so I am stuck!

• Hint: Use the evenness of $x^4e^{-x^2/(2t)}$ to write $$\int_{-\infty}^\infty x^4e^{-x^2/(2t)}\,dx=2\int_0^\infty x^4e^{-x^2/(2t)}\,dx$$ before making the substitution $u=x^2/(2t)$. (The integral you derived is incorrect: $u^{3/2}$ is either undefined or imaginary for $u\lt0$, and the $e^{-u}$ would make the integral over the negative reals diverge anyway. On a related note, the original integral only makes sense if $t\gt0$; it diverges if $t\lt0$.) Jan 15 at 11:50

The function is even, hence you can write it as

$$2\int_0^{+\infty} x^4 e^{-x^2/2t}\ \text{d}t$$

Using your substitution (please be careful of what you get), you can deal it via Gamma function, obtaining the result $$3 \sqrt{2 \pi } t^{5/2}$$

Details on the substitution

$$z = \dfrac{x^2}{2t} ~~~~~~~ x = \sqrt{2tz} ~~~~~~~ \text{d}x = \dfrac{t^{1/2}}{\sqrt{2z}}\ \text{d}z$$

Hence the integral becomes

$$2\int_0^{+\infty} 4 t^2z^2 e^{-z}\left(\dfrac{t^{1/2}}{\sqrt{2z}}\right)\ \text{d}z$$

$$\dfrac{8}{\sqrt{2}}t^{5/2}\int_0^{+\infty} z^{3/2}e^{-z}\ \text{d}z$$

Whence the above result.

$$I=\int x^4 e^{-x^2/2t}\ \text{d}t=\\Integrate -by- parts{\int}\mathtt{f}\mathtt{g}' = \mathtt{f}\mathtt{g} - {\int}\mathtt{f}'\mathtt{g}\\=-tx^3\mathrm{e}^{-\frac{x^2}{2t}}-{\displaystyle\int}-3tx^2\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x$$Now solving $${\displaystyle\int}-3tx^2\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x==-\class{steps-node}{\cssId{steps-node-1}{3t}}{\cdot}{\displaystyle\int}x^2\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x$$ $$=-tx\mathrm{e}^{-\frac{x^2}{2t}}-{\displaystyle\int}-t\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x$$ Now solving $${\displaystyle\int}-t\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x$$
Substitute $$u=\dfrac{x}{\sqrt{2}\sqrt{t}}$$
$${\displaystyle\int}-t\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x=-\class{steps-node}{\cssId{steps-node-2}{\dfrac{\sqrt{{\pi}}t^\frac{3}{2}}{\sqrt{2}}}}{\displaystyle\int}\dfrac{2\mathrm{e}^{-u^2}}{\sqrt{{\pi}}}\,\mathrm{d}u$$ note that $${\displaystyle\int}\dfrac{2\mathrm{e}^{-u^2}}{\sqrt{{\pi}}}\,\mathrm{d}u$$ This is a special integral ,Gauss error function which called $$=erf(u)$$so $$-\class{steps-node}{\cssId{steps-node-3}{\dfrac{\sqrt{{\pi}}t^\frac{3}{2}}{\sqrt{2}}}}{\displaystyle\int}\dfrac{2\mathrm{e}^{-u^2}}{\sqrt{{\pi}}}\,\mathrm{d}u==-\dfrac{\sqrt{{\pi}}t^\frac{3}{2}\operatorname{erf}\left(\frac{x}{\sqrt{2}\sqrt{t}}\right)}{\sqrt{2}}$$so plug in the second step $$-tx^3\mathrm{e}^{-\frac{x^2}{2t}}-{\displaystyle\int}-3tx^2\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x=\\=\dfrac{3\sqrt{{\pi}}t^\frac{5}{2}\operatorname{erf}\left(\frac{x}{\sqrt{2}\sqrt{t}}\right)}{\sqrt{2}}-tx^3\mathrm{e}^{-\frac{x^2}{2t}}-3t^2x\mathrm{e}^{-\frac{x^2}{2t}}$$ an ,finally $${\displaystyle\int}x^4\mathrm{e}^{-\frac{x^2}{2t}}\,\mathrm{d}x=\\=\dfrac{3\sqrt{{\pi}}t^\frac{5}{2}\operatorname{erf}\left(\frac{x}{\sqrt{2}\sqrt{t}}\right)}{\sqrt{2}}-tx^3\mathrm{e}^{-\frac{x^2}{2t}}-3t^2x\mathrm{e}^{-\frac{x^2}{2t}}+C$$ now apply limit bounds to find numerical value $$I=I = \int_{-\infty}^{\infty} x^4 e^{\frac{-x^2}{2t}} \ dx=\dfrac{3\sqrt{{\pi}}t^\frac{5}{2}}{\sqrt{2}}$$

$$I = \int_{-\infty}^\infty u^{3/2}e^{-u}du \\ \implies I = \int_0^\infty u^{3/2}e^{-u}du + \int_{-\infty}^0 u^{3/2}e^{-u}du$$ Changing the sign of the limits on the second term and swapping them has no effect, as both introduce one minus sign, so we can write $$I = 2\int_0^\infty u^{3/2}e^{-u}du = 2\Gamma(5/2).$$

Your substitution is invalid as it stands because $$x^2/2t$$ is not bijective on the integration domain. The integral is, however, twice the integral from $$0$$ to $$\infty$$, whereby the substitution and gamma definition can be applied and the result is $$(2t)^{5/2}\cdot\frac{3\sqrt\pi}4$$.


text:
Volume 352 - XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2019) - Working Group 7: Future of DIS
Shear forces and tensor polarization
O. Teryaev,* M. Gavrilova
*corresponding author
Full text: Not available
Abstract
The dilepton angular distribution in vector particle decays can be described through a set of five SO(3) rotational-invariant observables. These observables are derived as invariants of the spacial part of the hadronic tensor (density matrix) expressed in terms of angular coefficients. The restrictions on the invariants following from the positivity of the hadronic tensor are obtained. Special cases of SO(2) rotations are considered.
Open Access


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# Homework Help: Direct and limit comparison test?

1. Aug 5, 2008

### vigintitres

Does anyone have any knowledge on these? I look at an example of a direct or limit comparison and i see what they are doing, but I have no idea how they got the "comprable" term.... for example the sum (n = 1) to infinity n/(n^2 +1) you can use either test, but how do you choose what to compare it to? this is my issue and it occurs on other problems where you have to use comparison... I know for direct comparison you need to compare the original sum to something smaller or larger than itself and depending on what it does will tell you if it converges or diverges. I know this, but I do not know what to compare it to!! Do you just pick something out of thin air that is in the same general form as the sum and make it smaller or larger? aaaarrrghhhhh!!!!!

2. Aug 5, 2008

### foxjwill

Direct comparison:
Let's say we want to show that $$\sum_n a_n$$ converges by direct comparison. Basically, we use trial-and-error to find a series $$\sum_n b_n$$ such that for all n greater than some finite value M, $$b_n \geq a_n \geq 0$$. Think of it as the sequence $$b_n$$ squeezing $$a_n$$ into the x-axis.

3. Aug 5, 2008

### vigintitres

that made it clearer for that test, thank you, but I am still unsure about the limit test. It seems to be very similar

4. Aug 5, 2008

### snipez90

Well experience certainly helps. But I think the best way is to consider the behavior of the function for large values of n (for instance take a look at the limit as n -> +inf). Sometimes you do have to try an algebraic manipulation (often dividing top and bottom by some factor).

But really I would consider large values of the n and remember that for direct and limit comparison, you are often comparing to a geometric series or p-series. Taking your example as an example.

n/(n^2 +1) behaves like 1/n for large values of n. Then the sum behaves like a divergent p-series with p = 1 (very common, and remember p-series is divergent is p <= 1). Now consider the comparison test. It looks like it wouldn't help too much because our original series seems to be smaller than 1/n for all n (why would direct comparison fail in this case?).

Now try limit comparison. Find the limit [n/(n^2 + 1)]/[1/n] as n -> +inf. Can you now determine convergence/divergence of that series?

5. Aug 5, 2008

### snipez90

Remember for limit comparison, we take the expressions in the two series we are comparing and form the ratio. If the limit L of that ratio as n -> +inf exists and is greater than 0, then the test is conclusive. If we know one of the series was convergent, then the other converges as well. Similarly, if one was divergent, both are divergent.

Just remember that it often comes down to comparing a given series to a geometric series or a p-series when we're using direct/limit comparison.


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# Thread: Solve this PDE (Computer is fine, just want answer) dp/dt + (1-2p)*dp/dx = a (for 0<x

1. ## Solve this PDE (Computer is fine, just want answer) dp/dt + (1-2p)*dp/dx = a (for 0<x

Hi, I need help solving this PDE for p(x,t), I don't need working, just want a solution (although feel free to send working if you want).
The PDE is, (with derivatives as partial derivatives)

dp/dt + (1-2p)*dp/dx = a (for 0<x<1)
= 0 (for all other x values)
where "a" is a constant

the conditions are t> or =0 , and p(x,0)=1/2

2. Originally Posted by lukas
Hi, I need help solving this PDE for p(x,t), I don't need working, just want a solution (although feel free to send working if you want).
The PDE is, (with derivatives as partial derivatives)

dp/dt + (1-2p)*dp/dx = a (for 0<x<1)
= 0 (for all other x values)
where "a" is a constant

the conditions are t> or =0 , and p(x,0)=1/2

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

http://www.freemathhelp.com/forum/announcement.php?f=33


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# Mean of interpolated data or interpolation of means in geostatistics

Say I have a time series, with actual measurements of a variable $a$ in different locations. If I want to know the average of $p$ from time $t_1$ to $t_n$, I could say that $\overline{a_{p}}=\frac{\sum\limits_{t=1}^n a_{{p}_t}}{n}$, where $p$ is the coordinate of the point of measurement. So far, so good. Let's generalize and call this averaging function $m_p=f(a_p,t)$, where $f(a,t)$ is some deterministic function and $m$ is its result.

Now, say I want to calculate $m$ for a location $o$, where $o$ is a points for which I don't have actual measurements and $a_o$ was estimated through a an interpolating function $g(a,o)$. My intuition tells me that in this case, we should first estimate every $a_{o_t}$ before applying $f(a,t)$. In other words, considering that $a_o = g(a,o)$, we get $m_o$ by doing:

$m_o=f[g(a,o),t]=f(a_o,t)$

But I have seen so many papers that do the other way around. They first calculate $f(a,t)$ for every known $a$ and then interpolate the results using the same g() even though there is no guarantee that $m$ behaves like $a$, or:

$m_o=g[f(a,t),o]=g(m,o)$

In some cases, they use the same logic when instead of $t$, there is some other variable $b$, i.e., it's not a time series, but $f(a,b)$ is a deterministic function.

Are the models in those papers conceptually wrong? If they are wrong, is there a techcnical term to call this kind of mistake?

-

If your interpolation scheme is linear in the input $a$'s (and all interpolation schemes I can think of are), then there is no difference between the mean of interpolated values and the interpolation of the means.
Your notation is a little confusing, so let me put it this way. Suppose you know the values $a_{i,j} = a(p_i,t_j)$ for $m$ points $p_i$ at $n$ times $t_j$. The interpolated value at a point $o$ at any time $t_j$ can typically be expressed as a weighted sum of the values at known points, $$a(o,t_j) := w_1 a_{1,j} + w_2 a_{2,j} + \cdots + w_m a_{m,j}.$$ The mean of these interpolated values is $$\bar a(o) = \frac{1}{n}\sum_j a(o,t_j).$$ If you expand this out, you'll find that it's equal to \begin{align}\bar a(o) &= w_1 \frac{1}{n}\sum_j a_{1,j} + w_2 \frac{1}{n}\sum_j a_{2,j} + \cdots + w_m \frac{1}{n}\sum_j a_{m,j} \\ &= w_1 \bar a_1 + w_2 \bar a_2 + \cdots + w_m \bar a_m,\end{align} which amounts to interpolating the means. Presumably this is better from a computational perspective because if you want to find $\bar a(o)$ at many different $o$, you can keep the $\bar a_i$'s precomputed.
Rahul, I'm sorry for my confusing notation. I'm not very good at mathematics. You mean that if I am right in my suspicion if the data are to be interpolated using kriging? What if instead of just a simple average $m$ is something not linearly related to $a$? ($f(a,t)$ could be a hydrological model, for example). –  Adriano Dec 27 '10 at 2:57


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# Ricci curvature tensor

Jump to: navigation, search

This article defines a tensor (viz a section on a tensor bundle over the manifold) of type (0,2)

## Description

### Given data

A differential manifold $M$ with a linear connection $\nabla$ on it.

### Definition part

The Ricci curvature tensor is a $(0,2)$-tensor that takes as input two vector fields and outputs a scalar function, as follows.

Let $X$ and $Y$ be two vector fields. Then consider the map that sends a vector field $Z$ to $R(X,Z)Y$ (here $R$ denotes the Riemann curvature tensor).

This is a linear map. The Ricci curvature function $Ric(X,Y)$ is defined as the trace of this map.

Explicitly, it is given by:

$\operatorname{Tr}(Z \mapsto \nabla_X\nabla_ZY - \nabla_Z\nabla_XY - \nabla_{[X,Z]}Y)$

The Ricci curvature function is a tensor because the Riemann curvature function is also a tensor.

### For a Riemannian or pseudo-Riemannian manifold

Further information: Ricci curvature tensor of Levi-Civita connection

For a Riemannian manifold or pseudo-Riemannian manifold, we can give the Levi-Civita connection, a natural choice of linear connection. The Ricci curvature tensor of this connection, is termed the Ricci curvature tensor of the Riemannian or pseudo-Riemannian manifold.


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# Planck time

Jump to: navigation, search

In physics, the Planck time (tP) is the unit of time in the system of natural units known as Planck units.

Planck unit is the time required for light to travel in a vacuum a distance of 1 Planck length, which is approximately 5.39 × 10 −44 s. [1] The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as:[2]

${\displaystyle t_{\mathrm {P} }\equiv {\sqrt {\frac {\hbar G}{c^{5}}}}\approx 5.391\,16(13)\times 10^{-44}\ \mathrm {s} }$

where:

ħ = h2 π is the reduced Planck constant (sometimes h is used instead of ħ in the definition[1])
G = gravitational constant
c = speed of light in a vacuum
s is the SI unit of time, the second.

The two digits between parentheses denote the standard error of the estimated value.

## Physical significance

The Planck time is the unique combination of the gravitational constant G, the special-relativistic constant c, and the quantum constant ħ, to produce a constant with units of time. Because the Planck time comes from dimensional analysis, which ignores constant factors, there is no reason to believe that exactly one unit of Planck time has any special physical significance. Rather, the Planck time represents a rough time scale at which quantum gravitational effects are likely to become important. This essentially means that whilst smaller units of time can exist, they are so small their effect on our existence is negligible. The nature of those effects, and the exact time scale at which they would occur, would need to be derived from an actual theory of quantum gravity.

The reciprocal of the Planck time, which is Planck frequency, can be interpreted as an upper bound on the frequency of a wave. This follows from the interpretation of the Planck length as a minimal length, and hence a lower bound on the wavelength.

All scientific experiments and human experiences occur over time scales that are dozens of orders of magnitude longer than the Planck time,[3] making any events happening at the Planck scale hard to detect. As of November 2016, the smallest time interval uncertainty in direct measurements is on the order of 850 zeptoseconds (850 × 10−21 seconds)[4]

## References

1. ^ a b "Big Bang models back to Planck time". Georgia State University. 19 June 2005.
2. ^ CODATA Value: Planck Time – The NIST Reference on Constants, Units, and Uncertainty.
3. ^ "First Second of the Big Bang". How The Universe Works 3. 2014. Discovery Science.
4. ^ "Scientists have measured the smallest fragment of time ever". 2010-05-12. Retrieved 2012-04-19.

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# Calculating the Curvature of a Complex Manifold

1. Jan 15, 2009

### cduston

Hey everyone,
(First off, this is not a HW question, but I can move it there if you are unhappy about my choice) I'm trying to figure out how to calculate the curvature scalar of a complex manifold. As a test case, I am using $$\mathbb{C}P^1$$, which has the Fubini-Study metric on it:
$$g=\frac{dzd\bar{z}}{(1+z\bar{z})^2}$$.

Using Cartan's differential forms, I can get the curvature two-form to be
$$\Omega^1_{~1}=\theta\wedge\bar{\theta}$$,
Where my flat coordinate is
$$\theta=\frac{dz}{1+z\bar{z}}$$

However, I am stuck at the next step. I should be able to use the connection between the curvature two-form and the Riemann curvature in the following way:
$$\Omega^{\mu}_{~\nu}=\frac{1}{2}R^{\mu}_{~\nu\rho\eta}e^{\rho}\wedge e^{\eta}$$

Then I can get the scalar curvature from that. But what will the components of the Riemann tensor look like since my coordinate is complex? In other words, instead of a (2,0)-form my curvature is actually a (1,1)-form, perhaps best notated by $$\Omega^1_{~\bar{1}}$$. Then, will my Riemann tensor have components that look like $$R^{1}_{~\bar{1}1\bar{1}}$$? If so, when I calculate the scalar curvature, will my sum be over "complex indices" like
$$R=R_{1\bar{1}}+R_{\bar{1}1}+R_{11}+R_{\bar{1}\bar{1}}$$?
Things start to look rather strange...can anyone shed some light on this stuff?