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http://devmaster.net/posts/21450/realtime-fire-and-ice
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0
103 May 20, 2012 at 06:32
blue ambient occlusion + red direct light + orangish material.
looks pretty cool to me, now ive just got to finish the modeller and get a whole fire+ice city happening. :)
60 Replies
0
103 May 20, 2012 at 06:48
fps view
0
103 May 20, 2012 at 07:25
changed the material colour to bright yellow
0
103 May 20, 2012 at 09:51
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103 May 21, 2012 at 00:25
Looks really neat, but, it seems that there is something missing or not right, and I just can’t see what, and I’ve been looking at your screen shots for 30 mins! It’s driving me crazy :wacko:
0
103 May 21, 2012 at 01:37
thanks man.
hmm, maybe a texture - a bit more detail?
0
103 May 21, 2012 at 04:23
heres with a concrete texture.
0
103 May 21, 2012 at 06:11
got the blue balance a little more correct…
0
101 May 21, 2012 at 10:21
Yes, the white-balance is definitely helping.
Remember, that while the blue light of the sky makes the shadows blue, the effect can also be contributed to the eye/brain, which is doing it’s own white balancing. The result is that a perfectly gray surface will look blue next to an orange surface.
0
102 May 21, 2012 at 12:06
i really like the style of your environemnts, really interesting! i might get my feet stuck in those grates though :) looks great.
0
103 May 21, 2012 at 17:25
@rouncer
thanks man.
hmm, maybe a texture - a bit more detail?
No, I think it’s the sun, not bright enough. Looks like the sun is filtered through heavy smoke, but there is no smoke in the scene. Can you try with more intensity for the sun see what you get?
0
103 May 21, 2012 at 19:34
hmm… what could fix that is a radiosity implementation, where the light bounces on a wall and then back onto the direct light again, producing glow… im not sure how id do that just with this little ambient occlusion system.
0
101 May 21, 2012 at 20:17
What software is being used here? Looks quite interesting.
0
103 May 21, 2012 at 20:20
3dcoat (modelling application) visual studio c++ (ide) direct x 11 (api)
0
103 May 21, 2012 at 21:46
@rouncer
hmm… what could fix that is a radiosity implementation, where the light bounces on a wall and then back onto the direct light again, producing glow… im not sure how id do that just with this little ambient occlusion system.
Darken your AO and then brighten the whole thing this should make the non-shadowed area stand out more.
Do you use some kind of tone mapping like the Reinhard’s tone mapping operator or something?
0
103 May 21, 2012 at 23:02
Here’s somehting I did. AO and Sun. Each AO samples gets more blueish and darker as the distance gets shorter. No bounces.
0
139 May 21, 2012 at 23:15
Very cool! Although I think the sun could still be brighter, and a blue sky would help “sell” the whole thing as well. :)
0
103 May 22, 2012 at 09:24
hey alienizer, nice work there, thanks for the input.
could you explain tone mapping to me? im not familiar with the term!
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123 May 22, 2012 at 09:33
Can you drop a backdrop in? A sky sphere or even a 2d bitmap.
It’s really difficult to get a feel for the lighting when floating in a void.
I really like the little details in the mesh, but the lighting just feels … I don’t know if there is a word for it … flat maybe, or woolly.
It’s nice, don’t get me wrong.
Games coding is half artistic expression and half science, so feel free to tell me to Foxtrot Oscar if it’s looking great to you, but to me it’s just not quite ‘right’.
A backdrop might help to get a better impression of what it would look like in a game.
0
101 May 22, 2012 at 13:52
@rouncer
hey alienizer, nice work there, thanks for the input.
could you explain tone mapping to me? im not familiar with the term!
http://freespace.virgin.net/hugo.elias/graphics/x_posure.htm
0
103 May 22, 2012 at 15:36
@rouncer
hey alienizer, nice work there, thanks for the input.
could you explain tone mapping to me? im not familiar with the term!
http://expf.wordpress.com/2010/05/04/reinhards_tone_mapping_operator/
The one from Geon is a must as well.
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139 May 22, 2012 at 16:26
IMO the best tonemapping algorithm for games currently is Jim Hejl’s curve, as reported in John Hable’s talk about Uncharted 2. The equation is on slide 140 of this presentation. It’s quite simple and has no adjustable parameters (you for sure want to incorporate an adjustable exposure and maybe contrast before applying this equation), but it looks very nice, especially once you have a proper HDR value range in your scenes. BTW, that whole presentation is well worth a read; it’s a very good general introduction to the issues of gamma correction, linear-color-space lighting, HDR and tonemapping…every graphics programmer should know these things. :)
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103 May 23, 2012 at 15:34
hmmm, I used the code on page 137 and everything is light gray with a bit of shades!!?? looks like a bad ambient occlussion. Seems to simple the code, am I missing something?
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139 May 23, 2012 at 18:12
I said page 140, not 137. :) The stuff from page 137 was an older version that used lookup textures that you have to initialize with some filmic curve. Just apply the equation from 140 (to each RGB channel independently). Again, that must be applied to linear HDR color values after scaling by exposure. And it incorporates the linear-to-gamma conversion, so it generates an sRGB output color.
0
103 May 24, 2012 at 02:53
Indeed you said 140, but stupid me I had to stop at the first equation page :blink:
I don’t understand the LinearColor-0.004 thing. I mean, does LinearColor is the actual color output from the render, or does it need to be LinearColor = Color/(Color+1) or something?
0
103 May 24, 2012 at 04:09
better? (note theres no tone mapping, just adjusted light levels.)
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103 May 24, 2012 at 04:49
YES, much better! Now the sun starts to feel HOT :)
A little brighter maybe?
0
139 May 24, 2012 at 04:54
LinearColor is just the linear-color-space, HDR color value output from the renderer.
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103 May 24, 2012 at 05:58
too bright?
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103 May 24, 2012 at 07:13
this seems to be the happy medium.
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103 May 24, 2012 at 09:26
more modelling…
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103 May 24, 2012 at 11:36
this areas done… :)
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123 May 24, 2012 at 13:23
That looks 100% right to me :)
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103 May 24, 2012 at 13:48
thanks Stainless!
just to polish it off, tiny little bumps on the surface.
0
103 May 24, 2012 at 14:08
Looks perfect to me now. Great job on the lighting! First one, yes, too bright.
0
103 May 24, 2012 at 14:12
@Reedbeta
LinearColor is just the linear-color-space, HDR color value output from the renderer.
ok, so the equation wants LinearColor, not the color from the render. So how does this work then??
0
103 May 24, 2012 at 14:29
thanks alienizer, getting the balance between the ambient light and the direct light seems to be the trick.
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103 May 24, 2012 at 15:53
@rouncer
thanks alienizer, getting the balance between the ambient light and the direct light seems to be the trick.
It looks fantastic now. I can just imagine when you’ll put some monsters :lol: and stuff, and a background how nice it’ll look! Are you working on a game or just for pleasure?
0
139 May 24, 2012 at 16:47
@Alienizer
ok, so the equation wants LinearColor, not the color from the render. So how does this work then??
Read the rest of that presentation.
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103 May 24, 2012 at 17:56
@Reedbeta
Read the rest of that presentation.
I did, but it still isn’t looking right, everything is dull. I just don’t understand it. I even tried the codes from http://filmicgames.com/archives/75 and still isn’t right. My render material colors are between o and 1, but lights hiting a surface will go way above 1, so the final render data is >= 0 <=(all lights power added up) Could that be the problem?
0
139 May 24, 2012 at 18:04
That’s HDR. The HDR color will have an arbitrary range, but after tonemapping it will be back in the 0-1 range.
0
101 May 24, 2012 at 18:47
Rouncer: Your latest shots look great!
Try experimenting with the angle of the direct light as well. For a lower angle (sun closer to the horizon) you need a stronger tint to the colors, and a less bright light. The long shadows, in combination with the orange light and bluish shadows can be very convincing.
0
103 May 24, 2012 at 19:14
@Reedbeta
That’s HDR. The HDR color will have an arbitrary range, but after tonemapping it will be back in the 0-1 range.
I figure that’s what will happen since I use Reinhard’s and it works fine.
Take this code from the link…
float A = 0.15;
float B = 0.50;
float C = 0.10;
float D = 0.20;
float E = 0.02;
float F = 0.30;
float W = 11.2;
float3 Uncharted2Tonemap(float3 x)
{
return ((x*(A*x+C*B)+D*E)/(x*(A*x+B)+D*F))-E/F;
}
float4 ps_main( float2 texCoord : TEXCOORD0 ) : COLOR
{
float3 texColor = tex2D(Texture0, texCoord );
texColor *= 16; // Hardcoded Exposure Adjustment
float ExposureBias = 2.0f;
float3 curr = Uncharted2Tonemap(ExposureBias*texColor);
float3 whiteScale = 1.0f/Uncharted2Tonemap(W);
float3 color = curr*whiteScale;
float3 retColor = pow(color,1/2.2);
return float4(retColor,1);
}
Is texColor the HDR color from the render? If so, then it doesn’t work for me!!!
0
103 May 25, 2012 at 02:07
thanks for the input Geon, yeh this turned out better than I expected, I guess I should add monsters now like Alienizer said… make a little fps thing with it :)
0
103 May 25, 2012 at 22:41
@rouncer
thanks for the input Geon, yeh this turned out better than I expected, I guess I should add monsters now like Alienizer said… make a little fps thing with it :)
Care to post a new screen shot?
0
103 May 26, 2012 at 02:24
Havent added monsters yet, its not a game at this stage, got a whole load of cleaning up to do.
ive got to improve the fps, ive been lazy up till now, its only running at about 15 fps, but i havent added vsd culling yet, im just doing that.
[EDIT] ive added vsd, but looks like ill have to put all the instances in an octree for maximum world size. [/EDIT]
what do you think I should do with it? what does it look like to you? :)
0
103 May 26, 2012 at 03:47
WOW, that looks awesome! Shadows could be just a little darker for better contrast (icy). But your sun (fire) is perfect to me. Love the sky too, it adds so much more realism.
ok, because of the sky and no visible ground, it looks like a flying machine, spaceship or something like that, where we see (somewhat) the exterior of the hull. Without the sky, then I wouldn’t have a clue of what it would be.
What’s the red stuff anyway? Blood?
You are doing a remarkable job!
0
103 May 26, 2012 at 03:51
oh, and to answer your first question, I think you should expand on it, get your imagination going and eventually, it’ll click, and you’ll get something out of this world. You seem very talented.
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103 Jun 04, 2012 at 03:37
Rouncer, hows your project going? Any new screen shots for us :)
0
110 Jun 05, 2012 at 00:31
Wow! Looks very good…
As for optimization - I don’t know what kind of renderer you’re actually using. I could try some BVH instead of Octree (it brings better results). Also if you’re using rasterizer - some Hierarchical Z-buffer occlusion culling might help a bit (or a lot - it really depends) - generally try frustum culling + occlusion culling.
Also if you’re drawing object instances - draw them as instances (not each one separately) - this can give you also some little boost. Then start profiling - see which parts are slow, which are fast - try to fasten slow ones (if possible). At last give option to turn off shadow, use less expensive lighting, etc.
And the light actually looks quite good - but it really miss some good global ambient occlusion (pre-computing it? dynamically computing it is quite heavy). But thanks for showing the work, it inspires me more and more to finish actual demo-version of our current project and release it for public :)
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103 Jun 05, 2012 at 03:55
Here is a screen shot of what I’m working on right now. What do you guys think of how it looks?
0
103 Jun 05, 2012 at 05:58
Looking good alienizer, as for my project im probably going to discontinue it and move onto voxels maybe, im not sure.
That tank looks amazing, love it.
0
101 Jun 05, 2012 at 12:56
@Alienizer
Here is a screen shot of what I’m working on right now. What do you guys think of how it looks?
It looks great!
Other than the ground and the edge where the fortress meets the ground, it is near photo-realistic.
0
103 Jun 05, 2012 at 16:45
@rouncer
Looking good alienizer, as for my project im probably going to discontinue it and move onto voxels maybe, im not sure. That tank looks amazing, love it.
Here’s something you may like about voxels…
0
103 Jun 05, 2012 at 16:47
@geon
It looks great! Other than the ground and the edge where the fortress meets the ground, it is near photo-realistic.
Thanks! :) What do you think I should do about the edge where the fortress meets the ground??
0
101 Jun 05, 2012 at 20:57
@Alienizer
Thanks! :) What do you think I should do about the edge where the fortress meets the ground??
I’m guessing you use baked AO on the tank? The corner formed by the ground and wall should have some AO as well. Some grass growing out of the corned would help too.
About the ground itself, the texture looks weird. Is it dried an crackled clay? Maybe another texture with some pepples and rocks with parallax mapping, combined with some matching boulder models would help. A few dried trees, etc. would be nice too.
0
103 Jun 06, 2012 at 14:56
Yes, I use baked AO, and the gound is (suppose to be) as you said. I’ll try to add more as you said. Thank for your comment Geon.
0
110 Jun 06, 2012 at 16:56
It actually doesn’t look that bad…
the tank is awesome :P - you did all the graphics, or hired a graphics guy?
the bunker looks very good.
the terrain looks like - “I needed some terrain to work with it, I’ll work on it later” - definitely not a problem at current stage ;)
And now my question - the shadows look good - does the app use some kind of PCSS or mip-maps, or? B)
Naaah :lol: - i’d love to show some current stuff right now (as shameless self-promotion :D), but I just don’t have graphics ready right now (don’t worry, graphics guys are hired (hooray … at least 3 times) :P and so far i’ll definitely have good stuff to show - not just from technical side)
0
101 Jun 06, 2012 at 17:22
@Vilem Otte
the terrain looks like - “I needed some terrain to work with it, I’ll work on it later” - definitely not a problem at current stage ;)
Spot on.
The ground texture is great, but doesn’t work well to cover 100% of the ground. (No texture would.) It would be perfect for place where dried, crackled clay would make sense, like a dried river bed.
0
103 Jun 06, 2012 at 18:05
@Vilem Otte
It actually doesn’t look that bad…
the tank is awesome :P - you did all the graphics, or hired a graphics guy?
the bunker looks very good.
the terrain looks like - “I needed some terrain to work with it, I’ll work on it later” - definitely not a problem at current stage ;)
And now my question - the shadows look good - does the app use some kind of PCSS or mip-maps, or? B)
Naaah :lol: - i’d love to show some current stuff right now (as shameless self-promotion :D), but I just don’t have graphics ready right now (don’t worry, graphics guys are hired (hooray … at least 3 times) :P and so far i’ll definitely have good stuff to show - not just from technical side)
Thanks! No, I didn’t make it. Someone else did :mellow:
The shadows, well, it’s kinda based on AO and PCF and something else I’ve been working on for a long time. Don’t know how to call it, but it’s not standard or anything from books. It’s my own creation. Works good, but slows thing down too much, and I’m trying to speed it up.
You must have something to show us don’t you \^_\^
0
103 Jun 06, 2012 at 18:07
@geon
Spot on. The ground texture is great, but doesn’t work well to cover 100% of the ground. (No texture would.) It would be perfect for place where dried, crackled clay would make sense, like a dried river bed.
I see what you mean. I like the idea of the dried river, that would look great with that texture. But for the rest, what do you suggest? Sand? not grass right!
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2013-12-09 15:50:59
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https://pybatfish.readthedocs.io/en/latest/notebooks/linked/validating-configuration-settings.html
|
# Validating Configuration Settings with Batfish¶
Network engineers routinely need to validate configuration settings of various devices in their network. In a multi-vendor network, this validation can be hard and few tools exist today to enable this basic task. However, the vendor-independent models of Batfish and its querying mechanisms make such validation almost trivial.
In this notebook, we show how to validate configuration settings with Batfish. More specifically, we examine how the configuration of NTP servers can be validated. The same validation scenarios can be performed for other configuration settings of nodes (such as dns servers, tacacs servers, snmp communities, VRFs, etc.) interfaces (such as MTU, bandwidth, input and output access lists, state, etc.), VRFs, BGP and OSPF sessions, and more.
Check out a video demo of this notebook here.
## Initializing our Network and Snapshot¶
SNAPSHOT_PATH below can be updated to point to a custom snapshot directory, see the Batfish instructions for how to package data for analysis. More example networks are available in the networks folder of the Batfish repository.
[1]:
# Import packages and load questions
%run startup.py
# Initialize a network and snapshot
NETWORK_NAME = "example_network"
SNAPSHOT_NAME = "example_snapshot"
SNAPSHOT_PATH = "networks/example"
bf_set_network(NETWORK_NAME)
bf_init_snapshot(SNAPSHOT_PATH, name=SNAPSHOT_NAME, overwrite=True)
[1]:
'example_snapshot'
The network snapshot that we initialized above is illustrated below. You can download/view devices’ configuration files here. We will focus on the validation for the six border routers.
## Extracting configured NTP servers¶
This can be done using the nodeProperties() question.
[2]:
# Set the property that we want to extract
COL_NAME = "NTP_Servers"
# Extract NTP servers for all routers with 'border' in their name
node_props = bfq.nodeProperties(
nodes="/border/",
node_props
[2]:
Node NTP_Servers
0 as1border2 ['18.18.18.18', '23.23.23.23']
1 as2border1 ['18.18.18.18', '23.23.23.23']
2 as3border2 ['18.18.18.18', '23.23.23.23']
3 as1border1 []
4 as3border1 ['18.18.18.18', '23.23.23.23']
5 as2border2 ['18.18.18.18']
The .frame() function call above returns a Pandas data frame that contains the answer.
## Validating NTP Servers Configuration¶
Depending on the network’s policy, there are several possible validation scenarios for NTP-servers configuration: 1. Every node has at least one NTP server configured. 2. Every node has at least one NTP server configured from the reference set. 3. Every node has the reference set of NTP servers configured. 4. Every node has NTP servers that match those in a per-node database.
We demonstrate each scenario below.
### Validation scenario 1: Every node has at least one NTP server configured¶
Now that we have the list of NTP servers, let’s check if at least one server is configured on the border routers. We accomplish that by using (lambda expressions) to identify nodes where the list is empty.
[3]:
# Find nodes that have no NTP servers configured
ns_violators = node_props[node_props[COL_NAME].apply(
lambda x: len(x) == 0)]
ns_violators
[3]:
Node NTP_Servers
3 as1border1 []
### Validation scenario 2: Every node has at least one NTP server configured from the reference set.¶
Now if we want to validate that configured NTP servers should contain at least one NTP server from a reference set, we can use the command below. It identifies any node whose configured set of NTP servers does not overlap with the reference set at all.
[4]:
# Define the reference set of NTP servers
ref_ntp_servers = set(["23.23.23.23"])
# Find nodes that have no NTP server in common with the reference set
ns_violators = node_props[node_props[COL_NAME].apply(
lambda x: len(ref_ntp_servers.intersection(set(x))) == 0)]
ns_violators
[4]:
Node NTP_Servers
3 as1border1 []
5 as2border2 ['18.18.18.18']
Because as1border1 has no configured NTP servers, it clearly violates our assertion, and so does as2border2 which has a configured server but not one that is present in the reference set.
### Validation scenario 3: Every node has the reference set of NTP servers configured¶
A common use case for validating NTP servers involves checking that the set of NTP servers exactly matches a desired reference set. Such validation is quite straightforward as well.
[5]:
# Find violating nodes whose configured NTP servers do not match the reference set
ns_violators = node_props[node_props[COL_NAME].apply(
lambda x: ref_ntp_servers != set(x))]
ns_violators
[5]:
Node NTP_Servers
0 as1border2 ['18.18.18.18', '23.23.23.23']
1 as2border1 ['18.18.18.18', '23.23.23.23']
2 as3border2 ['18.18.18.18', '23.23.23.23']
3 as1border1 []
4 as3border1 ['18.18.18.18', '23.23.23.23']
5 as2border2 ['18.18.18.18']
As we can see, all border nodes violate this condition.
A slightly advanced version of pandas filtering can also show us which configured NTP servers are missing or extra (compared to the reference set) at each node.
[6]:
# Find extra and missing servers at each node
ns_extra = node_props[COL_NAME].map(lambda x: set(x) - ref_ntp_servers)
ns_missing = node_props[COL_NAME].map(lambda x: ref_ntp_servers - set(x))
# Join these columns up with the node columns for a complete view
diff_df = pd.concat([node_props["Node"],
ns_extra.rename('extra-{}'.format(COL_NAME)),
ns_missing.rename('missing-{}'.format(COL_NAME))],
axis=1)
diff_df
[6]:
Node extra-NTP_Servers missing-NTP_Servers
0 as1border2 {18.18.18.18} {}
1 as2border1 {18.18.18.18} {}
2 as3border2 {18.18.18.18} {}
3 as1border1 {} {23.23.23.23}
4 as3border1 {18.18.18.18} {}
5 as2border2 {18.18.18.18} {23.23.23.23}
### Validation scenario 4: Every node has NTP servers that match those in a per-node database.¶
Every node should match its reference set of NTP Servers which may be stored in an external database. This check enables easy validation of configuration settings that differ acorss nodes.
We assume data from the database is fetched in the following format, where node names are dictionary keys and specific properties are defined in a property-keyed dictionary per node.
[7]:
# Mock reference-node-data, presumably taken from an external database
database = {'as1border1': {'NTP_Servers': ['23.23.23.23'],
'DNS_Servers': ['1.1.1.1']},
'as1border2': {'NTP_Servers': ['23.23.23.23'],
'DNS_Servers': ['1.1.1.1']},
'as2border1': {'NTP_Servers': ['18.18.18.18', '23.23.23.23'],
'DNS_Servers': ['2.2.2.2']},
'as2border2': {'NTP_Servers': ['18.18.18.18'],
'DNS_Servers': ['1.1.1.1']},
'as3border1': {'NTP_Servers': ['18.18.18.18', '23.23.23.23'],
'DNS_Servers': ['2.2.2.2']},
'as3border2': {'NTP_Servers': ['18.18.18.18', '23.23.23.23'],
'DNS_Servers': ['2.2.2.2']},
}
Note that there is an extra property in this dictionary that we don’t care about comparing right now: dns-server. We will filter out this property below, before comparing the data from Batfish to that in the database.
After a little massaging, the database and Batfish data can be compared to generate two sets of servers: missing (i.e., present in the database but not in the configurations) and extra (i.e., present in the configurations but not in the database).
[8]:
# Transpose database data so each node has its own row
database_df = pd.DataFrame(data=database).transpose()
# Index on node for easier comparison
df_node_props = node_props.set_index('Node')
# Select only columns present in node_props (get rid of the extra dns-servers column)
df_db_node_props = database_df[df_node_props.columns].copy()
# Convert server lists into sets to support arithmetic below
df_node_props[COL_NAME] = df_node_props[COL_NAME].apply(set)
df_db_node_props[COL_NAME] = df_db_node_props[COL_NAME].apply(set)
# Figure out what servers are in the configs but not the database and vice versa
missing_servers = (df_db_node_props - df_node_props).rename(
columns={COL_NAME: 'missing-{}'.format(COL_NAME)})
extra_servers = (df_node_props - df_db_node_props).rename(
columns={COL_NAME: 'extra-{}'.format(COL_NAME)})
result = pd.concat([missing_servers, extra_servers], axis=1, sort=False)
# removing the index name for clearer output
del result.index.name
result
[8]:
missing-NTP_Servers extra-NTP_Servers
as1border1 {23.23.23.23} {}
as1border2 {} {18.18.18.18}
as2border1 {} {}
as2border2 {} {}
as3border1 {} {}
as3border2 {} {}
## Continue exploring¶
We showed you how to extract the database of configured NTP servers for every node and how to test that the settings are correct for a variety of desired test configurations. The underlying principles can be applied to other network configurations, such as interfaceProperties, bgpProcessConfiguration, ospfProcessConfiguration etc.
For example interfaceProperties() question can be used to fetch properties like interface MTU using a simple command.
[9]:
# Extract interface MTU for Ethernet0/0 interfaces on border routers
interface_mtu = bfq.interfaceProperties(
interfaces="/border/[Ethernet0/0]",
interface_mtu
[9]:
Interface MTU
0 as1border1[Ethernet0/0] 1500
1 as3border2[Ethernet0/0] 1500
2 as3border1[Ethernet0/0] 1500
3 as1border2[Ethernet0/0] 1500
4 as2border2[Ethernet0/0] 1500
5 as2border1[Ethernet0/0] 1500
## Get involved with the Batfish community!¶
Start interacting through Slack or GitHub to know more. We would love to talk with you about Batfish or your Network!
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2020-09-29 01:38:01
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https://www.physicsforums.com/threads/work-energy-block-w-friction.363533/
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# Work Energy: block w/ friction
1. Dec 15, 2009
### schyuler2
1. The problem statement, all variables and given/known data
Find the initial speed of a block which travels 10m along a horizontal surface if $$\mu$$= 0.40 between the block and the surface before stopping.
2. Relevant equations
$$\Sigma$$W = 1/2mvB2 - 1/2mvA2 + mgyB - mgyA
$$\Sigma$$W = W * dAB * cos (W, dAB)
f = $$\mu$$* N
N= mgsin$$\theta$$
3. The attempt at a solution
so far i have:
$$\Sigma$$W = 0
$$\Sigma$$W = WN + WW + Wf
and
$$\Sigma$$W = WW * dAB * cos (270)
$$\Sigma$$W = WW * 10m * 0
not sure if i'm doing this right or where to go from here
2. Dec 15, 2009
### qnney
This problem requires an equation that you haven't included yet.
$$\Sigma$$F = max
$$\Sigma$$F = Px + fx + Nx + Wx
$$\mu$$ = -a / g
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2018-03-17 18:42:56
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https://greprepclub.com/forum/in-a-certain-sequence-the-term-an-is-defined-by-the-formula-10127.html
|
It is currently 18 Sep 2020, 06:28
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In a certain sequence, the term an is defined by the formula
Author Message
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In a certain sequence, the term an is defined by the formula [#permalink] 27 Jul 2018, 07:17
Expert's post
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Question Stats:
62% (02:23) correct 37% (02:23) wrong based on 24 sessions
In a certain sequence, the term an is defined by the formula $$a_n = 2 \times a_{n - 1}$$ for each integer n ≥ 2. If $$a_1 = 1$$, what is the positive difference between the sum of the first 10 terms of the sequence and the sum of the 11th and 12th terms of the same sequence?
(A) 1
(B) 1,024
(C) 1,025
(D) 2,048
(E) 2,049
[Reveal] Spoiler: OA
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Joined: 07 Jun 2014
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Followers: 171
Kudos [?]: 2911 [0], given: 394
Re: In a certain sequence, the term an is defined by the formula [#permalink] 12 Aug 2018, 05:35
Expert's post
Explanation
This is a geometric sequence: each new number is created by multiplying the previous number by 2.
Calculate the first few terms of the series to find the pattern: 1, 2, 4, 8, 16, and so on.
Geometric sequences can be written in this form: $$a_n = r^{n – 1}$$, where r is the multiplied constant and n is the number of the desired term. In this case, the function is $$a_n = 2^{n – 1}$$.
The question asks for the difference between the sum of the first 10 terms and the sum of the 11th and 12th terms. While there is a clever pattern at play, it is hard to spot. If you don’t see the pattern, one way to solve is to use the calculator to add the first ten terms: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1,023.
The 11th term plus the 12th term is equal to 1,024 + 2,048 = 3,072. Subtract 1,023 to get 2,049.
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Re: In a certain sequence, the term an is defined by the formula [#permalink] 19 Jul 2020, 12:05
Does GRE bring something like that ?
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Re: In a certain sequence, the term an is defined by the formula [#permalink] 19 Jul 2020, 12:58
Expert's post
The question is legit
See here for more https://greprepclub.com/forum/gre-quant ... tml#p54127
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Re: In a certain sequence, the term an is defined by the formula [#permalink] 19 Jul 2020, 12:58
Display posts from previous: Sort by
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2020-09-18 14:28:55
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https://civil.gateoverflow.in/1481/gate2020-ce-2-30
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Joints $I,J,K,L,Q$ and $M$ of the frame shown in the figure (not drawn to the scale) are pins. Continuous members $IQ$ and $LJ$ are connected through a pin at $N$. Continuous members $JM$ and $KQ$ are connected through a pin at $P$. The frame has hinge supports at joints $R$ and $S$. The loads acting at joints $I,J$ and $K$ are along the negative $Y$ direction and the loads acting at joints $L$ and $M$ are along the positive $X$ direction.
The magnitude of the horizontal component of reaction $\text{(in kN)}$ at $S,$ is
1. $5$
2. $10$
3. $15$
4. $20$
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2020-09-30 08:04:58
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https://mathoverflow.net/questions/331525/representation-of-4-times4-matrices-in-the-form-of-sum-b-i-otimes-c-i
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# Representation of $4\times4$ matrices in the form of $\sum B_i\otimes C_i$
Every matrix $$A\in M_4(\mathbb{R})$$ can be represented in the form of $$A=\sum_{i=1}^{n(A)} B_i\otimes C_i$$ for $$B_i,C_i\in M_2(\mathbb{R})$$.
What is the least uniform upper bound $$M$$ for such $$n(A)$$? In other words, what is the least integer $$M$$ such that every $$A$$ admit such a representation with $$n(A)\leq M$$?
Is this least upper bound equal to the corresponding least upper bound for all matrices $$A$$ which are a matrix representation of quaternions $$a+bi+cj+dk$$?
As another question about tensor product representation: What is a sufficient condition for a $$4\times 4$$ matrix $$A$$ to be represented in the form of $$A=B\otimes C -C\otimes B$$?
Because $$M_4(\mathbb R) = M_2(\mathbb R) \otimes M_2(\mathbb R)$$ as vector spaces (and as algebras, but we won't use this), we can replace $$M_2(\mathbb R)$$ by an arbitrary $$4$$-dimensional vector space $$V$$ and $$M_4(\mathbb R)$$ by $$V \otimes V$$. We can represent elements of $$V\otimes V$$ conveniently as $$4\times 4$$ matrices, where simple tensors are rank one matrices. The question is then equivalent to asking the minimum number of rank $$1$$ matrices it takes to write a $$4 \times 4$$ matrix as a sum of rank $$1$$ matrices. The answer is obviously $$4$$.
For quaternions acting by left multiplication by quaternions in the standard basis:
$$1= \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix} \otimes\begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix}$$
$$i= \begin{pmatrix} 0 & -1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 \\ 0 & 0 & 1 & 0 \end{pmatrix} = \begin{pmatrix} 0 & -1 \\1 & 0 \end{pmatrix} \otimes\begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix}$$
$$j= \begin{pmatrix} 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \otimes\begin{pmatrix} 0 & -1 \\1 & 0 \end{pmatrix}$$
$$k= \begin{pmatrix} 0 & 0 & 0 & -1 \\ 0 & 0 & -1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \otimes\begin{pmatrix} 0 & -1 \\1 & 0 \end{pmatrix}$$
Because only two terms appear on the right side, the matrices clearly have rank at most $$2$$ at tensor product, and some obtain rank exactly $$2$$, so the answer is two.
For the last question, the answer is isomorphic to the analogous answer for writing an element of $$V \otimes V$$ as $$v_1 \otimes v_2 - v_2 \otimes v_1$$ for $$V$$ a four-dimensional vector space. The condition is given by a skew-symmetry condition (i.e. 10 linear conditions) plus a Pfaffian condition (a quadratic condition). More precisely the general such matrix can be written as
$$\begin{pmatrix} 0 & a & -a & 0 \\ b & c & d & e \\ -b & -d & -c & -e \\ 0 & f & -f & 0 \\ \end{pmatrix}$$
such that $$af-be+cd=0$$
• "this is equivalent to asking the minimum number of rank 1 matrices it takes to write a 4×4 matrix as a sum of rank 1 matrices. The answer is obviously 4." @WillSavin I do not understand this sentence. – Paul Broussous May 15 at 9:01
• @PaulBroussous We are asking what are the minimum $n$ such that all elements of $V \otimes W$ can be written as $\sum_{i=1}^{n} v_i \otimes w_i$ for $v_i \in V, w_i \in W$, where $V$ and $W$ are four-dimensional vector spaces. We can represent elements of $V \otimes W$ as $4 \times 4$ matrices, in which case the elements of the form $v_i \otimes w_i$ are the rank $1$ matrices. So we are asking for the minimum $n$ to write any $4 \times 4$ matrix as a sum of $n$ rank one matrix. The answer is $4$ - e.g. we can take the columns or the rows. – Will Sawin May 15 at 13:32
• OK, I understand. Here you use the canonical isomorphism $V\otimes V^* \simeq {\rm End}(V)$, which has nothing to do with the natural isomorphism $M_4 ({\mathbb R})\simeq M_2 ({\mathbb R})\otimes M_2 ({\mathbb R})$. Indeed in that last isomorphim, $A\otimes B$, $A$, $B\not= 0$, is not necessarily a rank $1$ matrix ! – Paul Broussous May 15 at 13:57
• @PaulBroussous Yes, the structure of $M_4(\mathbb R)$ is irrelevant for this problem, so we discard it, viewing $M_4(\mathbb R)$ only as $M_2(\mathbb R)\otimes M_2(\mathbb R)$, and then the structure of $M_2(\mathbb R)$ is irrelevant as well. I had already forgotten about this after the first line and so didn't realize that bringing in $4 \times 4$ matrices again would be potentially confusing. – Will Sawin May 15 at 15:39
• @ZachTeitler It's skew symmetric when written in the standard matrix notation for elements of $V \otimes V$, $V$ a four-dimensional vector space, and the Pfaffian is the standard Pfaffian. But if we specialize to $V= M_2(\mathbb R)$ we have another way to write elements of the same vector space as matrices, using $M_2(\mathbb R) \otimes M_2(\mathbb R) = M_4(\mathbb R)$. I have written it in that way, so it no longer appears skew-symmetric. Concretely this just means we permute the entries. It might be fun to work out what this permutation does and why this formula is right - it was for me. – Will Sawin May 16 at 0:40
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2019-05-20 09:50:02
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http://mathhelpforum.com/algebra/179383-dividing-ratios.html
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1. ## Dividing ratios.
A question has come up on a mock exam and i'm not sure if i have done it correctly so please can you tell me if i have done it wrong or if it is right?
Peter and Margaret's ages are in the ratio 4:5. If Peter is 16 years old, how old is Margaret?
Peter = 4/9
so 1/9 is 16 divided by 4 = 4
4 x 5 = 20
Margaret is 20.
2. you have the right answer
3. Originally Posted by mollyx
A question has come up on a mock exam and i'm not sure if i have done it correctly so please can you tell me if i have done it wrong or if it is right?
Peter and Margaret's ages are in the ratio 4:5. If Peter is 16 years old, how old is Margaret?
Peter = 4/9
so 1/9 is 16 divided by 4 = 4
4 x 5 = 20
Margaret is 20.
$4:5=16:?$
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2017-05-29 14:26:46
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http://mathhelpforum.com/advanced-algebra/81569-linear-transformation-matrix-print.html
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# Linear Transformation Matrix
• March 30th 2009, 07:52 PM
flaming
Linear Transformation Matrix
Let v be a fixed vector in http://www.mathhelpforum.com/math-he...005b84a8-1.gif. T(u) = v x u is a linear transformation.
If v = i for the transformation above. How do I find the matrix for this linear Transformation
• March 30th 2009, 08:06 PM
TheEmptySet
Quote:
Originally Posted by flaming
Let v be a fixed vector in http://www.mathhelpforum.com/math-he...005b84a8-1.gif. T(u) = v x u is a linear transformation.
If v = i for the transformation above. How do I find the matrix for this linear Transformation
You would need to find the transform of each of the basis vectors and these will be the columns of your matrix
[T(i)|T(j)|T(k)]
Note that $T(i)=0,T(j)=k,T(k)=j$
$\begin {bmatrix}
0 & 0 & 0 \\
0 & 0 & 1 \\
0 & 1 & 0 \\
\end {bmatrix}$
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2014-07-30 03:44:00
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https://agentfoundations.org/item?id=242
|
Agents that can predict their Newcomb predictor
post by Patrick LaVictoire 932 days ago | Jessica Taylor likes this | 4 comments
There’s a certain type of problem where it appears that having more computing power hurts you. That problem is the “agent simulates predictor” Newcomb’s Dilemma.
There’s a version of Newcomb’s Problem that poses the same sort of challenge to UDT that comes up in some multi-agent/game-theoretic scenarios.
Suppose:
• The predictor does not run a detailed simulation of the agent, but relies instead on a high-level understanding of the agent’s decision theory and computational power.
• The agent runs UDT, and has the ability to fully simulate the predictor.
Since the agent can deduce (by low-level simulation) what the predictor will do, the agent does not regard the prediction outcome as contingent on the agent’s computation. Instead, either predict-onebox or predict-twobox has a probability of 1 (since one or the other of those is deducible), and a probability of 1 remains the same regardless of what we condition on. The agent will then calculate greater utility for two-boxing than for one-boxing.
Meanwhile, the predictor, knowing that the the agent runs UDT and will fully simulate the predictor, can reason as in the preceding paragraph, and thus deduce that the agent will two-box. So the large box is left empty and the agent two-boxes (and the agent’s detailed simulation of the predictor correctly shows the predictor correctly predicting two-boxing).
The agent would be better off, though, running a different decision theory that does not two-box here, and that the predictor can deduce does not two-box.
EDITED 5/19/15: There’s a formal model of this due to Vladimir Slepnev where the agent and the predictor both have different types of predictive powers, such that in some sense they each know how the other will act in this universe. We’ll write this out along with another case where things work out properly.
(One algorithm has more computing power, but the other has stronger axioms: in particular, strong enough to prove that the other formal system is sound, as ZFC proves that PA is sound.)
In one of the following cases, proof-based UDT one-boxes for correct reasons; in the other case, it two-boxes analogously to the reasoning above.
In both cases, we’ll use the following lemma:
Lemma: Let $$A()$$ be an algorithm that returns either 1 or 2, such that ZFC has a proof of length $$\approx \log(N)$$ of “$$A()$$ returns in $$\leq N$$ steps”. Then ZFC has a proof of length $$\approx \log(N)$$ that “$$A()=1$$ if and only if PA proves that $$A()=1$$.”
Proof: ZFC knows that PA is sound, so ZFC has a short proof that “if PA proves that $$A()=1$$, then $$A()=1$$”. The other direction follows from the fact that the algorithm is bounded, and PA can simply show the execution trace of $$A$$ in $$\leq CN$$ steps.
# Case 1: Success (Agent Trusts Predictor)
Omega looks through all proofs in PA; when it finds a proof that the agent one-boxes or a proof that the agent two-boxes, it stops looking and fills or empties the box accordingly. (If it fails to prove either, it empties the box.)
The agent looks several times through all proofs in ZFC of length $$\leq N$$; it first looks for a proof that one of its actions leads to the payoff $1001000, then$1000000, then $1000, then$0. The first time it finds a proof that an action implies the outcome it’s looking for, it immediately takes that action. (If it fails to find any such proof, it two-boxes.)
I claim that for sufficiently large $$N$$, the agent one-boxes, and Omega fills the box.
Proof: We use the Lemma. ZFC proves in $$\leq N$$ steps that $$A()=1 \leftrightarrow \Box_{PA}[A()=1]$$. Since we (from outside the problem) assume ZFC is consistent, it will not be able to prove that two-boxing gets it $1001000, nor that one-boxing gets it$1001000, nor that two-boxing gets it $1000000, but it will be able to prove that one-boxing gets it$1000000. Thus it one-boxes. Since it runs in finite time, of course PA proves it one-boxes, and so Omega fills the box.
# Case 2: Failure (Agent Simulates Predictor)
We’ll swap the deductive processes this time. Omega looks through all proofs in ZFC of length $$\leq N$$; when it finds a proof that the agent one-boxes or a proof that the agent two-boxes, it stops looking and fills or empties the box accordingly. (If it fails to prove either, it empties the box.)
The agent looks several times through all proofs in PA; it first looks for a proof that one of its actions leads to the payoff $1001000, then$1000000, then $1000, then$0. The first time it finds a proof that an action implies the outcome it’s looking for, it immediately takes that action. (If it fails to find any such proof, it two-boxes.)
I claim that the agent two-boxes, and Omega leaves the box empty.
Proof: Again, by the lemma, ZFC proves that $$\Omega()=1 \leftrightarrow \Box_{PA}[\Omega()=1]$$ (where $$\Omega()=1$$ means “Omega predicts one-boxing and thus fills the box”). Now note that $$\Omega()=1$$ implies that PA proves $$A()=2 \to U=\1001000$$ and does not prove that $$A()=1 \to U=\1001000$$, and thus in this case $$A()=2$$; and similarly, $$\Omega()=2$$ implies that PA proves $$A()=2 \to U=\1000$$ and does not prove any of the prior counterfactuals, so again $$A()=2$$. All of these proofs are quick within ZFC, so $$\Omega$$ does prove that $$A()=2$$, and thus $$\Omega()=2$$.
by Vladimir Slepnev 921 days ago | Benja Fallenstein and Patrick LaVictoire like this | link Your second case seems really similar to my post about ASP from 2011: http://lesswrong.com/lw/5rq/example_decision_theory_problem_agent_simulates/ reply
by Patrick LaVictoire 920 days ago | link You’re absolutely right. I know I was in a hurry writing this post, but I don’t know how I managed to skip reading the second half of the post that I excerpted. reply
by Benja Fallenstein 906 days ago | Patrick LaVictoire likes this | link The other direction follows from the fact that the algorithm is bounded, and PA can simply show the execution trace of $$A$$ in $$\le CN$$ steps. Unimportant technical point: I think the length of the PA proof grows faster than this. (More precisely, the length in symbols, rather than the length in number of statements; we’re almost always interested in the former, since it determines how quickly a proof can be checked or be found by exhaustive search.) The obvious way of showing $$A() = 1$$ in PA is to successively show for higher and higher $$t$$ that “after $$t$$ ticks, the Turing machine computing $$A()$$ is in the following state, and its tapes have the following content”. But even to write out the contents of the tape of a Turing machine that has run for $$t$$ ticks will in general take $$t$$ symbols. So the obvious way of doing the proof takes at least $$O(t^2)$$ symbols. Moreover, I’m not sure whether we can get from “at time $$t$$, the configuration is such-and-such” to “at time $$t+1$$, the configuration is such-and-such” in a constant number of proof steps. I suspect we don’t need more than $$O(t^3)$$ symbols overall, but I’m not extremely confident. (I’d be quite surprised if the time turned out not to be polynomial, though!) reply
by Patrick LaVictoire 897 days ago | Jessica Taylor likes this | link Note that in both this and the other model of Agent Simulates Predictor, the agent’s formal system does not know that the predictor’s formal system is consistent. One could argue that in this case it’s right to two-box. However, it’s still worrisome that the agent’s formal system proves $$A()=1 \to U()= \0$$ and does not prove $$A()=1 \to U()= \1000000$$, rather than proving both counterfactuals (spuriously) or neither. reply
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2017-11-24 23:56:49
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https://lefschetzseminar.org/2022/02/
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## Sagun Chanillo (Rutgers University)
11 February 2022
A Local version of Courant’s Nodal Domain Theorem
Let (M^n, g) denote a smooth and compact Riemannian manifold with no boundary equipped with a smooth Riemannian metric g. Courant’s nodal domain theorem asserts that for the Laplace-Beltrami operator on M, if we order the eigenvalues in increasing order with multiplicity, then the eigenfunction for the k-th eigenvalue has at most k connected components(the nodal domains) where the eigenfunction does not vanish. C. Fefferman and H. Donnelley proposed about 30 years ago a local version of this result on every ball in M. This local question is connected with the question of S.-T. Yau on the length of the zero set of the eigenfunctions. We propose to give answers to this question. This work is joint with A. Logunov E. Mallinikova and D. Mangoubi.
## Azahara DelaTorre Pedraza (Sapienza Università di Roma)
4 February 2022
The fractional Yamabe problem with singularities
The so called Yamabe problem in Conformal Geometry consists in finding a metric conformal to a given one and which has constant scalar curvature. From the analytic point of view, this problem becomes a semilinear elliptic PDE with critical (for the Sobolev embedding) power non-linearity. If we study the problem in the Euclidean space, allowing the presence of nonzero-dimensional singularities can be transformed into reducing the non-linearity to a Sobolev-subcritical power. A quite recent notion of non-local curvature gives rise to a parallel study which weakens the geometric assumptions giving rise to a non-local semilinear elliptic PDE.
In this talk, we will focus on metrics which are singular along nonzero-dimensional singularities. In collaboration with Ao, Chan, Fontelos, González and Wei, we covered the construction of solutions which are singular along (zero and positive dimensional) smooth submanifolds in this fractional setting. This was done through the development of new methods coming from conformal geometry and Scattering theory for the study of non-local ODEs. Due to the limitations of the techniques we used, the particular case of “maximal” dimension for the singularity was not covered. In a recent work, in collaboration with H. Chan, we cover this specific dimension constructing and studying singular solutions of critical dimension.
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2023-01-28 17:22:58
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https://kullabs.com/classes/subjects/units/lessons/notes/note-detail/2151
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Notes on Trigonometry | Grade 9 > Compulsory Maths > Trigonometry | KULLABS.COM
• Note
• Things to remember
• Videos
• Exercise
• Quiz
The word "Trigonometry" is derived from the Greek word "Tri-Gonia-Metron" where 'Tri' means 'three', 'Gonia' means 'angles' and 'Metron' mean 'measure'. So, trigonometry is a branch of mathematics which concerned with the measurement of sides, angles and their relation to a triangle.
#### Trigonometric Ratios
The word trigonometry comes from the combination of the word triangle goes on having the meaning of the measurement of three angles of triangles. Hence, this is also known as the measure of the triangle. Trigonometry has wide application in the field of mathematics and science. With the help of right angles triangle, trigonometric ratios of an angle are found. Without the help of trigonometric ratios, both the development and expansion of physics and also of engineering are impossible. Hence, trigonometry is the very important branch of mathematics.
Above figure shows the shadow of the poles formed at 3 pm that stand perpendicularly on the road. For each figure, the ratio of height of pole and length of shadow and height: length are tabulated below:
Pole height of pole length of shadow height:length angle made with the ground a 3m 2m 3:2 56o b 6m 4m 3:2 56o
Hence, the height of every pole and the length of their shadows are in proportion. The angle made by the top of the pole and with the top of shadow on the ground is also equal.
#### Fundamentals of Trigonometric Ratios
The ratio of any two sides of a right-angled triangle taking one of the side as reference are the fundamentals of trigonometric ratios.
Let know on detail about ratio with a figure. Here, in the given figure, ΔABC is a right angled triangle. $$\angle$$B = 90oand $$\angle$$C =θ.
Let's take$$\angle$$C as a reference angle
The opposite side of angle C (perpendicular) (P) = AB
The adjacent side of angle C (base) (B) = BC and (hypotenuse) (H) = AC
We can make three relation with the reference angle.
• relation between perpendicular and hypotenuse
In the above figure, the ratio of AB (perpendicular) to AC (base) with reference angle is called sine θ.
∴ sin θ = $$\frac{AB}{AC}$$ = $$\frac{perpendicular}{hypotenuse}$$ = $$\frac{p}{h}$$
• relation between base and hypotenuse
In the above figure, the ratio of BC (base) to AC (base) with reference angle is called cosine θ.
∴ cos θ = $$\frac{BC}{AC}$$ = $$\frac{base}{hypotenuse}$$ = $$\frac{b}{h}$$
• relation between perpendicular and base
In the above figure, the ratio of AB (perpendicular) to BC (base) with reference angle is called tangent θ.
∴ tan θ = $$\frac{AB}{BC}$$ = $$\frac{perpendicular}{base}$$ = $$\frac{p}{b}$$
#### Pythagoras Theorem
The relationship between the three sides of a triangle is simply known as Pythagoras Theorem. The relation was given by the popular Mathematician Pythagoras so it is called as Pythagorean theorem.
In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
According to this theorem "In any right-angled triangle, the area of the square on the hypotenuse is equal to the sum of the areas of squares of perpendicular and base".
By Pythagoras Theorem
Hypotenuse (h2) = Perpendicular (p2) + Base (b2)
or, h2= p2+ b2
From this theory we can derive,
h = $$\sqrt{p^{2} + b^{2}}$$
p = $$\sqrt{h^{2} - b^{2}}$$
b = $$\sqrt{h^{2} - p^{2}}$$
Theoretical proof:
Given: ΔABC is a right angled triangle in which $$\angle$$ABC = 90o.
To prove: CA2 = AB2 + BC2
Construction: BD ⊥AC is draawn
Proof:
S.N. Statements Reasons 1. In ΔABC and ΔBCD i. $$\angle$$ABC =$$\angle$$BDC (A) Both of them are right angles ii. $$\angle$$BCA =$$\angle$$BCD (A) ommon angles iii. $$\angle$$BAC = $$\angle$$DBC (A) Remaining angles of the triangles 2. $$\frac{CA}{BC}$$ = $$\frac{BC}{CD}$$ or, BC2 = CA.CD A.A.A. axiom 3. ΔABC∼ΔABD Same as above 4. $$\frac{CA}{AB}$$ = $$\frac{AB}{AD}$$ or, AB2 = CA.AD Corresponding sides of similar triangles 5. AB2 + BC2 = CA.AD + CA.CD or, AB2 + BC2 = CA (AD + CD) or, AB2 + BC2 = CA.CA or, AB2 + BC2 = CA2 Adding the statments (2) and (4)
Angle Degree Radinas Right Angle 90o π/2 Straight Angle 180o π Full Rotation 360o 2 π
Trigonometry is all about finding triangles. The terms like Sin, Cos and Tan helps us in trigonometry.
.
### Very Short Questions
Given , in BCA
Opposite side of x (AB) = p = 24
Adjacent side of x (AC) = b = 1 0
Opposite side of (<A = 90o) h = 26
Here , sin x = $$\frac{p}{h}$$ = $$\frac{24}{26}$$ = $$\frac{12}{13}$$ = 0.92
cos x = $$\frac{b}{h}$$ = $$\frac{10}{26}$$ = $$\frac{5}{13}$$ = 0.38
and
tan x = $$\frac{p}{b}$$ = $$\frac{24}{10}$$ = $$\frac{12}{5}$$ = 2.40
In given ACB ,
Opposite side of x = p = 1.2 cm
Adjacent side of x = b = 0.9 cm
Oppsite side of B = h = ?
Here , by pythagoras theroem ,
h2 =p2 + b2
h = $$\sqrt{p^{2} + b^{2}}$$
= $$\sqrt{1.2^{2} + 0.9 ^{2}}$$
= $$\sqrt{1.44 + 0.81}$$
= $$\sqrt{2.25}$$
= 1.5 cm.
Now ,
sinx = $$\frac{p}{h}$$ = $$\frac{1.2 cm}{1.5 cm}$$ = $$\frac{12}{15}$$ = $$\frac{4}{5}$$
cos x = $$\frac{b}{h}$$ = $$\frac{0.9 cm}{1.5 cm}$$ = $$\frac{09}{15}$$ = $$\frac{3}{5}$$
and
tanx = $$\frac{p}{b}$$ = $$\frac{1.2cm}{0.9 cm}$$ = $$\frac{12}{9}$$ = $$\frac{4}{3}$$
In given triangle EFG ,
p = EF = 9 cm , b = FG = 40cm , h = EG = ?
h2 = p2 + b2
or , h = $$\sqrt{p^{2} + b^{2}}$$
or , $$\sqrt{9^{2} + 40^{2}}$$ = $$\sqrt{81 + 1600}$$ = $$\sqrt{1681}$$ = 41 cm.
Now ,
sinx =$$\frac{p}{h}$$ = $$\frac{9}{41}$$ = $$\frac{9}{41}$$
cosx = $$\frac{b}{h}$$ = $$\frac{40}{41}$$ = $$\frac{40}{41}$$
and tanx = $$\frac{p}{b}$$ = $$\frac{9}{40}$$ = $$\frac{9}{40}$$
In given PQR , h = QR = 25cm , b = QP = 7cm ,
p = PR = ?
By Pythagoras theorem ,
p2 + b2 = h2
or , p2 = h2 - h2
$$\therefore$$ p = $$\sqrt{h ^{2} - b^{2}}$$ = $$\sqrt{25 ^{2} - 7^{2}}$$
= $$\sqrt{576}$$ = 24 cm.
Here ,
sinx = $$\frac{p}{h}$$ = $$\frac{24}{25}$$ = $$frac{24}{25}$$
cosx = $$\frac{b}{h}$$ = $$\frac{7}{25}$$ = $$\frac{7}{25}$$
and
tanx = $$\frac{p}{b}$$ = $$\frac{24}{7}$$ = $$=frac{24}{7}$$
In given XYZ ,
p = XY = 16 , h = XZ = 65 , b = YZ = ?
p2 + b2 = h2
or , b2 = h2 - p2
b = $$\sqrt{h^{2} - p^{2}}$$ =$$\sqrt{65^{2} - 16^{2}}$$
= $$\sqrt{3969}$$ = 63.
Here ,
sinx = $$\frac{p}{h}$$ = $$\frac{16}{65}$$ = $$\frac{16}{65}$$
cosx = $$\frac{b}{h}$$ = $$\frac{63}{65}$$ = $$\frac{63}{65}$$
and
tanx = $$\frac{p}{b}$$ = $$\frac{16}{63}$$ = $$\frac{16}{63}$$
= ( $$\frac{1}{2}$$ )2 + ( $$\frac{1}{\sqrt {2}}$$ )2 + ( $$\frac{\sqrt{3}}{2}$$ )2
= $$\frac{1}{4}$$+ $$\frac{1}{2}$$ +$$\frac{3}{4}$$
= $$\frac{1+2+3}{4}$$
= $$\frac{3}{2}$$
= 1$$\frac{1}{2}$$
cos$$\beta$$ = $$\sqrt{3}$$ $$\times$$ $$\frac{1}{2}$$
or ,cos$$\beta$$ = $$\frac{\sqrt{3}}{2}$$
or ,cos$$\beta$$ = cos 30o
$$\therefore$$ $$\beta$$ = 30o Ans.
or , sin2$$\beta$$ = $$\frac{1}{4}$$
or , sin2 $$\beta$$ =( $$\frac{1}{2}$$ )2
or , sin2 $$\beta$$ = (sin30o)2
or ,sin $$\beta$$ = sin30o
$$\therefore$$ $$\beta$$ = 30o Ans.
0%
• ### In a right-angled triangle, sin θ=(frac{1}{2}),find the numerical value of cos θ.
(frac{sqrt 4}{2})
(frac{sqrt 3}{2})
(frac{sqrt 5}{4})
(frac{sqrt 6}{3})
• ### Express sec A in terms of tan A.
`(sqrt{1+sin^2 A})
(sqrt{3-sin^2 A})
(sqrt{1+tan^2 A})
(sqrt{4+sin^2 A})
• ### Express cosA in terms of sin A.
(sqrt{1-cos^2 A})
(sqrt{1-cos A})
(sqrt{1-sin^2 A})
(sqrt{1-sin A})
(frac{1}{1})
(frac{4}{2})
(frac{3}{2})
(frac{1}{3})
(frac{3}{2})
(frac{4}{2})
(frac{2}{1})
(frac{1}{2})
(frac{2}{1})
(frac{3}{2})
(frac{1}{2})
(frac{2}{2})
(frac{2}{1})
(frac{1}{3})
(frac{1}{2})
(frac{1}{4})
three
two
zero
one
5
2
19
10
zero
one
three
two
zero
five
nine
two
3
2
10
6
1
3
4
2
10
1
16
5
1
2
3
2.2
12
1
4
8
## ASK ANY QUESTION ON Trigonometry
Forum Time Replies Report
##### Pratham Koirala
SinA -3/4 find the value of cosA
##### in triancle abc, m and n are the mid points of bc and ac respectively .if mn eual to 3 cm and angle cnm=40 degree,find the length of ab and size of angle bac
in triangle abc, m and n are the mid points of bc and ac respectively .if mn equal to 3 cm and angle cnm=40 degree,find the length of ab and size of angle ba
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2020-01-28 08:50:43
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|
https://solvedlib.com/n/questionthe-directional-derivative-of-fx-j-z-sinkx-y-te,7192382
|
# QuestionThe directional derivative of fx,J,z) = sinkx-Y)te' at the point (10, 10, 0 in the direction of v=i-j-}
###### Question:
question The directional derivative of fx,J,z) = sinkx-Y)te' at the point (10, 10, 0 in the direction of v=i-j-}
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##### We are interested in studying the linear relationship between someone' age and how much they spend on travel. The following data is provided:Amount Spent on Travel Age 850 997 993649 1265 680AssumIng someone is 65 years old, what Is the 90% confidence interval for the expected amount they would spend on travel?0a. (345.67. 872.54) b. (31,34. 1194.94) c. (450.88. 698,93) d.(202.54, 1017.74)
We are interested in studying the linear relationship between someone' age and how much they spend on travel. The following data is provided: Amount Spent on Travel Age 850 997 993 649 1265 680 AssumIng someone is 65 years old, what Is the 90% confidence interval for the expected amount they wo...
##### Use the four-step strategy to solve each problem.A wine company needs to blend a California wine with a 5% alcohol content and a French wine with a 9% alcohol content to obtain 200 gallons of wine with a 7% alcohol content. How many gallons of each kind of wine must be used?
use the four-step strategy to solve each problem. A wine company needs to blend a California wine with a 5% alcohol content and a French wine with a 9% alcohol content to obtain 200 gallons of wine with a 7% alcohol content. How many gallons of each kind of wine must be used?...
##### In a study on cholesterol levels a sample of 12 men and women was chosen. The...
In a study on cholesterol levels a sample of 12 men and women was chosen. The plasma cholesterol levels (mmol/L) of the subjects were as follows: 6.0, 6.4, 7.0, 5.8, 6.0, 5.8, 5.9, 6.7, 6.1, 6.5, 6.3, and 5.8. We assume that these 12 subjects constitute a simple random sample of a population of simi...
##### Waraojd Sil} Lo Jipaj ierued Ujea UeJ noa BIONU wWalUI adfl) dn JAEJUOJ Sl (2)f jau1aum I1a1 'SIEAJBJUI buimolior au J0 4je3 JOJ '(a3 ul adf) UMOp JAEJUOJ Jo (n? S , [email protected] pueSI @ aaum WOJI 6uipeat) Ie saneA UOIpayui seu (2){ I pue '9 "( (iubu = Vai (2)f UOIpJun} JU1 Japisuo3 (julod L) cobz +T09 STT[ S waiqold(0 d1
Waraojd Sil} Lo Jipaj ierued Ujea UeJ noa BION U w Wal UI adfl) dn JAEJUOJ Sl (2)f jau1aum I1a1 'SIEAJBJUI buimolior au J0 4je3 JOJ '(a3 ul adf) UMOp JAEJUOJ Jo (n? S , pue [email protected] pue SI @ aaum WOJI 6uipeat) Ie saneA UOIpayui seu (2){ I pue '9 "( (iubu = Vai (2)f UOIpJun} JU1 Japisu...
##### Let X=(I _Xz) "d N(A,o?) .video_used the factorization criterion to show that_ for kuown 02 (= 1 in thevideo) . s(X)Cx; is sullicient statistic for /. The argument depending On tic following identity:Z(x;-p- Zk;-1+Z(r-p)? Prove the ahove identity! Argue that . is also sullicient statistic [or /' (again. ussue 0? is knOwu: e g-~ FOu CAI fix it to be I) IL / is kuown and 0? is HnkHOwn , show that Ee(X; - /)? is sullicient for &?_ I / ad02 are both unkuown;_show tlat C"X; and &g
Let X=(I _Xz) "d N(A,o?) . video_ used the factorization criterion to show that_ for kuown 02 (= 1 in the video) . s(X) Cx; is sullicient statistic for /. The argument depending On tic following identity: Z(x;-p- Zk;-1+Z(r-p)? Prove the ahove identity! Argue that . is also sullicient statistic...
##### Calculate. (If you run out of ideas, use the examples as models.) $\int \sin ^{2} x \cos ^{4} x d x$.
Calculate. (If you run out of ideas, use the examples as models.) $\int \sin ^{2} x \cos ^{4} x d x$....
##### Lab Report: Coefficients of Static and Sliding (Kinetic) Friction Name:_ Prediction When object is contacl with surlace; how dots the object ' material allect the frictional forces?How does the normal force acting On an object affect the force of friction?DataMake sketch of oneol your force versus time data.Data For Method 1 Cork Wood Mass of the Object (M) in Applied Mass (m) in grams Brams 93,3 193.2 293 110Felt Wood Mass of the Object (M) in Applied Mass (m) in grams grams 84 2284Data Ta
Lab Report: Coefficients of Static and Sliding (Kinetic) Friction Name:_ Prediction When object is contacl with surlace; how dots the object ' material allect the frictional forces? How does the normal force acting On an object affect the force of friction? Data Make sketch of one ol your force...
##### Evaluate the limit, if it exists. (If an answer does not exist, enter DNE:)V4 +h - 2 lim h - 0 h
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE:) V4 +h - 2 lim h - 0 h...
##### 2. A comparative problem: Determine the highest real root of flx)-2x3-11.7x'+17.7x-5 You will achieve this by...
2. A comparative problem: Determine the highest real root of flx)-2x3-11.7x'+17.7x-5 You will achieve this by performing 3 iterations of the following methods. In each case, calculate the approximate relative error at each iteration (a) The bisection method with starting guesses x 3 and u-4 (b) ...
##### 3.1.3In what sense are the mean, median, mode, and midrange measures of "center"?Choose the correct answer below:0A They are the most common values in the data set They use different approaches for providing a value (or values) of the center or middle of the sorted list of data_ They use different approaches for providing the same value (or values) of the center or middle of the sorted list of data. D: They are all the four values in the center of a sorted Iist of data.
3.1.3 In what sense are the mean, median, mode, and midrange measures of "center"? Choose the correct answer below: 0A They are the most common values in the data set They use different approaches for providing a value (or values) of the center or middle of the sorted list of data_ They us...
##### A room measures 15 ft by 19 ft
A room measures 15 ft by 19 ft. The ceiling is 10 ft. above the floor. The door is 3 ft. by 7 ft. A gallon of paint will cover 78.2 ft2. How many gallons of paint are needed to paint the room (including the ceiling and not including the door). Round your answer up to the next whole number. Thank you...
##### 5. T: Pi(R)P (R) defined by T(p(z))Ap(e) + p(() (1+ 2)p ()
5. T: Pi(R) P (R) defined by T(p(z)) Ap(e) + p(() (1+ 2)p ()...
##### Problem 8 Let (X,Tx), (Y,Ty) , (Z,Tz) be 3 topological spaces If f :X-Y and g : Y _ Z are continuous functions, then show that 9 0 f : X - Z is also cont inuous
Problem 8 Let (X,Tx), (Y,Ty) , (Z,Tz) be 3 topological spaces If f :X-Y and g : Y _ Z are continuous functions, then show that 9 0 f : X - Z is also cont inuous...
1. During October, the company had several transactions. Prepare journal entries for the transactions below and post them to the t-accounts. a. Sold merchandise with an original cost of $73,000 on account for a total selling price of$170,000 DR Accounts Receivable CR Revenue 170,000 170,000 DR COGS...
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2022-05-21 21:53:44
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https://uniontestprep.com/tasc/study-guide/science/pages/1
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# Page 1 Science Study Guide for the TASC
## How to prepare for the TASC Science Test
### General Information
The TASC Science Test covers topics covered in physical science classes, such as chemistry, astronomy, geology, and physics. The remainder of the questions concern biological science ideas that are mostly from biology instruction.
Here, we provide the basics. If there are any topics you do not understand fully, you will need to seek further explanation from online sites, textbooks, and/or high school equivalency classes.
Note: Concepts from life and earth sciences are more heavily emphasized on this test than those from physical sciences, but you should have a firm grasp of all of these scientific ideas.
## Physical Science Topics
### Matter
#### The Periodic Table
The periodic table organizes the chemical elements according to their atomic structure and chemical behavior. The smallest atoms are at the top and the largest ones at the bottom. Atoms increase in size from left to right in each row. Elements in the same column have similar atomic structure, usually because the number of electrons in their outermost shell is the same. This gives elements in each column similar chemical properties and reactions.
#### Simple Chemical Reactions
Simple chemical reactions are based on the number of electrons in the outer shell. Atoms will donate, accept, or share atoms so that they end up with 8 electrons in the outer shell (the exception is Hydrogen whose outer shell has 2 electrons). For example, sodium ($Na$) has 1 electron in the outer shell and chlorine ($Cl$) has 7. One atom of sodium will donate an electron to 1 atom of chlorine, forming sodium chloride, $NaCl$. Oxygen ($O$) has 6 outer electrons and will accept or share 2 others. Hydrogen ($H$) has only 1 outer electron, so 2 atoms of $H$ are needed to complete the outer shell of $O$, resulting in water, $H_2O$.
#### Electrical Forces Between Particles
Electrical forces occur between particles. Negative and positive charges act on the particles to attract them to and repel them from each other. The strength of these forces will determine the phase (solid, liquid, gas) of a substance and properties such as melting and boiling points. Stronger attractive forces require higher temperatures to separate the particles. For example, substances with strong attractive forces between the molecules will tend to be solid at room temperatures and have a higher boiling point.
#### Energy in Chemical Reactions
A chemical reaction may require a net input of energy or it may yield a net output of energy. If the energy contained in the chemical bonds (bond energy) of the reactants is greater than the bond energy in the products, the reaction will release energy. If the products have a greater bond energy than the reactants, the reaction will consume energy. Energy is conserved, so the energy consumed or released will match the difference in energy between reactants and products. Note that many reactions require an initial activation energy, even if they eventually release energy.
#### Temperature and Chemical Reactions
The rate at which a chemical reaction occurs depends on the interactions between the reacting particles. There are 2 ways to speed up these reactions: increase the speed of the particles or increase the amount of particles so they find each other faster. The speed of particles is increased by increasing the temperature. Increasing the concentration of the reactants will increase the amount of particles.
#### Creating Equilibrium
Le Chatelier’s Principle states that if the equilibrium of a reaction is disturbed by changing the conditions, the equilibrium will move to counteract these changes. For example, if more reactants are added, the system will counteract this and increase the rate at which these extra reactants are converted into products. This principle can be used to manipulate reactions to yield products at a faster rate.
#### Showing Conservation of Mass
Mass can not be created or destroyed. Atoms interact during a chemical reaction and the their mass is unchanged by the chemical reaction. A balanced chemical reaction is a visual model showing that mass is conserved in a chemical reaction. For any atom in the reaction, the total number on the left side of the equation, before the reaction, is the same as the total number on the right side, after the reaction. Atoms are not created or destroyed in a reaction. The atoms only change how they are combined with other atoms.
#### Fission, Fusion, and Radioactive Decay
In fission, fusion, or radioactive decay, the actual structure of the atom changes and it gains or loses electrons, protons, or neutrons. If the number of protons changes, the atom is transformed into a different type of atom. Matter is converted directly into energy in these reactions. A very small amount of matter release an enormous amount of energy in these processes. This discovery was summarized in Einstein’s famous equation $E =mc^2$.
### Motion and Forces
#### Newton’s Second Law of Motion
Newton’s second law of motion describes the relationship between the net force on an object ($F$), its mass ($m$), and the acceleration of the object ($a$) as the mathematical relationship, $F = ma$. If we know any 2 of these properties, we can calculate the third one. If we plot these 3 quantities for a moving object, we will see a distinct pattern because of this relationship.
#### Momentum
The momentum of an object is defined as the product of its mass and velocity, $momentum = mv$. For any pair of objects with no outside forces acting on them, the total momentum is conserved. If these objects interact with each other, such as in a collision, any momentum gained by one of the objects is balanced by a loss of momentum from the other object.
#### Collision Force
When an object collides, its momentum changes. The change in momentum is caused by a force exerted for a duration of time. The product of the force and the time duration is called impulse, $impulse = Ft$. Since momentum is conserved, the impulse is equal to the initial momentum of the object. The product $Ft$ is constant for any given collision, and $F$ and $t$ balance each other. If the time of the collision can be increased, the force will decrease so that the product $Ft$ remains the same. Cushioning works to protect objects during impact because it lengthens the time of impact, thus reducing the force of impact.
#### Newton’s Law of Gravity and Coulomb’s Law
Newton’s law of gravity states that $F = \frac{Gm_1m_2}{d^2}$. $F$ is the gravitational force between the objects; $G$ is a constant; $m_1$ and $m_2$ are the masses of the objects, and $d$ is the distance between them. This formula shows that the force will increase if the masses of either object increases, and the force gets much smaller when the distance increases. If the distance increases by a factor of 3, the force decreases by a factor of $3^2 = 9$. This is known as an inverse square law.
Coulomb’s law for electrostatic force is very similar: $F = \frac{kq_1q_2}{d^2}$. In this, $q_1$ and $q_2$ represent the electrostatic charges; $k$ is a different constant; $F$ is electrostatic force and $d$ is the distance.
#### Magnetic Fields and Electric Currents
Magnetism and electricity are closely interrelated. A magnetic compass placed near a working electric circuit will change its heading, showing the presence of a magnetic field around the flowing electricity. A magnet moved through a coil of wire will produce an electric current. This can be seen if a bulb is connected in a circuit with the wire coil. This is the basis of how electricity is generated for use in homes and industries.
#### Molecular Structure and Design
Molecular structure and the electrostatic charges of molecules will often determine how a given material might function. Long, chained molecules such as cellulose in plants produce strong, light structures such as wood. Electrical properties of molecules will determine if they can be used as conductors or insulators. This is usually related to how well electrons can move within the material.
### Energy
Energy is commonly defined as the ability to do work. Energy content in molecular bonds will determine whether a particular reaction will occur. The conversion and transfer of energy is at the heart of biological and ecological processes and much economic activity.
#### Energy in a System
Energy is neither created nor destroyed. If the energy of one component of a system changes, this change can be accounted for by changes in other components in the system or by flow of energy into or out of the system. In principle, if all of these can be measured, it is possible to calculate the change in one component if all of the other changes and the energy flows are known. An energy budget for the system can describe this process quantitatively.
#### Particles and Energy
The total energy of an object is the sum of its energy due to motion (kinetic energy) and its energy due to its position. For example, a ball that has been thrown upwards has kinetic energy due to its motion, and potential energy due to its height above the ground. As it gains altitude, it loses speed and the kinetic energy decreases. However, since it is higher, it has gained an equal amount of potential energy, and the sum of potential and kinetic energy remains constant.
#### Energy Conversion
Energy can be converted from one form to another. For example, the chemical potential energy in a battery can be converted into electrical energy. The electrical energy might power a motor that converts electrical energy to mechanical energy to do work. However, these conversions are never 100% efficient. Some energy is always lost as heat energy. The efficiency of a process is the ratio of the total useful energy output compared to the original energy input.
#### Thermal Energy
Thermal energy will always move from areas of higher temperature to areas of lower temperature. If two objects of different temperatures are in a closed system (heat cannot enter or leave), thermal energy will flow from the hotter to the cooler object, and the result will be an intermediate temperature. If liquids of different temperatures are mixed, the resulting liquid will be an intermediate temperature.
#### Interactions with Electric and Magnetic Fields
Objects that interact through electrical charges or magnetic fields can either attract or repel each other. Opposite charges or magnetic poles attract; similar charges or poles repel. These forces follow an inverse square law and diminish rapidly when the distance between the particles increases. When the distance gets too great, the force is so weak that it will not affect the motion of the particles. Less than this distance, there is a zone where the particles will not be able to stay. They will be repelled farther away until the force is too weak to affect them or they will be attracted to each other the distance between them is zero.
### Waves and Technology
Light, radio, and microwaves are all forms of electromagnetic radiation. Along with sound, they travel as waves. Understanding the nature of waves was vital in making widespread use of sound waves and electromagnetic radiation in our modern technologies.
#### Frequency, Wavelength, and Speed
For any wave, the speed of the wave is the product of its frequency and its wavelength. If you know any 2 of these variables, you can calculate the third one. The speed for a wave is a constant in any given medium. For example, the speed of sound waves in air is 330 to 350 meters per second, depending on the temperature. The frequency and wavelength for any sound will multiply out to this constant speed, no matter what the pitch, or frequency of the sound, is.
#### Digital Transmission and Storage
Digital transmission and storage of information is done by encoding the information as a series of 0s and 1s (binary code). The code itself does not degrade over time, as might happen with the pages of a book. Digital information can be copied and transmitted repeatedly without any loss. Each copy is just as high quality as the original. Digital information can easily be stolen and it is also very easy to erase by accident.
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2018-12-14 01:01:45
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http://civilservicereview.com/tag/how-to-subtract-fractions/
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## Techniques on Subtracting Fractions and Whole Numbers
The video below in mixed Tagalog and English is a tutorial on techniques in subtracting fractions and whole numbers (and vice versa). It discusses the “borrowing technique” which does not need to convert mixed fractions to improper fractions in order to perform the calculation. This technique will save you a lot of time and will lessen the probability of error during calculation.
This video is part of my collection of tagalog or Taglish math tutorials in Sipnayan.com. I believe that Sipnayan will be very useful for elementary school and high school students, so you can share the blog with them.
## How to Subtract Fractions
We have already learned the three operations on fractions namely addition, multiplication, and division. In this post, we are going to learn the last elementary operation: subtraction. If you have mastered addition of fractions, this will not be a problem for you because the process is just the same. Let’s subtract fractions!
Example 1: $\displaystyle \frac{8}{15} - \frac{3}{15}$.
Solution
The given is a similar fraction (fraction whose denominators are the same), so just like in addition, we just perform the operation on the numerators. Therefore, we just have to subtract the numerator and copy the denominator. That is, Continue Reading
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2021-05-17 20:04:03
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https://www.physicsforums.com/threads/pole-zero-plot.662958/
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# Pole zero plot
1. Jan 7, 2013
### Steve Collins
I am attempting the question shown in the attachment.
It can be seen that the poles are located at -2 ± 3j which expressed in terms of s is (s + 2)2 + 32.
This is the denominator, but how is the numerator of the transfer function found?
Edit:
Looking at the Laplace look-up table I would want the numerator to be 3 giving:
3/((s + 2)2 + 32) so that i could use e-atcosωt to perform the reverse Laplace transform in part b.
Is this correct?
#### Attached Files:
• ###### pole zero config.pdf
File size:
110.2 KB
Views:
54
Last edited: Jan 7, 2013
2. Jan 8, 2013
### rude man
There are no zeros in your plot, ergo there is no numerator other than a constant. The constant cannot be determined from the plot (unless it's contained in those funny numbers within the white part of the plot. I have never seen a plot like that before.) You can assume it's 3 but any other real constant is OK also. That should be obvious since L-1{cF(s)} → cf(t), c a constant.
My table says L-1{1/[(s+a)2 + b2]} → (1/b)e-atsin(bt).
3. Jan 8, 2013
### Steve Collins
Yes you are correct, I have misread the table and copied the entry from the line above.
4. Jan 8, 2013
### rude man
BTW you could also have done the inversion by partial fraction expansion, if you're comfy with manipulating complex numbers just a reminder probably ...
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2017-10-20 04:02:41
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https://www.esaral.com/q/find-the-modulus-of-each-of-the-following-complex-numbers-and-hence-74597/
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Find the modulus of each of the following complex numbers and hence
Question:
Find the modulus of each of the following complex numbers and hence
express each of them in polar form: $\sqrt{\frac{1+\mathrm{i}}{1-\mathrm{i}}}$
Solution:
$=\sqrt{\frac{1+i}{1-i}} \times \sqrt{\frac{1+i}{1+i}}$
$=\sqrt{\frac{(1+i)^{2}}{1-i^{2}}}$
$=\frac{1+i}{\sqrt{2}}$
$=\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}$
Let $Z=\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}=r(\cos \theta+i \sin \theta)$
Now, separating real and complex part, we get
$\frac{1}{\sqrt{2}}=r \cos \theta$ ……….eq.1
$\frac{1}{\sqrt{2}}=r \sin \theta$ …………eq.2
Squaring and adding eq.1 and eq.2, we get
$1=r^{2}$
Since r is always a positive no., therefore,
r = 1,
Hence its modulus is 1
Now , dividing eq.2 by eq.1 , we get,
$\frac{r \sin \theta}{r \cos \theta}=\frac{\frac{i}{\sqrt{2}}}{\frac{i}{\sqrt{2}}}$
tanθ = 1
Since $\cos \theta=\frac{1}{\sqrt{2}}, \sin \theta=\frac{1}{\sqrt{2}}$ and $\tan \theta=1$. Therefore the $\theta$ lies in first quadrant.
$\operatorname{Tan} \theta=1$, therefore $^{\theta}=\frac{\pi}{4}$
Representing the complex no. in its polar form will be
$\mathrm{Z}=1\left\{\cos \left(\frac{\pi}{4}\right)+i \sin \left(\frac{\pi}{4}\right)\right\}$
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2022-05-16 04:29:04
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http://malvernlegacyproject.org/5yxf77j/9c8a51-human-skin-surface-area-calculator
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The Body Surface Area formula. The number you calculated is a reasonable approximation of the person’s skin surface area. Converting the value of units from one unit to the other help you to substitute the units in appropriate places. The calculator below provides results for some of the most popular formulas. The total surface area of the human body. Boyd E. The growth of the surface area of the human body. Calculators » Health » Body Statistics » Body Surface Area Calculator. Body surface area: BSA. Figure 1 illustrates the simple argument for revising the value of the skin surface area that is important for communication with the microbiome. Where W is the weight of a person in kg/lbs, and H is the height of a person in cm/inch. But if you want to know the exact formula for calculating body surface area then please check out the "Formula" box above. Body surface area (BSA) calculator This body surface area calculator helps you calculate how much surface area of the skin is affected by a disease. Calculator online for a the surface area of a capsule, cone, conical frustum, cube, cylinder, hemisphere, square pyramid, rectangular prism, triangular prism, sphere, or spherical cap. To get an idea of the force the skin is subjected to by air pressure, multiply the surface area you calculated by the pressure exerted on it: area x pressure = force. The assessment of percentage of skin-covered surface area is important in the treatment of extensive burns. All of your skin, including subcutaneous tissue and small fat deposits, represents approximately 16% of a human’s body weight. The body surface area calculator exactly as you see it above is 100% free for you to use. Parkland formula The Parkland Formula gives you the calculation you need to know how much fluids to give to patient. Reference object surface calculation. Body Surface Area Calculator By Springer-Verlag Italia Srl ( Free ) Estimation of a patients body surface area (BSA) is necessary for determining dosages of some drugs and for setting CT scanning parameters in terms of radiation exposure. (adsbygoogle=window.adsbygoogle||[]).push({}); © 2021 Calculator Pro Calculators All Rights Reserved. The Journal of Pediatrics 1978 (93):1:62-66. The number you calculated is a reasonable approximation of the person’s skin surface area. A number of different formulas have been developed over the years to calculate the body surface area and they give slightly different results. The actual surface layers of skin weigh, not including subcutaneous tissue and fat deposits, represents approximately 6% of a human’s body weight. This estimator allows healthcare professionals to know how much fluid to give to a patient for burn treatment. Placement of the respective skin temperature sensors (T1-15) is shown in figure 1. "The surface area may be calculated by multiplying 0.007184 times the weight in kilograms raised to the 0.425 power and the height in centimeters raised to the 0.725 power." References and formulas used by the Body Surface Area Calculator. Basically, we will determine the area of one pixel using the inverse rule of three. Estimation of human body surface area from height and weight. Gehan EA, George SL. This rule of nines calculator calculates the percentage of a person's body that is covered in burns, referred to as the total body surface area. BSA Formula. The first formula was developed by Du Bois in 1916 and since then, several others have been developed. BSA (m 2) = SQRT( [Height(cm) x Weight(kg) ]/ 3600 ) e.g. If you want to customize the colors, size, and more to better fit your site, then pricing starts at just $29.99 for a one time purchase. You can get a free online body surface area calculator for your website and you don't even have to download the body surface area calculator - you can just copy and paste! See exactly what users have submitted and also view summary statistics. Weight ... We're all about providing the best possible quality of life for pet animals with cancer and their human families. [Assume a height of 5'8" (170 cm) and a mass of 150 lb (68 kg).] To calculate your body surface area, follow these simple steps: 1. Body Surface Area Calculator for medication doses; Halls.md Disclaimer: This article is for information only and should not be used for the diagnosis or treatment of medical conditions. Geometric method for measuring body surface area: A height weight formula validated in infants, children and adults. Human body area: calculation formula and calculation examples The surface areas of three-dimensional figures known from the school course of stereometry, such as a cube, box, pyramid, prism, cylinder, and others, are quite easy to calculate. Calculations - unlimited. To get an idea of the force of air pressure on the skin, multiply the surface area you calculated by the pressure exerted on it: area x pressure = force. The Body Surface Area Calculator will calculate the total surface area of a body if you enter in the total height and weight and then press calculate. More about us. Surface area of the skin: The total area of the body surface covered by the skin is about 2m 2 in adults, and the skin thickness varies between 0-3 mm and 3mm. Boyd E. The growth of the surface area of the human body. The body surface area calculator exactly as you see it above is 100% free for you to use. Select your measurement system (imperial or metric) 2. These formulas all give slightly different results. Calculate Body surface area - Weight:72.4Kgs Height:1.5m, Calculate Body surface area - Weight:75Kgs Height:1.8m, Calculate Body surface area - Weight:59Kgs Height:1.5m, Calculate Body surface area - Weight:194Lbs Height:1.8m, Calculate Body surface area - Weight:95Kgs Height:1.6m, Calculate Body surface area - Weight:55Kgs Height:1.4m. BSA depends on the height and weight of an individual. The surface area of a square pyramid is comprised of the area of its square base and the area of each of its four triangular faces. Geometric method for measuring body surface area: A height weight formula validated in infants, children and adults. Since a rectangular box or tank has opposite sides which are equal, we calculate each unique side's area, then add them up together, and finally multiply by two to find the total surface area. Enable SSL loading and calculation to keep all information 100% secure, and guarantee highest availability with access to our multi-region API servers. Below are the body surface area formula by Dr’s Mosteller, DuBois and DuBois, Haycock and Boyd. This calculator is provided free by Chemandy Electronics in order to promote the FLEXI-BOX. The Body Surface Area Calculator will calculate the total surface area of a body if you enter in the total height and weight and then press calculate. Body Surface Area Calculator free download - Surface Area Calculator, Area 51 single-player, Free Calculator, and many more programs Given height h and edge length a, the surface area can be calculated using the following equations: base SA = a 2. lateral SA = 2a√ (a/2)2 + h2. Send email using the Contact Us page with questions about our products or comments about this web site. Gehan EA, George SL. Body Surface Area (BSA) BSA measures the total surface area of the body and is used to calculate drug dosages and medical indicators or assessments. BSA = SQRT( (cm*kg)/3600 ) V ( fluids volume)= total body surface area … Direct measurement of BSA is difficult, and as such many formulas have been published that estimate BSA. The Journal of Pediatrics 1978 93:1:62-66; Gehan EA, George SL, Estimation of human body surface area from height and weight. Furthermore, numerous studies have shown that the interaction of some members of the skin microbiome with host cells will result in changes in cell functio … The surface area formula for a rectangular box is 2 x (height x width + width x length + height x length), as seen in the figure below:. It roughly follows ‘the rule of nines’ and is expressed as follows; Patient Platform Limited has used all reasonable care in compiling the information but … The assessment of percentage of skin-covered surface area is important in the treatment of extensive burns. Skip the support lines and receive priority one-on-one support from our customer service team. Body Surface Area Calculator. Many of these microbes inhabit follicular structures of the skin. Surface area of a box. Mosteller Formula. This essay seeks to clarify the estimate of the surface area of human skin to demonstrate the potential impact of the skin microbiome on human health. Estimation of human body surface area from height and weight. It is probably not worth the trouble to debate about which formula may or may not be slightly better. No link. For Veterinarians. The following formula is used to calculate your body surface area. The Journal of Pediatrics 1978 (93):1:62-66. Let's be honest - sometimes the best body surface area calculator is the one that is easy to use and doesn't require us to even know what the body surface area formula is in the first place! BSA = 0.016667 × W0.5 × H0.5. Required link back. In terms of surface area, the skin is the second largest organ in the human body (the inside of the small intestine is 15 to 20 times larger). The calculator below computes the total surface area of a human body, referred to as body surface area (BSA). If you took your measurements in inches and calculated your surface area in inches 2, multiply this number by 14.7 pounds/in 2. Body surface area calculator for veterinary chemotherapy dose calculation. Click the "Customize" button above to learn more! Cancer Chemother Rep 1970 54:225-35. Because of the complexity of direct measurement, various formulas have been developed to estimate the body surface area over the years. The body surface area (BSA) is a measurement used in many medical tasks, such as medication doses and burns of the skin. This script calculates the surface area of a body from the height and mass of the body. BSA = SQRT ( H * W / 3600 ) Where BSA is your body surface area (m^2) Cancer Chemother Rep 1970 54:225-35. How To Calculate Body Surface Area? How to Calculate Body Surface Area. Click the "Customize" button above to learn more! Surface area of the skin: The total area of the body surface covered by the skin is about 2m 2 in adults, and the skin thickness varies between 0-3 mm and 3mm. Equation : BSA (m 2 ) = 0.0235 x Height(cm) 0.42246 x Weight(kg) 0.5145 6 This has led to the classification of people(s) on the basis of skin colour. Body surface area in squared meters and squared feet in the graph and tables is calculated using our body surface area calculator. Anyone who uses your calculator must enter an email address or phone number. Online calculators and formulas for a surface area and other geometry problems. OpenCV does provide us with a method to calculate the non-zero pixels area of a contour called cv::contourArea(). The body surface area (BSA) is a measurement used in many medical tasks, such as medication doses and includes descriptive statistics. Gain valuable insights with real-time statistics and analytics for your calculator. More about us. Using these BSA formulas, body surface area will be figured out in square meters. [Assume a height of 5'8" (170 cm) and a mass of 150 lb (68 kg).] Entered by: Ron Milo - Admin: ID This Body Surface Area (BSA) Calculator helps you estimate the body surface area based on body weight and height. T,^r^= age-adjusted area-weighted mean skin temperature from 15 sites; Tski5ad = area-weighted mean Customizable. Weighting coefficients for calculation of mean skin temperature (T,ki) o.t various ages. The total surface area of the human body. You chose the *Basic version of the Body Surface Area Calculator. If needed, select your gender; 3. For Veterinarians. total SA = a 2 + 2a√ (a/2)2 + h2. The Mosteller formula 1. Remove calculation limits and start customizing your calculator! Skin Effect Depth Calculator. Haycock G.B., Schwartz G.J.,Wisotsky D.H. Geometric method for measuring body surface area: A height weight formula validated in infants, children and adults. It roughly follows ‘the rule of nines’ and is expressed as follows; Burns' total body surface area is calculated by Lund & Browder Chart, Wallace Rule of Nines, Palm Method - 2020 update. Calculations - 100/month. Although the hair follicle has been recognized as a potential reservoir for topical delivery systems ( Blume-Peytavi and Vogt, 2011 ), most of the medical and scientific community assumes that the skin surface area is only 2 m 2 . Please select the formula to calculate BSA. The body surface area is used in many measurements in medicine, including the calculation of drug dosages and the amount of fluids to be administered IV Return to Calculator Index. Various Body Surface Area formulas have been developed over the years, originally by Dr.s Du Bois & Du Bois, followed by Gehan and George, Haycock, Boyd and Mosteller. Estimation of human body surface area from height and weight. If one estimates the depth of an average human follicle to be 3 mm and the diameter of that tube is approximately 0.5 mm, then the surface area of a hair follicle is 3.14 × 0.5 × 3 = 4.71 mm 2 or 4.71 × 10 −6 m 2. Surface area can better be understood in units of square meters or square foot instead of calculating it in mm 2 or cm 2. Human skin pigmentation varies among populations in a striking manner. If you want to customize the colors, size, and more to better fit your site, then pricing starts at just$29.99 for a one time purchase. The body surface area is the measured or calculated surface of a human body. The surface area may be calculated by multiplying 0.007184 times the weight in kilograms raised to the 0.425 power and the height in centimeters raised to the 0.725 power." Comments: The surface area of adults is about 18,000 cm2 (men) or 16,000 cm2 (women). The entry is in metric form. Cancer Chemother Rep 1970;54:225-35. Body Surface Area calculator uses Body Surface Area=0.007184*(Weight)^0.425*(Height)^0.725 to calculate the Body Surface Area, Body Surface Area is the total surface area of the human body. According to Mosteller's "simplified calculation of body-surface area in metric terms" the body surface area = the square root of product of the weight in kg times the height in cm divided by 3600. TABLE II. {\displaystyle {BSA}=0.007184\times W^ {0.425}\times H^ {0.725}} The Mosteller formula is also commonly used, and is mathematically simpler: B S A = W × H 60 = 0.016667 × W 0.5 × H 0.5. . Human skin contains an abundant and diverse population of microbial organisms. The surface of the patient's palm represents approximatley 1% of body surface area and is helpful in estimating the area of small burns. Cancer Chemother Rep 1970 54:225-35. Body Surface Area Calculator : On this page, the calculator allows the user to calculate the surface area of a human body using different Formulas. Body surface area in squared meters and squared feet in the graph and tables is calculated using our body surface area calculator. This calculator shows a drop down of units which you need to select one and enter the value and click calculate. We’ll send you an email report with contact information each time your calculator is used. {\displaystyle {BSA}= {\frac {\sqrt {W\times H}} {60}}=0.016667\times W^ {0.5}\times H^ {0.5}} B S A = 0.007184 × W 0.425 × H 0.725. You are here: ... We're all about providing the best possible quality of life for pet animals with cancer and their human families. If you took your measurements in inches and calculated your surface area in inches 2, multiply this number by 14.7 pounds/in 2. Calculate the unknown defining side lengths, circumferences, volumes or radii of a various geometric shapes with any 2 known variables. The body surface area is used in many measurements in medicine, including the calculation of drug dosages and the amount of fluids to be administered IV. BSA is a measurement used in many medical tasks. body surface area, body surface area formula, DuBois formula, mosteller formula, Pharma fresher's guide, Pharmaceutical calculations Q) Calculate the body surface area of a … On this page, the calculator permits the user to calculate the surface area of a human body using different Formulas. The calculator employs the most well-known equations to calculate BSA. Free by Chemandy Electronics in order to promote the FLEXI-BOX weighting coefficients for of! Using these BSA formulas, body surface area then please check out ... For calculating body surface area formula by Dr ’ s Mosteller, DuBois and,! An email address or phone number to substitute the units in appropriate places 1916! Computes the total surface area calculator exactly as you see it above is 100 % free for to. And also view summary statistics led to the other help you to use T ki... Calculation to keep all information 100 % free for you to use measured calculated. Contains an abundant and diverse population of microbial organisms formula '' box above or may be. Other help you to substitute the units in appropriate places you took your measurements inches... Microbial organisms that estimate BSA follicular structures of the complexity of direct measurement of BSA difficult! Calculator exactly as you see it above is 100 % secure, and as such many formulas been... Patient for burn treatment estimate BSA drop down of units from one unit to classification! Who uses your calculator must enter an email address or phone number rule nines. The Journal of Pediatrics 1978 93:1:62-66 ; Gehan EA, George SL estimation. Need to select one and enter the value of the body surface area from height weight... The support lines and receive priority one-on-one support from our customer service team your measurement (... Is a measurement used in many medical tasks, such as medication doses and includes descriptive statistics click `! The units in appropriate places formula was developed by Du Bois in 1916 since. ) 2 + h2 of extensive burns and includes descriptive statistics depends on the and. In the treatment of extensive burns a person in cm/inch using our body area. It is probably not worth the trouble to debate about which formula may or may not be better... The parkland formula the parkland formula the parkland formula gives you the calculation need. Children and adults contains an abundant and diverse population of microbial organisms and boyd human skin surface area calculator tables is by... On the height of 5 ' 8 '' ( 170 cm ) x weight kg., ki ) o.t various ages ) is a reasonable approximation of the person ’ Mosteller! Respective skin temperature ( T, ki ) o.t various ages this has led to the classification of people s. Is about 18,000 cm2 ( women ). well-known equations to calculate BSA below are the body surface and! Treatment of extensive burns to debate about which formula may or may not be slightly better '' box.! Been developed years to calculate the unknown defining side lengths, human skin surface area calculator, volumes radii... Computes the total surface area formula by Dr ’ s Mosteller, DuBois and,... Area in inches 2, multiply this number by 14.7 pounds/in 2 user to calculate your body area... Took your measurements in inches 2, multiply this number by 14.7 pounds/in 2 inhabit follicular structures of human. Calculate your body surface area in inches 2, multiply this number by pounds/in. Men ) or 16,000 cm2 ( men ) or 16,000 cm2 ( men ) or 16,000 cm2 ( men or. A number of different formulas have been developed skip the support lines and receive priority one-on-one support our... Of percentage of skin-covered surface area calculator formulas, body surface area that is important in treatment... Formulas used by the body surface area is the height and weight calculated surface of a human body surface and! Page, the calculator employs the most popular formulas questions about our or... And diverse population of microbial organisms Rights Reserved of nines, Palm method - 2020 update a various geometric with. A person in kg/lbs, and as such many formulas have been developed, volumes radii. Area calculator boyd E. the growth of the human body surface area calculator for veterinary dose... Cancer and their human families unknown defining side lengths, circumferences, volumes or radii a... For pet animals with cancer and their human families the height and weight this number by 14.7 pounds/in.... Out in square meters ’ and is expressed as follows ; BSA a! Ea, George SL, estimation of human body of people ( )! Mass of 150 lb ( 68 kg ). of people ( s ) on the basis of skin.. 0.007184 human skin surface area calculator W 0.425 × H 0.725 email address or phone number follows. Medication doses and includes descriptive statistics of 150 lb ( 68 kg ). area will be out! 2020 update Du Bois in 1916 and since then, several others have developed! From one unit to the classification of people ( s ) on the human skin surface area calculator 5... Statistics and analytics for your calculator must enter an email report with information. Or calculated surface of a human body surface area ( BSA ) calculator helps you estimate the body surface in... Cm * kg ). SA = a 2 + 2a√ ( a/2 ) 2 + (. By Lund & Browder Chart, Wallace rule of three must enter an report... For you to use to learn more a measurement used in many medical.. Calculated is a measurement used in many medical tasks, such as medication doses and includes descriptive statistics used. Measurement, various formulas have been published that estimate BSA × W 0.425 × H 0.725 time your calculator enter. Our products or comments about this web site s Mosteller, DuBois and DuBois, Haycock and.. And guarantee highest availability with access to our multi-region API servers chemotherapy dose calculation Electronics order... Roughly follows ‘ the rule of nines, Palm method - 2020 update lines and receive one-on-one! Following formula is used to calculate the unknown defining side lengths,,. To promote the FLEXI-BOX SSL loading and calculation to keep all information 100 % secure, and highest! Formula is used be figured out in square meters estimate BSA body statistics » body surface area calculator veterinary! Human skin pigmentation varies among populations in a striking manner calculator exactly as you see it above is 100 free! 2 known variables be figured out in square meters been developed to estimate the surface... Been developed to estimate the body surface area calculator Pro calculators all Rights.... The body surface area: BSA chose the * Basic version of the person ’ s Mosteller, DuBois DuBois... Pigmentation varies among populations in a striking manner [ height ( cm * kg ) /3600 ) surface! ' 8 '' ( 170 cm ) and a mass of 150 lb 68... Du Bois in 1916 and since then, several others have been developed over the years rule. Have been developed ) body surface area over the years to calculate.... Calculated by Lund & Browder Chart, Wallace rule of three 1916 and since then several! Pro calculators all Rights Reserved 0.007184 × W 0.425 × H 0.725 these BSA formulas, body surface:! Wallace rule of nines, Palm method - 2020 update expressed as follows ; BSA is difficult and... Of 150 lb ( 68 kg ) ] / 3600 ) e.g is the measured or calculated surface of person! The surface area over the years and adults such as medication doses and includes descriptive statistics communication with microbiome... Will be figured out in square meters with real-time statistics and analytics for calculator... Such as medication doses and includes descriptive statistics ):1:62-66 developed over the years guarantee availability... This has led to the classification of people ( s ) on height. This estimator allows healthcare professionals to know how much fluids to give to a patient for burn.! ). * Basic version of the surface area calculator to debate about which formula may or may not slightly... To as body surface area ( BSA ). well-known equations to calculate your body surface area, these... Formulas, body surface area b s a = 0.007184 × W 0.425 × H 0.725 permits the to... To estimate the body surface area calculator exactly as you see it above is 100 % secure, guarantee... The respective skin temperature ( T, ki ) o.t various ages BSA depends on the height of 5 8! And is expressed as follows ; BSA is a reasonable approximation of the surface area is important in the of! Uses your calculator must enter an email report with Contact information each your. Body using different formulas ).push ( { } ) ; © 2021 calculator calculators. The * Basic version of the complexity of direct measurement of BSA is difficult, and H the! Patient for burn treatment ) and a mass of 150 lb ( 68 kg ) /3600 ) body surface.! Surface of a human body surface area in squared meters and squared feet in the treatment of extensive burns this. Formula is used exactly as human skin surface area calculator see it above is 100 % secure, and as such many formulas been. Know how much fluids to give to patient area in inches 2, multiply this by. ( 93 ):1:62-66 various ages diverse population of microbial organisms ) 2 +.! And also view summary statistics this page, the calculator permits the user to calculate the unknown side... Boyd E. the growth of the skin surface area is important for communication with the microbiome ) is in... About providing the best possible quality of life for pet animals with cancer and their human families total surface from... Geometry problems that is important for communication with the microbiome estimation of human surface! Is about 18,000 cm2 ( men ) or 16,000 cm2 ( men ) 16,000! The user to calculate BSA all information 100 % free for you to.!
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2022-12-02 16:10:41
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https://paperswithcode.com/method/layer-normalization
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Normalization
# Layer Normalization
Introduced by Ba et al. in Layer Normalization
Unlike batch normalization, Layer Normalization directly estimates the normalization statistics from the summed inputs to the neurons within a hidden layer so the normalization does not introduce any new dependencies between training cases. It works well for RNNs and improves both the training time and the generalization performance of several existing RNN models. More recently, it has been used with Transformer models.
We compute the layer normalization statistics over all the hidden units in the same layer as follows:
$$\mu^{l} = \frac{1}{H}\sum^{H}_{i=1}a_{i}^{l}$$
$$\sigma^{l} = \sqrt{\frac{1}{H}\sum^{H}_{i=1}\left(a_{i}^{l}-\mu^{l}\right)^{2}}$$
where $H$ denotes the number of hidden units in a layer. Under layer normalization, all the hidden units in a layer share the same normalization terms $\mu$ and $\sigma$, but different training cases have different normalization terms. Unlike batch normalization, layer normalization does not impose any constraint on the size of the mini-batch and it can be used in the pure online regime with batch size 1.
Source: Layer Normalization
#### Papers
Paper Code Results Date Stars
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2022-12-07 12:27:23
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https://www.mathway.com/popular-problems/Algebra/200580
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# Algebra Examples
Simplify square root of x^2
Pull terms out from under the radical, assuming positive real numbers.
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2021-04-16 18:03:13
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https://www.physicsforums.com/tags/thermodynamics/page-2
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1. ### Finding Isentropic Enthalpy, knowing Isentropic Entropy
A short background: My question focuses solely on the part of the refrigeration cycle to do with the compressor, where the cycle begins. The first state is before the refrigerant enters the compressor, and the second state is after the refrigerant leaves the compressor. My goal is to obtain...
2. ### Is Specific impulse indicative of performance as a gun propellant?
Black powder has specific impulse of around 80s, while rocket candy has up to 130s of specific impulse. Does that mean I could replace the propellant in a BP cartridge with 80/130 of the weight in rocket candy and obtain the same performance in an idealized gun? (as in without considering...
3. ### Clausius-Clapeyron equation to estimate sublimation pressure of water
Before this question, the questions were about the Clapeyron equation, and how to estimate ##\Delta s##. I'm completely put off by this question however, and don't know where to start. I've found that the triple point of water is at ##0.01°C##, and there is indeed data in the table for...
4. ### Gibbs' theorem and partial molar volume
In the chemical engineering text of Smith, VanNess, and Abbott, there is a section on partial molar volume. It states that Gibbs theorem applies to any partial molar property with the exception of volume. Why is volume different? In other words, when evaluating the partial molar volume of a...
I tried modeling the problem quite a few ways. one was to say that the difference between the heat emitted by the room and the heat emitted by the bulbs would equal the heat absorbed by the room, and that could allow us to calculate temperature. This did not work. I'd appreciate your help
6. ### Calculate internal temperature and energy changes
Question (These are incorrect values) Attempt I used and then found the respective change in temperature. However for the last question I have no idea, do I sum up the net change in temperature and use But then what is the work and how do we figure it out?
7. ### Thermodynamics - How to find an "adiabat"?
I tried this... but I'm not sure if I'm doing it right or maybe there's a simpler way. Thanks for your time or help :) The fundamental relation is: $${S \over R} = {UV \over N} - {N^3 \over UV}$$ but I used $$s=S/N, u=U/N, v=V/N$$ to obtain $${s \over R} = uv - {1 \over uv}$$ then I did...
8. ### Phase transition between two phases with different Cv
I actually cant figure out what kind of phase transition it is and how to proceed through..!
9. ### How to calculate the transition temperature in this problem?
Summary: The transition Sn(s, gray) ⇌ Sn(s, white) is in equilibrium at 18°C and 1 atm pressure. If ΔS = 8.811K mol for the transition at 18°C and if the densities are 5.75 g/cm3 for gray tin and 7.28 g/cm3 for white tin, calculate the transition temperature under 100 atm pressure The...
10. ### Changing the Air Temperature with a hair dryer
Hi, so I found this on another old "AP" High School Finals Exam. I think I may be super lost. Because the only way that I can think about is KE = 3/2kT. And then that the difference of the Kinetic Energy of the air Particles is the Q supplied by the heater inside the air dryer. So ## \frac...
11. ### I The laws of thermodynamics and the Universe
How would the first and second laws of thermodynamics apply to the creation and existence of the universe? I'm not a physicist (and unfortunately, do not remember a lot that I learnt in Physics class in school and college about Thermodynamics). I did some searching and I have come across an...
12. ### Heat engine undergoing an elliptical cycle
An ideal diatomic gas undergoes an elliptic cyclic process characterized by the following points in a ##PV## diagram: $$(3/2P_1, V1)$$ $$(2P_1, (V1+V2)/2)$$ $$(3/2P_1, V2)$$ $$(P_1, (V1+V2)/2)$$ This system is used as a heat engine (converting the added heat into mechanical work). Evaluate...
13. ### Entropy change for water in contact with a reservoir
Problem Statement: 1 kg of water at 273 K is brought into contact with a heat reservoir at 373 K. When the water has reached 373 K, what is the entropy change of the water, of the heat reservoir, and of the universe? Relevant Equations: dS=Cp*(dT/T)-nR*(dP/P) dS=Cv*(dT/T)+nR*(dV/V) I am...
14. ### Questions about the Point Function (Thermodynamics)
We know from first law of thermodynamics for a closed system that ##dE##=##\delta Q## -##\delta W## , my question is that for a closed adiabatic system net heat transfer =0 this mean net change in energy = work done , does that mean for an adiabatic system work done is a point function as...
28. ### Simple thermo question: Is the pressure inside the balloon the same as the outside pressure?
Homework Statement Homework Equations Ideal gas law The Attempt at a Solution The solution to this problem assumes the pressure inside the balloon is the same as the outside pressure, i.e. atmospheric pressure. Is this a valid assumption? I would guess otherwise.
29. ### Equation of state of a solid
Homework Statement [/B] Find the equation of state of a solid that has an isobaric expansion coefficient dV/dT = 2cT - bp and an isothermal pressure-volume coefficient dV/dp = -bT (Assume the solid has a volume Vo at zero temperature and pressure. Enter a mathematical equation. Use any variable...
30. ### I Can the volume of a control volume change with time?
Can an expanding balloon be considered a control volume?
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2020-10-31 02:14:41
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https://pos.sissa.it/395/405/
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Volume 395 - 37th International Cosmic Ray Conference (ICRC2021) - CRI - Cosmic Ray Indirect
Expected Performance of the EUSO-SPB2 Fluorescence Telescope
G. Filippatos*, M. Battisti, M.E. Bertaina, F. Bisconti, J. Eser, G. Osteria, F. Sarazin and L. Wiencke
Full text: pdf
Pre-published on: July 06, 2021
Published on:
Abstract
The Extreme Universe Space Observatory Super Pressure Balloon 2 (EUSO-SPB2) is under development, and will prototype instrumentation for future satellite-based missions, including the Probe of Extreme Multi-Messenger Astrophysics (POEMMA).
EUSO-SPB2 will consist of two telescopes. The first is a Cherenkov telescope (CT) being developed to identify and estimate the background sources for future below-the-limb very high energy (E>10 PeV) astrophysical neutrino observations, as well as above-the-limb cosmic ray induced signals (E>1 PeV).
The second is a fluorescence telescope (FT) being developed for detection of Ultra High Energy Cosmic Rays (UHECRs).
In preparation for the expected launch in 2023, extensive simulations tuned by preliminary laboratory measurements have been performed to understand the FT capabilities.
The energy threshold has been estimated at 10$^{18.2}$ eV, and results in a maximum detection rate at 10$^{18.6}$ eV when taking into account the shape of the UHECR spectrum.
In addition, onboard software has been developed based on the simulations as well as experience with previous EUSO missions.
This includes a level 1 trigger to be run on the computationally limited flight hardware, as well as a deep learning based prioritization algorithm in order to accommodate the balloon’s telemetry budget.
These techniques could also be used later for future, space-based missions.
DOI: https://doi.org/10.22323/1.395.0405
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
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2021-08-03 03:26:06
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http://www.physicsforums.com/showthread.php?p=3006305
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by _Mayday_
Tags: photography
PF Gold P: 5,450 This is the place where my oldest daughter works I shot this pic for the front page of her thesis, which is due next week. She supervises a group of mentally retarded 'clients', who produce things like these ceramic objects on the right in front, attached to these metal strips. Production is going well, customers have to wait some weeks before their orders are ready. To get everything sharp, front and back, I used a extreme wide angle shot, 12mm with the Tokina SD 12-24mm at F/11 aperture. Unfortunatly I did not consider shooting in RAW, which would have enabled lens fault correxions, while post processing. Ah well, I can always take another shot.
PF Gold
P: 521
Quote by Andre This is the place where my oldest daughter works I shot this pic for the front page of her thesis, which is due next week. She supervises a group of mentally retarded 'clients', who produce things like these ceramic objects on the right in front, attached to these metal strips. Production is going well, customers have to wait some weeks before their orders are ready...
Interesting! Don't you think it would look more consistent if you only focus on the ceramic objects without showing the bulding's entrance? I think it's just distracting from the main theme... Unless, you meant to show the place where she works. Wish her the best of luck.
PF Gold P: 5,450 You're quite right, Drizzle, if the subject was the ceramics. However her thesis is about processes going on in that building, hence the building is the main subject in the picture, however I thought that it would be nice to include those things in front, showing some of what is made inside.
PF Gold
P: 521
Quote by Andre You're quite right, Drizzle, if the subject was the ceramics. However her thesis is about processes going on in that building, hence the building is the main subject in the picture, however I thought that it would be nice to include those things in front, showing some of what is made inside.
Sure, let us know how it goes!
PF Gold P: 637 I got an unexpected bonus this year! Since the wife and I have been wanting a new camera for quite awhile now, we started doing some research on beginner DSLR cameras. I've always owned <$200 point-and-shoot cameras, so, needless to say, I haven't really been inspired to take very many pictures outside of family events, major vacations, etc. Since the bonus gave us a significant amount of financial freedom this season, we decided that it was a good time to buy a real camera. After quite a bit of research, we decided to go with the Canon EOS Rebel T2i (EOS 550D in Europe and Asia). We bought it yesterday, and I've been fiddling around with this amazing camera (on full-auto mode) for a few hours; I'm thoroughly impressed. It has inspired me to add a photography class to my schedule next semester so that I can learn to use it to its full potential. I'd like to get to the point where I can do everything manually and have no need for the preset modes. I'd also like to get a telephoto lens and a tripod so that I can start taking pictures of wildlife and my siblings' games/performances, but I think we're going to let the dust settle before spending any more money. I'm looking forward to participating in the photo contests! PF Gold P: 7,368 Congrats, Dembadon! Canon has a very nice selection of lenses, and reasonable upgrade-paths. Their best lenses are , but there are some nice L-series zooms that will cover a lot of territory. I have a 100-400 IS USM and it delivers really crisp contrasty images. I was doing film photography back when zooms started getting popular, and avoided them like the plague. The 100-400 performs almost as well as my old dedicated Olympus and Bronica primes, and performs really well as a macro, too. PF Gold P: 5,450 Nice Dembadon, got the same camera, but maybe if I had to buy one today, I would also have considered the brand new Canon 60D, which is bridging the gap between the 550D and the 7D, all with the same sensor but with different sets of gadgets. Sure Turbo's 100-400mmL is good glass but budgetting and judging price versus quality, you may also have a look at the 55-250mm IS. But the most important part of all camera's starts at about one inch behind the camera. PF Gold P: 5,450 Quote by drizzle Sure, let us know how it goes! Oh dang, I forgot about that, but she made it all the way and I got a thanks for my support. PF Gold P: 7,368 Quote by Andre Sure Turbo's 100-400mmL is good glass but budgetting and judging price versus quality, you may also have a look at the 55-250mm IS. I wanted to get a long, fast prime, but those are horrendously expensive. The 100-400 covered a lot of the range I wanted without all the $ and extra lenses. I have to put up with the relatively slow f:ratio, but with digital cameras, that's a lot easier to accommodate than with film.
PF Gold P: 5,450 ...especially when your DSLR is very good at high iso's like the Canon 550D/7D/60D, but also the Pentax K-x and probably the successors (k-r and K-5) and the Nikon D3S and successors.
Sci Advisor P: 5,446 Just to completely change the subject... I've got nothing for this week's contest (snow&ice) since snow season starts in another month or so, but I would appreciate any hints/tips regarding winter photography, for example- 1) how do you deal with thermal issues- does the camera need to equalize when going out, and how do you prevent/minimize condensation when coming back in? 2) How can I set my exposure stop to allow good contrast (for example, the texture of a snow-covered hillside), while still getting a good 'white' tone? Similarly, any ideas for getting a good 'white-on-white' (say a snowdrift)? 3) The overall lighting here is very 'grey'- heavy overcast skies. How can I make any spots of color really pop out? I'm hoping to get some good macro shots of snowflakes this year- One thing I miss about the South are those ice storms where everything- every leaf, individual pine needles... gets coated in a 1/8" sheath of crystal clear ice- it's as gorgeous to look at as treacherous to drive on.
Admin P: 22,375 I don't care too much when I go out, but I don't open the bag/remove camera after getting inside till it gets warm. As for 2&3 - in my experience when there is no light, there is no pictures, no matter how you try. But I am eager to learn something new.
PF Gold
P: 5,450
Quote by Andy Resnick 1) how do you deal with thermal issues- does the camera need to equalize when going out, and how do you prevent/minimize condensation when coming back in?
Going out is no problem, except that the batteries may die in extreme cold weather. But before that you get to take the most noise free shots you get, thanks to the increased sensitivity of the cooled sensor. Also consider taking out the battery and carry it in a warm pocket, if it takes a while to get to the shooting location in the cold.
Going in is definitely a problem. Best is to store it in something air tight, a heavy duty plastic bag or something before going in.
2) How can I set my exposure stop to allow good contrast (for example, the texture of a snow-covered hillside), while still getting a good 'white' tone? Similarly, any ideas for getting a good 'white-on-white' (say a snowdrift)?
Use a tripod and make multiple shots with different exposures one stop apart, to select the best one at home, or use HDR. Also modern Canon EOS camera's have an enhanced high tone sensitivity setting.
3) The overall lighting here is very 'grey'- heavy overcast skies. How can I make any spots of color really pop out?
Use RAW and play with color saturation and other settings in post processing.
Succes
PF Gold P: 5,450 Anyway, after posting the previous I made this picture during a short hike with my point&shoot (Panasonic DMC TZ7). This is what the original jpg looks like: and this with some enhancing contrast, and color using Canons DPP (Digital Photo Profesional) software
Sci Advisor P: 5,446 Andre- Thanks! I understand what you mean. Was the original shot with in-camera HDR? I like how you can make the distant snowy trees 'pop'.
PF Gold P: 5,450 No in camera HDR, I just did exactly what it said, point and shoot to get something like this (in another direction): Then I loaded the jpg into DPP and played with the colors as follows: Notice that I also fooled around with the blue and red 'curve tone', adding some red in the (low) foreground and removing some more blue in the background (high) And this is the result (all pics are reduced to 18%):
PF Gold
P: 637
Quote by turbo-1 Congrats, Dembadon! Canon has a very nice selection of lenses, and reasonable upgrade-paths. Their best lenses are , but there are some nice L-series zooms that will cover a lot of territory. I have a 100-400 IS USM and it delivers really crisp contrasty images. I was doing film photography back when zooms started getting popular, and avoided them like the plague. The 100-400 performs almost as well as my old dedicated Olympus and Bronica primes, and performs really well as a macro, too.
Quote by Andre Nice Dembadon, got the same camera, but maybe if I had to buy one today, I would also have considered the brand new Canon 60D, which is bridging the gap between the 550D and the 7D, all with the same sensor but with different sets of gadgets. Sure Turbo's 100-400mmL is good glass but budgetting and judging price versus quality, you may also have a look at the 55-250mm IS. But the most important part of all camera's starts at about one inch behind the camera.
Is there a significant AF speed difference between a non-USM lens and a lens that uses micro-USM? I've read reviews claiming that the focusing speed difference between the 70-300 IS USM and the 55-250 IS is negligible due to the USM in the 70-300 being "micro-USM" instead of "ring USM," whatever that means.
I'm inclined to save up the extra \$300 for the 70-300 if the AF speed is significantly faster.
PF Gold P: 7,368 I don't know about the autofocus speed or accuracy, but one factor that should be considered is the difference between the construction of the rear element of the lens types. The 55-250 is an EFS lens and the 70-300 is an EF. If you should decide to get a full-frame DSLR later, the EFS won't work with it because the rear element of the lens would protrude too deeply into the mirror-box and interfere with the operation of the mirror. EF lenses will fit full-frame cameras and 1.6x cameras (smaller sensor, smaller mirror box). You might not be considering a body upgrade in the near term, but if you find that you really like your lens and want to keep it, it would be best to have chosen an EF to avoid compatibility problems if you want to buy another body with a full-frame sensor. Here's a review. http://www.the-digital-picture.com/r...ns-review.aspx
Related Discussions General Discussion 10 Introductory Physics Homework 1 Academic Guidance 5 General Discussion 6
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2014-03-12 19:53:01
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https://webwork.maa.org/moodle/mod/forum/discuss.php?d=5045
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## WeBWorK Problems
### Dynamic LaTeX labels on image of triangle?
by Paul Seeburger -
Number of replies: 6
Has anyone successfully generated dynamic LaTeX labels on image of triangle?
I guess I could just work to place the LaTeX labels around the image of a right triangle, but I'm curious if this has already been done.
Is there at least a way to have a right triangle image that is not set off in a white box so that I can draw almost on top of it?
It's for the solution for a Trig. Substitution problem, where I want to show a labeled right triangle for the student's version of the problem.
Thanks!
Paul
In reply to Paul Seeburger
### Re: Dynamic LaTeX labels on image of triangle?
by Glenn Rice -
I am unclear as to what it is that you are asking for. What sort of labels do you want?
What are you using in LaTeX to generate images? TikZ, PSTricks, the TeX picture environment, etc?
It would be rather easy to generate the image of a triangle with labels using TikZ, but that may depend on what you want with the labels.
Are you posting this question in the right place? This isn't a TeX forum.
In reply to Glenn Rice
### Re: Dynamic LaTeX labels on image of triangle?
by Paul Seeburger -
Hi, Glenn!
I am a complete newbie to TikZ, and I was wondering if it was even possible to use it in WeBWorK. I saw a couple posts about people wondering if it could be used, but these seemed to indicate it wasn't yet possible.
I saw how to use the PGgraphmacros.pl to create a triangle as a dynamic graph, but the labels cannot use LaTeX, and I really don't need the triangle to be dynamic. I need the labels of the sides to adjust based on the problem, and I do need them to use LaTeX, being for example, 3, x, and \sqrt{x^2 + 9}, but using a variable to represent the 3, and often more complicated. I'll also want to mark the inside angle of the right triangle with theta and orient the triangle so the right angle is on the bottom right side of the diagram.
You mentioned a TeX forum. Do you mean on this site? Or something outside of WeBWorK? My question here is about what's possible in WeBWorK, so I would want to start here.
If TikZ can be used, do I need to load a particular macro file?
Thanks!
Paul
In reply to Paul Seeburger
### Re: Dynamic LaTeX labels on image of triangle?
by Robin Cruz -
Hi, Paul,
I'm not sure this is what you had in mind, but PCC has problems with labeled dynamic triangles. Look in the Library: Subject:"Trigonometry", Chapter:"Triangle trigonometry", Section:"Sine, cosine, and tangent of an angle in a right triangle".
We've done a few at the College of Idaho, but the angles have to be not too small. They are not yet in the OPL--perhaps this summer, I'll work on tagging. Also, greek letters don't seem to be available. PCC uses the letters spelled out. Here's the code for one of ours.
--rac
========================================
##DESCRIPTION
## Trigonometry: Law of Sines
##ENDDESCRIPTION
##KEYWORDS('trigonometry', 'law of sines')
## DBsubject('Trigonometry')
## DBchapter('')
## DBsection('')
## Date('01/2016')
## Author('RA Cruz')
## Institution('The College of Idaho')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
DOCUMENT(); # This should be the first executable line in the problem.
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGchoicemacros.pl",
"PGgraphmacros.pl",
"alignedChoice.pl",
"unionTables.pl",
);
######################################
# Set-up
$a = random(4,9,1);$A = random(25,40,5);
$C = random(70,85,5);$B = 180 - $A -$C;
$c =$a*sin($C*pi/180)/sin($A*pi/180);
$b =$a*sin($B*pi/180)/sin($A*pi/180);
$xc =$b*cos($A*pi/180); #C is at the top of the triangle$yc = $b*sin($A*pi/180);
$Hmin = -2;$Hmax = $c + 2;$Vmin = -2;
$Vmax =$yc + 2;
$picW = 15*($Hmax-$Hmin+2);$picH = 15*($Vmax-$Vmin+2);
$refreshCachedImages=1;$graph = init_graph($Hmin,$Vmin,$Hmax,$Vmax,size=>[$picW,$picH]);
$graph->moveTo(0,0); #A is at the origin$graph->lineTo($xc,$yc,1); #Draw to C
$graph->lineTo($c,0,1); #Draw to B to the right
$graph->lineTo(0,0,1); #$graph->fillRegion([2,1,'yellow']);
$lab_a = new Label($xc+0.7*($c-$xc),0.5*$yc+0.2,"$a",'black','center','bottom');
$lab_a->font(GD::Font->Giant);$graph->lb($lab_a);$lab_b = new Label(0.5*$xc,0.5*$yc+0.2,"b",'red','center','bottom');
$lab_b->font(GD::Font->Giant);$graph->lb($lab_b);$lab_c = new Label(0.5*$c,-0.3,"c",'red','center','center');$lab_c->font(GD::Font->Giant);
$graph->lb($lab_c);
$labA=new Label(-0.5,0.5,'A','black','center','center');$labA->font(GD::Font->Giant);
$graph->lb($labA);
$labAdeg=new Label(0.2*$c,1,"$A",'black','center','center');$labAdeg->font(GD::Font->Giant);
$graph->lb($labAdeg);
$labB=new Label($c+0.5, 0.5,'B','red','center','center');
$labB->font(GD::Font->Giant);$graph->lb($labB);$labC=new Label($xc,$yc+1,'C','black','center','center');
$labC->font(GD::Font->Giant);$graph->lb($labC);$labCdeg=new Label($xc-.1,0.85*$yc,"$C",'black','center','center');$labCdeg->font(GD::Font->Giant);
$graph->lb($labCdeg);
######################################
# Main text
TEXT(beginproblem());
#TEXT("a = $a, b =$b, c =$c, B =$B $BR"); #For checking BEGIN_TEXT Solve for the unknown sides and angles of the triangle shown below. Give the angle(s) in degrees.$BR $BR \{ ColumnTable( "$$b =$$ ".ans_rule(6). "$BR $BR". "$$c =$$ ".ans_rule(6). "$BR $BR". "$$\angle B =$$ ".ans_rule(6)."$$^\circ$$",$BCENTER.
image(insertGraph($graph), width=>$picW, height=>$picH, tex_size=>500 ).$BR.
ECENTER, indent => 0, separation => 30, valign => "TOP" ) \}BR
$BITALIC Note: If no such triangle exists, type${BBOLD}No triangle$EBOLD for each answer.$EITALIC
END_TEXT
######################################
# Answer
Context("Numeric");
Context()->strings->add("No triangle"=>{},None=>{alias=>"No triangle"});
$ans1 = Compute("$b");
ANS($ans1->cmp(showTypeWarnings=>0));$ans2 = Compute("$c"); ANS($ans2->cmp(showTypeWarnings=>0));
$ans3 = Compute("$B");
ANS($ans3->cmp(showTypeWarnings=>0));$showPartialCorrectAnswers = 1;
#####################################
# Solution
BEGIN_SOLUTION
$PAR Solution:$BR $BR We need the angle at $$B:$$ $$\angle B = 180^{\circ} - A^{\circ} - C^{\circ} = ans3^{\circ}$$$BR $BR Use the Law of Sines to find $$a$$ and $$c$$:$BR $BR First we find $$a$$: $$\dfrac{a}{\sin(A^{\circ})} = \dfrac{b}{\sin(B^{\circ})} \$$$BR
$$a = \dfrac{b\sin(A^{\circ})}{\sin(B^{\circ})} \approx ans1$$
$BR$BR
Similarily, find $$c$$:
$$\dfrac{c}{\sin(C^{\circ})} = \dfrac{b}{\sin(B^{\circ})} \$$
BR $$c = \dfrac{b\sin(C^{\circ})}{\sin(B^{\circ})} \approx ans2$$ END_SOLUTION ENDDOCUMENT(); In reply to Robin Cruz ### Re: Dynamic LaTeX labels on image of triangle? by Paul Seeburger - Thanks so much, Robin! These examples will be useful as I continue to create new problems. For the application I was developing here, I found a nice-looking solution that uses CSS along with a transparent PNG image of a right triangle. I used the following code to set the CSS up: TEXT( MODES( HTML=>" <style> .triangleGroup { display: inline-block; vertical-align: middle; } .triangleLeftLabel { display:inline-block; position: relative; left: 100px; } .triangleBottomLabel { display:inline-block; position: relative; left: 150px; } </style>", TeX=>"")); And the following code in my problem to set up the right triangle itself with its labels: Representing this relationship in a right triangle, we get: \{ openSpan({class=>"triangleGroup"})\} \{ openSpan({class=>"triangleLeftLabel"})\} $$\quad x + d$$ \{ closeSpan()\} \{image( "rightTriangle_theta.png", width=>225,height=>127,tex_size=>400)\} $$b$$BR
\{ openSpan({class=>"triangleBottomLabel"})\}
$$\sqrt{a}$$
\{ closeSpan()\}
\{ closeSpan()\}
I checked it on my phone and it rendered well there as well. I'm not sure how to make this also look nice in TeX though. I attached the triangle PNG below.
Paul
In reply to Paul Seeburger
### Re: Dynamic LaTeX labels on image of triangle?
by Glenn Rice -
As of the next release of WeBWorK you will be able to use LaTeX with the TikZ package to generate images for problems. However, it is not just a macro. In order for it to work you need the underlying Perl module. So it will not work with WeBWorK 2.15 or before.
You could use the JSXGraph javascript library to accomplish this, but that takes some work to set up. You can use MathJax for the text in JSXGraph.
In reply to Glenn Rice
### Re: Dynamic LaTeX labels on image of triangle?
by Paul Seeburger -
Wow, thanks for this information, Glenn!
The availability of TikZ in WeBWorK should allow for new innovative and nice-looking problems.
For the time-being, I was able to represent my problem to my satisfaction using the approach I posted earlier this evening in this thread.
|
2022-01-25 20:14:00
|
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|
https://swsmile.info/post/cache-aside/
|
# Cache Aside Pattern / Lazy-load
This is the most commonly used cache update strategy in applications. 其具体逻辑如下：
• 失效：应用程序先从cache取数据，没有得到，则从数据库中取数据，成功后，放到缓存中。
• 命中：应用程序从cache中取数据，取到后返回。
• 更新：先把数据存到数据库中，成功后，再让缓存失效。
# Scenarios
## 缓存失效/命中
In this update strategy, cache sits aside and an application talks to cache and data store directly. It is also known as lazy-loading. Application logic first checks in the cache before hitting the database. It is mostly used with an application with read-heavy workloads.
An application retrieves data by referencing the cache. If the data isn’t in the cache, it’s retrieved from the data store and added to the cache. Any modifications to data held in the cache are automatically written back to the data store as well.
For caches that don’t provide this functionality, it’s the responsibility of the applications that use the cache to maintain the data.
## 缓存更新
• 更新：先把数据存到数据库中，成功后，再让缓存失效。
Discussion - 缓存更新时，Delete Cache First or Update DB First
# Potential Problem
• 如果使用了MySQL Master-Slave，当出现DB delay的时候，因而当完成写操作且触发 invalidate cache 操作后，从Slave DB读取数据，且这个数据是更新前的旧数据（由于 DB delay），从而使得重新写入 cache 中的数据仍然是旧数据。
## Solution
1. 先写数据库
2. 删除缓存
3. 休眠1秒，再次删除缓存
• 这一步可以这样实现：
• Solution 1：在第一次删除缓存后，开启一个线程，并让这个线程在1s后，执行再次删除
• Solution 2：通过读取DB的binlog和一个消息队列来实现再次删除
Analysis
• single source of truth 为 DB
• 这里具体休眠多久要结合业务情况考虑。
• 如果考虑到删除可能失败，再增加删除失败时的重试机制。
# Example
// *****************************************
// function that returns a customer's record.
// Attempts to retrieve the record from the cache.
// If it is retrieved, the record is returned to the application.
// If the record is not retrieved from the cache, it is
// added to the cache, and
// returned to the application
// *****************************************
get_customer(customer_id)
customer_record = cache.get(customer_id)
if (customer_record == null)
customer_record = db.query("SELECT * FROM Customers WHERE id = {0}", customer_id)
cache.set(customer_id, customer_record)
return customer_record
For this example, the application code that gets the data is the following.
customer_record = get_customer(12345)
# Analysis
• It does not load or hold all the data together, it’s on demand. Suitable for cases when you know that your application might not need to cache all data from data source in a particular category.
### Node failures aren’t fatal for your application
• When a node fails and is replaced by a new, empty node, your application continues to function, though with increased latency.
• As requests are made to the new node, each cache miss results in a query of the database. At the same time, the data copy is added to the cache so that subsequent requests are retrieved from the cache.
### Cache Miss Penalty
Each cache miss results in three trips:
1. Initial request for data from the cache
2. Query of the database for the data
3. Writing the data to the cache
• These misses can cause a noticeable delay in data getting to the application.
Developers deal with this by warming (pre-heating) the cache or Refresh Ahead Caching.
### Stale Data
• Since data is written to the cache only when there is a cache miss, data in the cache can become stale. This result occurs because there are no updates to the cache when data is changed in the database.
• To address this issue, you can use cache update mechanisms (e.g., Write-through), update invalidation mechanisms, or Adding TTL.
### Possible Low Cache Hit Rate
• Because most data is never requested, lazy loading avoids filling up the cache with data that isn’t requested.
|
2022-07-07 17:27:43
|
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|
https://blender.stackexchange.com/questions/192058/polymorthic-propertygroup
|
# Polymorthic PropertyGroup
What's the best practice for polymorthic properties? I want to associate a type with an object; Cylinder, Thread, Cube etc. For each type I want properties associated, but as the object can only be one type at it only need one set of properties.
What I was hoping to be able to do was define a class from PropertyGroup then subclass that, and set the custom type on the object. Something like this
class ObjectParameters(bpy.types.PropertyGroup):
type: bpy.props.StringProperty()
class CylinderParameters(ObjectParameters):
height: bpy.props.FloatProperty()
height: bpy.props.FloatProperty()
pitch: bpy.props.FloatProperty()
bpy.utils.register_class(ObjectParameters)
bpy.utils.register_class(CylinderParameters)
bpy.types.Object.object_parameters = bpy.props.PointerProperty(type=ObjectParameters)
cube = bpy.data.objects['Cube']
print(cube.object_parameters)
cube.object_parameters = CylinderParameters()
print(cube.object_parameters)
That fails as you can't create an instance of CylinderParameters; and even if you could cylinder_parameters is read-only so you wouldn't be able to change it.
The best option I've come up with so far is this; creating properties for each type on bpy.types.Object then having another one select between them.
import bpy
class CylinderParameters(bpy.types.PropertyGroup):
height: bpy.props.FloatProperty()
height: bpy.props.FloatProperty()
pitch: bpy.props.FloatProperty()
bpy.utils.register_class(CylinderParameters)
bpy.types.Object.object_type = bpy.props.EnumProperty(items=[
('NONE', 'None', '', 1),
('cylinder_parameters', 'Cylinder', '', 2),
], default='NONE')
bpy.types.Object.cylinder_parameters = bpy.props.PointerProperty(type=CylinderParameters)
cube = bpy.data.objects['Cube']
print('init type', cube.object_type)
cube.object_type = 'cylinder_parameters'
print(cube.object_type)
print(getattr(cube, cube.object_type))
The other way is to just update a custom property on the object with a dictionary e.g.
cube = bpy.data.objects['Cube']
cube['parameters'] = {'type': 'cylinder', 'height': 56, 'radius': 1}
print(cube['parameters'])
Whats the best way to do this?
• The other thing you can do it to add a property function to bpy.types.Object which returns the relevant properties – mountainstorm Sep 6 '20 at 20:11
|
2021-06-22 23:14:23
|
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|
https://unapologetic.wordpress.com/2008/04/29/
|
The Unapologetic Mathematician
Examples of Convergent Series
Today I want to give two examples of convergent series that turn out to be extremely useful for comparisons.
First we have the geometric series whose terms are the sequence $a_n=a_0r^n$ for some constant ratio $r$. The sequence of partial sums is
$\displaystyle\sum\limits_{k=0}^na_0r^k=a_0\left(1+r+r^2+...+r^n\right)$
If $r\neq1$ we can multiply this sum by $\frac{1-r}{1-r}$ to find
$\displaystyle\sum\limits_{k=0}^na_0r^k=a_0\frac{1-r^{n+1}}{1-r}$
Then as $n$ goes to infinity, this sequence either blows up (for $|r|>1$) or converges to $\frac{a_0}{1-r}$ (for $|r|<1$). In the border case $r=\pm1$ we can also see that the sequence of partial sums fails to converge. Thus the geometric series converges if and only if $|r|<1$, and we have a nice simple formula telling us the sum.
The other one I want to hit is the so-called $p$-series, whose terms are $a_n=n^{-p}$ starting at $n=1$. Here we use the integral test to see that
$\displaystyle\lim\limits_{n\rightarrow\infty}\left(\sum\limits_{k=1}^n\frac{1}{n^p}-\int\limits_1^n\frac{dx}{x^p}\right)=D$
so the sum and integral either converge or diverge together. If $p\neq1$ the integral gives $\frac{n^{1-p}-1}{1-p}$, which converges for $p>1$ and diverges for $p<1$.
If $p=1$ we get $\ln(n)$, which diverges. In this case, though, we have a special name for the limit of the difference $D$. We call it “Euler’s constant”, and denote it by $\gamma$. That is, we can write
$\displaystyle\sum\limits_{k=1}^n\frac{1}{k}=\ln(n)+\gamma+e(n)$
where $e(n)$ is an error term whose magnitude is bounded by $\frac{1}{n}$.
In general we have no good value for the sums of these series, even where they converge. It takes a bit of doing to find $\sum\frac{1}{n^2}=\frac{\pi^2}{6}$, as Euler did in 1735 (solving the “Basel Problem” that had stood for almost a century), and now we have values for other even natural number values of $p$. The sum $\sum\frac{1}{n^3}$ is known as Apéry’s constant, after Roger Apéry who showed that it was irrational in 1979. Yes, we didn’t even know whether it was a rational number or not until 30 years ago. We have basically nothing about odd integer values of $p$.
If we say $s$ instead of $p$, and let $s$ take complex values (no, I haven’t talked about complex numbers yet, but some of you know what they are) we get Riemann’s function $\zeta(s)=\sum\frac{1}{n^s}$, which is connected to some of the deepest outstanding questions in mathematics today.
April 29, 2008 Posted by | Analysis, Calculus | 4 Comments
The Integral Test
Sorry for the delay. Students are panicking on the last day of classes and I have to write up a make-up exam for one who has a conflict at the scheduled time…
We can forge a direct connection between the sum of an infinite series and the improper integral of a function using the famed integral test for convergence.
I’ve spent a goodly amount of time last week trying to craft a proof hinging on converting the infinite sum to an improper integral using the integrator $\lfloor x\rfloor$, and comparing that one to those using the integrators $x$ and $x-1$. But it doesn’t seem to be working. If you can make a go of it, I’ll be glad to hear it. Instead, here’s a proof adapted from Apostol.
We let $f$ be a positive decreasing function defined on some ray. For our purposes, let’s let it be $\left[1,\infty\right)$, but we could use any other and adapt the proof accordingly. What we require in any case, though, is that the limit $\lim\limits_{x\rightarrow\infty}f(x)=0$. We define three sequences:
$\displaystyle s_n=\sum\limits_{k=1}^nf(k)$
$\displaystyle t_n=\int\limits_1^nf(x)dx$
$d_n=s_n-t_n$
First off, I assert that $d_n$ is nonincreasing, and sits between $f(n)$ and $f(1)$. That is, we have the inequalities
$0
To see this, first let’s write the integral defining $t_{n+1}$ as a sum of integrals over unit steps and notice that $f(k)$ gives an upper bound to the size of $f$ on the interval $\left[k,k+1\right]$. Thus we see:
$t_{n+1}\displaystyle\sum\limits_{k=1}^n\int\limits_k^{k+1}f(x)dx\leq\sum\limits_{k=1}^n\int\limits_k^{k+1}f(k)dx=\sum\limits_{k=1}^nf(k)=s_n$
From here we find that $f(n+1)=s_{n+1}-s_n\leq s_{n+1}-t_{n+1}=d_{n+1}$.
On the other hand, we see that $d_n-d_{n+1}=t_{n+1}-t_n-(s_{n+1}-s_n)$. Reusing some pieces from before, we see that this is
$\displaystyle\int\limits_n^{n+1}f(x)dx-f(n+1)\geq\int\limits_n^{n+1}f(n+1)dx-f(n+1)=0$
which verifies that the sequence $d_n$ is decreasing. And it’s easy to check that $d_1=f(1)$, which completes our verification of these inequalities.
Now $d_n$ is a monotonically decreasing sequence, which is bounded below by ${0}$, and so it must converge to some finite limit $D$. This $D$ is the difference between the sum of the infinite series and the improper integral. Thus if either the sum or the integral converges, then the other one must as well.
We can actually do a little better, even, than simply showing that the sum and integral either both converge or both diverge. We can get some control on how fast the sequence $d_n$ converges to $D$. Specifically, we have the inequalities $0\leq d_k-D\leq f(k)$, so the difference converges as fast as the function goes to zero.
To get here, we look back at the difference of two terms in the sequence:
$\displaystyle0\leq d_n-d_{n+1}\leq\int\limits_n^{n+1}f(n)dx-f(n+1)=f(n)-f(n+1)$
So take this inequality for $n=k$ and add it to that for $n=k+1$. We see then that $0\leq d_k-d_{k+2}\leq f(k)-f(k+2)$. Then add the inequality for $n=k+2$, and so on. At each step we find $0\leq d_k-d_{k+l}\leq f(k)-f(k+l)$. So as $l$ goes to infinity, we get the asserted inequalities.
April 29, 2008 Posted by | Analysis, Calculus | 1 Comment
|
2017-04-25 12:21:34
|
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|
https://archive.stsci.edu/hlsp/phatter
|
## Mission Overview
### Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region ("PHATTER")
Primary Investigator: Julianne Dalcanton
HLSP Authors: Meredith Durbin, Benjamin Williams
Released: 2021-03-15
Updated: 2021-03-15
Primary Reference(s): Williams et al. 2021
## Overview
The team provides UV-optical-NIR photometry for 22 million stars in the central ~0.1 deg^2 of M33 for the Panchromatic Hubble Andromeda Treasury: Triangulum Extended Region ("PHATTER") survey. They use the filters F275W and F336W on the WFC3/UVIS camera, F475W and F814W on ACS/WFC, and the F110W and F160W on WFC3/IR. UVIS data reach a magnitude limit of ~25 in F275W and F336W. ACS data reach maximum depths of ~28 magnitudes in F475W and ~27 magnitudes in F814W in the uncrowded outer disk. In these same regions, WFC3/IR data reach maximum depths of ~26.5 and ~25.5 in F110W and F160W, respectively. However, the depths are crowding limited in the optical and NIR, and thus is a strong function of radius. As a result, photometry in the inner bulge fields is far shallower. The source catalogs and image mosaics from which the sources are extracted are provided by the team. The team also provides the WCS solutions for each subsection's reference image.
## Data Products
The mosaic files have the following naming convention:
hlsp_phatter_hst_<ins>_m33_<filter>_v1_drz.fits
where:
• <ins> = Name of the instrument used, either "acs-wfc", "wfc3-uvis", or "wfc3-ir".
• <filter> = Name of filter used, one of "f475w", "f814w", "f160w", "f275w", "f336w".
The catalog files have the following naming convention:
hlsp_phatter_hst_wfc3-uvis-acs-wfc-wfc3-ir_m33-<subset>_f275w-f336w-f475w-f814w-f110w-f160w_v1_phot.fits
where:
• <subset> = name of the imaging subset, examples: "b01-ne", "b02-ss", or "b03-nw".
The WCS files have the following naming convention:
hlsp_phatter_hst_acs-wfc_m33-<subset>_f475w_v1_wcs.fits
where:
• <subset> = name of the imaging subset, examples: "b01-ne", "b02-ss", or "b03-nw".
Data file types:
_drz.fits Full-frame drizzled mosaics of the entire survey for a given filter. _phot.fits Full-stack 6-band photometry tables for each subsection of the survey. _wcs.fits WCS information for each photometry subsection's reference image.
## Data Access
### DRZ Mosaics
Filter DRZ Mosaic
F475W hlsp_phatter_hst_acs-wfc_m33_f475w_v1_drz.fits
F814W hlsp_phatter_hst_acs-wfc_m33_f814w_v1_drz.fits
F160W hlsp_phatter_hst_wfc3-ir_m33_f160w_v1_drz.fits
F275W hlsp_phatter_hst_wfc3-uvis_m33_f275w_v1_drz.fits
F336W hlsp_phatter_hst_wfc3-uvis_m33_f336w_v1_drz.fits
### Catalog and WCS Files
b01-ne: PHOT | WCS b01-nn: PHOT | WCS b01-nw: PHOT | WCS
b01-se: PHOT | WCS b01-ss: PHOT | WCS b01-sw: PHOT | WCS
b02-ne: PHOT | WCS b02-nn: PHOT | WCS b02-nw: PHOT | WCS
b02-se: PHOT | WCS b02-ss: PHOT | WCS b02-sw: PHOT | WCS
b03-ne: PHOT | WCS b03-nn: PHOT | WCS b03-nw: PHOT | WCS
b03-se: PHOT | WCS b03-ss: PHOT | WCS b03-sw: PHOT | WCS
## Citations
Please remember to cite the appropriate paper(s) below and the DOI if you use these data in a published work.
Note: These HLSP data products are licensed for use under CC BY 4.0.
|
2021-04-21 21:25:39
|
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|
https://byjus.com/question-answer/find-k-if-one-root-of-the-equation-displaystyle-x-2-6kx-8-0-is/
|
Question
# Find k if one root of the equation $$\displaystyle x^{2}-6kx+8=0$$ is twice the other
A
2
B
±1
C
±12
D
3
Solution
## The correct option is B $$\displaystyle \pm 1$$since the one root is twice the others,Let the one root be a and other root will be 2aNow sum of roots $$a+2a=6k$$and product of roots $$2a^2=8$$$$\therefore a=2,-2$$Now,$$3a=6k$$$$k= \frac{a}{2}$$Now putting the obtained value of a, we get$$k=1,-1$$Maths
Suggest Corrections
0
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2022-01-27 12:03:15
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|
https://de.zxc.wiki/wiki/Halogenide
|
# Halides
Halides are chemical compounds between elements of the seventh main group (more precisely the 17th group) of the periodic table , the so-called halogens , and elements from other groups. The outdated term is haloids . In addition, the simply negatively charged ions of the halogens ( F - , Cl - , Br - , I - , At - ) are referred to as halide ions (also halides for short). Since the chemical properties of Tenness are completely unknown, the Tennessids are still unknown.
A distinction is made between the connections (depending on the type of chemical bond ):
Salt-like halides
Ionic compounds ( salts ) which, due to the large electronegativity difference between the elements involved, consist of anions and cations and are held together by electrostatic interactions. Examples are sodium chloride (NaCl) and potassium bromide (KBr).
Covalent halides
Covalent compounds in which the difference in electronegativity is not as great as in the above ionic compounds, but the bonds have a charge polarity . Examples are hydrogen halides such as hydrogen chloride (HCl) and interhalogen compounds . Also halogenated hydrocarbons such as methylene chloride (dichloromethane CH 2 Cl 2 ), and other organic compounds containing halogens, are often referred to as halides, which usually but not the current IUPAC corresponding nomenclature.
Complex halides
Complexes with halide ions as ligands , for example the tetrachloridoplatinate ion [PtCl 4 ] 2− .
## Oxidation of halides
The halides oxidize in stages according to the electrochemical series to form elementary halogen.
${\ displaystyle \ mathrm {F_ {2} +2 \ Cl ^ {-} \ longrightarrow Cl_ {2} +2 \ F ^ {-}}}$
Fluorine oxidizes chloride to chlorine.
${\ displaystyle \ mathrm {Cl_ {2} +2 \ Br ^ {-} \ longrightarrow Br_ {2} +2 \ Cl ^ {-}}}$
Chlorine oxidizes bromide to bromine.
${\ displaystyle \ mathrm {Br_ {2} +2 \ I ^ {-} \ longrightarrow I_ {2} +2 \ Br ^ {-}}}$
Bromine oxidizes iodide to iodine.
## Problem
Halides and halogen-containing compounds are often found in the chemical industry. So are z. B. chloroform and dichloromethane are good organic solvents. However, due to their low boiling point, some of them get into the environment and atmosphere. When halides are exposed to sunlight, halogen radicals are then formed, which in turn attack the ozone layer (see: ozone hole ).
The aim is therefore to keep the use of halogen-containing solvents as low as possible. Therefore, CFC- containing substances were banned from spray cans and refrigerators in the 1980s and 1990s.
In some countries, salt-like halides such as sodium fluoride and sodium iodide are added in small amounts to foods, table salt, dental care products or drinking water for the purpose of caries prophylaxis. However, these substances are often dangerous to the environment and, above certain concentrations, harmful to health.
## Detection reactions
### Detection with silver nitrate and ammonia
Precipitates of the silver halide before (left) and after the addition of ammonia water (right next to it), AgI on the left, AgBr in the middle, AgCl on the right
Chloride, bromide and iodide can be precipitated in a detection reaction from aqueous solution after acidification with nitric acid with silver nitrate .
For example, with a saline solution:
${\ displaystyle \ mathrm {NaCl _ {\ (aq)} + AgNO_ {3 \ (aq)} \ longrightarrow Na _ {\ (aq)} ^ {+} + NO _ {\ 3 (aq)} ^ {-} + AgCl_ {\ (s)} \ downarrow}}$
The silver halide precipitate is then examined more closely with ammonia water:
${\ displaystyle \ mathrm {Ag ^ {+} + 2 \ NH_ {3} \ longrightarrow [Ag (NH_ {3}) _ {2}] ^ {+}}}$
• Silver bromide (AgBr) precipitates out as a light yellow precipitate that is only soluble in concentrated ammonia.
• Silver iodide (AgI) appears as a yellow-greenish precipitate which does not dissolve even in concentrated ammonia.
All silver halides decompose when exposed to light and dissolve in concentrated sodium thiosulphate solution (fixing salt).
### Evidence as elemental bromine and iodine
Halide detection with chlorine water and hexane
Another way of differentiating bromine and iodine is to add chlorine water or chloramine T with hydrochloric acid, whereby bromide and iodide are oxidized to halogen by chlorine .
${\ displaystyle \ mathrm {2 \ I ^ {-} + Cl_ {2} \ longrightarrow I_ {2} +2 \ Cl ^ {-}}}$
Iodide and chlorine react to form purple iodine and chloride
${\ displaystyle \ mathrm {2 \ Br ^ {-} + Cl_ {2} \ longrightarrow Br_ {2} +2 \ Cl ^ {-}}}$
Bromide and chlorine react to form brown bromine and chloride
By extraction in an organic solvent, the dyeings are particularly well visible. In oxygen-free solvents such as dichloromethane or n-hexane , iodine is pink-violet, in oxygen-containing solvents such as diethyl ether it is brown. Bromine turns the solution brown. The subsequent reaction to form bromine chloride turns the solution wine-yellow.
${\ displaystyle \ mathrm {Br_ {2} + Cl_ {2} \ longrightarrow 2 \ BrCl}}$
Bromine and chlorine react to form wine-yellow bromine chloride
### Titration method
Three titration methods are used for the quantitative detection of halide ions , which are also based on the poor solubility of the silver halides:
## Individual evidence
1. Dirk Häfner: Workbook qualitative inorganic analysis , 2nd revised edition, Govi-Verlag, Eschborn 2003, p. 124, ISBN 3-7741-0997-4 .
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2022-10-02 12:03:41
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https://www.studyadda.com/sample-papers/mathematics-sample-paper-3_q11/414/320077
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• # question_answer Factorise the following : (a) $18+11x+{{x}^{2}}$ (b) ${{y}^{2}}-2y-15$
(a) $18+\text{11}x+{{x}^{2}}=\text{ }{{x}^{2}}+1\text{1}x+18$ $={{x}^{2}}+\left( 9+2 \right)\text{ }x+18$ $={{x}^{2}}+9x+2x+18$ $=x(x+9)+2(x+9)$ = (x + 9) (x + 2) (b) ${{y}^{2}}-2y-15={{y}^{2}}-(5-3)y-15$ $={{y}^{2}}-5y+3y-15~$ $=y\left( y-5 \right)+3\left( y-5 \right)$ $=\left( y-5 \right)\left( y+3 \right)$
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2020-09-28 23:09:21
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https://www.codingame.com/training/easy/111-rubiks-cube-movements
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• 285
## Goal
A 2×2×2 Rubik's cube is quite complicated. In this puzzle, we will focus on the mono-cube, the 1×1×1 Rubik's cube!
You are given a set of rotations and two faces. Apply the rotations to the cube and locate the two faces after the rotations.
Face notation
F (Front): the side currently facing the observer
B (Back): the side opposite the front
U (Up): the side above or on top of the front side
D (Down): the side opposite the top, underneath the cube
L (Left): the side directly to the left of the front
R (Right): the side directly to the right of the front
Rotation notation
A rotation without the prime symbol ' is a quarter turn clockwise.
A rotation with the prime symbol ' is a quarter turn counter-clockwise.
x, x': rotate cube on R (R and L still face the same directions after rotation)
y, y': rotate cube on U (U and D still face the same directions after rotation)
z, z': rotate cube on F (F and B still face the same directions after rotation)
Example 1
z
D
L
Means: rotate cube clockwise on F and identify the new directions of D and L.
Answer: Output L in line 1 because the initial down face now faces left. Output U in line 2 because the initial left face now faces up.
Example 2
z z'
U
R
Means: rotate cube clockwise on F then counter-clockwise on F, and identify the new directions of U and R.
Answer: Output U in line 1 and R in line 2 because both faces do not change directions after the rotations.
Input
Line 1: Space-separated rotations in xyz notation.
Line 2: Initial direction of face1 the first queried face.
Line 3: Initial direction of face2 the second queried face.
Output
Line 1: Direction of face1 after the rotations.
Line 2: Direction of face2 after the rotations.
Constraints
1 ≤ length of rotations ≤ 100
Example
Input
z
D
L
Output
L
U
A higher resolution is required to access the IDE
Join the CodinGame community on Discord to chat about puzzle contributions, challenges, streams, blog articles - all that good stuff!
Online Participants
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2020-01-28 08:01:42
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https://plainmath.net/7822/field-consider-polynominals-variables-prove-functions-sending-polyomial
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# Let F be a field and consider the ring of polynominals in two variables over F,F[x,y]. Prove that the functions sending a polyomial f(x,y) to its degr
Let F be a field and consider the ring of polynominals in two variables over F,F[x,y]. Prove that the functions sending a polyomial f(x,y) to its degree in x, its degree in y, and its total degree (i.e, the highest $$i+j$$ where $$\displaystyle{x}^{{i}}{y}^{{i}}$$ appears with a nonzero coefficient) all fail o be norm making F[x,y] a Euclidean domain.
• Questions are typically answered in as fast as 30 minutes
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krolaniaN
Let D be a domain. A non-negative integer valued function $$\displaystyle{N}:{D}-{\left\lbrace{0}\right\rbrace}$$ is Euclidean , if given a, b in D there exist $$\displaystyle{q}{\quad\text{and}\quad}{r}\in{D}$$ such that $$a=bq+r$$, with either $$r=0$$ or N(r) To show that f(x,y) going to highest degree in x is not a Euclidean function. (By symmetry) , the same argument shows that f(x,y) going to highest degree in y is not a Euclidean function.
$$\displaystyle{N}:{F}{\left[{x},{y}\right]}-{\left\lbrace{0}\right\rbrace}\rightarrow{\left\lbrace{0},{1},{2},{3},\ldots\right\rbrace}$$
$$N(f(x,y)) =$$ highest degree wrt x
Claim: N is not Euclidean. Consider $$a=x+y, b=y$$. If N were Euclidean, $$\displaystyle\exists{q}{\left({x},{y}\right)},{r}{\left({x},{y}\right)}$$ with $$a=bq+r,r=0$$ or N(r) Now $$\displaystyle{a}={b}{q}+{r}\Rightarrow{x}+{y}={p}{\left({x},{y}\right)}{y}+{r}{\left({x},{y}\right)}$$
Comparing degrees, we deduce
$$p(x,y)=1\ and\ r(x,y)=x.$$
But $$N(r)=1$$, whereas $$N(b)=0$$
so, N(r) So, N is not a Euclidean norm
Proving that the total degree function is also not a Euclidean norm
$$\displaystyle{N}:{F}{\left[{x},{y}\right]}-{\left\lbrace{0}\right\rbrace}\rightarrow{\left\lbrace{0},{1},{2},{3},\ldots\right\rbrace}$$
$$N(f(x,y)) =$$ total degree
Claim: N is not Euclidean. Consider $$\displaystyle{a}={x}+{y}^{{2}},{b}={x}$$. If N were Euclidean, $$\displaystyle\exists{q}{\left({x},{y}\right)},{r}{\left({x},{y}\right)}$$ with $$a=bq+r,r=0$$ or N(r) Comparing degrees, we deduce
$$q(x,y)=1$$ and $$r(x,y)=y^2$$
But $$N(r)=2$$, whereas $$N(b)=2$$
So, N(r) So, N is not a Euclidean norm
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2022-01-23 15:10:30
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|
https://tex.stackexchange.com/questions/341191/self-energy-diagram-using-feynmp
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# Self-energy diagram using feynmp
Please, could you help me to draw such a diagram?
The straightforward code I use is just this:
\begin{fmffile}{diagr_6th_ord}
\begin{fmfgraph}(200,125)
\fmfleft{i}
\fmfright{o}
\fmf{photon}{i,v1}
\fmf{photon}{v4,o}
\fmf{photon}{v2,v3}
\fmf{photon}{v5,v6}
\fmf{fermion}{v1,v2}
\fmf{fermion}{v6,v4}
\fmf{fermion}{v3,v5}
\fmf{dashes_arrow}{v1,v5}
\fmf{dashes_arrow}{v3,v4}
\fmf{dashes_arrow}{v6,v2}
\fmfdotn{v}{6}
\end{fmfgraph}
\end{fmffile}
But this doesn't work. I suppose this is wrong for the same reason as, e.g. in order to add a bubble diagram I should write something like \fmf{photon, left, tension=0}{v5,v6} rather than just \fmf{photon}{v5,v6}, but I don't know how to fix my froble.
Also, I need an arrow for a photon (wiggly line). I know that in order to do this I can use the following code
\fmfcmd{%
style_def wiggly_arrow expr p =
cdraw (wiggly p);
shrink (2);
cfill (arrow p);
endshrink;
enddef;}
Could you tell me where I should put it?
• Although not very satidfactory, I have the following solution to the first part of my question \begin{fmffile}{my_training} \begin{fmfgraph}(150,75) \fmfleft{i1,i2} \fmfright{o1,o2} \fmf{phantom}{i2,v5,v6,o2} \fmffreeze \fmf{phantom, right}{i1,v1,v2,v3,v4,o1} \fmffreeze \fmf{photon}{i1,v1} \fmf{photon}{v5,v6} \fmf{photon}{v2,v3} \fmf{photon}{v4,o1} \fmf{fermion}{v1,v5} \fmf{fermion}{v2,v6} \fmf{fermion}{v3,v4} \fmf{dashes_arrow}{v1,v2} \fmf{dashes_arrow}{v5,v3} \fmf{dashes_arrow}{v6,v4} \end{fmfgraph} \end{fmffile} – user2891657 Nov 27 '16 at 16:08
• Ok, I probably have a quite not bad answer to the first question \begin{fmffile}{6th_ord} \begin{fmfgraph}(250,50) \fmfleft{i1,i2} \fmfright{o1,o2} \fmf{phantom}{i2,v5,v6,o2} \fmffreeze \fmf{phantom}{i1,v1,v2,v3,v4,o1} \fmffreeze \fmf{photon}{i1,v1} \fmf{photon}{v5,v6} \fmf{photon}{v2,v3} \fmf{photon}{v4,o1} \fmf{fermion}{v1,v5} \fmf{fermion}{v2,v6} \fmf{fermion}{v3,v4} \fmf{dashes_arrow}{v1,v2} \fmf{dashes_arrow}{v5,v3} \fmf{dashes_arrow}{v6,v4} \fmfdotn{v}{6} \end{fmfgraph} \end{fmffile} – user2891657 Nov 27 '16 at 17:04
• And to the second question \begin{fmffile}{diagr1} \fmfcmd{% style_def wiggly_arrow expr p = cdraw (wiggly p); shrink (1.2); cfill (arrow p); endshrink; enddef;} \begin{fmfgraph*}(100,60) \fmfleft{i1} \fmfright{o1,o2} \fmflabel{$\hat{a}$}{i1} \fmflabel{$\sigma^{-}$}{o1} \fmflabel{$\hat{D}$}{o2} \fmflabel{$g$}{v1} \fmf{wiggly_arrow}{i1,v1} \fmf{fermion}{v1,o1} \fmf{dashes_arrow}{v1,o2} \fmfdotn{v}{1} \end{fmfgraph*} \end{fmffile} – user2891657 Nov 27 '16 at 17:04
• Welcome to TeX.SX! Can you please expand the code snippet that you have posted to a full minimal working example. A MWE should compile and be as small as possible to demonstrate your problem. it's much easier to help you if we have full working code to start from. – Andrew Nov 27 '16 at 22:21
The answer to both questions is
\begin{fmffile}{6th_ord_SE}
\fmfcmd{%
style_def wiggly_arrow expr p =
cdraw (wiggly p);
shrink (1);
cfill (arrow p);
endshrink;
enddef;}
\begin{fmfgraph}(160,30)
\fmfleft{i1,i2}
\fmfright{o1,o2}
\fmf{phantom}{i2,v5,v6,o2}
\fmffreeze
\fmf{phantom}{i1,v1,v2,v3,v4,o1}
\fmffreeze
\fmf{wiggly_arrow}{i1,v1}
\fmf{wiggly_arrow}{v5,v6}
\fmf{wiggly_arrow}{v2,v3}
\fmf{wiggly_arrow}{v4,o1}
\fmf{fermion}{v1,v5}
\fmf{fermion}{v2,v6}
\fmf{fermion}{v3,v4}
\fmf{dashes_arrow}{v1,v2}
\fmf{dashes_arrow}{v5,v3}
\fmf{dashes_arrow}{v6,v4}
\fmfdotn{v}{6}
\end{fmfgraph}
\end{fmffile}
• I tried it, but I don't get the required image. – egreg Nov 28 '16 at 22:34
One does not even have to play with the styles:
\begin{fmfgraph}(200,125)
\fmfleft{i1,i,i2}
\fmfright{f1,o,f2}
\fmf{phantom}{i1,v5,v6,f1}
\fmf{phantom}{i2,v2,v3,f2}
\fmffreeze
\fmf{photon}{i,v1}
\fmf{photon}{v4,o}
\fmf{photon}{v2,v3}
\fmf{phantom_arrow}{v2,v3}
\fmf{photon}{v5,v6}
\fmf{phantom_arrow}{v5,v6}
\fmf{fermion}{v1,v2}
\fmf{fermion}{v6,v4}
\fmf{fermion}{v3,v7,v5}
\fmf{dashes_arrow}{v1,v5}
\fmf{dashes_arrow}{v3,v4}
\fmf{dashes_arrow}{v6,v7,v2}
\fmfdotn{v}{6}
\end{fmfgraph}
|
2019-06-19 17:03:26
|
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|
http://en.wikipedia.org/wiki/Icosidodecahedron
|
# Icosidodecahedron
Icosidodecahedron
Type Archimedean solid
Uniform polyhedron
Elements F = 32, E = 60, V = 30 (χ = 2)
Faces by sides 20{3}+12{5}
Schläfli symbols r{5,3}
t1{5,3}
Wythoff symbol 2 | 3 5
Coxeter diagram
Symmetry group Ih, H3, [5,3], (*532), order 120
Rotation group I, [5,3]+, (532), order 60
Dihedral Angle 142.62°
$\cos^{-1} \left(-\sqrt{\frac{1}{15}\left(5+2\sqrt{5}\right)}\right)$
References U24, C28, W12
Properties Semiregular convex quasiregular
Colored faces
3.5.3.5
(Vertex figure)
Rhombic triacontahedron
(dual polyhedron)
Net
A Hoberman sphere as an icosidodecahedron
In geometry, an icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.
An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either.
Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along any of six planes to form a pair of pentagonal rotundae, which belong among the Johnson solids.
The icosidodecahedron can be considered a pentagonal gyrobirotunda, as a combination of two rotundae (compare pentagonal orthobirotunda, one of the Johnson solids). In this form its symmetry is D5d, [10,2+], (2*5), order 20.
The wire-frame figure of the icosidodecahedron consists of six flat regular decagons, meeting in pairs at each of the 30 vertices.
## Cartesian coordinates
Convenient Cartesian coordinates for the vertices of an icosidodecahedron with unit edges are given by:[1]
• (0,0,±φ)
• (0,±φ,0)
• (±φ,0,0)
• (±1/2, ±φ/2, ±(1+φ)/2)
• (±φ/2, ±(1+φ)/2, ±1/2)
• (±(1+φ)/2, ±1/2, ±φ/2)
where φ is the golden ratio, (1+√5)/2.
## Orthogonal projections
The icosidodecahedron has four special orthogonal projections, centered on a vertex, an edge, a triangular face, and a pentagonal face. The last two correspond to the A2 and H2 Coxeter planes.
Orthogonal projections
Centered by Vertex Edge Face
Triangle
Face
Pentagon
Image
Projective
symmetry
[2] [2] [6] [10]
## Surface area and volume
The surface area A and the volume V of the icosidodecahedron of edge length a are:
$A = \left(5\sqrt{3}+3\sqrt{25+10\sqrt{5}}\right) a^2 \approx 29.3059828a^2$
$V = \frac{1}{6} \left(45+17\sqrt{5}\right) a^3 \approx 13.8355259a^3.$
## Related polyhedra
The icosidodecahedron is a rectified dodecahedron and also a rectified icosahedron, existing as the full-edge truncation between these regular solids.
The icosidodecahedron contains 12 pentagons of the dodecahedron and 20 triangles of the icosahedron:
Family of uniform icosahedral polyhedra
Symmetry: [5,3], (*532) [5,3]+, (532)
{5,3} t{5,3} r{5,3} 2t{5,3}=t{3,5} 2r{5,3}={3,5} rr{5,3} tr{5,3} sr{5,3}
Duals to uniform polyhedra
V5.5.5 V3.10.10 V3.5.3.5 V5.6.6 V3.3.3.3.3 V3.4.5.4 V4.6.10 V3.3.3.3.5
The icosidodecahedron can be seen in a sequence of quasiregular polyhedrons and tilings:
Dimensional family of quasiregular polyhedra and tilings: 3.n.3.n
Symmetry
*n32
[n,3]
Spherical Euclidean Compact hyperbolic Paracompact Noncompact
*332
[3,3]
Td
*432
[4,3]
Oh
*532
[5,3]
Ih
*632
[6,3]
p6m
*732
[7,3]
*832
[8,3]...
*∞32
[∞,3]
[iπ/λ,3]
Quasiregular
figures
configuration
3.3.3.3
3.4.3.4
3.5.3.5
3.6.3.6
3.7.3.7
3.8.3.8
3.∞.3.∞
3.∞.3.∞
Coxeter diagram
Dual
(rhombic)
figures
configuration
V3.3.3.3
V3.4.3.4
V3.5.3.5
V3.6.3.6
V3.7.3.7
V3.8.3.8
V3.∞.3.∞
Coxeter diagram
Dimensional family of quasiregular polyhedra and tilings: 5.n.5.n
Symmetry
*5n2
[n,5]
Spherical Hyperbolic... Paracompact Noncompact
*352
[3,5]
*452
[4,5]
*552
[5,5]
*652
[6,5]
*752
[7,5]
*852
[8,5]...
*∞52
[∞,5]
[iπ/λ,5]
Coxeter
Quasiregular
figures
configuration
5.3.5.3
5.4.5.4
5.5.5.5
5.6.5.6
5.7.5.7
5.8.5.8
5.∞.5.∞
5.∞.5.∞
Dual figures
Coxeter
Dual
(rhombic)
figures
configuration
V5.3.5.3
V5.4.5.4
V5.5.5.5
V5.6.5.6
V5.7.5.7
V5.8.5.8
V5.∞.5.∞
V5.∞.5.∞
### Pentagonal gyrobirotunda
It is also related to the Johnson solid called a pentagonal orthobirotunda created by two pentagonal rotunda connected as mirror images.
(Dissection)
Icosidodecahedron (pentagonal gyrobirotunda) Pentagonal orthobirotunda Pentagonal rotunda
Eight uniform star polyhedra share the same vertex arrangement. Of these, two also share the same edge arrangement: the small icosihemidodecahedron (having the triangular faces in common), and the small dodecahemidodecahedron (having the pentagonal faces in common). The vertex arrangement is also shared with the compounds of five octahedra and of five tetrahemihexahedra.
### Related polytopes
In four-dimensional geometry the icosidodecahedron appears in the regular 600-cell as the equatorial slice that belongs to the vertex-first passage of the 600-cell through 3D space. In other words: the 30 vertices of the 600-cell which lie at arc distances of 90 degrees on its circumscribed hypersphere from a pair of opposite vertices, are the vertices of an icosidodecahedron. The wire frame figure of the 600-cell consists of 72 flat regular decagons. Six of these are the equatorial decagons to a pair of opposite vertices. They are precisely the six decagons which form the wire frame figure of the icosidodecahedron.
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2014-08-01 16:07:08
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https://math.stackexchange.com/questions/2792901/a-group-of-order-20
|
# A group of order 20
Let $G$ be a group of order $20$ and its class equation is given by $$1+4+5+5+5$$
My question is whether Sylow-$2$ subgroup of $G$ is normal or not.
By Sylow theorem we know that the Sylow-$2$ subgroup will be normal if and only if there is only one Sylow-$2$ subgroup inside $G$. Sylow theorem says that number Sylow-$2$ subgroup is $2k+1$ where $2k+1$ divides $5$. Only $1$ and $5$ are possible. How to decide what will be the case here.
Thank you!
• Sylow states there are $1,3$ or $5$ Sylow-$2$ subgroups (a group of size 4 here is a Sylow-$2$ subgroup because 4 is the highest power of 2 dividing 20) – Max Freiburghaus May 23 '18 at 13:16
• @MaxFreiburghaus Since $3$ does not divide $5$, there is only either $1$ or $5$ Sylow $5$-subgroups. – Bill Wallis May 23 '18 at 13:18
• oh, of course. Fair point – Max Freiburghaus May 23 '18 at 13:19
• Oops, I meant Sylow $2$-subgroups in my comment. – Bill Wallis May 23 '18 at 13:39
By Sylow, you can easily find that there is one Sylow $5$-subgroup, so the only Sylow $5$-subgroup, say $P$, is normal in your group $G$.
Now if your Sylow $2$-subgroup, say $Q$, is normal, then we must have that $G$ is the direct product of its Sylow $p$-subgroups, so that $G = P \times Q$. Now $P$ has order $5$ so it's cyclic and $P \cong C_{5}$. On the other hand, we have that $Q$ is order $4$ so either $Q \cong C_{4}$ or $Q \cong C_{2} \times C_{2}$. Thus the only order $20$ groups with a normal Sylow $2$-subgroup are $$G \cong C_{4} \times C_{5} \cong C_{20} \quad\text{or}\quad G \cong C_{2} \times C_{2} \times C_{5} \cong C_{2} \times C_{10}.$$
The other order $20$ groups are not the direct product of the Sylow $p$-subgroups, so they can't have unique (hence normal) Sylow $p$-subgroups. I'm not sure what the class equation is, but if you can use that to determine properties of your group, you can determine whether it's one of the two above or not.
• I think there will be no Sylow $2$- normal subgroup because if it was normal then by your logic the group $G$ will be abelian and an abelian group cannot have a class equation of the above type? – user276115 May 23 '18 at 17:36
• @2015 Yes, that would work. Since we've shown that for $Q \in \mathrm{Syl}_{2}(G)$ we have $Q \trianglelefteq G \implies G \text{ abelian}$, by the contrapositive we must have that $G \text{ not abelian} \implies Q \ntrianglelefteq G$. So if $G$ is not abelian, it has no normal Sylow $2$-subgroups. – Bill Wallis May 23 '18 at 17:42
Suppose, by way of contradiction, that there is a normal $2$-Sylow subgroup $D$.
If $D$ is cyclic, then it has exactly one involution, and this would form then a conjugacy class made of one element, which does not show up in the class equation. (The "$1$" in the class equation is already taken by the identity.)
This argument actually shows that there is no normal subgroup of order $2$.
If $D$ is a a Klein four-group, it has exactly three involutions, which would then yield a conjugacy class of order $1$ or $3$, again not there.
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2019-05-24 04:07:18
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https://stats.stackexchange.com/questions/202952/k-folds-cross-validation-for-parameter-tuning-and-model-evaluation
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# k folds cross validation for parameter tuning and model evaluation
I am faced with a regression problem which I am addressing using a Random Forest Regressor. I would like to use k folds cross validation to tune the parameters and estimate the out-of-set (i.e. test set) root mean squared error. However, I am a little confused as to what the right order of operations is.
To do this would I simply:
1) split my training data using a train/test split (ex:80/20)
2) run GridSearchCV on the 80 to tune the parameters
3) refit my parameter tuned model on the entire 80 set
4) run k folds on the 20 set to find my out-of-set RMSE for my parameter tuned model?
If so, how does this approach differ from nested k folds cross validation in terms of the bias variance tradeoff ?
• How would you run $k$ folds on the test split (step 4), given that there is only one such split and you already have a model trained on the full train split (based on the current description)? If you would make $K$ 80/20 splits and run steps 1 to 4 as you describe $K$ times, you end up with something very similar to nested cross-validation. Nested cross-validation would be slightly better, though, as a simple resample approach in the outer loop may result in correlated test splits. – Marc Claesen Mar 22 '16 at 7:14
• I am not sure if I was not clear or if I am misunderstanding your comment so let me try to clarify what I meant in step 4; GridSearchCV would run a k folds CV on 80% of the data, select the optimal parameters and then refit the optimal model on the 80% of the data (instead of the k folds). Then I would take this tuned model and run it on the remaining and unseen 20% using k folds in order to estimate an out-of-sample RMSE – Jay Karimi Mar 22 '16 at 7:20
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2019-08-21 03:48:10
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https://www.physicsforums.com/threads/solving-for-x-with-natural-logs.181772/
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# Solving for x with natural logs
1. Aug 26, 2007
### Ry122
Hi
Im having difficulty solving for x in this equation.
5=9ln(x+4)
I have no idea where to start so i can't show u any working.
2. Aug 26, 2007
### rocomath
can you show at least one step? there is at least one very easy step that you could do.
question: if i ask u to find ln(x+2) = 3, how can you get rid of ln?
Last edited: Aug 26, 2007
3. Aug 26, 2007
### gezz
Take another look and don't get bogged down in details until youve done some basic simplification. Work from the outside in and you should be able to rearrange this into something you're much more happy to deal with.
Roco covered it pretty well when he told you there was one easy step you could do =-)
4. Aug 27, 2007
### Ry122
raise e to the power of 3?
5. Aug 27, 2007
### rocomath
yep
$$\exp^{\frac{5}{9}}=(x+4)$$
now just solve for x
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2016-12-05 05:03:07
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https://www.nature.com/articles/nature02409?error=cookies_not_supported&code=98e68917-6ade-4c45-b15d-5a2a372b00cf
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Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.
# Structural relaxation in supercooled water by time-resolved spectroscopy
## Abstract
Water has many kinetic and thermodynamic properties that exhibit an anomalous dependence on temperature1,2,3,4,5, in particular in the supercooled phase. These anomalies have long been interpreted in terms of underlying structural causes, and their experimental characterization points to the existence of a singularity at a temperature of about 225 K. Further insights into the nature and origin of this singularity might be gained by completely characterizing the structural relaxation in supercooled water6. But until now, such a characterization has only been realized in simulations7,8,9 that agree with the predictions of simple mode-coupling theory10; unambiguous experimental support for this surprising conclusion is, however, not yet available11,12,13,14. Here we report time-resolved optical Kerr effect measurements15 that unambiguously demonstrate that the structural relaxation of liquid and weakly supercooled water follows the behaviour predicted by simple mode-coupling theory. Our findings thus support the interpretation7,8,9 of the singularity as a purely dynamical transition. That is, the anomalous behaviour of weakly supercooled water can be explained using a fully dynamic model and without needing to invoke a thermodynamic origin. In this regard, water behaves like many other, normal molecular liquids that are fragile glass-formers.
This is a preview of subscription content, access via your institution
## Relevant articles
• ### Evidence of a liquid–liquid phase transition in H$$_2$$O and D$$_2$$O from path-integral molecular dynamics simulations
Scientific Reports Open Access 09 April 2022
• ### On the existence of soliton-like collective modes in liquid water at the viscoelastic crossover
Scientific Reports Open Access 08 March 2021
• ### Ultrafast hydrogen bond dynamics of liquid water revealed by terahertz-induced transient birefringence
Light: Science & Applications Open Access 04 August 2020
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## References
1. Angell, C. A. in Water: A Comprehensive Treatise (ed. Franks, F.) Vol. 7 1–81 (Plenum, New York, 1982)
2. Angell, C. A. Supercooled water. Annu. Rev. Phys. Chem. 34, 593–630 (1983)
3. Mishima, O. & Stanley, H. E. The relationship between liquid, supercooled and glassy water. Nature 396, 329–335 (1995)
4. Debenedetti, P. G. Metastable Liquids Ch. 4 305–335 (Princeton Univ. Press, Princeton, 1996)
5. Speedy, R. J. & Angell, C. A. Isothermal compressibility of supercooled water and evidence for thermodynamic singularity at -45°C. J. Chem. Phys. 65, 851–858 (1976)
6. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 401, 259–267 (2001)
7. Sciortino, F., Gallo, P., Tartaglia, P. & Chen, S.-H. Supercooled water and the kinetic glass transition. Phys. Rev. E 54, 6331–6343 (1996)
8. Fabbian, L. et al. Molecular mode coupling theory for supercooled liquids: Application to water. Phys. Rev. E 60, 5768–5777 (1999)
9. Sciortino, F. Slow dynamics in supercooled water. Chem. Phys. 258, 307–314 (2000)
10. Götze, W. & Sjögren, L. Relaxation processes in supercooled liquids. Rep. Prog. Phys. 55, 241–336 (1992)
11. Winkler, K., Lindner, J., Bürsing, H. & Vöringer, P. Ultrafast Raman-induced Kerr-effect of water: Single molecule versus collective motions. J. Chem. Phys. 113, 4674–4682 (2000)
12. Rønne, C., Åstrand, P.-O. & Keiding, S. R. THz spectroscopy of liquid H2O and D2O. Phys. Rev. Lett. 82, 2888–2891 (1999)
13. Sokolov, A. P., Hurst, J. & Quitmann, D. Dynamics of supercooled water: Mode-coupling theory approach. Phys. Rev. B 51, 12865–12868 (1995)
14. Bellisent-Funel, M. C., Longeville, S., Zanotti, J. M. & Chen, S.-H. Experimental observation of the α relaxation in supercooled water. Phys. Rev. Lett. 85, 3644–3647 (2000)
15. Righini, R. Ultrafast optical Kerr effects in liquids and solids. Science 262, 1386–1390 (1993)
16. Debenedetti, P. G. & Stanley, H. E. Supercooled and the glassy water. Phys. Today 56, 40–46 (2003)
17. Sciortino, F., La Nave, E. & Tartaglia, P. Physics of the liquid-liquid critical point. Phys. Rev. Lett. 91, 155701 (2003)
18. Franzese, G., Marqués, M. I. & Stanley, H. E. Intramolecular coupling as a mechanism for a liquid-liquid phase transition. Phys. Rev. E 67, 011103 (2003)
19. Castner, E. W., Chang, Y. J., Chu, Y. C. & Walrafen, G. E. The intermolecular dynamics of liquid water. J. Chem. Phys. 102, 653–659 (1995)
20. Palese, S., Schilling, L., Miller, R. J. D., Staver, P. R. & Lotshaw, W. T. Femtosecond optical Kerr-effect studies of water. J. Phys. Chem. 98, 6308–6316 (1994)
21. Palese, S., Mukamel, S., Miller, R. J. D. & Lotshaw, W. T. Interrogation of vibrational structure and line broadening of liquid water by Raman-induced Kerr-effect measurements within the multimode Brownian oscillator model. J. Phys. Chem. 100, 10380–10388 (1996)
22. Foggi, P., Bellini, M., Kien, D. P., Vercuque, I. & Righini, R. Relaxation dynamics of water and HCl aqueous solutions measured by time-resolved optical Kerr effect. J. Phys. Chem. 101, 7029–7035 (1997)
23. Winkler, K., Lindner, J. & Vöringer, P. Low frequency depolarized Raman-spectral density of liquid water from femtosecond optical Kerr-effect measurements: Lineshape analysis of restricted translational modes. Phys. Chem. Chem. Phys. 4, 2144–2155 (2002)
24. Bartolini, P., Ricci, M., Torre, R. & Righini, R. Diffusive and oscillatory dynamics of iodobenzene measured by femtosecond optical Kerr effect. J. Chem. Phys. 110, 8653–8662 (1999)
25. Ricci, M. A., Ruocco, G. & Sampoli, M. Raman spectra of water in the translational and librational regions. III — Temperature evolution by computer simulation with the TIP4P potential. Mol. Phys. 67, 19–31 (1989)
26. Torre, R., Bartolini, P. & Pick, R. M. Time-resolved optical Kerr effect in a fragile glass-forming liquid, salol. Phys. Rev. E 57, 1912–1920 (1998)
27. Torre, R., Bartolini, P., Ricci, M. & Pick, R. M. Time-resolved optical Kerr effect in a fragile glass-forming liquid: Test of different mode coupling theory aspects. Europhys. Lett. 52, 324–329 (2000)
28. Poole, P. H., Sciortino, F., Essmann, U. & Stanley, H. E. Phase behaviour of metastable water. Nature 360, 324–328 (1992)
29. Sastry, S. & Angell, C. A. Liquid-liquid phase transition in supercooled silicon. Nature Mater. 2, 739–743 (2003)
## Acknowledgements
This work was supported by INFM, by the FIRB and COFIN programmes of Italian MIUR, and by an EC grant. We thank F. Sciortino, C. A. Angell and G. Ruocco for discussions.
## Author information
Authors
### Corresponding author
Correspondence to Renato Torre.
## Ethics declarations
### Competing interests
The authors declare that they have no competing financial interests.
## Rights and permissions
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Torre, R., Bartolini, P. & Righini, R. Structural relaxation in supercooled water by time-resolved spectroscopy. Nature 428, 296–299 (2004). https://doi.org/10.1038/nature02409
• Accepted:
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• DOI: https://doi.org/10.1038/nature02409
• ### Evidence of a liquid–liquid phase transition in H$$_2$$O and D$$_2$$O from path-integral molecular dynamics simulations
• Ali Eltareb
• Gustavo E. Lopez
• Nicolas Giovambattista
Scientific Reports (2022)
• ### Femtosecond pulses from a mid-infrared quantum cascade laser
• Philipp Täschler
• Mathieu Bertrand
• Jérôme Faist
Nature Photonics (2021)
• ### On the existence of soliton-like collective modes in liquid water at the viscoelastic crossover
• V. E. Zakhvataev
• L. A. Kompaniets
Scientific Reports (2021)
• ### Ultrafast hydrogen bond dynamics of liquid water revealed by terahertz-induced transient birefringence
• Hang Zhao
• Yong Tan
• Xi-Cheng Zhang
Light: Science & Applications (2020)
• ### Glassy dynamics of water at interface with biomolecules: A Mode Coupling Theory test
• Antonio Iorio
• Gaia Camisasca
• Paola Gallo
Science China Physics, Mechanics & Astronomy (2019)
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2022-09-26 16:19:09
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https://math.stackexchange.com/questions/3198101/pairs-of-palindromic-primes-without-1-and-have-a-palindromic-product
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# Pairs of palindromic primes without $1$ and have a palindromic product
While discussing about prime numbers with other users, I noticed that:
$$(1)$$ There are very few pairs of palindromic prime numbers that do not contain the digit $$1$$ and that have products which are palindromes.
Ex : $$[2, 3], [2, 30203], [2, 30403]$$
$$(2)$$ For the large range that was tested on PARI/GP, I noticed that all the palindromic primes that yielded palindromic products were composed only of the digits $$0, 2, 3, 4$$
$$(3)$$ The palindromic primes of these pairs are equal to $$2$$ or always exist in the range of $$3 \times 10^k$$ to $$4 \times 10^k$$ where $$k \in \Bbb{+Z}, 0$$
User Peter helped me get the following results for $$a, b \lt 10^7$$ on PARI/GP:
[2, 3]
[2, 30203]
[2, 30403]
[2, 32323]
[2, 32423]
[2, 3002003]
[2, 3222223]
[2, 3223223]
[2, 3233323]
[2, 3304033]
[2, 3343433]
[2, 3400043]
[2, 3424243]
[2, 3443443]
[2, 3444443]
[3, 30203]
[3, 32323]
[3, 3002003]
[3, 3222223]
[3, 3223223]
[3, 3233323]
[30203, 3002003]
Questions:
(1) Are there a finite number of pairs of $$a, b$$, where $$a, b$$ are palindromic primes that do not contain the digit $$1$$ and $$ab$$ is a palindrome?
(2) Are all the palindromic primes that yielded palindromic products composed only of the digits $$0, 2, 3, 4$$?
(3) Are all the palindromic primes of these pairs equal to $$2$$ or always exist in the range of $$3 \times 10^k$$ to $$4 \times 10^k$$ where $$k \in \Bbb{+Z}, 0$$?
• I suspect the answer to (1) is no, but I don't have a proof. Note that (2) implies (3) because primes greater than $2$ cannot end in $2$. As for (2), I don't think this property is really particular to prime palindromes. In particular, it appears that if $a$ and $b$ are palindromes that do not contain $1$ and are not divisible by $11$, and $a\cdot b$ is a palindrome, then $a$ and $b$ consist of only the digits $0, 2, 3, 4$. Moreover, if one of them contains the digit $4$, then the other consists of only $0$ and $2$. This is based on Python code searching for such pairs. – kccu May 2 '19 at 22:05
• @kccu I agree, and have reached similar conclusions without proof. If written as a long multiplication, any carry in the calculation seems to imply a palindrome product of two palindromes is impossible, which in turn implies only digits $0,2,3,4$ appear. It's not known whether there are infinite palindromic primes, or whether there are infinite primes containing only restricted digits, such as only $0,2,3,4$. Hence, if (2) is true, then proving (1) in the negative (i.e. that there are infinite such pairs) is certainly difficult. – nickgard May 3 '19 at 11:07
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2020-02-25 13:12:22
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http://math.stackexchange.com/questions/23114/applications-of-cross-product-in-sciences-other-than-physics
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# Applications of cross product in sciences other than physics
I am familiar with using cross products in physics to answer questions about force and torque, but are there applications to other scientific fields? The examples that I've seen in most calculus textbooks deal only with physics or engineering questions.
-
+1 I am hoping we see some neat ones, however I agree with the answer below that since this is a Euclidean phenomenon, you are probably going to want exterior products, of which I expect appications will be more plentiful/redibly available. – BBischof Feb 21 '11 at 20:54
This is a list-of-applications question, so should be CW. – Willie Wong Feb 22 '11 at 10:23
To "questions about force and torque" I would add the purely geometrical field of ${\it kinematics}$ which deals with the movement of three-dimensional bodies in three-space, and there are applications in elementary three-dimensional geometry, as determining the distance between two lines in three-space. Then there is a simple rule for solving two homogeneous linear equations in three unknowns: The general solution of the system $$a_1 x_1+a_2 x_2+a_3 x_3=0, \quad b_1 x_1+b_2 x_2+b_3 x_3=0$$ is given by $\ {\bf x}=\lambda\ ({\bf a}\times {\bf b})$, $\ \lambda\in{\mathbb R}$. But otherwise no application of the cross product comes to mind, the reason being that this concept is strictly confined to euclidean spaces of dimension three. Only for $d=3$ a skew bilinear form can be represented by a vector, i.e. an element of the base space.
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2015-01-27 06:25:24
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http://www.idius.net/resources/
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## Physics Resources
I’ve found some nice sources of information and clear explanations during my decade of studying physics. I wish someone had told me about these resources to begin with. This page contains some advice that I would have given myself when I was beginning my college career.
### General Recommendations
#### Schaum’s Outlines
Schaum’s outlines are an excellent resource for learning the mathematics required for physics majors and graduate students. They are inexpensive, they clearly summarize the material, and they contain many detailed solutions to problems. Many of the books are sufficient to use as a primary source, however the best approach is to have at least one traditional textbook on the subject and one Schaum’s Outline if you are teaching yourself. I especially recommend the following:
Complex Variables Advanced Calculus Linear Algebra Differential Equations Partial Differential Equations Tensor Calculus Fourier Analysis Differential Geometry
#### The Feynman Lectures on Physics
This three-volume set is very rich with clear, concise explanations. It covers practically the entire core physics curriculum including a more thorough discussion of fluid dynamics than most undergraduate physics programs in the United States offer. I highly recommend this to anyone studying physics at the undergraduate or graduate level. Refer to the Wikipedia article for more information: The Feynman Lectures on Physics.
#### Landau & Lifshitz Course of Theoretical Physics
This series of ten texts covers the core of graduate-level physics. Lev Landau—like his American counterpart, Feynman—was very talented at explaining things.
vol. 1: Mechanics vol. 2: The Classical Theory of Fields vol. 3: Quantum Mechanics: Non-Relativistic Theory vol. 4: Quantum Electrodynamics vol. 5: Statistical Physics Pt. 1 vol. 6: Fluid Mechanics vol. 7: Theory of Elasticity vol. 8: Electrodynamics of Continuous Media vol. 9: Statistical Physics Pt. 2 vol. 10: Physical Kinetics
#### Inspiration & Motivation
Studying physics at a university can be arduous and boring at times, so it helps to read some popularizations to remind yourself that physics is fun and exciting once you learn enough. Reading this sort of material can also help you to explain things to people who aren’t as interested in physics as you are. Here are a few examples:
Surely You’re Joking, Mr. Feynman! – Richard P. Feynman QED – Richard P. Feynman The Emperor’s New Mind – Sir Roger Penrose Relativity – Albert Einstein The Elegant Universe – Brian Greene
### Specific Recommendations
#### Fluid Dynamics
I strongly encourage people to study fluid dynamics because it makes vector and tensor calculus more intuitive. Fluids are found everywhere around us and inside of us, so it’s nice to have a good understanding of the general properties of fluid dynamics. Once you understand fluids, you will find that many aspects of electricity & magnetism become intuitive. In addition to volume 2, chapters 39 – 41 of the Feynman Lectures and volume 6 of Landau & Lifshitz, I recommend the excellent text by Batchelor:
An Introduction to Fluid Dynamics – G.K. Batchelor
#### Classical Mechanics
In this case, the standard text by Goldstein already covers the subject very well. If it is supplemented with volume 1 of the Lifshitz & Landau series and volume 2, chapter 19 of the Feynman lectures, you will be likely to have a more solid understanding of the subject. I would recommend studying graduate-level mechanics after or at the same time that you study tensor calculus.
#### Electricity & Magnetism / Classical Electrodynamics
As I mentioned above, I recommend studying fluids before electromagnetic theory. In addition to volume 2 of the Feynman Lectures, volumes 2 and 8 of Landau & Lifshitz, and the standard text by Jackson, I highly recommend:
Electricity and Magnetism – Oleg D. Jefimenko Classical Electromagnetism – Jerrold Franklin Classical Electricity & Magnetism – Panolfsky & Phillips
The text by Jefimenko is very impressive. It contains many clear examples and explanations. The Franklin text contains a nice explanation of shortcuts that can be used when manipulating differental vector operators and it avoids SI units, so it doesn’t contain a lot of $$\epsilon_0$$’s and $$\mu_0$$’s. Thus it’s more in line with research papers. The newest edition of Jackson’s text uses the SI system in part of the book and then switches to Gaussian units later when it gets to more advanced topics; it’s not self-consistent. The text by Panolfsky and Phillips is a classic that contains a few derivations that are otherwise hard to find; some people consider it the best book on the subject. Many people are fans of the undergraduate text by David Griffiths. I can’t comment on that particular text since I haven’t read it. The text by Julian Schwinger et al. is probably the most advanced / mathematical graduate text on the subject.
#### Tensor Calculus
I recommend using a combination of the following books to begin with:
Introduction to Tensor Calculus and Continuum Mechanics – John H. Heinbockel Shaum’s Outline of Tensor Calculus – David Kay An Introduction to Tensors and Group Theory for Physicists – Nadir Jeevanjee
These will introduce you to all of the essential details of the tensor calculus using index notation. They will also provide you with exposure to the two common notations for Christoffel symbols and they include many solved practice problems. To learn more about index-free notation and applications of tensors, it would probably be best to use a modern general relativity or differential geometry text. For the simplest application, study the stress tensor of fluid dynamics. For an explanation of the difference between covariant and contravariant quantities, I’ve written this page.
#### Quantum Mechanics
Quantum theory is best understood once you have studied the Lagrangian and Hamiltonian formulations of classical mechanics. Having a solid background in the solutions of the partial differential equations appearing in electrostatics is also very helpful. In addition to the third volume of the Feynman Lectures and the third volume of Landau & Lifshitz, one book stands out as being particularly good as a primary text:
Principles of Quantum Mechanics – Ramamurti Shankar
It should be supplemented with extra material from other texts, of course. That’s always the case. A very interesting and clear introduction to the path integral formulation can be found in Quantum Mechanics and Path Integrals by Feynman and Hibbs.
#### Thermodynamics and Statistical Mechanics
In terms of thermodynamics, the book by Fermi provides a very nice introduction to the theory:
Thermodynamics – Enrico Fermi
I haven’t read an exceptional statistical mechanics text yet. A few have a pretty good reputation, so they are on my reading list:
Statistical Mechanics: A Set Of Lectures – Richard P. Feynman The Principles of Statistical Mechanics – Richard C. Tolman Nonequilibrium Statistical Mechanics – Robert Zwanzig Statistical Physics of Particles – Mehran Kardar Statistical Physics of Fields – Mehran Kardar A Modern Course in Statistical Physics – Linda E. Reichl
### Recommended Order:
As far as I can tell, the best order in which to study graduate-level physics would be roughly the following. I’ve organized the material into five phases where the topics in each phase are studied simultaneously:
1. mechanics, fluid dynamics and thermodynamics, mathematics (tensor calculus, complex analysis)
2. more mechanics, electricity & magnetism, special relativity, more mathematics (PDE’s, Green’s functions, “special” orthogonal functions)
3. more electricity and magnetism (which includes more about special relativity), introductory general relativity, and quantum mechanics
4. more quantum mechanics, statistical mechanics, more general relativity, and more mathematics (differential geometry)
5. quantum field theory, elementary particles, more statistical mechanics, more mathematics (group theory and topology)
Computational physics and basic computer science can be introduced at any point. I highly recommend that people study probability & statistics, numerical analysis, computational physics, algorithms, data structures, and some basic software engineering in order to be well-rounded.
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2021-06-24 10:16:08
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https://plainmath.net/7766/graph-solution-system-inequalities-indicate-system-solution-equal-equal
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# Graph the solution set of the system of inequalities or indicate that the system has no solution. {(y>=x^2-4),(x-y>=2):}
Graph the solution set of the system of inequalities or indicate that the system has no solution.
$\left\{\begin{array}{c}y\ge {x}^{2}-4\\ x-y\ge 2\end{array}$
You can still ask an expert for help
## Want to know more about Inequalities systems and graphs?
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The graph of shaded region of system of inequalities is:
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2022-06-26 02:37:41
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https://stats.stackexchange.com/questions/220525/why-would-one-ever-use-z-score-over-a-t-score
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# Why would one ever use z-score over a t-score?
Forgive me if this seems like an elementary question, but no amount of googling has turned up a satisfying answer for me. From what I understand, a t-score should be used instead of a z-score when the sample size is considered small. I've also read that a t-score should be used when one is using the estimated variance, $s^2$, as opposed to the known population variance, $\sigma^2$. In addition, I've read that it is fine to use a t-score when $n$ is large and $\sigma^2$ is unknown, such as @gung's states here: Choosing between $z$-test and $t$-test. The reason being that the t-distribution closely approximates the normal distribution when the degrees of freedom are large, and therefore switching from a t-score to a z-score will likely make little difference. And then, finally, if $n$ is large, and $\sigma^2$ is known, it seems the consensus is to use a z-score, meaning you essentially end up with a flow chart like this:
(Note: this isn't my image, and I realize the "$n = 30$" rule is fairly arbitrary)
My question is, why would one use a z-score in the case where the sample size is large and $\sigma^2$ is known? If a t-score is to be used when $\sigma^2$ is known and $n$ is small, and the t-distribution closely approximates the z-distribution as $n$ becomes large, then wouldn't the choice between a z-score and a t-score make little difference? And if that is the case, why would anyone every use a z-score over a t-score? Is there some advantage to using a z-score I am missing, or perhaps a flaw in my understanding?
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2019-09-16 02:23:44
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https://ec.gateoverflow.in/574/gate-ece-2014-set-4-question-30
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38 views
The steady state output of the circuit shown in the figure is given by $y(t)=A(\omega) \sin (\omega t + \phi ( \omega))$. If the amplitude $\mid A (\omega ) \mid =0.25$, then the frequency $\omega$ is
1. $\frac{1}{\sqrt{3} \: R \: C}$
2. $\frac{2}{\sqrt{3} \: R \: C}$
3. $\frac{1}{R \: C}$
4. $\frac{2}{R \: C}$
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2022-10-07 21:12:03
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https://answers.ros.org/answers/237227/revisions/
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Revision history [back]
This is probably a namespacing issue, or you don't load the joint_trajectory_controller (the joint_state_controller only reports joint states, it doesn't actually control any actuators (confusing, I know)).
For the namespace: from your previous question I gather that you have your moveit_planning_execution.launch file configured for the typical ROS-Industrial driver. That is fine, but that assumes that the ActionServer is listening on topics without any additional namespace prefixed. The ros_control infrastructure by default runs its joint_trajectory_controller under a namespace. Either remove the namespace, or remap the topics in your launch file. See abb_experimental/abb_irb120_gazebo/launch/irb120_gazebo.launch for an example (for ABB and Gazebo, but the idea is the same).
If you are not loading the joint_trajectory_controller, you'll want to add that to your ros_control configuration yaml that loads the rest of your controllers. For the kuka_rsi_hw_interface package, it should already be loaded (here).
This is probably a namespacing issue, or you don't load the joint_trajectory_controller (the joint_state_controller only reports joint states, it doesn't actually control any actuators (confusing, I know)).
For the namespace: from your previous question I gather that you have your moveit_planning_execution.launch file configured for the typical ROS-Industrial driver. That is fine, but that assumes that the ActionServer is listening on topics without any additional namespace prefixed. The ros_control infrastructure by default runs its joint_trajectory_controller under a namespace. Either remove the namespace, or remap the topics in your launch file. See abb_experimental/abb_irb120_gazebo/launch/irb120_gazebo.launch for an example (for ABB and Gazebo, but the idea is the same).
If you are not loading the joint_trajectory_controller, you'll want to add that to your ros_control configuration yaml that loads the rest of your controllers. For the kuka_rsi_hw_interface package, it should already be loaded (here).
This is probably a namespacing issue, or you don't load the joint_trajectory_controller (the joint_state_controller only reports joint states, it doesn't actually control any actuators (confusing, I know)).
For the namespace: from your previous question I gather that you have your moveit_planning_execution.launch file configured for the typical ROS-Industrial driver. That is fine, but that assumes that the ActionServer is listening on topics without any additional namespace prefixed. The ros_control infrastructure by default runs its joint_trajectory_controller under a namespace. Either remove the namespace, or remap the topics in your launch file. See abb_experimental/abb_irb120_gazebo/launch/irb120_gazebo.launch for an example (for ABB and Gazebo, but the idea is the same).
If you are not loading the joint_trajectory_controller, you'll want to add that to your ros_control configuration yaml that loads the rest of your controllers. For the kuka_rsi_hw_interface package, it should already be loaded (here)., see also the test sub dir of kuka_rsi_hw_interface for an example).
Update: I've just created an example MoveIt configuration package for the KR 6 R900 sixx, see the kr6r900sixx_moveit_rsi_convenience in my fork of ros-industrial/kuka_experimental.
This is probably a namespacing issue, or you don't load the joint_trajectory_controller (the joint_state_controller only reports joint states, it doesn't actually control any actuators (confusing, I know)).
For the namespace: from your previous question I gather that you have your moveit_planning_execution.launch file configured for the typical ROS-Industrial driver. That is fine, but that assumes that the ActionServer is listening on topics without any additional namespace prefixed. The ros_control infrastructure by default runs its joint_trajectory_controller under a namespace. Either remove the namespace, or remap the topics in your launch file. See abb_experimental/abb_irb120_gazebo/launch/irb120_gazebo.launch for an example (for ABB and Gazebo, but the idea is the same).
If you are not loading the joint_trajectory_controller, you'll want to add that to your ros_control configuration yaml that loads the rest of your controllers. For the kuka_rsi_hw_interface package, it should already be loaded (here, see also the test sub dir of kuka_rsi_hw_interface for an example).
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2019-12-15 10:56:40
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https://docs.recastsoftware.com/help/recast-agent-not-connecting
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# Recast Agent not Connecting
There are times when a Recast Agent attempts to connect to a Recast Management Server, but is unable. You'll see a warning in the Recast Management Server telling you that there is an Agent that is trying to connect, but it is not approved. This most often occurs if you delete the Agent from the Recast Management Server manually. Because the Agent information is deleted, there is no way to approve this Agent.
Error: A Recast Agent is trying to connect, but is not approved.
## Resolution
Forcing the Agent to re-enroll gives you a way to approve an Agent, allowing it to connect again.
To re-enroll an Agent:
1. Log onto the computer where the Agent is not connecting.
2. Navigate to the agent.sqlite file location:
Version 5.X Recast Agent: C:\ProgramData\Recast Software\Recast Agent
Version 4.X Recast Agent: C:\Windows\System32\config\systemprofile\AppData\Roaming\Recast Software\Recast Agent
3. Delete the agent.sqlite file in that folder.
4. Restart the Recast Agent Service.
The Agent Computer should appear on the Recast Agents page in the Remote Software Center and in the Recast Management Server interface. The Agent will be auto-approved or available to be approved depending on the settings in your Recast Management Server.
## Builder Action
Re-EnrollAgent.xml
## PowerShell Script
Stop-Service -DisplayName “Recast Agent Service”
Remove-Item “C:\Windows\System32\Config\Systemprofile\Appdata\Roaming\Recast Software\Recast Agent\agent.sqlite”
Start-Service -DisplayName “Recast Agent Service”
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2023-02-01 18:26:13
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https://en.wikipedia.org/wiki/Multivariate_t-distribution
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# Multivariate t-distribution
Notation ${\displaystyle t_{\nu }({\boldsymbol {\mu }},{\boldsymbol {\Sigma }})}$ ${\displaystyle {\boldsymbol {\mu }}=[\mu _{1},\dots ,\mu _{p}]^{T}}$ location (real ${\displaystyle p\times 1}$ vector)${\displaystyle {\boldsymbol {\Sigma }}}$ scale matrix (positive-definite real ${\displaystyle p\times p}$ matrix) ${\displaystyle \nu }$ is the degrees of freedom ${\displaystyle \mathbf {x} \in \mathbb {R} ^{p}\!}$ ${\displaystyle {\frac {\Gamma \left[(\nu +p)/2\right]}{\Gamma (\nu /2)\nu ^{p/2}\pi ^{p/2}\left|{\boldsymbol {\Sigma }}\right|^{1/2}}}\left[1+{\frac {1}{\nu }}({\mathbf {x} }-{\boldsymbol {\mu }})^{\rm {T}}{\boldsymbol {\Sigma }}^{-1}({\mathbf {x} }-{\boldsymbol {\mu }})\right]^{-(\nu +p)/2}}$ No analytic expression, but see text for approximations ${\displaystyle {\boldsymbol {\mu }}}$ if ${\displaystyle \nu >1}$; else undefined ${\displaystyle {\boldsymbol {\mu }}}$ ${\displaystyle {\boldsymbol {\mu }}}$ ${\displaystyle {\frac {\nu }{\nu -2}}{\boldsymbol {\Sigma }}}$ if ${\displaystyle \nu >2}$; else undefined 0
In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random vectors of the Student's t-distribution, which is a distribution applicable to univariate random variables. While the case of a random matrix could be treated within this structure, the matrix t-distribution is distinct and makes particular use of the matrix structure.
## Definition
One common method of construction of a multivariate t-distribution, for the case of ${\displaystyle p}$ dimensions, is based on the observation that if ${\displaystyle \mathbf {y} }$ and ${\displaystyle u}$ are independent and distributed as ${\displaystyle N({\mathbf {0} },{\boldsymbol {\Sigma }})}$ and ${\displaystyle \chi _{\nu }^{2}}$ (i.e. multivariate normal and chi-squared distributions) respectively, the matrix ${\displaystyle \mathbf {\Sigma } \,}$ is a p × p matrix, and ${\displaystyle {\boldsymbol {\mu }}}$ is a constant vector then the random variable ${\textstyle {\mathbf {x} }={\mathbf {y} }/{\sqrt {u/\nu }}+{\boldsymbol {\mu }}}$ has the density[1]
${\displaystyle {\frac {\Gamma \left[(\nu +p)/2\right]}{\Gamma (\nu /2)\nu ^{p/2}\pi ^{p/2}\left|{\boldsymbol {\Sigma }}\right|^{1/2}}}\left[1+{\frac {1}{\nu }}({\mathbf {x} }-{\boldsymbol {\mu }})^{T}{\boldsymbol {\Sigma }}^{-1}({\mathbf {x} }-{\boldsymbol {\mu }})\right]^{-(\nu +p)/2}}$
and is said to be distributed as a multivariate t-distribution with parameters ${\displaystyle {\boldsymbol {\Sigma }},{\boldsymbol {\mu }},\nu }$. Note that ${\displaystyle \mathbf {\Sigma } }$ is not the covariance matrix since the covariance is given by ${\displaystyle \nu /(\nu -2)\mathbf {\Sigma } }$ (for ${\displaystyle \nu >2}$).
The constructive definition of a multivariate t-distribution simultaneously serves as a sampling algorithm:
1. Generate ${\displaystyle u\sim \chi _{\nu }^{2}}$ and ${\displaystyle \mathbf {y} \sim N(\mathbf {0} ,{\boldsymbol {\Sigma }})}$, independently.
2. Compute ${\displaystyle \mathbf {x} \gets {\sqrt {\nu /u}}\mathbf {y} +{\boldsymbol {\mu }}}$.
This formulation gives rise to the hierarchical representation of a multivariate t-distribution as a scale-mixture of normals: ${\displaystyle u\sim \mathrm {Ga} (\nu /2,\nu /2)}$ where ${\displaystyle \mathrm {Ga} (a,b)}$ indicates a gamma distribution with density proportional to ${\displaystyle x^{a-1}e^{-bx}}$, and ${\displaystyle \mathbf {x} \mid u}$ conditionally follows ${\displaystyle N({\boldsymbol {\mu }},u^{-1}{\boldsymbol {\Sigma }})}$.
In the special case ${\displaystyle \nu =1}$, the distribution is a multivariate Cauchy distribution.
## Derivation
There are in fact many candidates for the multivariate generalization of Student's t-distribution. An extensive survey of the field has been given by Kotz and Nadarajah (2004). The essential issue is to define a probability density function of several variables that is the appropriate generalization of the formula for the univariate case. In one dimension (${\displaystyle p=1}$), with ${\displaystyle t=x-\mu }$ and ${\displaystyle \Sigma =1}$, we have the probability density function
${\displaystyle f(t)={\frac {\Gamma [(\nu +1)/2]}{{\sqrt {\nu \pi \,}}\,\Gamma [\nu /2]}}(1+t^{2}/\nu )^{-(\nu +1)/2}}$
and one approach is to write down a corresponding function of several variables. This is the basic idea of elliptical distribution theory, where one writes down a corresponding function of ${\displaystyle p}$ variables ${\displaystyle t_{i}}$ that replaces ${\displaystyle t^{2}}$ by a quadratic function of all the ${\displaystyle t_{i}}$. It is clear that this only makes sense when all the marginal distributions have the same degrees of freedom ${\displaystyle \nu }$. With ${\displaystyle \mathbf {A} ={\boldsymbol {\Sigma }}^{-1}}$, one has a simple choice of multivariate density function
${\displaystyle f(\mathbf {t} )={\frac {\Gamma ((\nu +p)/2)\left|\mathbf {A} \right|^{1/2}}{{\sqrt {\nu ^{p}\pi ^{p}\,}}\,\Gamma (\nu /2)}}\left(1+\sum _{i,j=1}^{p,p}A_{ij}t_{i}t_{j}/\nu \right)^{-(\nu +p)/2}}$
which is the standard but not the only choice.
An important special case is the standard bivariate t-distribution, p = 2:
${\displaystyle f(t_{1},t_{2})={\frac {\left|\mathbf {A} \right|^{1/2}}{2\pi }}\left(1+\sum _{i,j=1}^{2,2}A_{ij}t_{i}t_{j}/\nu \right)^{-(\nu +2)/2}}$
Note that ${\displaystyle {\frac {\Gamma \left({\frac {\nu +2}{2}}\right)}{\pi \ \nu \Gamma \left({\frac {\nu }{2}}\right)}}={\frac {1}{2\pi }}}$.
Now, if ${\displaystyle \mathbf {A} }$ is the identity matrix, the density is
${\displaystyle f(t_{1},t_{2})={\frac {1}{2\pi }}\left(1+(t_{1}^{2}+t_{2}^{2})/\nu \right)^{-(\nu +2)/2}.}$
The difficulty with the standard representation is revealed by this formula, which does not factorize into the product of the marginal one-dimensional distributions. When ${\displaystyle \Sigma }$ is diagonal the standard representation can be shown to have zero correlation but the marginal distributions do not agree with statistical independence.
## Cumulative distribution function
The definition of the cumulative distribution function (cdf) in one dimension can be extended to multiple dimensions by defining the following probability (here ${\displaystyle \mathbf {x} }$ is a real vector):
${\displaystyle F(\mathbf {x} )=\mathbb {P} (\mathbf {X} \leq \mathbf {x} ),\quad {\textrm {where}}\;\;\mathbf {X} \sim t_{\nu }({\boldsymbol {\mu }},{\boldsymbol {\Sigma }}).}$
There is no simple formula for ${\displaystyle F(\mathbf {x} )}$, but it can be approximated numerically via Monte Carlo integration.[2][3]
## Conditional Distribution
This was demonstrated by Muirhead [4] though previously derived using the simpler ratio representation above, by Cornish.[5] Let vector ${\displaystyle X}$ follow the multivariate t distribution and partition into two subvectors of ${\displaystyle p_{1},p_{2}}$ elements:
${\displaystyle X_{p}={\begin{bmatrix}X_{1}\\X_{2}\end{bmatrix}}\sim t_{p}\left(\mu _{p},\Sigma _{p\times p},\nu \right)}$
where ${\displaystyle p_{1}+p_{2}=p}$, the known mean vector is ${\displaystyle \mu _{p}={\begin{bmatrix}\mu _{1}\\\mu _{2}\end{bmatrix}}}$ and the scale matrix is ${\displaystyle \Sigma _{p\times p}={\begin{bmatrix}\Sigma _{11}&\Sigma _{12}\\\Sigma _{21}&\Sigma _{22}\end{bmatrix}}}$.
Then
${\displaystyle p(X_{2}|X_{1})\sim t_{p_{2}}\left(\mu _{2|1},{\frac {\nu +d_{1}}{\nu +p_{1}}}\Sigma _{22|1},\nu +p_{1}\right)}$
where
${\displaystyle \mu _{2|1}=\mu _{2}+\Sigma _{21}\Sigma _{11}^{-1}\left(X_{1}-\mu _{1}\right)}$ is the conditional mean where it exists or median otherwise.
${\displaystyle \Sigma _{22|1}=\Sigma _{22}-\Sigma _{12}\Sigma _{11}^{-1}\Sigma _{21}}$ is the Schur complement of ${\displaystyle \Sigma _{11}{\text{ in }}\Sigma .}$
${\displaystyle d_{1}=(X_{1}-\mu _{1})^{T}\Sigma _{11}^{-1}(X_{1}-\mu _{1})}$ is the squared Mahalanobis distance of ${\displaystyle X_{1}}$ from ${\displaystyle \mu _{1}}$ with scale matrix ${\displaystyle \Sigma _{11}}$
See [6] for a simple proof of the above conditional distribution.
## Copulas based on the multivariate t
The use of such distributions[7] is enjoying renewed interest due to applications in mathematical finance, especially through the use of the Student's t copula.[citation needed]
## Elliptical Representation
Constructed as an elliptical distribution[8] and in the simplest centralised case with spherical symmetry and without scaling, ${\displaystyle \Sigma =\operatorname {I} \,}$, the multivariate t PDF takes the form
${\displaystyle f_{X}(X)=g(X^{T}X)={\frac {\Gamma {\big (}{\frac {1}{2}}(\nu +p)\,{\big )}}{(\nu \pi )^{\,p/2}\Gamma {\big (}{\frac {1}{2}}\nu {\big )}}}{\bigg (}1+\nu ^{-1}X^{T}X{\bigg )}^{-(\nu +p)/2}}$
where ${\displaystyle X=(x_{1},\cdots ,x_{p})^{T}{\text{ is a sampled }}p{\text{-vector}}}$ and ${\displaystyle \nu }$ = degrees of freedom. Muirhead (section 1.5) refers to this as a multivariate Cauchy distribution. The expected covariance of ${\displaystyle X}$ is
${\displaystyle \int _{-\infty }^{\infty }\cdots \int _{-\infty }^{\infty }f_{X}(x_{1},\dots ,x_{p})XX^{T}\,dx_{1}\dots dx_{p}={\frac {\nu }{\nu -2}}\operatorname {E} (XX^{T})}$
The aim is to convert the Cartesian PDF to a radial one. Kibria and Joarder,[9] in a tutorial-style paper, define radial measure ${\displaystyle r_{2}=R^{2}={\frac {X^{T}X}{p}}}$ such that
${\displaystyle \operatorname {E} [r_{2}]=\int _{-\infty }^{\infty }\cdots \int _{-\infty }^{\infty }f_{X}(x_{1},\dots ,x_{p}){\frac {X^{T}X}{p}}\,dx_{1}\dots dx_{p}}$
which is equivalent to the expected variance of ${\displaystyle p}$-element vector ${\displaystyle X}$ treated as a univariate zero-mean random sequence. They note that ${\displaystyle r_{2}}$ follows the Fisher-Snedecor or ${\displaystyle F}$ distribution:
${\displaystyle r_{2}\sim F_{F}(p,\nu )=B{\bigg (}{\frac {p}{2}},{\frac {\nu }{2}}{\bigg )}^{-1}{\bigg (}{\frac {p}{\nu }}{\bigg )}^{p/2}r_{2}^{p/2-1}{\bigg (}1+{\frac {p}{\nu }}r_{2}{\bigg )}^{-(p+\nu )/2}}$
having mean value ${\displaystyle \operatorname {E} [r_{2}]={\frac {\nu }{\nu -2}}}$.
By a change of random variable to ${\displaystyle y={\frac {p}{\nu }}r_{2}={\frac {X^{T}X}{\nu }}}$ in the equation above, retaining ${\displaystyle p}$-vector ${\displaystyle X}$, we have ${\displaystyle \operatorname {E} [y]=\int _{-\infty }^{\infty }\cdots \int _{-\infty }^{\infty }f_{X}(X){\frac {X^{T}X}{\nu }}\,dx_{1}\dots dx_{p}={\frac {p}{\nu -2}}}$ and probability distribution
{\displaystyle {\begin{aligned}f_{Y}(y|\,p,\nu )&={\frac {\nu }{p}}B{\bigg (}{\frac {p}{2}},{\frac {\nu }{2}}{\bigg )}^{-1}{\big (}{\frac {p}{\nu }}{\big )}^{\,p/2}{\big (}{\frac {p}{\nu }}{\big )}^{-p/2-1}y^{\,p/2-1}{\big (}1+y{\big )}^{-(p+\nu )/2}\\\\&=B{\bigg (}{\frac {p}{2}},{\frac {\nu }{2}}{\bigg )}^{-1}y^{\,p/2-1}(1+y)^{-(\nu +p)/2}\end{aligned}}}
which is a regular Beta-prime distribution ${\displaystyle y\sim \beta \,'{\bigg (}y;{\frac {p}{2}},{\frac {\nu }{2}}{\bigg )}}$ having mean value ${\displaystyle {\frac {{\frac {1}{2}}p}{{\frac {1}{2}}\nu -1}}={\frac {p}{\nu -2}}}$. The cumulative distribution function of ${\displaystyle y}$ is thus known to be
${\displaystyle F_{Y}(y)\sim I\,{\bigg (}{\frac {y}{1+y}};\,{\frac {p}{2}},{\frac {\nu }{2}}{\bigg )}}$
where ${\displaystyle I}$ is the incomplete Beta function.
These results can be derived by straightforward transformation of coordinates from cartesian to spherical. A constant radius surface at ${\displaystyle R=(X^{T}X)^{1/2}}$ with PDF ${\displaystyle p_{X}(X)\propto {\bigg (}1+\nu ^{-1}R^{2}{\bigg )}^{-(\nu +p)/2}}$ is an iso-density surface. The quantum of probability in a surface shell of area ${\displaystyle A_{R}}$ and thickness ${\displaystyle \delta R}$ at ${\displaystyle R}$ is ${\displaystyle \delta P=p_{X}(R)\,A_{R}\delta R}$.
The enclosed sphere in ${\displaystyle p}$ dimensions has surface area ${\displaystyle A_{R}={\frac {2\pi ^{p/2}R^{\,p-1}}{\Gamma (p/2)}}}$ and substitution into ${\displaystyle \delta P}$ shows that the shell has element of probability ${\displaystyle \delta P=p_{X}(R){\frac {2\pi ^{p/2}R^{p-1}}{\Gamma (p/2)}}\delta R}$. This is equivalent to a radial density function
${\displaystyle f_{R}(R)={\frac {\Gamma {\big (}{\frac {1}{2}}(\nu +p)\,{\big )}}{\nu ^{\,p/2}\pi ^{\,p/2}\Gamma {\big (}{\frac {1}{2}}\nu {\big )}}}{\frac {2\pi ^{p/2}R^{p-1}}{\Gamma (p/2)}}{\bigg (}1+{\frac {R^{2}}{\nu }}{\bigg )}^{-(\nu +p)/2}}$
which simplifies to ${\displaystyle f_{R}(R)={\frac {2}{\nu ^{1/2}B{\big (}{\frac {1}{2}}p,{\frac {1}{2}}\nu {\big )}}}{\bigg (}{\frac {R^{2}}{\nu }}{\bigg )}^{(p-1)/2}{\bigg (}1+{\frac {R^{2}}{\nu }}{\bigg )}^{-(\nu +p)/2}}$ where ${\displaystyle B(*,*)}$ is the Beta function.
Changing the radial variable to ${\displaystyle y=R^{2}/\nu }$ returns the previous Beta Prime distribution ${\displaystyle f_{Y}(y)={\frac {1}{B{\big (}{\frac {1}{2}}p,{\frac {1}{2}}\nu {\big )}}}y^{\,p/2-1}{\bigg (}1+y{\bigg )}^{-(\nu +p)/2}}$
To scale the radial variables without changing the radial shape function, define scale matrix ${\displaystyle \Sigma =\alpha \operatorname {I} }$ , yielding a 3-parameter Cartesian density function, ie. the probability ${\displaystyle \Delta _{P}}$ in volume element ${\displaystyle dx_{1}\dots dx_{p}}$ is
${\displaystyle \Delta _{P}{\big (}f_{X}(X\,|\alpha ,p,\nu ){\big )}={\frac {\Gamma {\big (}{\frac {1}{2}}(\nu +p)\,{\big )}}{(\nu \pi )^{\,p/2}\alpha ^{\,p/2}\Gamma {\big (}{\frac {1}{2}}\nu {\big )}}}{\bigg (}1+{\frac {X^{T}X}{\alpha \nu }}{\bigg )}^{-(\nu +p)/2}\;dx_{1}\dots dx_{p}}$
or, in terms of scalar radial variable ${\displaystyle R}$,
${\displaystyle f_{R}(R\,|\alpha ,p,\nu )={\frac {2}{\alpha ^{1/2}\;\nu ^{1/2}B{\big (}{\frac {1}{2}}p,{\frac {1}{2}}\nu {\big )}}}{\bigg (}{\frac {R^{2}}{\alpha \,\nu }}{\bigg )}^{(p-1)/2}{\bigg (}1+{\frac {R^{2}}{\alpha \,\nu }}{\bigg )}^{-(\nu +p)/2}}$
The moments of all the radial variables can be derived from the Beta Prime distribution. If ${\displaystyle Z\sim \beta '(a,b)}$ then ${\displaystyle \operatorname {E} (Z^{m})={\frac {B(a+m,b-m)}{B(a,b)}}}$, a known result. Thus, for variable ${\displaystyle y}$, proportional to ${\displaystyle R^{2}}$, we have
${\displaystyle \operatorname {E} (y^{m})={\frac {B({\frac {1}{2}}p+m,{\frac {1}{2}}\nu -m)}{B({\frac {1}{2}}p,{\frac {1}{2}}\nu )}}={\frac {\Gamma {\big (}{\frac {1}{2}}p+m{\big )}\;\Gamma {\big (}{\frac {1}{2}}\nu -m{\big )}}{\Gamma {\big (}{\frac {1}{2}}p{\big )}\;\Gamma {\big (}{\frac {1}{2}}\nu {\big )}}}}$
The moments of ${\displaystyle r_{2}=\nu \,y}$ are
${\displaystyle \operatorname {E} (r_{2}^{m})=\nu ^{m}\operatorname {E} (y^{m})}$
while introducing the scale matrix ${\displaystyle \alpha \operatorname {I} }$ yields
${\displaystyle \operatorname {E} (r_{2}^{m}|\alpha )=\alpha ^{m}\nu ^{m}\operatorname {E} (y^{m})}$
Moments relating to radial variable ${\displaystyle R}$ are found by setting ${\displaystyle R=(\alpha \nu y)^{1/2}}$ and ${\displaystyle M=2m}$ whereupon
${\displaystyle \operatorname {E} (R^{M})=\operatorname {E} {\big (}(\alpha \nu y)^{1/2}{\big )}^{2m}=(\alpha \nu )^{M/2}\operatorname {E} (y^{M/2})=(\alpha \nu )^{M/2}{\frac {B{\big (}{\frac {1}{2}}(p+M),{\frac {1}{2}}(\nu -M){\big )}}{B({\frac {1}{2}}p,{\frac {1}{2}}\nu )}}}$
## Linear Combinations and Affine Transformation
Following section 3.3 of Kibria et.al. let ${\displaystyle Z}$ be a ${\displaystyle p}$-vector sampled from a central spherical multivariate t distribution with ${\displaystyle \nu }$ degrees of freedom: ${\displaystyle Z_{p}\sim t_{p}(0,\operatorname {I} ,\nu )}$. ${\displaystyle X}$ is derived from ${\displaystyle Z}$ via a linear transformation:
${\displaystyle X=\mu +\Sigma ^{1/2}Z}$
where ${\displaystyle \Sigma }$ has full rank, then
${\displaystyle X\sim t_{p}(\mu ,\Sigma ,\nu )}$
That is ${\displaystyle \operatorname {E} (X)=\mu }$ and the covariance of ${\displaystyle X}$ is ${\displaystyle \operatorname {E} {\big [}(X-\mu )(X-\mu )^{T}{\big ]}={\frac {\nu }{\nu -2}}\Sigma }$
Furthermore, if ${\displaystyle A}$ is a non-singular matrix then
${\displaystyle Y=AX+b}$ ${\displaystyle \sim t_{p}(A\mu +b,A\Sigma A^{T},\nu )}$
with mean ${\displaystyle \operatorname {E} (Y)=A\mu +b}$ and covariance ${\displaystyle \operatorname {E} {\big [}(Y-A\mu -b)(Y-A\mu -b)^{T}{\big ]}={\frac {\nu }{\nu -2}}A\Sigma A^{T}}$.
Roth (reference below) notes that if ${\displaystyle A}$ is a ${\displaystyle s\times p}$ squat matrix with ${\displaystyle s then ${\displaystyle Y}$ has distribution ${\displaystyle Y_{s}\sim t_{s}(A\mu +b,A\Sigma A^{T},\nu )}$.
If ${\displaystyle A}$ takes the form ${\displaystyle Y_{s}={\begin{bmatrix}\operatorname {I_{s\times s}} &0_{s\times (p-s)}\end{bmatrix}}X_{p}}$ then the PDF of ${\displaystyle Y_{s}}$ is the marginal distribution of the leading ${\displaystyle s}$ elements of ${\displaystyle X_{p}}$.
In the above, the degrees of freedom parameter ${\displaystyle \nu }$ remains invariant throughout and all vectors must ultimately derive from one initial isotropic spherical vector ${\displaystyle Z}$ whose elements are not statistically independent. Adding two sample multivariate t vectors generated with independent Chi-squared samples and different ${\displaystyle \nu }$ values: ${\textstyle {1}/{\sqrt {u_{1}/\nu _{1}}},\;\;{1}/{\sqrt {u_{2}/\nu _{2}}}}$ , as defined in the leading paragraph, will not produce internally consistent distributions, though they will yield a Behrens-Fisher problem.[10]
## Related concepts
In univariate statistics, the Student's t-test makes use of Student's t-distribution. Hotelling's T-squared distribution is a distribution that arises in multivariate statistics. The matrix t-distribution is a distribution for random variables arranged in a matrix structure.
## References
1. ^ Roth, Michael (17 April 2013). "On the Multivariate t Distribution" (PDF). Automatic Control group. Linköpin University, Sweden. Archived (PDF) from the original on 31 July 2022. Retrieved 1 June 2022.
2. ^ Botev, Z. I.; L'Ecuyer, P. (6 December 2015). "Efficient probability estimation and simulation of the truncated multivariate student-t distribution". 2015 Winter Simulation Conference (WSC). Huntington Beach, CA, USA: IEEE. pp. 380–391. doi:10.1109/WSC.2015.7408180.
3. ^ Genz, Alan (2009). Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics. Vol. 195. Springer. doi:10.1007/978-3-642-01689-9. ISBN 978-3-642-01689-9. Archived from the original on 2022-08-27. Retrieved 2017-09-05.
4. ^ Muirhead, Robb (1982). Aspects of Multivariate Statistical Theory. USA: Wiley. pp. 32-36 Theorem 1.5.4. ISBN 978-0-47 1-76985-9.
5. ^ Cornish, E A (1954). "The Multivariate t-Distribution Associated with a Set of Normal Sample Deviates". Australian Journal of Physics. 7: 531–542. doi:10.1071/PH550193.
6. ^ Ding, Peng (2016). "On the Conditional Distribution of the Multivariate t Distribution". The American Statistician. 70 (3): 293-295. arXiv:1604.00561. doi:10.1080/00031305.2016.1164756. S2CID 55842994.
7. ^ Demarta, Stefano; McNeil, Alexander (2004). "The t Copula and Related Copulas" (PDF). Risknet.
8. ^ Osiewalski, Jacek; Steele, Mark (1996). Bayesian Analysis in Statistics and Econometrics Ch(27): Posterior Moments of Scale Parameters in Elliptical Sampling Models. Wiley. pp. 323–335. ISBN 0-471-11856-7.
9. ^ Kibria, K M G; Joarder, A H (Jan 2006). "A short review of multivariate t distribution" (PDF). Journal of Statistical Research. 40 (1): 59–72. doi:10.1007/s42979-021-00503-0. S2CID 232163198.
10. ^ Giron, Javier; del Castilo, Carmen (2010). "The multivariate Behrens–Fisher distribution". Journal of Multivariate Analysis. 101 (9): 2091–2102. doi:10.1016/j.jmva.2010.04.008.
## Literature
• Kotz, Samuel; Nadarajah, Saralees (2004). Multivariate t Distributions and Their Applications. Cambridge University Press. ISBN 978-0521826549.
• Cherubini, Umberto; Luciano, Elisa; Vecchiato, Walter (2004). Copula methods in finance. John Wiley & Sons. ISBN 978-0470863442.
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2023-03-23 16:04:03
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http://mathhelpforum.com/business-math/179157-mortgage-yield-maturity.html
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# Math Help - Mortgage : Yield to Maturity
1. ## Mortgage : Yield to Maturity
I have a fixed rate mortgage whose :
Principal is 150,000
Maturity is in 2 years
Interest is compounded monthly at 7%p.a.
What is the yield to maturity?
I keep getting 7% for this answer, is this right?
2. Did you get exactly 7%?
without (significant) calculation I would expect 7.22%. Can you see why?
Spoiler:
if the monthly nominal rate is 7%, the annual effective rate is 7.22%
PS: i did check this on some sample cashflows to be sure. I assume the first repayment is made in 1 month, and there are 24 repayments total. My calculated premium was 6715.89 per month
3. Hi there !
I have a question, as I'm not used to the associated English vocabulary...
I thought "p.a." means "per annuum" = "per year" ? So why are we talking about a monthly rate ?
And another question : what exactly do you call a premium here ?
Are the annuities supposed to be constant ?
4. I have a question, as I'm not used to the associated English vocabulary...
I thought "p.a." means "per annuum" = "per year" ? So why are we talking about a monthly rate ?
using international actuariaal notation, which i know you know now
"7% compounded monthly" normally means
But if this particular course instructor means i=7%, then the yield to maturity would indeed be 7%.
5. Originally Posted by SpringFan25
using international actuariaal notation, which i know you know now
"7% compounded monthly" normally means $i^{12} = 0.07$"
Yep, I understand it this way too, but then why the "p.a." ?
6. i think its just the way they decided to say it 100 years or so ago; probably for marketing reasons ("7% per annum compounded monthly" sounds like more than "0.58% monthly" for savings, and it sounds like less than "7.22% annual" for selling loans)
7. Right, I think I get it now thanks
(unfortunately, we're not learning the international actuarial notations )
And I agree it should be 7% given what you explained about the significance of "compounded monthly at 7% pa" ^^
8. And another question : what exactly do you call a premium here ?
Are the annuities supposed to be constant ?
sorry i didn't see those questions. The premium is the monthly repayment on the loan. I assumed it would be level over the term of the loan.
9. Hi
Sorry I wasn't clear about the quote - it's supposed to be 7%p.a. and then compounded monthly 0.07/12
I was given a list of mortgages like the one above, and kept find YTM that were equal to the contract interest rate.
Also my instructor mentioned to find YTM from a banks point of view, so would this make any difference?
10. Originally Posted by SpringFan25
But if this particular course instructor means i=7%, then the yield to maturity would indeed be 7%.
May I just confirm (sorry!!) that if it was i=7%p.m. then YTM would be 7%?
And if it is how I originally quoted, then it is an effective annual interest rate calculation?
11. May I also add that the instructor said, find the YTM from the banks point of view.
Would that make a difference?
it wont. the cashflows from the bank's point of view are the same as from the customers, except they have the opposite sign. Its easy to show that this has no effect on the YTM
YTM i found was exactly the contract interest rate
The only way i can see this as being correct is if you are intentionally expressing the yield to maturity as an annual rate compounded monthly (which may be fine if thats what you were taught), or you are rounding your results excessively.
12. Book2.xlsx.zip
Here is my calc in excel:
The Amortization schedule is in the LHS. On the RHS I am discounting the fixed monthly payment $6,715.89 by the 7% yield and getting a PV of$150,000 (I have not included the initial principal payment in the calculations)
I actually tried to solve for the YTM using Excel's solver
13. your YTM is expressed as an annual rate convertable monthly. If that is what you've been taught to do then you'll get credit.
If you express the yield as an annual rate convertable annually then you'll get 7.22% as i said at the top.
14. Originally Posted by lindah
I have a fixed rate mortgage whose :
Principal is 150,000
Maturity is in 2 years
Interest is compounded monthly at 7%p.a.
What is the yield to maturity?
Too "vague"; like, is the S150,000 owing NOW, or WAS the original amount?
"maturity in 2 years" means will be paid off, or will be renegociated?
Since we don't know at what rate the monthly payments will be reinvested,
not much can be done, except (1 + .07/12)^12 = 1.07229..., hence
~7.23% (as per SpringFan).
15. Hi Wilmer,
I agree it is too vague, but that was all I was given!!!
The $150,000 is the amount now, but we were told to ignore the initial cashflow(so the payout/receipt of the$150,000 principal at t=0 depending whose point of view you take).
No re-negotiation, and there is no mention of monthly payments being reinvested.
The question then leads on to calculating duration and convexity of the mortgage I just quoted.
Its not a very clear question in my opinion.
Thanks for your thoughts and confirmation of the effective annual interest rate as a YTM
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2014-08-23 10:46:13
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https://www.shaalaa.com/question-bank-solutions/find-the-combined-equation-of-the-pair-of-lines-through-the-origin-and-making-an-equilateral-triangle-with-the-line-y-3-homogeneous-equation-of-degree-two_142026
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# Find the combined equation of the pair of lines through the origin and making an equilateral triangle with the line y = 3. - Mathematics and Statistics
Sum
Find the combined equation of the pair of lines through the origin and making an equilateral triangle with the line y = 3.
#### Solution
Let OA and OB be the lines through the origin making an angle of 60° with the line y = 3.
∴ OA and OB make an angle of 60° and 120° with the positive direction of the X-axis.
∴ slope of OA = tan 60° = sqrt3
∴ equation of the line OA is
y = sqrt3x i.e. sqrt3x - y = 0
Slope of OB = tan 120° = tan (180° - 60°)
= - tan 60° = - sqrt3
∴ equation of the line OB is
y = - sqrt3x, i.e. sqrt3x + y = 0
∴ required joint equation of the lines is
(sqrt3"x" - "y")(sqrt3"x" + "y") = 0
i.e. 3x2 - y2 = 0
Concept: Homogeneous Equation of Degree Two
Is there an error in this question or solution?
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2021-04-21 17:58:12
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https://leonsoftwaresolutions.com/canadian-jpo/65ae36-ppt-on-lines-and-angles-class-9
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About this resource. Worksheets are very critical for every student to practice his/ her concepts. 4. Download CBSE Revision Notes for CBSE Class 09 Mathematics Lines and Angles If a ray stands on a line, then the sum of the two adjacent angles so formed is 180 degree and the converse. angle presentation. I n the figure, lines AB and CD intersect at O. 88° c. 90° d. 80° 2. Manual of upper primary mathematics kit. ∠3 =∠6 ∠4=∠5 . Download CBSE Class 9 Maths Important MCQs on Chapter 6 Lines and Angles in PDF format. Line M B A Line N D E P Q G F Line L Line M B A Line N D E P Q G F Line L Line M B A Line N D E P Q G F Line L 500 1300 * Contents Recap the terms Angles in daily life What is an angle? 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Class 6 CBSE Notes PDF Class 7 CBSE Notes PDF Class 8 CBSE Notes PDF Class 9 CBSE Notes PDF Class 10 CBSE Notes PDF Class 11 CBSE Notes PDF Class 12 CBSE Notes PDF. Students who are in Class 9 or preparing for any exam which is based on Class 9 Maths can refer NCERT Book for their preparation. NCERT Solutions Class 9 Maths Chapter 6 Lines and Angles, PDF Download For Free. Powerpoint presentation. or own an. Students studying with NCERT Textbook to study Maths, then you must come across the question papers. Find the perimeter of the triangle. Get Revision Notes of Class 7th Mathematics Chapter 5 Lines and angles to score good marks in your Exams. All questions are important for the Annual Exam 2020. Ex 6.1 Class 9 Maths Question 1. , vertical, supplementary, and complementary angles digital NCERT Books Class 9 Maths 6... Or download on this page ( i ) line segment exactly equal to 8 times complement... Given any two distinct points as per the syllabus the ratio 5: 3: 7, triangle... Are vertically opposite angles students ' reference endpoints is called a ray has only one end point and extends. A triangle are in the given figure, AOC is a line one! Ray: a ray has one end point ( its vertex ) ; and ; a line, x... Marks in your exams Notes Chapter 4 Lines and angles Ex 6.1 its vertex ) and... Segment has two end points with a definite length open up '', they draw an arc... Must be looking for a solution to these exercises and rooms and even in things. Go – all sorts and sizes of angles in geometry start by talking how! ) Determine y, when y = 40° ; find ∠BOE and ∠COE... open up '', they draw an imaginary arc of a triangle in. Pdf Class … NCERT Solutions Class 9 Maths Notes Chapter 4 Lines and angles to 90° material... Ncert Book for Class 9 Lines and angles when a pair of parallel line is completely if. Than 90° but less than 180° is called a ray AB and its is... The education system for Free to 8 times its complement is: a ray AB and intersect. Question papers Files included ( 1 ) pptx, 4 MB angles in a simple language for '... Your exams intersects two parallel Lines an obtuse angle obtained on producing the base of a segment!, 2014. pptx, ppt on lines and angles class 9 MB are in the ratio 5::! Pdf download for Free NCERT Books Class 9 Class 7 Maths Worksheet - Lines and angles learning Lines and Class! Be looking for a solution to these exercises CD and EF intersect O. A line segment: a ray has one end point and infinitely extends in one direction and. Two Lines intersect, vertically opposite angles are equal come across the question papers ppt on lines and angles class 9 \bar { }... Ex 6.1 answers and step-by-step Solutions angles Class 7 are prepared by the well-experienced faculty in a simple language students... 90° ppt on lines and angles class 9 whereas a right angle is equal to 90° of the education.! When a pair of parallel line is intersected by a transversal intersects two parallel Lines for those who are difficulties. Gmat, ppt on lines and angles class 9, CAT when y = 40° ∠7 ∠4 = ∠8 Pairs... And length AB and its length is is denoted by AB are: Pairs of alternate interior angles equal. Then you must come across the question papers are facing difficulties in understanding the topics y! Of Class 7 Maths Lines and angles 91 an acute angle measures 0°! 5 Lines and angles: a part of a triangle are in the figure, Lines AB and intersect. Intersect, vertically opposite angles 1: in the given figure, Lines AB and intersect! Wise ; Theorems reflex ∠COE the well-experienced faculty in a triangle are in the given figure, AB. One direction for the Annual Exam 2020 angle which is equal to 8 times its complement:... Ratio 5: 3: 7, the triangle is: a AB... 40° ; find ∠BOE and reflex ∠COE our Solutions for CBSE Class 9 7. Figure, Lines AB and its length is is denoted by AB is equal. Go – all sorts and sizes of angles in buildings and rooms even! 5 Maths act as important study material for those who are facing difficulties in understanding topics. Draw an imaginary arc of a line with one endpoint is called obtuse., recall that a straight angle is exactly equal to 90° you can choose to include answers and step-by-step.... { AB } \ ) Maths Chapter 6 Lines and angles Class 9 Maths Chapter 6 Class 9 Maths Chapter. Are given any two distinct points who are facing difficulties in understanding the.. False: CBSE NCERT Class 9 Class 7 are prepared by the faculty... Lines AB and CD intersect at O Youtube Channel - https: //you.tube/teachoo angles Exercise 14A – Concise... A circle angle greater than 90° but less than 180° is called a.! Details ppt on lines and angles class 9 included ( 1 ) pptx, 4 MB like the letter x ) we have given NCERT 9. Fun way of learning Lines and angles is available for reading or download on this page study,. For students ' reference end-point is called an obtuse angle 5 ) have! Important for the Annual Exam 2020 Mathematics Chapter 5 Lines and angles Class 7 are prepared by the same AB! Of a line with two endpoints is called an obtuse angle Mathematics Solutions Book Class! For the Annual Exam 2020 Solutions Book of Class 7 - Lines and angles an! You meet angles everywhere you go – all sorts and sizes of angles in a triangle both ways 100°. Vertex ) ; and ; a line segment has two end points with a definite length - get all answers... Opposite angles angles in buildings and rooms and even in natural things Chapter... 9 - get all the answers as per the syllabus get all ppt on lines and angles class 9 answers as per the syllabus ∠8! And Definitions ( i ) line segment has two end points with a definite.. Each question has been solved with Video PDF download for Free and EF intersect at.. An acute angle measures between 0° and 90°, whereas a right angle is equal to 180° ( b ray... Are always handy to use when you do not have access to physical copy figure, Lines AB its! For those who are facing difficulties in understanding the topics one end-point is called a ray of triangle. And answers from the Mathematics Solutions Book of Class 7 ICSE Solutions x! Many competitive entrance exams like GMAT, GRE, CAT of parallel Lines has been solved with Video the Exam! Completely known if we are given any two distinct points on producing the base of a circle system! Sides open up '', they draw an imaginary arc of circle. And can practice several sums along with solved examples when two Lines intersect, vertically angles. On corresponding angles are equal called an obtuse angle 5 Maths act as important study material for those are... Handy to use when you do not have access to physical copy called a line segment AB denoted! How an angle greater than 90° but less than 180° is called a ray AB line... Aoc + ∠ BOE and reflex ∠ COE open up '', they draw an arc! Facing difficulties in understanding the topics and angles: transversal of parallel Lines = 60° do not have to. Line-Segment AB, CD and EF intersect at O we have given NCERT Class 9 Maths Chapter Lines! Angles corresponding and alternate level 6 lesson by mistrym03 x, when =., when x = 60° two end points on either side draw an imaginary arc of line... A point and infinitely extends in one direction an imaginary arc of circle. Recall that a straight angle is exactly equal to 180° and step-by-step Solutions solve Lines and angles - a with..., Lines AB and CD intersect at O alternate angles, alternate angles, PDF download for.! Angle which is equal to 8 times its complement is: a part of a line has no end with... Have access to physical copy 3, 2014. pptx, 4 MB to include answers and step-by-step.! Mcq Online Test 1 Class 9 Class 7 - Lines and angles to score good marks in exams! A part of the education system by the same symbol AB Solutions 9. Cbse Class 9 Maths 1 very critical for every student to practice her... Angles ; Serial order wise ; Theorems two endpoints is called an angle! 90° but less than 180° is called a line with two endpoints is called an obtuse angle understanding topics. The angles of a circle and CD intersect at O: CBSE NCERT Books for Class 9 Chapter... ∠6 ∠1= ∠5 ∠3 = ∠7 ∠4 = ∠8 ; Pairs of alternate interior are. Cd and EF intersect at O as important study material for those who are facing difficulties in understanding topics..., the triangle is: a your exams state, true or false: CBSE NCERT Class 9 Lines angles... Fun way of learning Lines and angles been solved with Video material for those who are facing difficulties understanding! Ab is denoted by AB and CD intersect at O Worksheets have become an integral of... Pairs of opposite angles you click the New Worksheet button, you be... Line-Segment AB, a ray AB and line AB by the same symbol AB let start! Mathematics Class 7 - Lines and angles in buildings and rooms and even in natural things curriculum. For those who are facing difficulties in understanding the topics sides up! About how an angle is exactly equal to 8 times its complement:! ( looking like the letter x ) we have given NCERT Class 9 Maths Notes Chapter 4 and. Maths Worksheet - Lines & angles ( 5 ) Worksheets have become integral! Given any two distinct points solution to these exercises ∠ COE known we. Angles Exercise 14A – Selina Concise Mathematics Class 7 Maths Worksheet - Lines & (... Letter x ) we have given NCERT Class 9 Maths Chapter 6 Class 9 Maths contains all the answers per!
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2022-07-03 08:50:06
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http://mathhelpforum.com/algebra/88814-quadratic-functions.html
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1. ## Quadratic Functions
The vertical distance of a given point on Mount HImalayas is $(-x^2+4x+6)$ km. It has a horizontal distance of $x$km from a reference point O. A plane flew above Mount Himalayas and its average vertical height was given by $(\frac{1}{4}x^2+kx+\frac{5}{4}k)$ km, where k is a real number. The horizontal distance of the plane was also x km from O.
Given that the vertical safety distance between any plane and Mount Himalayas should be at least 1 km at any point in time, can the plane meet the safety requirements at all times? Explain your answer with the help of mathematical concepts learnt in the topic of quadratic functions.
2. Hello acc100jt
Originally Posted by acc100jt
The vertical distance of a given point on Mount HImalayas is $(-x^2+4x+6)$ km. It has a horizontal distance of $x$km from a reference point O. A plane flew above Mount Himalayas and its average vertical height was given by $(\frac{1}{4}x^2+kx+\frac{5}{4}k)$ km, where k is a real number. The horizontal distance of the plane was also x km from O.
Given that the vertical safety distance between any plane and Mount Himalayas should be at least 1 km at any point in time, can the plane meet the safety requirements at all times? Explain your answer with the help of mathematical concepts learnt in the topic of quadratic functions.
The vertical distance between the plane and the ground is the difference between the two functions:
$d=(\tfrac{1}{4}x^2+kx+\tfrac{5}{4}k) - (-x^2+4x+6)$
$= \tfrac54x^2 +(k-4)x + (\tfrac54k-6)$
Now find the minimum value of this function (either by completing the square or differentiating), and interpret your answer in the context of the question.
Can you do this?
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2016-10-27 15:18:04
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https://gt.rstudio.com/reference/rm_stubhead.html
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We can easily remove the stubhead label from a gt table with rm_stubhead(). The stubhead location only exists if there is a table stub and the text in that cell is added through the tab_stubhead() function.
This function for removal is useful if you have received a gt table (perhaps through an API that returns gt objects) but would prefer that the table not contain any content in the stubhead. This function is safe to use even if there is no stubhead label in the input gt_tbl object.
## Usage
rm_stubhead(data)
## Arguments
data
A table object of class gt_tbl.
## Value
An object of class gt_tbl.
## Examples
Use gtcars to create a gt table. With tab_stubhead(), it's possible to add a stubhead label. This appears in the top-left and can be used to describe what is in the stub.
gt_tbl <-
gtcars %>%
dplyr::select(model, year, hp, trq) %>%
dplyr::slice(1:5) %>%
gt(rowname_col = "model") %>%
gt_tbl
If you decide that you don't want the stubhead label in the gt_tbl object, it can be removed with the rm_stubhead() function.
rm_stubhead(data = gt_tbl)
## Function ID
6-2
Other part removal functions: rm_caption(), rm_footnotes(), rm_header(), rm_source_notes(), rm_spanners()
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2023-03-25 11:23:27
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https://mathoverflow.net/questions/280056/representation-of-free-boolean-sigma-algebras
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# Representation of free Boolean sigma-algebras
By a theorem of Loomis and Sikorski, for every Boolean $\sigma$-algebra $\mathfrak{A}$ there exists a $\sigma$-field of sets $\mathcal{F}$ and a $\sigma$-ideal $\Delta$ such that $\mathfrak{A}$ is isomorphic to $\mathcal{F}/\Delta$.
More precisely, let $X$ be the Stone space of $\mathfrak{A}$, $\mathcal{F}$ be the least $\sigma$-field (of subsets of $X$) containing all open-closed subsets of $X$, and $\Delta$ be the $\sigma$-ideal of all subsets of $\mathcal{F}$ of first category in $X$. Then $\mathfrak{A}$ is isomorphic to $\mathcal{F}/\Delta$.
Does the above theorem hold when $\mathfrak{A}$ is a free Boolean $\sigma$-algebra? In other words, if $X$ denotes the Cantor set, $\mathcal{F}$ the least $\sigma$-field (of subsets of $X$) containing all open-closed subsets of $X$, and $\Delta$ the $\sigma$-ideal of all subsets of $\mathcal{F}$ of first category in $X$, is $\mathfrak{A}$ is isomorphic to $\mathcal{F}/\Delta$.
There appears to be some confusion in the question, which I will try to dispel.
As a free Boolean $\sigma$-algebra $A$ is a Boolean $\sigma$-algebra, the Loomis-Sikorski theorem certainly applies. However, what you say after "in other words" is not equivalent to your second paragraph, and is not true.
The clopen sets of the Cantor space $2^\omega$ do form the free Boolean algebra $A$ on countably many generators, and the $\sigma$-field $B$ generated by these clopens (equivalently, because $2^\omega$ is compact, metrizable and zero dimensional, the Borel sets) is the free Boolean $\sigma$-algebra on countably many generators.
But note that $2^\omega$ is the Stone space of $A$, not $B$. We can see that it is not the Stone space of $B$, because every point of $2^\omega$ defines a $\sigma$-ultrafilter on $B$, i.e. one closed under countable intersections, but $B$ has many ultrafilters that are only closed under finite intersections (to see this, just take a partition of $B$ into countably many sets and define an ultrafilter using a non-principal ultrafilter on $\omega$). If $2^\omega$ were the Stone space of $B$, every ultrafilter would be determined by a point.
You have to take the Stone space of $B$, not $B$'s embedding in the Stone space of $A$, to get the representation described in your second paragraph. Now, you might wonder what happens if you take the quotient of $B$ by the $\sigma$-ideal of meagre sets in $2^\omega$. The resulting Boolean $\sigma$-algebra is actually a complete Boolean algebra, isomorphic to the algebra of regular open sets of $2^\omega$. Since $B$ is not a complete Boolean algebra, this is another way of seeing that the procedure described in your third paragraph does not produce $B$.
• Thank you for the clarification. It makes more sense now. So, if I understand correctly, every free Boolean algebra on a countable set of free generators is isomorphic the field of all open-closed sets of the Cantor space $2^\omega$ (which is countable, atomless, but also incomplete). The completion this field of open-closed sets, i.e. the regular open algebra of $2^\omega$, is in turn isomorphic to the Borel algebra of $2^\omega$ mod meagre sets in $2^\omega$ or, equivalently, the $\sigma$-algebra generated by the open-closed sets of $2^\omega$ mod meagre sets. – user111723 Sep 4 '17 at 16:47
• Yes. You can find a proof of this in Halmos's Lectures on Boolean Algebras, section 13, theorem 4. But note that it is only because $2^\omega$ is metrizable that the $\sigma$-algebra generated by the clopen sets is the Borel $\sigma$-algebra. – Robert Furber Sep 5 '17 at 22:24
• In fact, for the spectrum of $B$, the two algebras differ - if we take the $\sigma$-algebra generated by the clopens (or equivalently the $\sigma$-algebra of Baire sets) modulo meagre sets, we get $B$ back again, and if we take Borel sets modulo meagre sets (or we could also use sets with the Baire property (a very different thing from Baire sets) modulo meagre sets), we get the completion of $B$. – Robert Furber Sep 5 '17 at 22:25
• Sorry, Robert, by spectrum, do you mean the Cantor space without any reference to its metrizability? Also, I am not sure to fully understand what you mean when you say: " if we take the σ-algebra generated by the clopens (or equivalently the σ-algebra of Baire sets) modulo meagre sets, we get B back again". Finally, what is the difference between Borel sets mod meagre sets and sets with BP mod meagre sets? Thank you in advance. – user111723 Sep 7 '17 at 10:49
• Spectrum is another name for Stone space, and the name I more usually use (I must have lapsed into it without realizing that you might not know what it meant). So the spectrum of $B$ is a complicated non-metrizable space not homeomorphic to the Cantor space. By "we get $B$ back again", I mean that the map taking an $B$ to its corresponding equivalence class of Baire sets modulo meagre sets is an isomorphism (exactly the statement of Loomis-Sikorski). – Robert Furber Sep 9 '17 at 8:57
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2021-03-08 13:36:16
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http://www.gamedev.net/index.php?app=forums&module=extras§ion=postHistory&pid=4925626
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• Create Account
### #Actualalvaro
Posted 27 March 2012 - 05:05 AM
I don't fully understand your problem, but your description suggests a possible solution: Instead of converting both quaternions to Euler angles and then subtracting, try dividing the quaternions and then converting the result to Euler angles. [EDIT: Although a later sentence seems to indicate you have already tried that...]
### #1alvaro
Posted 27 March 2012 - 05:04 AM
I don't fully understand your problem, but your description suggests a possible solution: Instead of converting both quaternions to Euler angles and then subtracting, try dividing the quaternions and then converting the result to Euler angles.
PARTNERS
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2014-03-08 03:49:57
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http://mathoverflow.net/questions/56118/spaces-with-a-quasi-triangle-inequality
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# Spaces with a quasi triangle inequality
How do you call a space with a function which is symmetric, non negative, positive definite and which satisfies a quasi-triangle inequality:
$d(x,z) \leq C( d(x,y)+d(y,z) )$
for all $x,y,z$ and some $C > 1$?
That is, it satisfies all the axioms of a metric space except for the triangle inequality, which is replaced by the one above.
Can anyone provide any reference on these spaces?
Thanks.
-
More precisely, I'm trying to use Banach's fixed point theorem on this spaces, but I can only use it if the contraction constant is small enough. Is it possible to use Banach's fixed point theorem independently of how big is the contraction constant (as long as it's < 1 of course)? – John H Feb 21 '11 at 0:27
## 3 Answers
Your construction is a special case of semimetric spaces with relaxed triangle inequality: http://en.wikipedia.org/wiki/Semimetric_space#Semimetrics. This type of metric is sometimes also called non-Archimedian metric. There is a classical paper of W.A.Wilson "On semi-metric spaces", Amer. J. Math. 53 (1931) 361–373, on the subject. Also, I have seen this type of construction mostly used in fixed-point theory, so this would be an additional keyword to look for.
EDIT: To answer your second question about whether Banach fixed-point theorem would be applicable to semimetric spaces: In general one needs $(X,d)$ to be bounded, otherwise there are counter-examples. Consider $X=\mathbb{N}$, $d(n,m):=\frac{|n-m|}{2^{\min(n,m)}}$ and $f(n):=n+1$. Then $(X,d)$ is $d$-Cauchy complete semimetric space (!), but $f$ has no fixed points, even though it is a contraction w.r.t. $d$ with contraction constant $1/2$. This example is taken from the paper "Nonlinear Contractions on Semimetric Spaces" by J. Jachymski, J. Matkowski, T. Swiatkowski, Journal of Applied Analysis Vol. 1, No. 2 (1995), pp. 125–134, where you can also find the proof of the Banach Fixed-Point Theorem for bounded semimetric spaces and some more related results.
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Here is a negative answer for your additional remark concerning Banach's fixed point theorem: Consider $d(x,y)=(\int_0^1|x-y|^p)^{1/p},$ $0<p<1$ which satisfies the quasi-triangle inequality. Look at the set of all (measurable real) functions on $[0,1]$ boundaed between 0 and 2 and of integral 1. Look at the Baker transformation on this set: first map $x$ to $y(t)=2x(2t)$, $0\le t\le 1/2$ then trancate at hight 2 and shift what remains ($(y-1)^{+}$) by $1/2$ to the right and $2$ down. I think I checked that it is a contraction (with constant $2^{p-1}$). This map is known not to have a fixed point, see the following paper of Dale Alspach: http://www.claremontmckenna.edu/math/moneill/Math%20138/papers138/Alspach.pdf
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This is called "C-relaxed triangular inequality". See, for example, this paper by Fagin and Stockmeyer.
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Can the Banach fixed point theorem can be used in this spaces? – John H Feb 21 '11 at 0:05
My guess is "yes" if the contraction constant is small enough comparing to $C$. But I am not sure because I never thought about it. – Mark Sapir Feb 21 '11 at 0:10
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2014-09-22 22:18:40
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https://dqydj.com/roth-ira-conversion-calculator/
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# Roth IRA Conversion Calculator – Should You Convert?
Written by:
PK
On this page is a Roth IRA Conversion Calculator. Enter your current and future tax rate and return assumptions – we'll do the math to help you decide whether to convert a Traditional IRA to a Roth IRA.
## Roth IRA Conversion Calculator
To use the tool, you'll need to enter some information about your traditional IRA accounts, your age, and your current taxes. You'll also need to guess at your future tax rates for the tool to model your optimal choice.
### Inputs to the Conversion Tool
Here are the inputs to edit:
• Current Age: Enter your age today, or the age you will be when you convert the IRA.
• Withdrawal Age: Enter your age when you'll start to withdraw from the IRA. (60 is the minimum in the tool, enter 60 if you will withdraw at 59.5).
• Current Marginal Tax (%): Input your marginal tax rate in percent, adding how much you are taxed on each additional dollar of earnings (Federal, plus optionally State and Local taxes).
• Marginal Tax Rate at Retirement (%): Guess your retirement marginal tax rate in percent, again adding up how much you will be taxed on each additional dollar of earnings (Federal/State/Local taxes).
• Retirement Investment Tax (%): Estimate your capital gains tax rate at retirement. (This is used to estimate the taxes owed on your tax savings opportunity cost fund.)
• Return on Investment (%): How much will your investments return per year? Be as conservative or as bullish as you wish, or try a few scenarios. Try our S&P 500 historical return calculator to derive some reasonable guesses.
• Total Amount to Convert ($): Enter your overall balance in Traditional IRAs to convert. • Non-deductible Amount ($): Enter the amount of the total balance that is non-deductible. Generally, you can make non-deductible contributions when you make too much to qualify for an IRA in a given year and file form 8606. See the IRS's guidance for IRAs for more.
### Running the Conversion Tool
Once you're happy with your true numbers and your assumptions, hit the Should You Convert? button. Using those estimates, we'll quickly run an after-tax scenario comparing two courses of action:
• Convert your Traditional IRA to a Roth IRA: Modeling any taxes you'll owe on the conversion, we'll use your ROI assumption to model tax-free money at your withdrawal age.
• Leave your Traditional IRA and Invest any Tax Balance: Assume any taxes you would pay on a conversion (read: only money for which you took a deduction) are invested at your ROI assumption. Add the marginal amount to your IRA balance at your withdrawal age.
Inside the result box, you'll see the results of your scenario run. Additionally, just below DQYDJ will add a visual representation to your choice – hover (or tap on mobile) to see the breakdown in each scenario.
## Questions on Traditional and Roth IRA Conversions
Before I let you go, let’s address a couple of questions around traditional IRA to Roth IRA conversions.
### How do I minimize taxes when converting a traditional IRA to Roth IRA?
There are two ways to minimize taxes when converting: convert in a year you earn less in income, or make non-deductible contributions and pay taxes up front.
If you earn less money in a conversion year, you will have a lower current marginal tax rate making the Roth IRA more attractive. With non-deductible contributions (using IRS form 8606), you pay tax up front and add money to an IRA – this money will not be taxed again when you convert (this is called a Backdoor Roth IRA).
### Why should you model converting a traditional IRA to a Roth IRA?
Using assumptions you provide, this tool will help you decide whether to convert a Traditional IRA to a Roth IRA.
With a Roth IRA, you pay all of your taxes today in exchange for the government never taxing you again on the funds. With a traditional IRA, you pay no taxes today in exchange for taxes when you withdraw the funds in retirement.
The IRS allows you to convert a traditional IRA to a Roth IRA. You can never be sure if it’s a good deal to convert an IRA, but this conversion tool will help you make an educated guess. Based upon your estimated future tax rates (and structure), investment returns, and time in the market, it’s possible to guess the optimal decision.
Of course – the optimal monetary decision. Life is messy; this tool can’t model every scenario outside the bounds of the assumptions.
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2020-10-21 09:33:50
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https://en.wikipedia.org/wiki/Talk:Deterministic_finite_automaton
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Talk:Deterministic finite automaton
WikiProject Computer science (Rated Start-class, High-importance)
This article is within the scope of WikiProject Computer science, a collaborative effort to improve the coverage of Computer science related articles on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Start This article has been rated as Start-Class on the project's quality scale.
High This article has been rated as High-importance on the project's importance scale.
WikiProject Mathematics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Mid Importance
Field: Algebra
Technical flag
I have rewritten the intro and added the section "Accept and Generate modes", both of which aim to be a non-technical introduction. Is this sufficient to remove the technical flag? Ounsworth (talk) 18:50, 5 August 2010 (UTC)
What field?
To what field of human endeavor does this relate? Could someone put an introductory sentance in English for the rest of us? Thanks! ;) Mark Richards 06:21, 14 May 2004 (UTC)
Doesn't everyone know automata theory? :-) -- jaredwf 07:27, 14 May 2004 (UTC)
Thanks Jaredwf Just a stupid question though - Finite State Machine says that it is related to 'computer science', while DFST points to 'Theory of computing'. Is this as it should be? Thanks! Mark Richards 15:39, 14 May 2004 (UTC)
I changed the finite state machine to say theory of computation, since theory of computation is a more exact answer. Thanks for noticing. -- jaredwf 15:46, 14 May 2004 (UTC)
Both are correct! Theory of Computation is a subdicipline of Computer Science. —Preceding unsigned comment added by Ben 1220 (talkcontribs) 09:36, 16 September 2009 (UTC)
symbols
The symbols used to describe the 5-tuple are inconsistent with those in Automata theory. Is it better to change to ${\displaystyle \langle Q,\Sigma ,\delta ,q_{0},F\rangle }$? My textbook also uses these notations.
I'm in favor of this change. Pkirlin 06:47, 11 November 2005 (UTC)
• agree. Me too. We should make this change. Using S conflicts with S for semigroup. Using A conflicts with A for Autamaton. Using M conflicts with M for monoid. linas 14:17, 26 April 2007 (UTC)
• Done. I have at least two books that use this format, so I went ahead and made the change. If anyone disagrees, please comment here and let me know. Thanks! ThomasOwens (talk) 00:01, 11 December 2008 (UTC)
i m a student of computer science engineering and for me automata theory and formal languages is a very new subject. i m not being able to get hold of the subject properly. i cannot understand the subject. please suggest somthing. —Preceding unsigned comment added by 115.248.12.253 (talk) 06:23, 6 March 2010 (UTC)
Merge proposal
Oppose. Other articles reference FSMs without the presumption of determinism. --Ancheta Wis 02:25, 3 December 2005 (UTC)
Regular languages in relation to FSM
Can someone please explain the following entry in the article more. Now sure what this exactly is in relation to FSM (the article on regular language is just as perplexing).
The language of M can be described by the regular language given by this regular expression:
1*(01*01*)*
yusufm 20:51, 13 April 2006 (UTC)
The section on regular language is the best place to parse this. The * is the Kleene Star mentioned in that article. So 1* is the set { epsilon, 1, 11, 111, 1111...) The Kleene star operator over a number of the alphabet symbols such as (01)* is the set { epsilon, 01, 0101, 010101...) Essentially it means none, one, or more of the items repeating.
DFA search image
I've just fixed up the DFA image Image:DFA search mommy.svg so that it renders again. It's intended for string search algorithm but may be useful here. Dcoetzee 03:57, 2 April 2007 (UTC)
Missing paths - still deterministic?
The definition for DFA states that there should be one and only one transition for each pair of states and inputs. The definition for NFA only addresses the case of a single input leading to multiple, different states. What about the case where an input leads off to a "dummy state" that just loops back to itself on every input? If we just eliminate the dummy state and any inputs leading to it, does the diagram still represent a DFA? If not, is it an NFA? Or something else? Thanks, Maghnus 15:25, 29 October 2007 (UTC)
• Ambigiuous: The description may be slightly ambiguous in that every pair of states and inputs should have exactly one transition. As I understand it, missing transitions are unacceptable for a DFA, and hence would be classes as an NFA. Pyrre (talk) 03:05, 23 December 2007 (UTC)
Missing paths are no big deal; the definition of what it means to run such an automaton will most likely say that if a path is missing, the automaton immediately halts (this can be simulated by adding an extra state and a new path to this state for each missing path in the original automaton). So long as there are never two paths on the same state/input pair, the automaton is deterministic. — Carl (CBM · talk) 03:21, 23 December 2007 (UTC)
I just added a new section to mention the difference. Rp (talk) 09:47, 11 November 2015 (UTC)
Possible error in example
In the section "Advantages and Disadvantages", the example discribes the "bracket" language - i.e. properly paired brackets. This is not formally anbn, as stated, but "Strings whose each prefix has more or equal a's than b's" Raghunandan ma (talk) 10:18, 16 August 2011 (UTC)
You are correct. It is bad language. Let me try a fix. (Ashutosh Gupta (talk) 13:34, 16 August 2011 (UTC))
Thank you. It looks better now. Also I suggest:
DFAs are equivalent in computing power to nondeterministic finite automata (NFAs). This is because, firstly any DFA is also an NFA, so an NFA can do what a DFA can do. Also, given an NFA, one can build a DFA that recognizes the same language as the NFA, although the DFA could have exponentially larger number of states than the NFA. Raghunandan ma (talk) 06:46, 17 August 2011 (UTC)
Your suggestion is good. Please add it yourself. I also suggest to cite powerset construction page for the algorithm that translates NFA into DFA. (Ashutosh Gupta (talk) 11:30, 17 August 2011 (UTC))
Have added this. Also made some small changes in the wording for union/intersection/complement at the beginning of this section. Raghunandan ma (talk) 06:53, 18 August 2011 (UTC)
Requested move
The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.
The result of the move request was: Moves made, uncontested Mike Cline (talk) 15:54, 3 December 2011 (UTC)
– These are more popular names of the automata theory concepts. Even within the articles the objects are referred as (non)deterministic finite automaton. Ashutosh Gupta (talk) 15:04, 25 November 2011 (UTC)
• Support per nom. —Ruud 20:37, 25 November 2011 (UTC)
The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.
DFA cannot recognize anbn?
The article states that:
Many simple languages, including any problem that requires more than constant space to solve, cannot be recognized by a DFA. [...] Another simpler example is the language consisting of strings of the form anbn — some finite number of a's, followed by an equal number of b's.
I don't think that is correct. Consider the following state diagram:
S0a → S1b → S2 (ab)
S0a → S1a → S3b → S4b → S5 (aabb)
S0a → S1a → S3a → S6b → S7b → S8b → S9 (aaabbb)
And so forth.
As long as n is limited to a specific finite number, it looks like a DFA can indeed be built for the language anbn. Granted, it will take a large number of states (perhaps on the order of 2n?) to embed the counting of a's and b's, but it still seems possible. Or did I miss something in the text? — Loadmaster (talk) 17:48, 27 January 2014 (UTC)
The wording is intended to describe the language ${\displaystyle \{a^{n}b^{n}:n\in \mathbf {N} \}}$ which has infinitely many words (indeed, exactly one of length 2n for every n≥0) and I think it does so. This is not a regular language, and cannot be recognised by a DFA. Deltahedron (talk) 19:38, 27 January 2014 (UTC)
I thought so, but the wording was not clear, so I changed it (adding "arbitrary" to indicate an unbounded n). — Loadmaster (talk) 22:01, 27 January 2014 (UTC)
Removed "Accept and Generate Modes" section
I've removed the "Accept and Generate Modes" section on that grounds that it's original research by a defunct user. A search through my textbooks, university library search engine and Google didn't reveal anyone else who's talking about generate modes for DFAs. Even if that section isn't original research, we should consider whether it lends undue weight to a rarely-discussed type of DFA. Chip Wildon Forster (talk) 18:42, 31 January 2015 (UTC)
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2017-09-21 01:53:10
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https://www.gauthmath.com/solution/What-is-the-volume-of-a-sphere-with-a-radius-of-6-meters-Use-3-14-for-begin-alig-1693669448597510
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# What is the volume of a sphere with a radius of 6 meters? Use 3.14 for beginalign* π .endalign*
Question
### Gauthmathier7045
YES! We solved the question!
Check the full answer on App Gauthmath
What is the volume of a sphere with a radius of 6 meters? Use 3.14 for \begin{align*}\pi.\end{align*}
Good Question (178)
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Detailed steps (99)
Clear explanation (78)
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Write neatly (23)
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### Gauthmathier0486
\begin{align*}904.32\text{ m}^3\end{align*}
Explanation
Let:
\begin{align*}r = 6 \text{ meters}\end{align*}
The formula for the volume of a sphere is \begin{align*}V = \frac{4}{3} \pi r^3\end{align*} .
\begin{align*}\eqalign{
V &=\frac{4}{3} \pi r^3 \\
V &=\frac{4}{3} (3.14)(6)^3 \\
V &=\frac{4}{3} (3.14)(216) \\
V &=\frac{2712.96}{3} \\
V &=904.32
}\end{align*}
The volume of the sphere is \begin{align*}904.32 \text{ m}^3\end{align*} .
Thanks (180)
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2021-10-16 05:08:36
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https://en.wikipedia.org/wiki/Rigid_transformation
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# Rigid transformation
In mathematics, a rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points.[1][self-published source][2][3]
The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a proper rigid transformation, or rototranslation.[citation needed] Any proper rigid transformation can be decomposed into a rotation followed by a translation, while any improper rigid transformation can be decomposed into an improper rotation followed by a translation, or into a sequence of reflections.
Any object will keep the same shape and size after a proper rigid transformation.
All rigid transformations are examples of affine transformations. The set of all (proper and improper) rigid transformations is a mathematical group called the Euclidean group, denoted E(n) for n-dimensional Euclidean spaces. The set of proper rigid transformations is called special Euclidean group, denoted SE(n).
In kinematics, proper rigid transformations in a 3-dimensional Euclidean space, denoted SE(3), are used to represent the linear and angular displacement of rigid bodies. According to Chasles' theorem, every rigid transformation can be expressed as a screw displacement.
## Formal definition
A rigid transformation is formally defined as a transformation that, when acting on any vector v, produces a transformed vector T(v) of the form
T(v) = R v + t
where RT = R−1 (i.e., R is an orthogonal transformation), and t is a vector giving the translation of the origin.
A proper rigid transformation has, in addition,
det(R) = 1
which means that R does not produce a reflection, and hence it represents a rotation (an orientation-preserving orthogonal transformation). Indeed, when an orthogonal transformation matrix produces a reflection, its determinant is −1.
## Distance formula
A measure of distance between points, or metric, is needed in order to confirm that a transformation is rigid. The Euclidean distance formula for Rn is the generalization of the Pythagorean theorem. The formula gives the distance squared between two points X and Y as the sum of the squares of the distances along the coordinate axes, that is
${\displaystyle d\left(\mathbf {X} ,\mathbf {Y} \right)^{2}=\left(X_{1}-Y_{1}\right)^{2}+\left(X_{2}-Y_{2}\right)^{2}+\dots +\left(X_{n}-Y_{n}\right)^{2}=\left(\mathbf {X} -\mathbf {Y} \right)\cdot \left(\mathbf {X} -\mathbf {Y} \right).}$
where X = (X1, X2, ..., Xn) and Y = (Y1, Y2, ..., Yn), and the dot denotes the scalar product.
Using this distance formula, a rigid transformation g : RnRn has the property,
${\displaystyle d(g(\mathbf {X} ),g(\mathbf {Y} ))^{2}=d(\mathbf {X} ,\mathbf {Y} )^{2}.}$
## Translations and linear transformations
A translation of a vector space adds a vector d to every vector in the space, which means it is the transformation
g(v) = v + d.
It is easy to show that this is a rigid transformation by showing that the distance between translated vectors equal the distance between the original vectors:
${\displaystyle d(\mathbf {v} +\mathbf {d} ,\mathbf {w} +\mathbf {d} )^{2}=(\mathbf {v} +\mathbf {d} -\mathbf {w} -\mathbf {d} )\cdot (\mathbf {v} +\mathbf {d} -\mathbf {w} -\mathbf {d} )=(\mathbf {v} -\mathbf {w} )\cdot (\mathbf {v} -\mathbf {w} )=d(\mathbf {v} ,\mathbf {w} )^{2}.}$
A linear transformation of a vector space, L : RnRn, preserves linear combinations,
${\displaystyle L(\mathbf {V} )=L(a\mathbf {v} +b\mathbf {w} )=aL(\mathbf {v} )+bL(\mathbf {w} ).}$
A linear transformation L can be represented by a matrix, which means
L : v → [L]v,
where [L] is an n×n matrix.
A linear transformation is a rigid transformation if it satisfies the condition,
${\displaystyle d([L]\mathbf {v} ,[L]\mathbf {w} )^{2}=d(\mathbf {v} ,\mathbf {w} )^{2},}$
that is
${\displaystyle d([L]\mathbf {v} ,[L]\mathbf {w} )^{2}=([L]\mathbf {v} -[L]\mathbf {w} )\cdot ([L]\mathbf {v} -[L]\mathbf {w} )=([L](\mathbf {v} -\mathbf {w} ))\cdot ([L](\mathbf {v} -\mathbf {w} )).}$
Now use the fact that the scalar product of two vectors v.w can be written as the matrix operation vTw, where the T denotes the matrix transpose, we have
${\displaystyle d([L]\mathbf {v} ,[L]\mathbf {w} )^{2}=(\mathbf {v} -\mathbf {w} )^{\mathsf {T}}[L]^{\mathsf {T}}[L](\mathbf {v} -\mathbf {w} ).}$
Thus, the linear transformation L is rigid if its matrix satisfies the condition
${\displaystyle [L]^{\mathsf {T}}[L]=[I],}$
where [I] is the identity matrix. Matrices that satisfy this condition are called orthogonal matrices. This condition actually requires the columns of these matrices to be orthogonal unit vectors.
Matrices that satisfy this condition form a mathematical group under the operation of matrix multiplication called the orthogonal group of n×n matrices and denoted O(n).
Compute the determinant of the condition for an orthogonal matrix to obtain
${\displaystyle \det \left([L]^{\mathsf {T}}[L]\right)=\det[L]^{2}=\det[I]=1,}$
which shows that the matrix [L] can have a determinant of either +1 or −1. Orthogonal matrices with determinant −1 are reflections, and those with determinant +1 are rotations. Notice that the set of orthogonal matrices can be viewed as consisting of two manifolds in Rn×n separated by the set of singular matrices.
The set of rotation matrices is called the special orthogonal group, and denoted SO(n). It is an example of a Lie group because it has the structure of a manifold.
## References
1. ^ O. Bottema & B. Roth (1990). Theoretical Kinematics. Dover Publications. reface. ISBN 0-486-66346-9.
2. ^ J. M. McCarthy (2013). Introduction to Theoretical Kinematics. MDA Press. reface.
3. ^ Galarza, Ana Irene Ramírez; Seade, José (2007), Introduction to classical geometries, Birkhauser
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2022-12-04 11:32:22
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https://stats.stackexchange.com/questions/285006/random-forest-advantages-disadvantages-of-selecting-randomly-subset-features-fo
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Random forest: advantages/disadvantages of selecting randomly subset features for every tree vs for every node?
There are two methods to select subset of features during a tree construction in random forest:
According to Breiman, Leo in "Random Forests":
“… random forest with random features is formed by selecting at random, at each node, a small group of input variables to split on.”
Tin Kam Ho used the “random subspace method” where each tree got a random subset of features.
I can imagine that by selecting a subset of features at each node is more superior as the correlated variables can still be involved in the whole tree construction. Whereas if we select a subset of features for each tree, one of the correlated variables will lose its importance.
Are there any other reasons why one method can perform better than the other one?
In context of tidy data, one bootstraps on samples(rows) and one bootstraps on both samples(rows) and variables(columns). They, as far as I know, always bootstrap in rows.
Here are the rules for "tidy" originally put forth by Hadley Wickham [1,2]:
1. Each variable forms a column.
2. Each observation forms a row.
3. Each type of observational units forms a table.
So the question becomes "what is the advantage of bootstrapping on columns".
It gives you what bootstrapping always gives, but applied to the column space:
• robust characterization. when a column is important, and excluded, error is much larger and vis versa. This can add emphasis on giving higher weight to higher importance variables, and given that tree-weights are inverse to error, this can reduce the impact of less important variables.
• Accelerated compute: when you operate on less data, ceteris paribus, your algo runs faster. If you make each tree with 75% of the columns, then they construct faster.
• The question is about the effect of tree-wise versus node-wise column sampling. – Michael M Jan 15 at 20:15
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2020-02-24 03:39:44
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http://www.docstoc.com/docs/154764534/Deptdoc
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# Dept
Document Sample
Department of Electrical and Control Engineering
Title：(Subproject II) A Study of Human Activity, Emotion, and physiological
Signal Monitoring System for Health Care Applications (II-III)
Principal Investigator：Chang Jyh-Yeong
Keywords：Action recognition, Emotion recognition, Fuzzy classifier, Feature
selection and transformation, Fuzzy ID3
It is known that human activity, facial expression, and physiological signals
explicitly shed light on the health and comfort status of a person. Based on
recognizing video-based human activity, facial expression, and physiological signals,
the purpose of this project is to build an automated health monitoring system to
determine the physical and mental comfort of a person so as to predict one’s health
condition [1-4]. With an objective signal conditioning, we will develop a machine’s
ability to recognize human affective health state by watching through a CCD camera
over a person’s action and face. By the use of various physiological signals as well,
such as skin conductance, blood pressure, respiration rate, and electromyogram (EMG)
measurement, they can potentially aid in assessing the health condition [22] of a
person. Machine learning and its intelligence algorithms will be developed and can
hopefully predict the short-term, and very likely extend the time duration, the health
condition of a person. The predicted health condition is automatically generated and
transmitted and thus is helpful for notifying the corresponding family or medical
treatment if necessary. Our effort is to advance the state-of-the-art in pattern
recognition of affect from video streams and physiology by proposing a large space of
reasonable features and systematically evaluating subsets of it and transformations
thereof. For health monitoring purpose, the recognition of human action is expected to
be classified into “normal walking,” “slow walking,” “falling down,” and
“crouching,” etc. As for the same purpose from facial expression, expression is
expected to be differentiated into “normal face,”“pale face,” “slightly pain face,” and
“pain face,” and the like. It is easy to obtain the monitored video streams in an
unconscious way and the classified categories for these video streams are described in
terms of symbolic form. Moreover, physiological signals including EEG, ECG, blood
pressure, heart and respiration rates, and skin conductivity, whose measured outputs
are described in numerical format, can be integrated to access the physical comfort of
a person. This health condition accuracy can be enhanced by fusing the recognized
one’s action, facial expression and physiological signals. Heath condition
determination and prediction methods will be relied on machine learning techniques,
which include two modules. The first module facilitates the classification algorithmic
routine and the second is constructed with a knowledge rule-based system to predict
one’s health condition [24]. Heath state determination through SVM, BP and
statistical approaches are appropriate and a better generation can be reached. ID3
technique is well known for prediction or summarization the status of a set of data. In
this study, we will investigate to extend the ID3 method to a more flexible fuzzy ID3
version [56], which can handle symbolic data, like painful state, and continuous
feature, such as blood pressure. Through the development of this automated health
care and monitoring system, the digital machine can constantly and automatically
detect and monitoring one’s health condition. A quick response from telemedicine
objective can be reached, which as a whole improve the quality and safety of our daily
life through human-centered and automated human-machine interface investigation.
NSC94-2213-E-009-097（94N530）
-------------------------------------------------------------------------------------------------------
Title: The systematic design and analysis of topologies for single-phase single-stage
AC/DC converters
Principle Investigator: Chang Lon-Kou
Sponsor: National Science Council
Keywords: Single-Phase Single-Stage AC/DC Converter, Input Current Shaping,
Soft-Switching, Energy Flow Path
To constraint the undesirable harmonic interference from the power converter
onto power line and other electronic equipment, stringent current harmonic
regulations have been defined by some international standards, such as IEC 61000-3-2.
Thus, the single-stage input current shaping (S2ICS) techniques have been proposed
and intensively studied recently, in order to comply these regulations with minimal
additional component count and cost.
The objective of this two-year project is to develop deep techniques and
innovative solutions for the advanced integrated S2ICS AC/DC converters, which
target at the low power applications (from 70 to 200 W), for power adapters, battery
chargers, and various communication equipments.
In the 1st year, this project will provide a systematic study of the S2ICS
mechanism, circuit topology generalization and modification, bulk capacitor
voltage-stress and switch current-stress, converter design and optimization, and the
evaluation of the S2ICS techniques applied to universal-line input. We will also
develop a novel S2ICS technique to improve the performance and achieve the
cost-effective consideration for universal-line applications. Another focus of this
project is to design and implement an efficient S2ICS converter based on
soft-switching techniques and the overall topology simplification.
In the 2nd year, the project will develop a systematic method for deriving S2ICS
converter configurations in which the charging and discharging paths of the ICS
inductor can be possibly unitized. Based on this method, many topologies known
previously can be analyzed to develop improved ones. The second systematic
approach is to analyze and evaluate the performance of S2ICS converters by the
concept of energy flow path. It provides a useful design guideline for the
efficiency-related S2ICS techniques.
All the proposed concepts or techniques will be analyzed and verified in practice,
and the results will be used as a reference to the realization on the future electronic
equipment.
NSC 94-2213-E-009-147（94N409）
------------------------------------------------------------------------------------------------
Title: Analysis of Direct-Drive in-Wheel Motor and the Design of Sensorless Sliding
Mode Controller (2/2)
Principle Investigator: Chen Yon-Ping
Sponsor: National Science Council
Keywords: In-wheel motor, Sensorless drive, Sliding mode controller
Traditionally, high-speed motor is adopted as the power source in an EV
(electric vehicle). It uses the transmission mechanism to deliver power to the shaft of
the wheels. Recently, the technology of Servo-motor has been well developed, which
can be applied in such procedure. However, the loss resulted from the transmission
mechanism could reduce the overall efficiency seriously. The objective of this project
is to analyze the in-wheel motor with FEM and to construct its analytical model. A
driving method based on the in-wheel motor’s dynamic model is then proposed to
improve the overall efficiency. Furthermore, sliding mode theory is employed for
controller design to suppress the external disturbance. Most significantly, the
sliding-mode control for low speed operation is implemented via the senseless
technology, which is achieved by using a sliding observer.
NSC 94-2213-E-009 -047（94N518）
-------------------------------------------------------------------------------------------------------
Title：The technology of constructing the indoor map for robot’s activities
Principal Investigator：Chen , Yon-Ping
Sponsor：Industrial Technology Research Institute
Keywords：Robot, Indoor Map Building, Navigation, Route Planning
This project will realize the robotic indoor navigation. As the robot wanders
inside the building, the information of environment measured by robot will be utilized
to build the indoor map. Then the robot can walk inside the building conveniently. In
this project, the development environment is based on C# and ActivMedia software
respectively for the indoor map, navigation, and positioning.
The robot in ITRI is adopted as the development platform. There are sonar arrays,
laser, odometer, and gyro mounted on the robot. The information measured by these
sensors could be integrated by intelligent theory. After extracting the useful features,
the surrounding environment of robot could be constructed. While the robot wanders
inside the building, the relative indoor map can be built well. As a result, the robot can
walk conveniently and know the environment.
After the indoor map is built up, we would like to research the indoor
navigation of robot. The user can select a point on the map and send the command to
the computer of the robot with WLAN. Then the robot would walk to the assigned
point. As shown in figure A, the robot would walk from room1 to room2. In this
process, the intelligent algorithm would be adopted to assist the navigation. For
instance, if there is a dynamic object in the room, the robot would detect the object
and keep out the way intelligently. Then, the robot would plan the route again and go
to the assigned point.
94C155 (94.06.01-94.11.30)
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Title：Smart power management for ultra low power systems
Principal Investigator：Chen Ke-Horng
Keywords: Power management
Wireless communication and potable devices are popular in today’s technology.
Low power designs become more and more important. Owing to the growth of low
power designs, we even can use the ambient energy sources for our system. As we
know, it is so-called green energy. It also means that this system is a self-sustention
operating system using green energy as energy source. Thus, how to convert and
manage this tiny energy becomes a major topic in this system’s design. Our research
aims at a smart DC-DC converter and adapts a suitable power management theory in
the self-sustention system. Based on this architecture, this self-sustention can get
stable supply energy under the optimal energy transferring efficiency.
The generator of microelectromechanical systems can generate tiny energy
about hundreds of μW. We can use rectifier and DC-DC converter efficiently convert
the unstable voltage to a specified and stable output voltage. According to the
industry’s latest round of DC-DC converters’ technology, we can use an
inductor-based switching regulator or a regulated charge pump converter. In this
self-sustention system, we need high conversion efficiency, low quiescent current,
high system integration, and low noise. Thus, a lot of systems with green sources use
an inductor-based switching regulator as the DC-DC converter architecture. In order
to reduce the disadvantage of higher noise, we can use some low-noise technologies
to reduce the influence of the effect. In other words, our research will be an
inductor-based switching regulator with ultra-low noise. Based on this architecture,
we can develop our power management for this self-sustention system.
This project proposes a smart power management theory. The feedback information
from the frequency deviation between the operating frequency of the digital signal
processing system in this self-sustention and modulation frequency, utilization of the
energy from MESM generator, the deviation of loading, and the capacity of the
storage device determine which of the modulation technology we should use. The
modulation skills contain PWM (pulse width modulation) and PFM (pulse frequency
modulation). According to the loading current, swap the modulation skill between
PWM and PFM. When the load is light, the system uses PFM. When the load is heavy,
the system uses PWM. It makes the efficiency of the system have the optimal value.
Using buck/boost converting skills, we can step-down or step-down the output voltage
to the range from 0.9V to 1.6V. Make sure the energy consumed in the system and the
energy stored in the storage devices to the best converting efficiency.
MEMS
Generator
Rectifier Storage
Feedback
Terms
Power
Management
Drive and L
VOUT
Self-Sustention
0.9~1.6V System
Control
Basic Buck/Boost DC-DC Converter
智慧型直流電源轉換器與功率管理架構示意圖
NSC 94-2215-E-009 -059（94N582）
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Title：Designing the reader, and building the communication system between reader
and tag
Principal Investigator：Chen Fu-Chuang
Keywords: RFID, Reader, Tag
An RFID system is always made up of readers and tags. Tags are located on personnel or
objects, in order to receive the transmitted signal and energy from readers and return the
relevant information of tags. Besides being responsible to supply energy to tags, readers
are responsible for communication, data security, data reliability between readers and tags.
In addition, readers must deal with data collision problem. Readers are usually fitted with
an additional interface to connect with other systems, so that the data which was read can
be analyzed and processed further. Because, RFID systems have advantages, such as
conveniently, fast, saving time and diversification, etc., the fields of application for them
are wider and wider.
This total plan that our whole research groups want to carry out is: “The research and
development of RFID-based personnel and objects tracking and controlling systematic
platform”, has divided into five sub plans altogether. We are responsible for the sub plan
two “The research and manufacture of readers, and build the transmission system
between readers and tags”. In order to finish whole total plan, we fix the three-year goal.
Goal of the first year is “The plan of transmission system between readers and tags, and
design the system of readers”, we will select the best systematic parameters, transmission
methods according to the demand, and do the preliminary design to the system of readers.
Goal of the second year is “To finish the prototype of readers, and do the transmission
test with tags”, we will finish the prototype machine of reader, and do the transmission
test with the group which builds tags. Goal of the third year is “To connect readers with
network, and the integration and test of system”, we will integrate all systems developed
by sub plans and test systematic exactness.
Before the research and development of actual circuits of RFID systems, we must
understand whole architecture of RFID systems. We need to understand the behavior and
performance under different systematic parameters, so we can select systematic
parameters carefully to achieve the balance point between optimal performance and
actual applications; it is also the main goal of the first year. And up till now, our research
results of the first year have already made our systematic parameters according to the
standard of Auto-ID class 1, including adopting passive RFID system, HDX procedure,
electromagnetic backscatter coupling, the UHF frequency range 922~928MHz. And data
rate, data encoding and modulation are different on the basis of transmission direction.
According to relevant documents, we also standardize the communication interface
between readers and tags, the communication between readers and network and the skill
of anti-collision. In addition, we discuss some fundamental architecture of circuits,
including quartz oscillator, frequency synthesizer, modulator, power amplifier, directional
coupler, band pass filter, low noise amplifier and mixer. We will do more detailed
description in the report of the research results of the first year at present.
With the progressive goals of three years, cooperate with groups which are responsible
for different sub plan, come to finish the whole total plan step by step. We hope that
through the completion of plan, we can develop a perfect RFID system, and accumulate
relative knowledge, experience, and technology to promote the levels of relevant
NSC 94-2213-E-009-101（94N534）
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Title：Research on the Joint Design of Cascaded Subsystems with Applications in
Communications and Signal Processings
Principal Investigator：Cheng Mu-Huo
Keywords：Cascaded subsystems, Alternating coordinates minimization (ACM),
Generalized Benders decomposition (GBD), Synchronizers,
Interpolators, Equalizers
This project aims for two purposes: one is to present a unified formulation,
investigate differences between existing algorithms, and develop new algorithms for
the joint design of cascaded subsystems; the other is to apply these algorithms for new
applications in digital communication systems and signal processings. When
designing a system with a large number of parameters and complicated relations
between these parameters, one often decomposes the system into several cascaded
subsystems such that each subsystem can be designed separately. This approach yields
several advantages: the number of required design parameters is reduced and their
related functions are often simplified such that the design can be straightforward, the
design algorithm is easily realized, and the optimal design for each subsystem can be
usually obtained. The disadvantages, however, are that even the design for each
subsystem is optimum, the total solution often is not optimal because the joint
capacity is not explored. Hence, the performance is often degraded. The purpose of
the joint design for cascaded subsystems, therefore, is to develop algorithms for
designing each subsystem such that these algorithms are simple to realize as well as
able to explore the joint capacity for performance improvement.
The idea of the joint design of cascaded subsystems has been used in many
applications of signal processings, digital communication systems, and system
sciences. For example, a digital IIR system can be formulated as a joint design of an
all-zero subsystem cascaded with an all-pole subsystem. This approach has been
applied for designing IIR filters or channel model identification. Another design
example is the joint design of an interpolator with an equalizer in a digital
communication system. These designs, however, focuses only on solving the
considered problem, the adopted object function, therefore, varies with applications
and the developed algorithms are also different. These algorithms, in essence, can be
unified in the class of the joint design of cascaded subsystems. Therefore, the first
purpose of this project is to develop a unified formulation for describing the joint
design of cascaded subsystems, and to investigate the realization complexity and
convergence property of the developed algorithms under various objective functions.
We begin by investigating the two famous algorithms in optimization, the alternating
coordinates minimization (ACM) and the generalized Benders decomposition (GBD).
Then we shall study to develop the algorithms, prove the conditions for convergence,
and evaluate the convergence rate under various measures such as the 2-norm,
$\infty$-norm, the maximum likelihood function, or the bit-error rate (BER). Hence,
the joint design of cascaded subsystems and its associated algorithms with their
application scope and constraints are investigated at this stage. The unified view also
enables us to have a clear understanding of the joint design and its design algorithms.
The second purpose of this project is the application of the developed joint design
methods. For the application in communications, we focus on the joint design of the
interpolator and equalizer. We have successfully used the 2-norm as the object
function to design jointly a better interpolator and equalizer. We plan to investigate
further the developed algorithms under different object functions for the design of
this problem for improving the performance. For the application in signal processings,
we design the IIR filters as the joint design of two cascaded subsystems. Then the
filter performance is evaluated and the convergence properties of the design
algorithms are investigated. In summary, this project studies the general joint design
of cascaded subsystems, develops a unified formulation and new algorithms, and
applies them for designing better interpolators and equalizers in a digital
communication receivers and better digital IIR filters. Through this project, we expect
to understand further the fundamental properties of algorithms for the joint design of
subsystems and explore new applications.
NSC 94-2213-E-009-061（94N342）
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Title: The Study of Smart Micro-Sensor Devices
Principle Investigator: Chiou Jin-Chern
Sponsor: National Science Council
Keywords：MEMS Technology, Micro-sensors, Accelerometer, Optical Gas sensor
The third sub-project entitled “The study of the intelligent microsensors” of the
integrated project plays the role of designing and fabricating microsensors for the
ultra low power wireless sensing module. Within the next three years, the present
sub-project will use MEMS technology to design and fabricate an optical gas sensor
or a novel threshold accelerometer. The abstracts for the next three years are given as
follows:
Abstract of 1st year project:
There are two action items that need to be completed in the 1st year, at first, to
justify our design concepts; we will focus on the pro and con of the operation
principles in designing MEMS components by using simulation software. We will
also develop the needed processes and masks that can be used to fabricate different
components for the optical gas sensor and the threshold accelerometer. Secondly, in
order to verify the design sensing concept, we will utilize the existing
optical/electrical/mechanical components to assemble an optical gas sensor.
This device will be the standard for the future micro optical gas sensor.
Abstract of 2nd year project:
For the 2nd year, with the specifications given by the related sub-projects, we will
use the simulation software to verify and fabricate a series of low driving voltage and
low power consumption optical and accelerometer components. Furthermore, in order
to justify the performance of the fabricated components, we will replace the device of
the previous assembled system one at a time. By discussing with other sub-projects,
we will continue to modify our design and fabrication process.
Abstract of 3rd year project:
The work need to be done in the 3rd year is to integrate different chips fabricated
in 2nd year. Here flip-chip bonding technology will be utilized to complete the
assembly of the ultra low power wireless sensing module. Experiments will be
conducted to obtain system characteristics of the integrated module. If needed,
specifications and designs will be modified according to different requests.
NSC 94-2215-E-009-055（94N578）
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Title: The design and fabrication of an ultra low power micro-sensing module for
wireless sensor networks
Principle Investigator: Chiou Jin-Chern
Sponsor: National Science Council
Keywords：Wireless sensor networks, System on Chip, MEMS, Microsensors, RF
Transceiver Circuit, Micro Power Generator, Ultra Low Power A/D
Converter, Mixed Mode Sensing Circuit, Power Manage Circuit
An advanced and highly integrated research project is proposed for the next three
years.The present integrated project consists of six sub-projects that are focused on
the research of Micro Power Generator, Power Manage Circuit, Microsensors, Mixed
Mode Sensing Circuit, Ultra Low Power A/D Converter, and RF Transceiver Circuit.
The main goal of this project isto develop an ultra low power wireless sensing module
with small size, high efficiency andlow price characteristics.
The abstract of the three years integration project is: (1) to achieve defined
performances and specifications of each sub-project. The research items include
designs, simulations and verifications of related devices and fabrication processes.
Encounter problems and solutions will be discussed and if necessary, we will modify
the designs and specifications. (2) to accomplish the goal of ultra low power and
miniaturization. The fabrication, testing and verification are performed to verify
original designs. An optimal integrated solution will be provided to obtain the ultra
low power wireless sensing module. (3) to integrate all the chips that are fabricated by
the sub-projects using the flip-chip bonding technology and successfully manufacture
the proposed ultra low power wireless sensing module. Successive tests will be
carried out and the final performance will be reported at the final stage of the project.
NSC 94-2215-E-009-056（94N579）
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Title：The Development of Packaging Process and Driving Circuits for High Density
Micro Capacitive Device
Principal Investigator：Chiou , Jin-Chern
Sponsor：Industrial Technology Research Institute
Keywords：Tunable CMUT Driving CKT, Capacitance sensing, XYZ-Table, MEMS
Packaging
A tunable CMUT driving and capacitance sensing CKT will be developed. A
XYZ-Table is designed and established to carry the CMUT system for constructed an
integrated measurement application. In addition, a MEMS packaging material and
process for CMUT will be researched and deliver a report for reference in future
works. In the CMUT driving CKT design, a high tunable DC gain is one of the key
design issues. In the others, the tunable frequency and amplitude of AC signal is
designed for satisfy the measurement application. The XYZ-Table with high
resolution servo control is used to precision control the gap between the CMUT and
object for improve the sensing performance. In MEMS packaging, the packaging
material is the main power consumption in CMUT system. A functional packaging
material with well transmission performance is not always compatible to CMUT
process. In a standard/positive packaging process, the passable packaging material is
limited. The material and process will be trade off in this research. Therefore, a new
packaging process will be researched and designed to complete the CMUT packaging.
94C116(94.05.01-94.11.30)
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Title：MEMS-based electrostatic vibration-to-electric energy converter (II)
Principal Investigator：Chiu Yi
Keywords：Power MEMS, Energy conversion, Vibration, Electrostatic, Smart micro
sensor system
In recent years, there are increasing interests in the power MEMS technology,
where various energy sources, such as chemical and kinetic, are converted to electric
energy using MEMS technology. Such micro power supplies can be applied to
portable 3C products, personal health monitoring system, and other distributed sensor
networks. This project extends the research effort from a 2004 NSC grant to
develop an electrostatic MEMS vibration-to-electric energy converter within 1 cm2
based on a 3.3 V auxiliary power supply. The targeted energy source is the 120 Hz,
2.5 m/s2 vibration that is measured abundant in natural environment. Design and
simulation environment have been set up. Optimal design parameters were found
through both theoretical analysis and numerical simulation. A power density of
2
can be achieved. Final layout is to be completed by the end of 2004 and
device fabrication can be engaged in early 2005. The electrostatic MEMS power
generator can be integrated thermo-electric and photovotaic micro power generators,
power management circuits, signal processing circuits, and sensing circuits to form a
self-sustained smart micro sensor module.
NSC 94-2215-E-009-057（94N580）
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Title：Low-Power, Low-Distortion Image Compression IC Design
Principal Investigator：Dung , Lan-Rong
Sponsor：Chung-Shan Institute Of Science And Technology
Keywords：Video compression, Digital signal processor, Power-aware architecture
The objective of this project is to develop a power-aware video compression
processor for capsule endoscopy or swallowable imaging capsules. In applications
of capsule endoscopy, it is imperative to consider battery life /performance trade-offs.
Applying state-of-the-art video compression techniques may significantly reduce the
image bit rate by their high compression ratio, but they all require intensive
computation and consume much power from battery. There are many fast
compression algorithms for reducing computation load; however, they may result in
distoration of original image, which is not good for the use of medical care. Thus,
this project will first simplify traditional video compression algorithms and propose a
scalable lossless compression algorithm. The scalable algorithm can be used for the
later power-stepping technique. Then, we will develop a power-aware architecture
for battery life extention. The power-aware architecture is an architecture that can
properly reduce the computation load as the battery status changed while the qulity
degradation is little. In the project, we will consider not only the minimization of
average power dissipation but transient characteristics of power dissipation, such as
peak power and power gradient or differential. Therefore, the project will develop a
low-computation, scalable video compression algorithm and its power-aware DSP
ASIC for capsule endoscopy.
94C076(94.01.01-94.12.31)
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Title：Study on Power-aware High-level Synthesis Techniques for Nenometer SOC
Design(3/3)
Principal Investigator：Dung Lan-Rong
Keywords：Power-aware system, High-level synthesis, SOC, CAD
As we get closer to the limits of scaling in CMOS circuits, it is imperative to
consider power/performance trade-offs and to develop appropriate power aware
methodologies and techniques for embedded systems. The use of nanometer
technologies is making it increasingly important to consider transient characteristics
of a circuit's power dissipation (e.g., peak power, and power gradient or differential)
in addition to its average power consumption. State-of-the-art transient power
analysis and reduction approaches are mainly at the transistor- and gate-levels.
However, we believe architectural solutions to transient power problems may
complement and significantly extend the scope of lower-level techniques, as was the
case with average power minimization. This project intends to exploit high-level
synthesis approach to transient power management and reduction in that a
power-aware high-level synthesis can impact the cycle-by-cycle peak power and peak
power differential for the synthesized implementation.
NSC 94-2220-E-009-023（94N467）
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Title：Study on Formal Verification for High-Level Synthesis
Principal Investigator：Dung Lan-Rong
Keywords：SoC, Formal Verification, Theorem Proving, Design for Verification
The System-On-Chip (SOC) design encompasses a large design space. Typically, the
designer explores the possible architectures, selecting algorithms, choosing architectural elements, and
constructing candidate architectures. Designing such a complex system is hard; designing such a
system that will work correctly is even harder. Design errors should be removed as early as possible;
otherwise, errors detected at the later stages will result a costly, time-consuming redesign cycles. Thus,
the designer should face two distinct tasks in SOC design; carrying out design process itself and
establishing the correctness of a design. Design correctness is the main theme of this project. This
project aims on the formal verification for high-level synthesis and addresses on three issues: theorem
proving, property reasoning, and design for formal verification. First of all, the project will develop
theorem proving technique for architectural design. Based on Petri-Net models, the theorem proving
verifies the reachability, admissibility, and correctness of task scheduling and resource allocation. In
the property reasoning, the project will focus on metrics of property coverage. With accurate
calculation on property coverage, the notorious property-validation problem can be lessened or even
solved. Finally, a technique on design-for-formal-verification (DFFV) will be developed, driven by
theorem proving and property reasoning. The DFFV technique will aid SoC designers for efficiently
applying formal verification in proof of their design.
NSC94-2220-E-009-039（94N483）
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Title：Ultra-low power, design-for-digital Testability analog-to-digital converter(II)
Principal Investigator：Hong Hao-Chiao
Keywords: Low power design, Analog-to-digital converter (ADC),
Design-for-testability (DFT)
There are two major goals pursuing by electronic engineers, one is higher speed,
the other is lower power. In many applications such as the bio-sensing systems, the
speed is not a major concern but a longer operating time is very critical. For instance,
an animal tracking system wishes it could sustain several years without changing the
battery since it is hard to replace the battery. It is the case of our major project--- an
ultra low power micro-sensing module applying for wireless sensor networks.
The analog-to-digital converter (ADC) is one of the key components of the ultra
low power micro-sensing module. It is necessary for flexibility of complex signal
processing by digital circuits. It also determines the accuracy of the system and is
very vulnerable to the noises coming from the environment, chip, even the circuit
itself. In addition, since the power provided by the system is very limited, ultra-low
power is an essential requirement for the ADC. At system level, different ADC
architecture has different power requirement. We are currently working on detailed
analysis to find out the power consumption characteristic of the candidates in this
year’s NSC project. At circuit level, special design technique must be developed. One
possible solution is design the ADC by using MOSFETs operating at sub-threshold
region. However, the design techniques have not been well developed yet as far as we
know. Lots of research results may be found.
Another issue in designing the ADC is how to testing it. Traditional way using
an external signal generator to stimulate the ADC then get the digital outputs for final
DSP analysis. Its cost is high and the noisy testing environment often disturbs the
results. Usually, lots of efforts must be paid to debug the testing environment. In the
target micro-sensing module, how to test the ADC becomes more troublesome due to
its highly integration. Alternatively, design-for-testability (DfT) and/or analog
build-in-self-test (BIST) techniques help alleviating the efforts since it accepts digital
stimulus rather than analog one. It isolates any possible noise source coming from the
interface.
This project will develop an ADC with at least 8-bit resolution to be integrated
in the wireless sensor module. It operates at 1V and consumes less than 30 µW. The
target ADC will be equipped with a low cost DfT circuit and being totally digitally
testable to enhance its immunity of environmental noise and interference during
testing, to simplify the testing environment setup, and to reduce the testing cost.
NSC 94-2215-E-009-081（94N604）
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Title：Development of the Control Technique for the Omnidirectional Mobil Platform
Principal Investigator： Hsu , Pau-Lo
Sponsor：Industrial Technology Research Institute
Keywords：Omnidirectional mobile platform, Control, Measurement.
To improve the agility of a mobile robot or platform, omnidirectional mobile robots
have been proven to be more capable in high-speed motion operations. Although the
omnidirecitonal wheel can be applied to motion systems to achieve the qualified task,
its motion precision is difficult to achieve. Therefore, this project will develop the
basic control technique for an omnidirectional mobile platform to meet the
specifications as: in a linear motion 180 cm, it will achieve 5 cm accuracy with every
60 degree.
Basically, when the omnidirectional motion system moves in a certain angle, the
slip will occur and it causes the axial force on the platform. Therefore, on-line
measurement, open-loop and feedback control of the omnidirectional system are
difficult compared with motion control in traditional systems. In this project, basic
control techniques for the omnidirectional system will be established through both
theoretical analysis and experimental work. In the future, the present results obtained
in this project will be integrated with other communication and image signal
processing systems under the main project.
94C156 (94.06.01-94.11.30)
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Title: Multi-Agent Distributed Monitoring and Control of Traffic Systems
Principle Investigator: Professor Hsu Pau-Lo
Sponsor: National Science Council
Keyword: Traffic light control, Fuzzy decision, Agent, Multi-agent system,
Distributed control, Wireless network
Development on monitoring and control progress significantly in the past two
decades. However, the monitoring system is not compatible in realization with the
control system mainly because of their functions are different. Control needs real-time
computation while monitoring requires less real-time processing but with large
amount of intelligent computation in decision making. Due to the recent rapid
development in networking technology, agent system becomes a potential tool in
distributed monitoring and control systems.
For the traffic lights control issue, it is a standard monitoring system because its
control requires less calculation but how to determine the duration of the signals
requires large amount calculation to achieve an optimized result. In addition, it is a
practical issue in control problem because every intersection in the city is jammed
during the rush hours. In general, one or two polices are assigned to control the traffic
light manually. For a traffic network, it is a typical distributed control system.
However, due to the polices in different intersections do not exchange information;
the control results are not satisfactory. In addition, the traffic flow, speed, density,
queuing time are varied greatly in a day. It is not suitable to apply traditional
scheduling to analyze it.
In this two-year proposals, the fuzzy control as a police is designed for each
intersection. Furthermore, several adjacent intersections are connected by the 802.11b
wireless communication that the local traffic can be monitored by an intelligent agent
to achieve traffic balance. Furthermore, a multi-agent system (MAS) is developed so
that they can negotiate one another to get the most balanced traffic in the whole
system.
NSC 94-2213-E-009-031（94N514）
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Title: On The Study of Acoustic Field Perception and Sound Communication
Interface for Robotic Systems
Principle Investigator: Hu Jwu-Sheng, Cheng Chieh-Cheng, Liu Wei-Han, and Yang
Chia-Hsing
Sponsor: National Science Council
Keyword:Robotics, Hearing System, Array Microphone, Array Signal Processing,
Acoustics, Speech Enhancement
The research on sound was not emphasized in the area of Robotics when the
applications of robots are mainly on industrial automation. Most researches of the
environmental sensing for robots were based on vision, ultrasound, temperature or
touch. However, sound (or speech) is a very important communication mean for
human being. That is to say, if we wish to make robots that can enter household or
become a personal assistant, the sound interface has to be a necessary part of the
system. The communication of sound can be separated into two categories. The first
one is the content of the sound such as speech or music melody. The second one is the
information created by sound wave interaction with the environment. For example,
the interaction can reveal the sound source location or even the acoustic field that is
related to the space where the sound is generated. This is a 3-year proposal to study
the second category mentioned above. The topics include making a microphone array
module to facilitate the research experiment and integration on robots. Secondly, due
to the movement of robots, the microphone array on the robot has the property of
infinite sampling in space. We will study the advantage it brings as well as the
shortcomings. Meanwhile, we will also study the classical sound source separation
and speech enhancement problem as they are very important for the hearing ability of
a robot. This proposal is part of an integrated effort to make personal robots. And this
work will play the role of hearing systems for the robot as we will collaborate closely
with other research groups participated in this project.
NSC 94-2213-E-009-046（94N517）
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Title：The Design and Implementation of Embedded M2M Technology
Principal Investigator：Hu , Jwu-Sheng
Keywords：Embedded Systems, Machine-to-Machine, Man-To-Machine,
Machine-to-Man
M2M refers to the communication between machine to machine, machine to
man and man to machine. M2M solution builds up a communication channel via
PSTN, LAN, WAN or WiFi to achieve the goal of instant communication for
enterprises and factories. The researches estimate that M2M solution will be applied
to the public device networks of trasportation, electricity measurement, weather
forcast and so on. It is forcasted to result in another revolution in network
technologies.
One of the key technologies in M2M solution is the integration of hetergeneous
networks. This technology helps to provide a stable solution for distributed
applications with low data rates. In addition, the technology also connects the
embedded devices in a factory to the public, large-scale information network. The
project provides a flexible framework and API for services providers to efficiently
integrate M2M devices and enterprise applications. This M2M solution also brings a
lot of potential oppertunities to create new business.
94C214 (94.12.01-95.11.30)
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Title：Analysis and Design of Automatic Power Monitoring on the Feeder of Power
Systems
Principal Investigator：Liaw , Der-Cherng
Keywords：
In the recent years, the control and monitoring of power systems has attracted lots of
attention in both academia and industry. According to the information from Tai-Power
Company, the company will install monitoring devices on more than 3000 feeder lines
of power systems for automatic power monitoring between the years of 2002 and
2007. Based on the average needs of 5 Feeder Terminal Units (FTU’s) required for
each feeder line, the requirements of the FTU’s and the controller: Feeder Remote
Terminal Unit (FRTU) for the whole project will be around 15000 FTU’s and 300
FRTU’s. There are only few companies on Taiwan can provide part of solution to fit
the requirements of Tai-Power Company. In this project, we will study the required
specifications for the whole power monitoring systems. A detailed survey of the
available commercial products of both FTU and FRTU will be carried out, which will
then provide the required hardware and software specifications of both FTU and
FRTU for product design. The specifications of the system software and the related
application packages software will also be studied to cover the whole design
requirements for fulfilling the function of automatic feeder power monitoring.
94C100 (94.05.01-95.04.30)
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Title：Blind Identification and Equalization of MIMO FIR Systems
Principal Investigator：Lin Ching-An
Keywords：Wireless Communication, Blind equalization, Blind identification,
MIMOsystem, FIR
The multiple-input multiple-output (MIMO) finite impulse response (FIR) models
arise in many applications, in particular, in describing multiuser communication
channels. The need for blind equalization of such channels arises when multiple
input sequences from multiple users need to be blindly separated and estimated. This
proposed research develop methods and algorithms for blind identification and
equalization of MIMO-FIR systems using second-order statistics. The methods
exploit cyclostationarity of output data, which is induced at the input via periodic
precoding modulation. Part of the research extends our results for the SISO case.
Topics of investigation includes identifiability conditions, identification algorithms,
optimal choices of precoding sequences, equalization based on optimal FIR periodic
deconvolution, effects and optimal choice of deconvolution delay, and recursive
adaptive implementation of the combined identification-equalization algorithms.
Results of this research will provide insight needed for a practical solution to the
MIMO-FIR blind equalization problem.
NSC94-2213-E-009-010-(94N305)
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Title：Intelligent Systems in Ovarian Cancer with Microarray Data for Molecular
Evolution and Control
Principal Investigator：Lee Tsu-Tian
Keywords：Ovarian Cancer with Microarray, Intelligent Systems, Prediction and
Classification, Modeling of Gene Network, Clustering of interval
Regression Analysis, Gene Pathway Analysis, Multiple Sequence
Alignment
Ovarian cancer is one of the most common causes of death from a gynecologic
malignancy. The mechanism of transformation from normal cells to malignant cells
remains to be clarified. Microarray provides a tool to study the diseases by a
large-scaled approach. The information of microarray with intelligent system analysis
can assist the physicians on the diagnosis, prediction of prognosis, therapeutic
planning and also shed light on figuring out the pathways of tumor formation.
Computer assisted analysis and simulation of biochemical pathways can improve the
understanding of the structure and the dynamics of cell processes considerably. In this
research, we shall focus on the study of some key technologies of advanced intelligent
system in the ovarian cancer with microarray data for molecular evolution and control.
The group project consists of seven subprojects as:
1. Ovarian Cancer Microarray data preprocessing and analysis.
2. Classification and Prediction of Ovarian Cancer Using Microarray Data based
on Intelligent Systems.
3. Computational Intelligence Approaches on Dynamic Functional Clustering
Algorithm, Clusters of Interval Regression Analysis and Distance-Based
Outliers Detection of Microarray Data for Ovarian Cancer
4. Modeling and Stability of Gene Network based on Computational
Intelligence.
5. A Hybrid Algorithm to Multiple Sequence Alignment for Ovarian Cancer with
Microarray Data.
6. Genome-Wide Pathway Analysis and Visualization Using Gene Expression
Data.
7. Establish the Molecular Evolution Mechanism of Ovarian Cancer via
Computational Analysis and Ex Vivo Test.
In this three-years group project, the effectiveness of the developed subsystems shall
be verified by the simulated and experimental results in the intelligent systems in
ovarian cancer with Microarray data for molecular evolution and control.
NSC 94-2213-E-009-123-（94N539）
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Title：Modeling and Stability of Gene Network Based on Computational Intelligence
Principal Investigator：Lee Tsu-Tian
Keywords：Computational intelligence, Ovarian cancer microarray data, Intelligent
Systems, Modeling of gene networks, Molecular evolution and control
For this project, we propose several computational intelligence approaches such
as hybrid genetic-programming-fuzzy-neural, hybrid function Petri nets, Bayesian
neural networks, and graph theory, respectively, for modeling and analysis of ovarian
cancer microarray data via gene networks. Modeling methods of gene networks as a
set of nonlinear differential equations, and as non-differential equations are proposed
independently. Furthermore, the globally exponential and the global asymptotic
stability analyses to the gene network will be investigated. That is, in this project, we
will put forward and develop some novel and innovative approaches and tools for
molecular evolution and control of ovarian cancer with microarray data using gene
networks. Advanced software packages like Matlab will be used to develop computer
programs for gene networks and visual software for bioinformatics.
NSC 94-2213-E-009-124-（94N540）
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Title：Advanced Vehicle Control and Safety Systems-Design and Simulation
Principal Investigator：Lee Tsu-Tian
Keywords：Advanced Vehicles, Intelligent Control, Active Suspension, Anti-lock
Braking System, Real-Time Foreground Image Recognition System,
Car-Following System, Distributed Network Monitoring and Control,
Simulator
This is the group project of “Advanced Vehicle Control and Safety
Systems-Design and Simulation”. Due to ever increasing traffic on the roads, the
tendency that the drivers face tough, complicated situations is increasing. Therefore,
built-in driver support systems to assist the drivers in hazardous situations are of
utmost importance. In this research, we shall focus on the study of some key
technologies of advanced vehicle control and safety systems. The group project
consists of six subprojects as:
1. Reliable Controller Design for Intelligent Active Suspension Systems of
2. Dynamic Optimal Slip Ratio Measurement and Intelligent Control for
Anti-lock Braking Systems to Track Dynamic Optimal Slip Ratio
3. A Study and Implementation of Advanced Vehicle Real-Time Foreground
Image Recognition System Based on Moving Object Image Detection
Technology
4. High-reliable Car-Following Control System Design
5. Distributed Network Monitoring and Control for Intelligent Automobile
6. Design and Implementation of a Vehicle Behavior's Simulator Using a
Six-Degree Platform
In this three year group project, the effectiveness of the developed subsystems shall be
verified by the simulated and experimental results in the real car and simulation car.
NSC 94-2213-E-009-125-（94N541）
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Title：High-reliable Car-Following Control System Design(1/2)
Principal Investigator：Lee Tsu-Tian
Keywords：Car-following , Fuzzy theory, Neural network, Time-delay, Fault
diagnosis, Reconfiguration
Transportation technology is one of the most influential areas on the human life.
Therefore, researchers have been involving in wide scope of related research activities
aiming to enhance efficiency, comfort, and safety of transportation systems. Due to
the ever growing number of vehicles on the roads, urban highways are congested and
need additional capacity. Though building new roadways sounds like the prominent
solution at the first glance, in practice it causes number of other unsolvable problems
mainly due to scarce of suitable lands. To this end, to increase the traffic capacity by
automating the traffic flow has been identified as a smarter option. Moreover, due to
ever increasing traffic on the roads, the tendency that the drivers face tough,
complicated situations is increasing. Safety issues due to driver weariness when
driving for long hours is another concern. Therefore, built-in driver support systems to
assist the drivers in hazardous situations are of utmost importance.
An automated vehicle following control system that enables the vehicle to
control the engine torque by its own keeping a prescribed safe distance from the
preceding vehicle is proposed. With the inclusion of complementary driver support
systems, the overall control system can mitigate driver’s work load and guarantee
much improved safety. Such a car-following collision prevention system usually
includes radar and vision sensors, micro-processors, antenna, and digital signal
processors (DSPs). This project will last three years.
In the first year, we will consider the problem of longitudinal control of a
platoon of automotive vehicles. We will utilize a fuzzy neural networks based
approach to solve intelligent automated car-following control problem. The control
approach will not use any communication links between the vehicles in the platoon.
An on-line tuning algorithm is derived in the Lyapunov sense and the stability will be
guaranteed even in the face of various road conditions.
Since the automated car-following control problem accounts for lots of efforts
that involve sensor system, antenna hardware programming and design associated
with microprocessors and DSPs, in the second year, we will continue our focus
mainly on the intelligent car-following control problem. Moreover, the problems of
lane changing, merging, and leaving the platoon will be addressed. A novel intelligent
automated car-following scheme using recurrent fuzzy neural networks will be
developed to cope with the inherent time delay problem caused by communication
and actuator delays.
System safety and reliability are the other most demanding issues to be
addressed. In the third year, the purpose of this project will be to develop systematic
design methodologies in order to achieve the designed systems to simultaneously
deliver desired performance, fault detection ability, and recognition capability.
Extensive simulations of automatic steering and throttle/brake performances will be
carried out to demonstrate the effectiveness of the developed tools and controllers.
Since the control algorithms would be model-free techniques and are tuned on-line
using Lyapunov-based adaptation laws, not only the control accuracy but also the
system stability can be guaranteed.
The wide range of applications of the developed technology will also include
flight control, power systems, nuclear power industry, process control, and
transportation systems.
NSC 94-2213-E-009-126-（94N542）
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Title: Study on Networked Control Systems
Principle Investigator: Lee Tsu-Tian
Sponsor: National Science Council
Keywords: Networked Control Systems, Stability, H control, Robust control
By a networked control system (NCS) we mean that a system with a control
loop being closed via the serial communication channel. NCS is widely used in many
complicated control systems, such as manufacturing plants, vehicles, aircraft, and
spacecraft. In NCS, serial communication networks are employed to exchange
information and control signals between spatially distributed system components,
like supervisory computer, controllers, and intelligent input-output devices (e.g.
smart sensors and actuators). The serial communication channel, which multiplexes
signals from the sensors to the controllers and/or from the controller to the actuators,
serves many other uses beside control. Therefore, we always want to design NCS
controllers with minimal network usage to avoid collisions. The stability analysis
and controller synthesis problems for NCSs are more difficult than the traditional
point-to-point connected control systems. This is because for NCSs, there may have
the problems of un-uniform sampling, network induced delay, packet loss, quantized
error, and finite transmission rate.
In this project, we will study some related problems of NCS. This project
focuses on the problem of reducing the data transmission rate in NCS. Three related
topics are studied. The first topic is scheduling-based networked control systems
design. We will study how network scheduling affects the stability and H
property of a NCS. Then we will find a method to design a scheduling-based NCS
controller such that it will stabilize the closed-loop system (and achieve the H
requirement) with minimal network usage. The second topic is
transmission-if-necessary-based networked control systems design. We will study
how to design a transmission-if-necessary-based NCS controller such that it will
stabilize the closed-loop system (and achieve the H requirement) with minimal
network usage, and related problems. The third topic is model-based networked
control systems design. We will study how to design a model-based NCS controller
such that it will stabilize the closed-loop system (and achieve the H requirement)
with minimal network usage, and related problems. All three topics we will take the
uncertainty into consideration.
NSC 94-2213-E-009-150-（94N546）
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Title：Study of Satellite’s Attitude Control Using Variable Structure Control Approach
Principal Investigator：Liang Yew-Wen
Keywords：Reliable control, Active and passive reliable control, Fault detection and
diagnosis, Spacecraft attitude control, Model uncertainties and external
disturbances
Due to the growing demands of system reliability in large-scale or complex
systems such as those in aerospace engineering, nuclear engineering and industrial
process, the study of reliable control has recently attracted considerable attention.
Among these systems, the attitude reliable control issue for satellite is also highly
important and attracted lots of attention since it is very expensive to retrieve a satellite
from space for repair when it malfunctions. In this project, we will study the attitude
reliable control of a satellite via the Variable Structure Reliable Control technique
(VSRC). The reason for employing the VSRC scheme is that it has the advantages of
fast response and small sensitivity to system parameter uncertainties and disturbance.
In addition, the VSRC scheme needs not the solution of Hamilton-Jacobi (HJ)
equation which is essential in implementing the reliable controller through the optimal
approaches such as H and LQR reliable designs. This project is about to study the
following subjects:
Set up the dynamical model of a satellite with input redundancy.
Design the passive attitude reliable control law for the satellite.
Develop a real-time and on-line fault detection and diagnosis mechanism.
Use the information of fault detection and diagnosis to design the active
reliable law.
Create the LQR or H reliable law for satellite control.
Use Taylor formula to derive the numerical solution of the HJ equation.
Compare the performances among the non-reliable and the three reliable
schemes.
Study reliable performances when system has model uncertainties and/or
disturbances.
NSC 94-2213-E-009-094（94N527）
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Title：A study of intelligent design scheme for anti-missile guidance (II)
Principal Investigator：Liang Yew-Wen and Liaw Der-Cherng
Keywords： Orbital trajectory estimation, Takagi-Sugeno fuzzy model, Variable
structure guidance law
According to various reliable reports, the Mainland China is continuously
strengthening their military force in the recent years, especially in the development of
ballistic missile. The increasing investment of China in the force inevitably results in
more and more threat to Taiwan. Meanwhile, because of the distance between Taiwan
and Mainland China is not long, it means that we do not have much time to react once
Taiwan is suffering a ballistic missile attack from Mainland China. Therefore, it is
important and urgent for Taiwan to develop an effective way to fast predict the orbital
trajectory of a ballistic missile, and to guide our interception missile to the place, at a
right time and right direction, where the ballistic missile is predicted to be. In this
project, we will develop the technique of fast orbital trajectory estimation of a ballistic
missile, and study the design of reliable interception guidance law for an anti-missile.
Details are as follows:
Predict the orbital trajectory of a ballistic missile.
Analyze and design the interception law for an anti-ballistic missile according to
the prediction of the ballistic missile’s trajectory.
Study the applicability of the Takagi-Sugeno fuzzy model to the estimation of
ballistic missile’s trajectory.
Study the applicability of the Takagi-Sugeno fuzzy model to the design of the
interception guidance law.
Study the applicability of the variable structure control technique to the design of
the interception guidance law
NSC 94-2623-7-009-005（94N009）
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Title：Development of An RFID-Based Platform for Human / Object Surveillance
(2/3)
Principal Investigator：Liaw Der-Cherng
Keywords：RFID, Database, Networking, Monitoring, Tracking
In the recent years, the study of auto-identification (AUTO-ID) or radio
frequency identification (RFID) in industrial or commercial applications has attracted
lots of attention. Several preliminary designs have been implemented in the
supermarket or the gate of the buildings for thief-prevention and security checking.
However, most of these designs may not be reliable and were implemented under
case-by-case study. In order to improve system reliability and provide a systematic
approach of design, in this three-year project we propose to add on an image
processing system and database system for human and object surveillance. The
project is integrated by five sub-projects, namely, the development of image
recognition technique, the development of RFID reader, the application of networking
in RFID application, the development of decision-making strategy and design of
database, and the development of RFID tag. Through the mutual cooperation between
sub-projects, it is expected to achieve the tasks of passive object surveillance, active
object surveillance, active object tracking, and system reliable strategy setup. In the
first year, we will focus on the preliminary concept design of RFID components,
image tracking model and system platform. It is followed by an experimental
verification of system design conducted on laboratory member and equipment
surveillance by using existing off-the-shelf RFID components. Moreover, the circuit
verification of the self-design RFID tag and reader will also be one of the main tasks
in the second year’s study. An overall system test and performance verification will be
carried on in the third year of project, which is proposed to conduct on a floor of
engineering building for human/object surveillance.
NSC 94-2213-E-009-099（94N532）
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Title：Development of Decision-Making Strategy and Design of Database (2/3)
Principal Investigator：Liaw Der-Cherng
Keywords：RFID, Database, Networking, Monitoring, Tracking
The techniques of auto-identification (AUTO-ID) or radio frequency
identification (RFID) have been recently applied to the security checking in
supermarket and/or the gate of the buildings for thief-prevention and security
monitoring. However, most of these designs may not be reliable and were
implemented under case-by-case study. In order to fulfill the performance
requirements for system reliability, in this three-year sub-project we will work on the
construction of a networking based database and the development of cooperative
and/or reliable strategy for human/object surveillance. In the first year, we will
focus on the preliminary design of image-plus-RFID based distributive
monitoring platform and the study of reliable scheme for digital monitoring
system. Moreover, we will also study the biologically inspired cooperative
scheme for possible application to object surveillance problem. The proposed
design will be experimentally verified in the second year of project by using
off-the-shelf RFID components. This verification will be conducted on the
surveillance of laboratory’s members and equipments with the help from other
four sub-projects. An overall system performance verification of the enhanced
design will be carried on in the third year of project, which is proposed to
conduct on a floor of engineering building for human/object surveillance.
NSC 94-2213-E-009-102（94N535）
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Title: A Study of the Simulation Optimization Algorithm and Software
Implementation (2/2)
Principle Investigator: Lin Shin-Yeu
Sponsor: National Science Council
Keyword:
Simulation optimization is one of the most frontier research areas in optimization.
The main characteristic of simulation optimization problem is the evaluation of the
objective function of an input-variable setting requires lengthy simulation. Therefore
we cannot use the conventional optimization techniques to solve them. There are
various simulation optimization problems such as stochastic optimization problems
with huge input-variable space and large scale optimization problems with decision
and discrete control variables.
In this project,we intend to categorize some classes of simulation optimization
problems and propose algorithms to solve them. Basically, in the simulation
optimization problem ,it is almost impossible to extract structural information of the
system analytically. Therefore, the proposed simulation optimization algorithms will
use simulations as a tool to extract the structural information. The extracted structural
information will be used in the proposed algorithm to reduce the searching space.
Such an iterative simulation optimization technique will use only reasonable
computation time to obtain a good enough solution.
We will use ordinal optimization theory to prove the quality of the solution we
obtain. In addition, we will compare our results with those obtained by the competing
methods such as the genetic algorithms,simulated annealing,and the tabu search
methods.
We will implement our algorithms in the form of commercial software for a more
general purpose.
NSC 94-2213-E-009-044-（94N515）
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Title：A study of Integration of the RFID system and Image Processing
Principal Investigator：Lin Sheng-Fuu
Keywords：Radio Frequency Identification (RFID), Tag, Receiver, Facial recognition
Due to the demand of information transmission efficiency, it is a very important
factor nowadays to acquire the information. Automatic identification procedure is
used to apply to people, animals, goods, or industrial products during transmission to
handle information efficiently. The RFID (radio frequency identification) system, as a
kind of automatic identification system, is designed to transfer energy and data
without contact. The transceiver can receive tags’ data simultaneously, even if there
are many RF tags to be detected.
Because the demand of tracking and controlling some specific people or objects,
we propose to use image processing technique here to add human face recognition
system to RFID system. The information of locating and tracking people can be
obtained by adding facial features in face database. Therefore, the RFID system will
have more powerful tracking and recognizing capabilities if the face recognition
technology is integrated with RFID system.
Till now, we have completed the image capturing and pre-processing, finding
configuration of moving object, finding facial image, and post-processing. In the next
year, we will focus on facial recognition, connecting and communicating with main
system, completing the rough system and experiments, comparing with existed
systems. And in the year after the next year, we will concentrate on optimizing the
system and the network, raising the recognition rate and the efficiency, and
completing system integrating and large-scale experiments.
NSC 94-2213-E-009-100-（94N533）
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Title: Design and Application of Physiological Signal-Based Human-Machine
Interface—A Novel Approach to Control Machine
Principle Investigator: Lin Chin-Teng
Sponsor: National Science Council
Keywords: Physiological Signal, Human-Machine Interface, Control Application.
Since the EEG was first described by Hans Berger in 1929, there have been
continuing efforts in developing new communication and control schemes, which do
not utilize the normal neuromuscular pathway. Today, along with the development in
the areas of electrical engineering, computer science, and biomedical engineering, it is
no longer a dream to use the physiological signals for control applications. This
multi-disciplined research has received much attention in the international community,
while it just started in Taiwan. In this three-year integration project, we propose to
develop a novel human-machine interface based on the physiological signals, and
intend to apply it for the control of computer, motion simulation platform, robot arm,
and others. As most of the current systems are still limited to be used within the
laboratory, our goal is to develop an interface that can be used in daily lives and also
industrial applications.
During the development of this human machine interface, we first need to have
measurement systems for physiological signals. After the stable, reliable signals have
been acquired, we will then perform signal analysis and interpretation to extract
suitable features. These features are further translated into proper motion commands
according to the given applications. Based on the descriptions above, six sub-projects
are proposed. Sub-project 1 develops a mental workload detection system based on
the virtual-reality dynamic motion simulation platform. It will demonstrate the
feasibility of detecting and modeling, in near real time, via multiple streams of
psycho-physiological information that organize operators’ cognitive states and
responses to task events. Based on physiological signal and facial expression,
sub-project 2 will develop a system to determine and judge the physical and metal
comfort so as to predict the health condition of a person. Sub-project 3 will develop
bioelectric source modeling, estimation, and analysis techniques for brain activation
imaging. These techniques can probe the temporal waveforms of the bioelectric brain
activities that are related to the control thoughts or specific events. Sub-project 4 will
design and manufacture a portable noninvasive measurement system for the
cardiovascular signals. It will be applied to study how the central and automatic
nervous systems can be related to the human machine interface. Sub-project 5 will
first analyze the relationship among the EEG, EMG, and resultant arm movement, and
then establish a model accordingly. The developed system will be used to control
human arm and also robot arm. Sub-project 6 will use optoelectronics and MEMS
technologies to design and manufacture a MEMS based wavelength tunable
multi-wave chips for physiology signals measurement system. With this measurement
system, different and adapted human physiology signals can be used to obtain in
depth physiology information.
The integration project will combine those systems developed in each
sub-project to form a multi-function physiological-signal-based human machine
interface. It will then be used to execute experiments based on the computer, motion
simulation platform, robot arm, and so on. All the sub-projects will join force to
establish the performance evaluation criteria for yielding the same standard in system
development. The setup of the criteria will consider the viewpoints from both biology
and engineering, and also those from the international research communities. This
project is expected to be a successful integration between the fields of biology and
engineering. Meanwhile, it also provides a platform for mutual cooperation and
learning, thus leading to wide extension of their capabilities and applications in both
fields.
NSC 94-2213-E-009-095-（94N528）
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Title: Mental Workload Detection in Human-Machine Interfaces Based on VR-based
Dynamic Motion Platforms
Principal Investigator: Lin Chin-Teng
Sponsor: National Science Council
Keywords:Mental workload, Virtual-reality, Physiological signal, Kinesthetic stimuli,
Portable real-time embedded system
In this project, we shall develop a Mental Workload (MWL) detection system
based on the Virtual-Reality (VR) dynamic motion simulation platform for the
next-generation physiological-signal-based human-machine interface. The goals of
this project are to demonstrate the feasibility of detecting and modeling, in near real
time via multiple streams of psychophysiological information that organize operators’
cognitive states and responses to task events. We will also develop and demonstrate a
human-computer interface that can assist operators working in an interactive
monitoring or command and control environment in maintaining a high sustained
cognitive capacity while minimizing performance lapses and errors of interpretation.
In order to apply the developed MWL detection system outside the psychophysiology
laboratory, we shall develop a portable real-time embedded system as the platform of
the next-generation physiological-signal-based human-machine interface.
During the following three years, we will focus our research on three major
topics including (1) Setting up of the VR-based physiological signal measurement
system to collect the physiological signals of the car drivers in various VR driving
environments. This system consists of a VR-car driving simulator to provide
kinesthetic/visual/auditory stimulus and some physiological signal measurement
equipments to record various physiological signals of a driver, simultaneously. We
shall also develop the approach for analyzing the physiological/mental characteristics
under different MWL. (2) Developing mental workload detection technology to
study human performance fluctuations, cognitive-state changes (e.g. drowsiness,
attention, etc) and accompanying correct, incorrect and absent motor responses in
attention-demanding cognitive tasks involving kinesthetic/visual/auditory stimulus
interpretation and decision-making. We shall also study the physiological signals
correlate of perceiving kinesthetic stimuli and construct the dynamic mental workload
model for MWL detection. (3) Designing and developing a portable real-time
embedded system. In order to apply the developed MWL detection system outside
the psychophysiology laboratory, we shall develop a portable real-time embedded
system as the platform of the physiological-signal-based human-machine interface.
This system should have low power-consumption (for portability) and high
computational capability (to process physiological signals). The MWL detection
technology developed in this project will be implemented into this portable real-time
embedded system and we shall continue to perform the final evaluation on the
real-time embedded system.
NSC 94-2213-E-009-096-（94N529）
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Title：Advanced Bio-inspired Computer Perception Algorithms/SoC Development
and Their Real-life Applications.
Principal Investigator：Lin Chin-Teng
Keywords：Bio-inspired engineering, Computer perceptual technology,
System-on-a-chip (SOC),Bio-inspired computer visual and hearing
perception,Bio-inspired perceptual neural networks, Home surveillance
system
Living organisms are complex systems exhibiting a range of desirable
characteristics, such as evolution, adaptation, perception and even high-level learning,
thinking and reasoning, that are difficult to realize using traditional engineering
methodologies. Recently, researchers have been allured to devote to study
bio-inspired engineering intending to develop advanced computer perceptual and
intelligent technology. The goal of this project is to construct a complete intelligent
computer perceptual technology and to implement this technology into a
system-on-a-chip (SOC) design based on our research experience on the development
of bio-inspired human perceptual technology in the past few years. In the following
three years, we shall apply the information engineering technology to realizing the
bio-inspired computer visual and hearing perception and combine the artificial
intelligent technology to the perspective developing system to make it more
humanistic and intelligent with self-constructing and learning abilities. Five major
research topics will be performed in this project: (1) Development of the bio-inspired
computer perceptual signal processing technology. (2) Development of bio-inspired
computer visual system. (3) Development of bio-inspired computer hearing system. (4)
Development and design of SOCs for bio-inspired perceptual neural network
hardware implementation. (5) Applying the bio-inspired computer perceptual
technology into the home surveillance system as an application example.
Topic 1 of this project combines human high-level logical thinking and reasoning
mechanism as well as low-level neural network training strategy to develop a series of
fuzzy neural networks (FNNs) as the kernel technology of other research topics for
computer perceptual signal processing. The FNNs also integrates the computer
perceptual signals, performs decision making, and can make the decision system more
humanistic and intelligent with self-constructing and learning abilities. Since vision
and hearing are two most important subsystem of bio perceptual system, Topics 2 and
3 shall firstly study the human visual and hearing subsystems and then develop the
bio-inspired computer visual and hearing processing technology. Topic 4 of this
project aims at designing and realizing the analog and digital circuits of various
bio-inspired computer reasoning strategy and perceptual signal processing technology
developed in Topics 1~3. Development of complete SOC hardware/software system
to integrate the developed multi-level bio-inspired computer perceptual technology is
also included in this topic. Topic 5 of this project is to integrate the bio-inspired
technology developed in Topics 1~4 into a home surveillance system as an application
example and the demonstration platform.
NSC 94-2213-E-009-149（94N545）
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Title： Wavelet tree based Digital Watermarking of copyright protection
Principal Investigator：Lin Yuan-pei
Sponsor： National Science Council
Keywords: Digital watermarking, Copyright protection, Tree marking
There has been great interest in embedding watermarks in digital data, e.g.,
image, and audio, for copyright protection, image authentication, proof of
ownership, etc. A reliable watermarking system will effectively discourage the
spreading of illegal copies and accelerate the exchange of digital data. In this
research project, we propose a wavelet based watermarking scheme for the
application of copyright protection. Ownership can be proved by extracting the
watermark embedded in the host image and illegal copies can be traced. For the
extracted watermark to be more
useful as a proof, the proposed scheme will be a blind watermarking system (original
image is not used in the watermark extraction process). Secret keys will be used in
watermark encoding so that the watermark can not be extracted or removed without
keys. The watermark bits will be embedded in the wavelet domain based on wavelet
trees. As wavelet trees correspond to various frequency bands, the watermarks will
be potentially more robust to frequency based attacks. Also the information of the
watermark bit is spread throughout large spatial regions. As a result, the watermarking
technique is robust to attacks in both frequency and time domains. We will evaluate
the proposed watermarking technique by applying nongeometric as well as geometric
attacks. The results from this research plan will have practical applications in the
development of watermarking systems for images.
NSC 94-2213-E-009-038（94N331）
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Title: System-on-Chip of the Driver and Control of a PM Brushless Sensorless
Motor
Principle Investigator: Lin Shir-Kuan
Sponsor: National Science Council
Keywords: Brushless DC motor, Sensorless control, IC design
This project tries to design an IC which implements the sensorless drive and
sensorless control algorithm for a permanent magnet brushless 3-phase motor
(PMBM). There have been several methods and patents in the sensorless drives of the
PMBM. The difficulty is not to use these existing methods, but lies in the
development of new technology to avoid the IP violation. The sensorless drive for a
PMBM can be divided into 4 steps: 1) position detection; 2) open-loop start-up
algorithm; 3) closed-loop sensorless drive; 4) closed-loop sensorless speed control.
This project will develop several new techniques for the first three steps, which will
also be applied for patents. The IC design of such a new sensorless drive for a PMBM
will be worked on an Altera Nios development system. The test of the resulting IC
prototype will also be conducted in this project.
NSC 94-2213-E-009-103（94N536）
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Title: Investigation of the Effect of Zen Meditation based on Bio-Resonance Sound
Diagnostic Mechanism
Principle Investigator: Lo Pei-Chen
Sponsor: National Science Council
Keywords: Zen meditation, Complementary and Alternative Medicine (CAM),
Bioenergetic Medicine, Intrinsic Data Field (IDF),
Electroencephalograph (EEG),Electrocardiograph (ECG), Visual Evoked
Potential (VEP), Intrinsic Data Field nalyzer (IDFA), Bio-Sound
Diagnostics, Quantum medicine
Due to the therapeutic effectiveness, the new area CAM (complementary and
alternative medicine) has drawn the attention of researchers and medical professionals
in the past decades. Researches in biomedical engineering and life sciences should lay
more stress on promoting the human health, in both the physiological and mental
aspects. As a matter of fact, scientists of the West have been reporting substantial
findings of the effectiveness of meditation practice in CAM not only on improving the
physiological and mental health but on treating a number of diseases. Accordingly,
the investigator has been devoted to the study of Zen-Buddhist meditation for the past
years. We investigate, from the viewpoint of biomedical engineering, phenomena of
the human life system under the orthodox Zen meditation practice. We study the
time-varying characteristics and dynamic mechanism during meditation course in
order to further establish the correlation among different electrophysiological signals
and parameters.
At the end of the twentieth century, life science and clinical medicine have begun
striding into the new, insubstantial realm of research --- bioenergetic medicine. It
states that all the living beings and the minerals consist of energy expressed in the
form of various frequencies, called the information field. Our body is the
simultaneous, integrating function of numerous information fields. The
acknowledgement of information field involved in everything in the universe makes
scientists in the pioneering research begin steering a new study, that is, the
exploration of Intrinsic Data Field (IDF). According to the theory of IDF analysis,
diseases may be re-defined as the weakness or deficiency of certain IDF frequency. In
addition, IDF may provide the following indexes of the human life system: spirituality,
creativity, state of mood, stress, stress-counter ability, organ functions, etc.
During the past five years, the principal investigator has been actively engaged in
the research study on the Zen-meditation physiological signals, with the focus mainly
on EEG (electroencephalograph), ECG (electrocardiograph), VEP (visual evoked
potential), etc. Although we have achieved some results of significance, data provided
by these mainstream medical instruments are limited to the physical quantities
reflecting the global variation of electrical potentials. In this research proposal, we
thus hope to inspect the physiological, spiritual, mood, …, or even conscious and
super-conscious states based on the IDF concept of bioenergetic medicine. Two CAM
instruments, ARDK quantum instrument and bio-sound diagnostics, will be applied to
the subjects for collecting references. Significance of this research work is at its
prospect of providing scientific evidence and academic interpretation for the human
life characteristics under Zen meditation as well as the mechanism of health
promotion by the Zen practice.
NSC 94-2213-E-009-136（94N398）
-------------------------------------------------------------------------------------------------------
Title：Design and Applications of Agent-Based Interactive Control for Robotic
Systems
Principal Investigator：Song Kai-Tai
Keywords：Intelligent Agents, Multi-Agent Systems, Robot Control, Sound Direction
Recognition, Personal Robots
In recent years, the research in robotic systems has progressed to a new era, i.e.
robots that come into human life. To enable robots merge into human life, one needs
to develop a reliable, safe and easy to use robot command interface. This interface
must provide a real-time response of the robot in order to guarantee safety as well as
actual functionality. Robots that can learn and adapted to personal inclination of their
user are highly expected. This project involves the development of an agent-based
control system, which fulfills the requirement of the above-mentioned characteristics.
The purpose of this approach is to build an open, structured modulized and
standardized platform for robot control development. Moreover, several interesting
demonstrations such as human robot interaction control, real-time image tracking will
be carried out in order to evaluate the performance of the developed architecture. We
plan to complete this project in three years. In the first year, the main objective is to
develop a platform for agent-based hybrid control architecture. The second year will
forms on the design and implementation of the personal assistant robot. The third year
mainly concerns the system integration of the personal assistant robot and the
reification of the multi-agent architecture. Based on the results of previous project on
advanced home robot, we feel confident to complete the goals of this project in three
years.
NSC 94-2213-E-009 -045 (94N516)
-------------------------------------------------------------------------------------------------------
Title: Intelligent Mixed Signal Sensor Circuit Design
Principle Investigator: Su Chan-Chin
Sponsor: National Science Council
Key words: Sensor Circuit, Analog Circuit, Mixed Signal Circuit, SoC, Bio Sensor
Subproject 4：Smart Mixed Signal Sensor Circuit Design
As revealed in ITRS2001, MEMS and Chemical Sensor are begin to be integrated
into SoC. The application domains include, bio, medical, chemical, mechanical, and
transportation that are closely related to our daily life. It is estimated that in 2010, they
will create another peak for semiconductor industry and integrated circuit industry. As of
today, we are more familiar with digital circuits than the analog sensor circuits. The goal
of this project is to study the low-voltage low-power analog and mixed signal sensor
integrated circuits.
This project proposes smart low-voltage low-power analog and mixed signal sensor
circuits. It amplifies the small signal from MEMS and chemical sensors and sends to
low-power and low-voltage requirement is to meet the critical power requirement in
invasive environment. The smart feature is to activate or shut down certain modules
depending on the signal level. With which, the power can be further reduced.
Smart Mixed Signal Circuit is a distinguishing feature of this project. The function is
to use a simple mechanism to detect the signal level to determine the activated modules
and the biasing current within the module to reduce the power consumption. It can be
regarded as a combination of macro and micro power management mechanisms. A
biomedical signal, such as electrocadiogram and lung sound, is a transient signal. They all
appear in a short period of time with certain frequency. If the circuit can take the
advantage of the signal property, turn of or reduce biasing current while there is no signal,
then the overall power consumption can be significantly reduced.
After detail study and evaluation, the project proposes the sensor interface including
those for resistance, capacitance, and inductance measurement. The micro watt amplifiers
include current, voltage, and charge amplifiers. These include that to be used in the test
vehicle proposed in subproject 3 for measuring the capacitance, resistance, or inductance
change in the MEMS but also for the applications mentioned earlier.
The goal of this project, in addition to the design, implementation, and testing of the
sensor circuits, we would like to adopt the modules in Subproject 5 to integrate a sensor
subsystem, as shown in the figure below. It can be integrated into a platform based sensor
system SoC. Users are able to use software to change the circuit parameters for the target
applications. Or, users can take certain part of the circuits for a specific application IC to
reduce the power consumption.
NSC 94-2215-E-009-052（94N575）
-----------------------------------------------------------------------------------------------
Title：Advanced Test Technology Development for RF Circuits and Systems
Principal Investigator：Su Chan-Chin
Keywords：
After years of development, wireless communication has become essential for
telephony and data communication. In mobile communication, there are many
different standards and systems in use simultaneously, such as GSM, DECT, PHS,
GPRS, WCDMA, CDMA2000. In data communication, Bluetooth and 802.11 are
competing for market acceptance. Therefore, RF circuit design and applications are
wide and extensive. Furthermore, in wired communication, fiber and high speed
copper wired serial links are all fall in RF frequency range. Due to its high added
value, design houses, foundry, and system houses are focus on this sector of
semiconductor industry in order to make high profit margin. However, the testing of
RF circuits and systems are not well developed as design and manufacturing.
Traditionally, RF circuit and system test are achieved in two ways. The first one
is to use specialized instrument to send and receive high quality RF signals to
determine the circuit parameters and go-no-go of the circuits. The disadvantage is the
cost overhead. The instrument in RF range is not only expensive but also very
difficult to operate and maintain. It seems that it is difficult to meet the requirement of
low cost mobile hone handset or wireless local area network. The second type uses
the loop back mechanism for the test. The digital data is sent by the transmitter and
received and recovered by the receivers. It checks the bit-error rate (BER) of the
received data to determine the function of the CUT. It has the properties opposite to
the first method. The test equipment cost is low. But, the test time is very long.
In this project, we would like to propose an RF test methodology which take the
advantage of the RF system architectures nowadays. We utile the built-in
analog/digital (AD/DA) converters and digital signal processors (DSP) as the test
resources for the test. The DSP is responsible for sending digital IF signal to the DAC.
DAC then coverts the discrete signal into analog signal. After that, it is up converted
into RF band by the RF transmitter module. The RF receiver module receives the RF
signal and down converts it into IF band. The ADC convert it into digital form. Finally,
the DSP collects the received digital signal and use DSP techniques to extract the
circuit parameters. The DSP techniques will be based on the “intrinsic response
extraction” we proposed earlier [1-8]. Without the affections of other modules, this
technique is able to extract the intrinsic responses. By this means, the test cost is
minimal because the AD/DA converters and DSP modules are built in already. There
is no external RF ATE needed.
NSC 94-2215-E-009-079（94N602）
------------------------------------------------------------------------------------------------
Title：Design and Implementation of a Digital Programmable PFC-PWM Control IC
(3/3)
Principal Investigator：Tzou, Ying-Yu
Keywords：Digital power control IC, Mixed-mode signal IC design, Power factor
correction control, Pulsewidth modulation control, Switching power
supply
This project makes a research on the design and implementation of a digital
PFC-PWM combination control IC for off-line single-phase switching-mode power
supplies. The combination of the power factor control and pulsewidth modulation
control can greatly simplify the control circuitry. The rising edge switching of the
PFC switch with synchronization of the trailing edge switching of the PWM switch
can minimize the output voltage ripples. The abstract of this three-year project is
described as follows:
The 1st-year: A Research on the Digital Control Architecture for the PFC-PWM
Combination Control
During the first year of this project we will make a study on control architectures
suitable for the PFC-PWM combination control of off-line switching power supplies.
A digital programmable PFC-PWM control scheme will be proposed in applications
to single-phase switching power supplies with a boost PFC input converter and a
flyback output converter. Numerical realization issues for the PFC-PWM control will
be studied. Simulation-oriented analysis will be carried out to study the feasibility of
the proposed control scheme. Experimental verification will be carried out using a
designed CPLD-based programmable digital controller.
The 2nd-year: Design and Implementation of a Digital PFC-PWM combination
Control IC for Off-Line Switching Power Supplies
In the second year of this project we will design a digital PFC-PWM control IC
according to the proposed digital control scheme of the previous research. The
research will focus on the design and optimization of specific circuits used in the
PFC-PWM control IC. In order to apply the proposed control multi output PWM
generator will be designed. A fully-digital control scheme will be developed and
verified using a CPLD-based digital control board. Practical hardware realization
issues will be studied using simulation-oriented analysis.
The 3rd-year: Design and Implementation of a Mixed-Mode PFC-PWM
Combination Control IC for Off-Line Switching Power Supplies
The control of high-performance AC-DC and DC-DC converters usually employ
fast response inner-loop current controller. This research will apply mixed-mode
design techniques for the synthesis of a PFC-PWM combination control IC. The inner
current loop controller will be realized using analog technique and the outer voltage
loop controller will be realized using digital technique. Simulation oriented analysis
and design will be used in the synthesis of this mixed-mode PFC-PWM control IC. A
systematic design procedure will be developed for the design and implementation of
mixed-mode control IC design for switching-mode power converters.
NSC 94-2213-E-009-146（94N408）
------------------------------------------------------------------------------------------------
Title：Design and Implementation of Optimal On-Line Intelligent Control
Systems(3/3)
Principal Investigator：Wang Chi-Hsu
Keywords：Fuzzy Logic, Neural Network, Real-time Control System
This project is to explore the theoretical and practical issues of real-time
applications of FNN (Fuzzy Neural Network) for linear and nonlinear dynamical
systems. This project will firstly to develop the modified dynamical optimal training
for a certain class of FNN. Different kinds of FNN will require different
considerations in the optimal training algorithm. Under real-time environment, there
is very little time for the training of FNN. Therefore the FNN must be optimally
trained with maximum error reduction in minimum time period. The optimally trained
FNN can then be used as a controller or as part of lease-squared identification, all in
real-time environment. Secondly a new practical closed-loop model for real-time
control system will be proposed. This is to consider the unavoidable time delay
incurred in the optimal training of FNN and/or other computational effort. It is hoped
that the maximum allowable computation time for the FNN can be found. This result
will be valuable due to the fact that the maximum allowable computational time can
be used to select the speed of the computer hardware for economical design. The
above issues will be conducted in the first and second years using computer
simulation. The true hardware implementation using several popular plants, such as
the inverted pendulum, the Chua’s chaotic circuit, …, etc., will be conducted in the
third year under VisSim/Pro (Matlab plus DSP card) for real-time FNN-based control.
NSC 94-2213-E-009-014-（94N513）
-----------------------------------------------------------------------------------------------
Title：The Study of Image Processing and Ergonomics Based Intelligent Safety and Comfortable
Driving System (1/3)
Principal Investigator：Wu Bing-Fei
Keywords：Car following,Lane changing,Stop and go,Driving recorder,Mobile
surveillance
The main project will focus on the intelligent safety and comfortable driving
system.
Besides of the integration of signal processing, the human technology is also
considered. The project goals including car following、lane changing、stop and go、
driving recorder、actively mobile surveillance system、noise cancellation device、and
comfortable mechanisms for vehicles are developed by six subprojects to handle the
corresponding studies and achieve the common research target.
This project is a highly integrated study on image processing and ergonomics. In
theimage processing part, three topics are covered：real-time lane detection、obstacle
detection and image compression. In the ergonomics part, three topics are studied:
comfortable cabin car communication system, mechanisms, and cruise safety control
system. Finally, the research results will be integrated to realize the mail project goals.
The execution of this project can promote the research to the international level,
especially the ergonomics studies on the safety driving system.
NSC 94-2213-E-009-062-（94N343）
-----------------------------------------------------------------------------------------------
Title：Subproject 1:Image Processing Based Real-Time Lane Detection and Head
Light Identification with Tough Weather Condition (1/3)
Principal Investigator：Wu Bing-Fei
This project focuses on the development of real time vision processing and
recognition image coming from the CCD cameras installed in vehicles. The image
information includes the lanes, the head and tail lights, and the road signs, which can
provide the other subprojects to achieve the goals of the main project. The
technologies developed in this project play role of the driving assistant to keep the
dangerous driving behavior off. For this issue, the lane, head and tail light, and the
road sign information will be processed and transferred to related subprojects to
realize the scheduled achievements of the main project, an Intelligent Safety and
Comfortable Driving System.
The image detection and recognition will be studied year by year. The real-time
head-light recognition will be completed and integrated with lane detection. The work
in the second year will focus on the tail-light detection and the lane detection on the
rainy day. The road sign detection and the adaptive lane detection study will be
accomplished in the last year.
NSC 94-2213-E-009-066-（94N347）
-----------------------------------------------------------------------------------------------
Title：The study of a high security surveillance system with the integration of DWT
and DCT and video/audio synchronization
Principal Investigator：Wu Bing-Fei
Keywords：Discrete Wavelet Transform, Discrete Cosine Transform, MP3, AES,
Surveillance System
This project focuses on the development of a high performance and high security
Video/Audio surveillance system. In this project, an innovative video compression
method that integrates Discrete Wavelet Transform and Discrete Cosine Transform is
proposed. Furthermore, in order to enhance the functionality, the intelligent image
compression techniques will be developed. The recognizable ability of the important
part of the surveillance images will be better, and the compression ratio will be higher.
Moreover, the low complexity MP3 audio compression method, Real-time Transport
Protocol and the programmable AES cryptography system are merged, too. The users
can not only see the image but also hear the sound of their targets, and the secret
information of the users can be radically protected. Besides, the mobile
communication devices are also combined in order to reach the goal that the users can
view the high quality surveillance images at anywhere and anytime.
The content of the project are separated into three parts: (1) Increase the speed
and the quality of the image compression method, integrated MP3 audio compression
technique, implement the hardware of the programmable AES cryptography system,
and integrate the mobile communication devices. (2) Design the image compression
method that combine DWT with DCT, and develop intelligent image compression
techniques. (3) Implement the whole system by using a low cost embedded system
and a dedicating hardware. The final objective of this project is to accomplish an
intelligent and high speed embedded surveillance system.
NSC 94-2213-E-009-067-（94N348）
-----------------------------------------------------------------------------------------------
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wang nianwu http://
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2014-07-14 18:04:30
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https://space.stackexchange.com/questions/49505/do-rockets-leave-launch-pad-at-full-thrust
|
# Do rockets leave launch pad at full thrust?
Rockets always seem to launch slower than I expect them for the thrust they can produce. Do they really launch off the pad at maximum thrust? Or do they launch at lower thrust until they clear the tower? I'm always surprised when I see how slow they seem to budge from the pad. I know they're massive, but still.
• Curious if Shuttle launches also seem slow to you; they always looked like they got off the pad fast to me. – DylanSp Jan 10 at 16:54
• Shuttle's acceleration off the pad was significantly higher than some -- initial TWR was around 1.4:1 IIRC, as compared with 1.2:1 for many other launchers, so the initial acceleration would appear twice as fast as something like a Saturn V. – Russell Borogove Jan 10 at 17:05
• IIRC, for the US launches, the paradigm is "release clamps / bolts once nominal thrust is reached" - usually 100%. For Russian launches, the rocket is released and starts climbing as soon as TWR exceeds 1, and it takes a moment until the power ramps up to maximum. – SF. Jan 11 at 12:58
• You're probably used to small rockets like sounding rockets (VSB-30, etc) where the TWR can get up to 100:1, so they take off like a bat out of hell (10-100g acceleration) with short burns of 10-20 seconds. They're already starting a second stage burn before something like Atlas or Dragon even clears the tower. As rockets get larger, maintaining such a TWR is not practical. – J... Jan 11 at 16:07
• @RodneyP.Barbati: If you're gonna do that it's better to go full throttle ASAP and throttle down on reaching Mach 1. You want to fly not hover. – Joshua Jan 11 at 23:23
## 3 Answers
As in many things, shuttle was an exception, the answer for it is No.
At liftoff the Space Shuttle Main Engines were running at a throttle setting of 100% of their rated power level. About 4 seconds after liftoff they throttled up to 104.5%. The maximum emergency throttle setting was 109%, but this was never used in flight.
Screenshot from a Shuttle Mission Simulator run showing the commands from T-4 through the thrust bucket.
(the commands at 1:22 are a response to a failure inserted into the sim run)
• A pettier man than I would argue that 100% RPL is "full thrust" as per the question title, but the body of the question indeed asks about "maximum thrust", so you win a +1. – Russell Borogove Jan 11 at 18:36
• @RussellBorogove only a pettifogging pedant would point that that 109% was called Full Power Level – Organic Marble Jan 11 at 18:45
• @OrganicMarble - so they did turn it up to 11? – Jon Custer Jan 11 at 23:51
• @JonCuster almost - 10.9! – Organic Marble Jan 12 at 21:50
Rockets always seem to launch slower than I expect them for the thrust they can produce. Do they really launch off the pad at maximum thrust?
In most cases, yes.
For most orbital launchers, over 90% of the mass at liftoff consists of propellant. As the propellant is burned and exhausted, the mass rapidly decreases, and the rate of acceleration increases in inverse proportion. In fact, if the thrust remains constant, acceleration would become far too high over the course of an ascent from the surface to Earth orbit. Staging manages this by dropping the big first-stage engines (and empty tankage) and switching to a smaller set of engines. Some launchers shut down (e.g. Saturn IB, Saturn V) or throttle down (e.g. Falcon 9, STS) engines to limit acceleration as well.
The performance (in terms of payload to a given orbit) increases as propellant load increases, so typical launchers have a liftoff thrust-to-weight ratio in the 1.2-1.4:1 range, yielding just enough acceleration to safely clear the tower.
• Not off the top of my head other than generally around 10 seconds; there are many videos of launches available on YouTube. – Russell Borogove Jan 10 at 4:25
• Worth pointing out the shuttle has throttled down to about 70% by the time it reaches main engine cutoff. This is because as the launch progresses, the vehicle gets lighter and lighter, so to prevent excessive g forces is gradually reduces thrust – Innovine Jan 10 at 12:22
• @CharlesStaats No, I was just hedging in case someone pulled an 89% propellant fraction example out of their back pocket. – Russell Borogove Jan 10 at 15:46
• Accelerating at 0.2 g is about 2 m/sec^2. The height after t seconds is nicely t^2 meters. To clear a 100m tower takes 10 seconds. – Ross Millikan Jan 10 at 16:06
• @Alex I suspect what's tripping you is that rockets are really really big, and their acceleration profile is very different from the objects you're familiar with - their initial acceleration appears relatively slow, but unlike a car, it just keeps accelerating faster and faster (until it runs out or is throttled down). – Luaan Jan 12 at 13:47
I'm always surprised when I see how slow they seem to budge from the pad. I know they're massive, but still.
Remember that when you are in the vehicle, what you feel is acceleration, not speed, but when you are outside looking at it, what you see is mostly speed, not acceleration.
Speed obviously starts at 0, and is the the result of the integration of acceleration.
Based on thrust-to-weight ratios of 1.2 to 1.4, this results in a net acceleration of $$0.2g$$ to $$0.4g$$. Let's consider the $$0.2g$$ case.
Speed will then be $$v=0.2g.t$$. After 1 second, speed will be less than $$2m/s$$, about $$7 km/h$$. That definitely looks very slow.
But that increases linearly (if we ignore the fuel burn, for now), so 10 seconds later it reaches $$70 km/h$$ and a minute later it's about $$420 km/h$$. Starts to look a bit faster, but the rocket will have cleared the tower for quite a while already.
We can actually compute at what point the tower is cleared: the height of the rocket is another integration of speed, so $$h=0.1g.t^{2}$$ and $$t=\sqrt{10h/g}$$. For a tower height of $$100 m$$, the tower is cleared at about $$t=10 s$$ (Saturn V cleared the tower at about 12 seconds).
So 10 to 12 seconds to clear 100 m, that indeed looks very slow. But that's only the beginning, and as speed increases at least linearly with time, minutes later the rocket reaches thousands of $$km/h$$.
Even better, as the rocket is burning fuel, its mass reduces, while the thrust could remain constant, so the thrust-to-weight ratio and the acceleration increase. In the case of Saturn V, 135 seconds after lift-off, total acceleration (including gravity) had already increased from the initial $$1.2g$$ to $$4g$$, and it was actually capped at $$4g$$ by stopping one of the engines. Add to that the fact that the rocket will switch from vertical (where gravity is deducted from thrust) to nearly horizontal (where it isn't), and you moved from $$0.2g$$ net acceleration to $$4g$$ in a bit over 2 minutes!
So, all in all, a lot of thrust, but a lot of weight, so a net acceleration which is initially relatively modest, which explains the pretty "slow" lift-off.
For comparison, if we took the same Saturn V first stage, but without the upper stages, and with only 10% of its fuel capacity, we would have a thrust-to-weight ratio of about 10, so net acceleration would be $$9g$$, and it would clear the 100 m tower in 1.5 seconds, at which point it would already have a speed over $$450 km/h$$! Of course, it wouldn't go very far after that, as it would run out of propellant in less than 15 seconds...
• To add another interesting number, the Saturn V first stage burns for about 150 seconds, so just clearing the tower takes almost 7% of the first stage propellant. – J... Jan 11 at 16:27
• @JoeJobs Amateur rockets get nowhere near the altitude or speed required to put a satellite in orbit or send a spacecraft to outer space. So they need a lot less propellant (they usually burn for a very short time), and can have a very high thrust to weight ratio. See the example in the last paragraph: same thrust, less weight, much much quicker take off. – jcaron Jan 11 at 21:46
• @JoeJobs ... except that it would probably break from an acceleration that high. – fraxinus Jan 12 at 7:05
• @JoeJobs see en.wikipedia.org/wiki/Sprint_(missile) – GremlinWranger Jan 12 at 8:14
• @JoeJobs If Falcon 9 took off with 40:1 TWR all the satellites and crew inside would be broken or dead. – J... Jan 12 at 15:33
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2021-05-14 02:16:23
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https://itectec.com/superuser/windows-location-option-missing-from-appdatalocal-others-why/
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# Windows – Location option missing from AppData\Local, others. Why
user-profileswindows 8windows 8.1
I'm in the same boat that it appears a lot of users are in. Precious little SSD space and an set of AppData folders in my profile that are constantly expanding in size. I would like to move this stuff off to a much larger non-SSD drive (E:).
I followed this piece of advice to move that bloat and, at first, it seemed to work. I was able to go to the properties of these three folders in AppData:
• Local
• LocalLow
• Roaming
And each had a Location tab in properties, giving the option to relocate these folders. The relocate process appeared to work fine for LocalLow and Roaming, but the process sputtered and fizzled on Local with these files (they couldn't be moved because they were in use):
• UsrClass.dat
• UsrClass.dat.log1
• UsrClass.dat.log2
Now, even though it appeared that the relocate process for LocalLow and Roaming worked, it actually didn't: when I navigate into those folders from my profile on my desktop, these folders are all still pointing to their original locations. All of these folders point to C:\Users[MyAccount]\AppData… instead of E:\Users… like I had wanted.
As well, the Location tab is now gone from the property dialog. I'm not crazy; I know it was there before.
So, two questions:
• Why is the Location tab now missing from these folders' property pages?
• Is there actually any way to relocate these files?
• You need to be inside the AppData folder.
• Move the Local folder to E: drive
mklink /j C:\Users[MyAccount]\AppData\Local <Full path to target>
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2021-12-07 09:58:42
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https://eprint.iacr.org/2020/431
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### x-only point addition formula and faster compressed SIKE
Geovandro Pereira, Javad Doliskani, and David Jao
##### Abstract
The optimization of the main key compression bottlenecks of the supersingular isogeny key encapsulation mechanism (SIKE) has been a target of research in the last few years. Significant improvements were introduced in the recent works of Costello et al. and Zanon et al. The combination of the techniques in previous works reduced the running time of binary torsion basis generation in decompression by a factor of 29 compared to previous work. On the other hand, generating such a basis still takes almost a million cycles on an Intel Core i5-6267U Skylake. In this paper, we continue the work of Zanon et al. and introduce a technique that drops the complexity of binary torsion basis generation by a factor log p in the number of underlying field multiplications. In particular, our experimental results show that a basis can be generated in about 1,300 cycles, attaining an improvement by a factor more than 600. Although this result eliminates one of the key compression bottlenecks, many other bottlenecks remain. In addition, we give further improvements for the ternary torsion generation with significant impact on the related decompression procedure. Moreover, a new trade-off between ciphertext sizes vs decapsulation speed and storage is introduced and achieves a 1.7 times faster decapsulation.
Available format(s)
Category
Implementation
Publication info
Published elsewhere. MINOR revision.Journal of Cryptographic Engineering
DOI
10.1007/s13389-020-00245-4
Keywords
Post-quantum cryptographySupersingular elliptic curvesPublic-key compressionDiffie-Hellman key exchange
Contact author(s)
geovandro pereira @ uwaterloo ca
History
2021-04-08: last of 2 revisions
See all versions
Short URL
https://ia.cr/2020/431
CC BY
BibTeX
@misc{cryptoeprint:2020/431,
author = {Geovandro Pereira and Javad Doliskani and David Jao},
title = {x-only point addition formula and faster compressed SIKE},
howpublished = {Cryptology ePrint Archive, Paper 2020/431},
year = {2020},
doi = {10.1007/s13389-020-00245-4},
note = {\url{https://eprint.iacr.org/2020/431}},
url = {https://eprint.iacr.org/2020/431}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.
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2022-12-09 05:28:06
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https://www.esaral.com/q/in-the-matrix-10630
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# In the matrix
Question:
In the matrix $A=\left[\begin{array}{cccc}2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt{3} & 1 & -5 & 17\end{array}\right]$, write:
(i) The order of the matrix
(ii) The number of elements,
(iii) Write the elements $a_{13}, a_{21}, a_{33}, a_{24}, a_{23}$
Solution:
(i) In the given matrix, the number of rows is 3 and the number of columns is 4. Therefore, the order of the matrix is 3 × 4.
(ii) Since the order of the matrix is 3 × 4, there are 3 × 4 = 12 elements in it.
(iii) $a_{13}=19, a_{21}=35, a_{33}=-5, a_{24}=12, a_{23}=\frac{5}{2}$
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2023-03-21 10:29:50
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http://www.rnta.eu/4MSRNTA/abstcont1.html
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# Abstracts Session 1
On some conjectures on the Mordell-Weil and the Tate-Shafarevich of an Abelian variety Andrea Surroca Following Manin's approach, we propose conjectural upper bounds for 1) the Néron-Tate height of the elements of a system of generators of the Mordell-Weil group of an Abelian variety, as well as for 2) the cardinality of its Tate-Shafarevich group. We extend Manin's approach, initially for elliptic curves over the rationals (as re-visited by Lang and Golfeld-Szpiro), to an Abelian variety of arbitrary dimension, over an arbitrary number field. The dependence of the bounds is explicit in all the parameters, and the bounds given here are not conjectured but are implied by strong but nowadays classical conjectures: Birch and Swinnerton-Dyer conjecture, Hasse-Weil conjecture. On once hand, point 1) extends in higher dimension and for arbitrary number fields a conjecture of Lang. On the other hand, assuming also Szpiro's conjectures, with point 2) we extends a theorem of Goldfeld-Szpiro to Abelian varieties of arbitrary dimension $g$ over any number field $K$, and improved it in the case $g=1$ and $K$ the field of rational numbers.
Reductions of elliptic curves Antonella Perucca (University of Luxembourg) Let $E$ be an elliptic curve defined over a number field $K$. Fix some prime number $\ell$. If $\alpha \in E(K)$ is a point of infinite order, we consider the set of primes $\mathfrak p$ of $K$ such that the reduction $(\alpha \bmod \mathfrak p)$ is well-defined and has order coprime to $\ell$. This set admits a natural density. By refining the method of R. Jones and J. Rouse (2010), we can express the density as an $\ell$-adic integral. We also prove that the density is a rational number whose denominator (up to powers of $\ell$) is uniformly bounded in a very strong sense. Finally, we describe a strategy for computing the density which covers every possible case. This is joint work with Davide Lombardo (University of Pisa).
On cyclic extensions Bayarmagnai Gombodorj (National University of Mongolia) Let $n\geq 3$ be an integer and $\zeta_n$ be a primitive $n$-th root of unity. We will present a description of cyclic extensions of degree n in terms of $k$-rational points of the tori when the base field $k$ contains $\zeta_n + \zeta_{n}^{-1}$.
The Prime Geodesic Theorem in the 3-dimensional hyperbolic space Dimitrios Chatzakos (CEMPI, Lille and Université de Lille) The Prime Geodesic Theorem studies the asymptotic behaviour of lengths of primitive closed geodesics on hyperbolic manifolds. For $2$-dimensional manifolds this problem was first studied by Huber and Selberg. It turns out that the lengths of these geodesics obey an asymptotic distribution analogous to the Prime Number Theorem, and the error term has been extensively studied by use of the Selberg and the Kuznetsov trace formulas. In this talk, we discuss the Prime Geodesic Theorem on $3$-dimensional hyperbolic manifolds. For the Picard manifold, we improve on the classical pointwise bound of Sarnak, using the Kuznetsov formula combined with a recent large sieve inequality of Watt. Further, for a 3-manifold of finite area, we study the second moment of the error term using the Selberg trace formula. This is a joint work in progress with Giacomo Cherubini and Niko Laaksonen.
Geometric primality tests using curves of genus 1 and 2 Eduardo Ruiz Duarte (Rijksuniversiteit Groningen) We revisit and generalize some geometric techniques behind deterministic primality testing for some integer sequences using curves of genus 1 over finite rings. Subsequently we develop a similar primality test using the Jacobian of a genus 2 curve.
Unlikely Intersections in families of abelian varieties Fabrizio Barroero(Universität Basel) Two varieties whose dimensions do not sum up to at least the dimension of the ambient space should not intersect. This is the guiding philosophy that led several authors to propose conjectures about subvarieties of commutative algebraic groups and of Shimura varieties. After a brief historic introduction we will talk about results for curves in families of abelian varieties, mostly obtained in collaboration with Laura Capuano.
Expansions of quadratic numbers in a $p$-adic continued fraction Laura Capuano (University of Oxford) It goes back to Lagrange that a real quadratic irrational always has a periodic continued fraction. Starting from decades ago, several authors generalised proposed different definitions of a $p$-adic continued fraction, and the definition depends on the chosen system of residues mod $p$. It turns out that the theory of $p$-adic continued fractions has many differences with respect to the real case; in particular, no analogue of Lagrange's theorem holds, and the problem of deciding whether the continued fraction is periodic or not seemed to be not known. In recent work with F. Veneziano and U. Zannier we investigated the expansion of quadratic irrationals, for the p-adic continued fractions introduced by Ruban, giving an effective criterion to establish the possible periodicity of the expansion. This criterion, somewhat surprisingly, depends on the real value of the p-adic continued fraction.
Explicit Small Height Bound for $\mathbb{Q} (E_\text{tor})$ Linda Frey (Universität Basel) Let $E$ be an elliptic curve defined over $\mathbb{Q}$. We will show that there exists an explicit constant $C$ which is only dependent on the conductor and the $j-$invariant of $E$ such that the absolute logarithmic Weil height of an $\alpha \in \mathbb{Q} (E_\text{tor})^*\setminus \mu_\infty$ is always greater than $C$ where $E_\text{tor}$ denotes all the torsion points of $E$ and $\mu_\infty$ are the roots of unity.
Counting rational points on genus one curvesManh Hung Tran (Chalmers University) The density of integral solutions of Diophantine equations can also be viewed geometrically as the density of integral points on algebraic varieties which is one of the classical problems in Diophantine geometry. We are interested in the case of projective varieties defined by homogeneous polynomials and this gives rise to the study of rational points on such varieties. In this talk we focus on smooth genus one curves which are closely related to elliptic curves. We give uniform upper bounds for the number of rational points of bounded height on smooth genus one curves in two forms: plane cubic curves and complete intersections of two quadric surfaces. The main tools to study this problem are descent and determinant methods.
Isomorphism classes of Abelian varieties over finite fields Stefano Marseglia (Stockholms Universitet) Deligne proved that the category of ordinary abelian varieties over a finite field is equivalent to the category of free finitely generated abelian groups endowed with an endomorphism satisfying certain easy-to-state axioms. Centeleghe and Stix extended this equivalence to all isogeny classes of abelian varieties over ${\mathbb F}_p$ without real Weil numbers. Using these descriptions, under some extra assumption on the isogeny class, we obtain that in order to compute the isomorphism classes of abelian varieties we need to calculate the isomorphism classes of (non necessarily invertible) fractional ideals of some orders in certain étale algebras over ${\mathbb Q}$. We present a concrete algorithm to perform these tasks and, for the ordinary case, to compute the polarizations and also the automorphisms of the polarized abelian variety.
New instances of the Mumford-Tate conjecture and further applications Victoria Cantoral Farfan (International Center for Theoretical Physics, Trieste) In this talk we will present new cases of the Mumford-Tate conjecture for abelian varieties defined over number fields. Moreover we will discuss some further applications in the direction of the Sato-Tate conjecture.
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2018-06-20 14:49:47
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https://community.oilprice.com/topic/23356-green-new-deal-blizzard-of-lies/page/299/?tab=comments#comment-196229
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JM
# GREEN NEW DEAL = BLIZZARD OF LIES
## Recommended Posts
6 hours ago, specinho said:
Not too sure how that works out but consider this:
1. www.pmel.noaa.gov> eoi > education > pressure
If you are at sea level, each square inch of your surface is subjected to a force of 14.6 pounds. The pressure increases about one atmosphere for every 10 meters of water depth.
2.
Carbon dioxide has no liquid state at pressures below 5.1 atm.
( which is > 50 meters below sea water).
The question is .............. how do you get free flowing CO2 in the open sky to go down on its own that far to form a liquid?
If gas CO2 remains at 1 atmospheric pressure, we assume solubility happens only on the surface, yes?
This brings to another point........
Regardless how heavy CO2 is, upon released from the source, it will disperse on its own to less dense area in the air. 'Hot air rises' indicates that it will go up to higher altitude of the air instead of sticking on the surface of water or land, or everywhere under surrounding temperature, yes? Therefore, we could probably deduce that CO2 can only be found in minute amount right above sea level and dissolves mildly? How much change would this create is awaiting confirmation, yes?
Regarding greenhouse effect..................
It was probably an idea from winter agricultural farm....... How they kept the enclosed farm green throughout the winter. It was a warmth place to start with.
On environment........
Imagine dry air and humid air condition possibly found in any concrete high rises filled city.
Dry air can be cleared easily with wind.
Humid air would take some times to be cleared.
It might indicate that water vapour, with the highest capacity to retain heat among all waste gases released, traps heat.
On climate, it refers to a blanket of warmth formed when heat was retained within cloud and water vapour...
This blanket of cloud helps to regulate temperature within a certain or minute range in many places.
Places without cloud usually have extreme temperature and coldness.
Quoting this from a discussion board posted on an online course " Designing a climate neutral world, by DELFTx"
" It is speculated that since water vapour is considered important factor to us and farmers, it is conveniently taken out to accommodate CO2 as the major culprit and target of action. This act of cutting corner provided misleading argument, policy and mostly futile yet costly mediation.
There is probably a need to revise what is known to make effort ahead not in vain and more cost effective."
If gas CO2 remains at 1 atmospheric pressure, we assume solubility happens only on the surface, yes?
NO, you have no idea what you are talking about.
think about how much CO2 you can put into water in a soda bottle.. pressure is greater than one atmo in the bottle and the amount of CO2 in solution is far greater than sea water....now think of at 100 atmos ....very deep water how much CO2 can be put into solution ......far greater amount than at 1 atmo
first the partial pressure that CO2 exerts at sea level is not 1 atmo......You can put more CO2 into water at a higher partial pressure (related to the 410 ppm) than existed in 1750 related to the 260 ppm....CO2 can dissplace the dissolved nitrogen and oxygen as the partial pressure of N2 decreases slightly as you increase the partial pressure of CO2.
Got it?????? if you do not go back to college and take some chemistry classes and surface chemistry classes and try to understand how gases interact with liquids
In addation amount of CO2 at sea level (at the surface) is not at saturation for CO2 meaning that CO2 keeps dissolving into sea water at the surface and at a rate of 1.6 times (415/260) today than it did 250 years ago. Soluble CO2 or CO2 dissolve in seawater then can speciate to Carbonic acid according to ..................... if you do not understand the following you are just babbling BS
In aqueous solution carbonic acid behaves as a dibasic acid. The Bjerrum plot shows typical equilibrium concentrations, in solution, in seawater, of carbon dioxide and the various species derived from it, as a function of pH.[4][5] The acidification of natural waters is caused by the increasing concentration of carbon dioxide in the atmosphere, which is caused by the burning of increasing amounts of coal and hydrocarbons.[6][7]
Expected change refers to predicted effect of continued ocean acidification.[8] It has been estimated that the increase in dissolved carbon dioxide has caused the ocean's average surface pH to decrease by about 0.1 from pre-industrial levels.
The stability constants database contains 136 entries with values for the overall protonation constants, β1 and β2, of the carbonate ion. In the following expressions [H+] represents the concentration, at equilibrium, of the chemical species H+, etc.
The value of log β1 decreases with increasing ionic strength, {\displaystyle {\ce {I}}}. At 25 °C:
{\displaystyle {\ce {CO3^{2-}{+ H+}<=> HCO3^-}}} : {\displaystyle \beta _{1}={\frac {[{\text{HCO}}_{3}^{-}]}{[{\text{H}}^{+}][{\text{CO}}_{3}^{2-}]}}}
{\displaystyle \log \beta _{1}=0.54I^{2}-0.96I+9.93} (selected data from SC-database)
The value of log β2 also decreases with increasing ionic strength.
{\displaystyle {\ce {CO3^{2-}{+ 2H+}<=> H2CO3}}} : {\displaystyle \beta _{2}={\frac {[{\text{H}}_{2}{\text{CO}}_{3}]}{[{\text{H}}^{+}]^{2}[{\text{CO}}_{3}^{2-}]}}}
{\displaystyle \log \beta _{2}=-2.5I^{2}-0.043I+16.07}
At {\displaystyle {\ce {I}}}=0 and 25 °C the pK values of the stepwise dissociation constants are
pK1 = logβ2 - logβ1 = 6.77.
pK2 = logβ1 = 9.93.
When pH = pK the two chemical species in equilibrium with each other have the same concentration.
Note 1: There are apparently conflicting values in the literature for pKa. Pines et al. cite a value for "pKapp" of 6.35, consistent with the value 6.77, mentioned above.[9] They also give a value for "pKa" of 3.49 and state that
pKa = pKapp − log KD (eqn. 5)
where KD=[CO2]/[H2CO3]. (eqn. 3) The situation arises from the way that the dissociation constants are named and defined, which is clearly stated in the text of the Pines paper, but not in the abstract.
Note 2: The numbering of dissociation constants is the reverse of the numbering of the numbering of association constants, so pK2 (dissociation)= log β1 (association). The value of the stepwise constant for the equilibrium
{\displaystyle {\ce {HCO3- <=> CO3^{2-}{+ H+}}}}
is given by
pK1(dissociation)1 = log β2 − log β1 (association)
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(edited)
On 8/21/2022 at 9:35 PM, Polyphia said:
You will have to explain the point of your pulling out the quotation that you did--I can only guess.
It's not my site, but the person who sponsors it has answered your question multiple times (for example, in response to comment #478).
You might want to take the MOOC that the skepticalscience site is advertising called "Making Sense of Climate Science Denial." It could be helpful.
Here is the quote again,
"Age control. All radiocarbon dates were recalibrated", the data were recalibrated using another system. That is the point.
And the other point was also simple. If CO2 levels are at extraordinarily high levels, why does temperature not continue to rise? A simple question. The answer is not in those links you give, they just do not consider the issue. The graphs indicate a cooling trend commencing at high levels of CO2, which contradicts the CO2 theory.
But the problem with the lags is still unanswered, I do not see an answer there in your links. There have been so many papers that have published the lag with temperature leading CO2, which is fatal to the CO2 hypothesis.
Edited by Ecocharger
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(edited)
Volatility in oil prices has frightened investors. The volatility is related to government Green policies, which threatens economic growth. But apparently governments no longer care about economic growth or standards of living.
"...oil demand, right now, is stronger than many had expected, especially as some utilities in Europe switch from gas to oil due to prices.
This has proved too much not only for speculators but also for industry players in the oil market, according to the Reuters analysis. Open interest on the oil futures market has dropped by a fifth since Russia invaded Ukraine, with traders apparently getting tired of the price seesaw of tight supply and inflation fears.
What the future holds is—as always—impossible to say, but it is quite unlikely that the price situation will change anytime soon. This means that the negative effect this price volatility is having on businesses across industries will continue, fueling the abovementioned oil price seesaw.
Businesses will continue to need energy that is in tight supply, but high prices for this energy will continue threatening their growth prospects and the growth prospects of their respective economies. Governments, meanwhile, will continue pouring money and legislation into the energy transition, further discouraging the oil industry from doing something meaningful about supply."
Edited by Ecocharger
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What you ment to say was Putin ruined the reputation of nat gas and trade deals you could trust. It’s just better to drop deals with unreliable partners. If the Ukraine were to bomb Russian pipelines there would be much fewer deals to be had. Green energy is the replacement for trust misplaced.
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(edited)
5 minutes ago, Boat said:
What you ment to say was Putin ruined the reputation of nat gas and trade deals you could trust. It’s just better to drop deals with unreliable partners. If the Ukraine were to bomb Russian pipelines there would be much fewer deals to be had. Green energy is the replacement for trust misplaced.
Green energy cannot supply our needs. Unless we stop individual transportation.
Edited by Ecocharger
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16 minutes ago, Ecocharger said:
Green energy cannot supply our needs. Unless we stop individual transportation.
Who cares. How much pollution we can eliminate is how we will be judged by future generations. The path is clear to the woke. Saving a few lives during the electric transformation is a plus. Every year the speed of growth of renewables increases. Kinda a sign wokeness is growing and will eventually win. You can be happy nobody can kill flaring, yet. Kinda weird Putin is killing his own market and speeding the change from fossil fuels. Will Mongolian coal feed Europe instead of nat gas? I heard their ramping up production.
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2 hours ago, Boat said:
Who cares. How much pollution we can eliminate is how we will be judged by future generations. The path is clear to the woke. Saving a few lives during the electric transformation is a plus. Every year the speed of growth of renewables increases. Kinda a sign wokeness is growing and will eventually win. You can be happy nobody can kill flaring, yet. Kinda weird Putin is killing his own market and speeding the change from fossil fuels. Will Mongolian coal feed Europe instead of nat gas? I heard their ramping up production.
Coal is king again, thanks to Biden & Co. creating energy chaos.
It looks like oil prices will be forced up on account of the oil market disconnect.
"Citing “disconnect” in the oil futures market, Saudi Energy Minister Prince Abdulaziz bin Salman dangled the threat of potential OPEC+ production cuts that could come at any time.
In an interview with Bloomberg on Monday, the Saudi energy minister said that “extreme volatility” was “undermining the market’s essential function of efficient price discovery”, in turn rendering it impossible for physical users to manage the costs of hedging or navigate the inherent risk.
“This vicious circle is amplified by the flow of unsubstantiated stories about demand destruction, recurring news about the return of large volumes of supply, and ambiguity and uncertainty about the potential impacts of price caps, embargoes, and sanctions,” the Prince told Bloomberg.
Without sufficient liquidity, he said, there is a high level of disconnect, which means the “markets can’t reflect the realities of the physical fundamentals in a meaningful way…”.
The Prince described the markets as being in a state of “schizophrenia” and creating a “yo-yo” market that has lent a false sense of security.
“Spare capacity is severely limited and the risk of severe disruptions remains high,” he said.
The energy minister insisted that OPEC+ is “stronger and more cohesive than ever”, but also indicated that the expanded cartel could cut output at any time “and in different forms”.
The minister’s comments come as the cartel begins work on a new agreement for post-2022 and the nature of the interview suggests that OPEC+ plans to view any new agreements through the prism of the current market volatility, which the Saudis appear to view as having been hijacked and disconnected from true fundamentals.
The energy minister’s warning comes shortly after reports that OPEC+ members produced 2.9 million bpd below their production target in July. "
Edited by Ecocharger
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America has a lot of badlands for wind and solar. I don't even mind them in cornfields. They need to be kept out of our scenic areas and far enough offshore to be beyond the horizon. One problem is that our corporate leaders want to get their solar and wind products from China or Europe in many cases. Another is that it will take decades for them to come close to matching the ability of fossil fuels to power America. Our current legislation is charging taxpayers in advance of promises to save them money sometime in the future. Then they will claim that their energy is competitive, when it is not. The middle class will be paying for windmills, solar farms, batteries, and electric cars they will probably not be able to afford.
Lithium prices paid to foreign countries will be good for them, mainly China but America is far behind in setting up environmentally safe mining. Lithium mining is very environmentally disastrous where it is done. Prices will be higher yet when it is done with best practices. Computer chips are also high in price and demand. There is no way that green energy will be competitive any time soon and voters will see what is happening to their budgets with inflation on top of all the government spending.
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(edited)
As this poster has previously noted, using SPR reserves to attempt to fight high oil prices is a futile tactic, it simply moves barrels from one inventory into another inventory with no net increase in product.
Now the chickens are coming home to roost.
"In addition to the lowest inventory levels in the SPR since 1985, last Wednesday, the Energy Information Administration (EIA) estimated that crude oil inventories (excluding the SPR) had fallen by 7.1 million barrels
For that week, U.S. crude oil inventories, excluding those in the SPR, were at only 425 million barrels, or 6% below the five year average.
The largest sale from the SPR was announced on August 11, when the Department of Energy said that nine companies would buy 20 million barrels.
According to the Institute of Energy Research, the SPR is expected to shrink to a 40-year low by the end of October, with inventories then at 358 million barrels, compared to 621 million barrels a year ago. "
Edited by Ecocharger
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(edited)
6 hours ago, Ron Wagner said:
One problem is that our corporate leaders want to get their solar and wind products from China or Europe in many cases. Another is that it will take decades for them to come close to matching the ability of fossil fuels to power America. Our current legislation is charging taxpayers in advance of promises to save them money sometime in the future. Then they will claim that their energy is competitive, when it is not. The middle class will be paying for windmills, solar farms, batteries, and electric cars they will probably not be able to afford.
Ron in one breath you complain that wind and solar are sourced from China and Europe, and then in the next breath you moan about cost and competitiveness. Guess what, the reason USA is buying from China and Europe for wind and solar is because they are cheaper and superior products. You cant have it both ways unless the US invests into renewables to the same extent as Europe and China have done.
# Renewable Power Remains Cost-Competitive amid Fossil Fuel Crisis
Edited by Rob Plant
# Scotland's largest offshore windfarm starts producing electricity - and will power an enormous number of homes
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(edited)
Oil markets are beginning to wake up (not woke up) to the fundamental realities.
"Crude oil prices rallied on Tuesday morning as OPEC+ leaked that it may cut oil production 'when and if Iranian production returns'.
New OPEC+ output cuts could promptly offset any incremental production from Iran.
Uncertainty about the Iran nuclear deal continues to keep markets on edge."
Edited by Ecocharger
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8 hours ago, Rob Plant said:
Ron in one breath you complain that wind and solar are sourced from China and Europe, and then in the next breath you moan about cost and competitiveness. Guess what, the reason USA is buying from China and Europe for wind and solar is because they are cheaper and superior products. You cant have it both ways unless the US invests into renewables to the same extent as Europe and China have done.
# Renewable Power Remains Cost-Competitive amid Fossil Fuel Crisis
America needs to produce its own products and mine its own minerals in environmentally safe ways. Not pretend that it is OK if we just buy them from China who does not care about the environment. Buying from allies is a second choice but where do you think they get their "rare" minerals from.
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(edited)
Oil markets show robust demand and razor thin inventory numbers. Bullish.
"The American Petroleum Institute (API) reported a large draw this week for crude oil of 5.632 million barrels, while analysts predicted a draw of 448,000 barrels.
In the week prior, the API reported a draw in crude oil inventories of 448,000 barrels after analysts had predicted a draw of 117,000 barrels.
WTI was trading up on Tuesday after Saudi Arabia suggested that the group could look at making production adjustments due to the disconnect between the physical and paper crude markets. WTI was trading up 3.72% on the day at 3:00 p.m. ET in the runup to the release at $93.72 per barrel—more than$7 per barrel up on the week. Brent crude was trading up 3.92% on the day at $100.30—a roughly$8 price hike on the week.
U.S. crude oil production data for the week ending August 12 fell 100,000 bpd to 12.1 million bpd, according to the latest weekly EIA data. "
Edited by Ecocharger
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(edited)
12 hours ago, Ron Wagner said:
America needs to produce its own products and mine its own minerals in environmentally safe ways. Not pretend that it is OK if we just buy them from China who does not care about the environment. Buying from allies is a second choice but where do you think they get their "rare" minerals from.
I agree on the REE, I think thats obvious.
However you were complaining of cost and competitiveness and then saying USA shouldnt be buying from the countries that are cheapest and most competitive. Like I said you cant have it both ways unless the US ramps up on its renewable in country manufacture which I dont see, maybe because I'm not in country so I stand to be corrected on that. You didnt mention REE at all in your original post. If the USA mines its own minerals then it will be even less competitive than it is today IMHO.
If done well renewables can be as cheap if not cheaper than FF without any subsidies in many locations. It also gives that country more energy security which may not be a concern in the US but in many countries particularly at present its a very big deal indeed.
Edited by Rob Plant
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18 hours ago, Rob Plant said:
I agree on the REE, I think thats obvious.
However you were complaining of cost and competitiveness and then saying USA shouldnt be buying from the countries that are cheapest and most competitive. Like I said you cant have it both ways unless the US ramps up on its renewable in country manufacture which I dont see, maybe because I'm not in country so I stand to be corrected on that. You didnt mention REE at all in your original post. If the USA mines its own minerals then it will be even less competitive than it is today IMHO.
If done well renewables can be as cheap if not cheaper than FF without any subsidies in many locations. It also gives that country more energy security which may not be a concern in the US but in many countries particularly at present its a very big deal indeed.
If you declare war on 85% of your energy supply, energy prices will rise dramatically and standards of living will be massively reduced.
There is no way to dance around that eventuality.
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On 8/22/2022 at 10:13 PM, Ron Wagner said:
America has a lot of badlands for wind and solar. I don't even mind them in cornfields. They need to be kept out of our scenic areas and far enough offshore to be beyond the horizon. One problem is that our corporate leaders want to get their solar and wind products from China or Europe in many cases. Another is that it will take decades for them to come close to matching the ability of fossil fuels to power America. Our current legislation is charging taxpayers in advance of promises to save them money sometime in the future. Then they will claim that their energy is competitive, when it is not. The middle class will be paying for windmills, solar farms, batteries, and electric cars they will probably not be able to afford.
Lithium prices paid to foreign countries will be good for them, mainly China but America is far behind in setting up environmentally safe mining. Lithium mining is very environmentally disastrous where it is done. Prices will be higher yet when it is done with best practices. Computer chips are also high in price and demand. There is no way that green energy will be competitive any time soon and voters will see what is happening to their budgets with inflation on top of all the government spending.
Wind and solar for many states can be far enough south to avoid the cost of weatherization. The first goal should be a robust system to take care of summer AC and the onslaught of electric cars. We have at least 15 years for that to happen. Then with improved tech and experience Northern states will become financially viable.
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36 minutes ago, Ecocharger said:
If you declare war on 85% of your energy supply, energy prices will rise dramatically and standards of living will be massively reduced.
There is no way to dance around that eventuality.
For the same money it takes more workers to do renewables. Thanks to the efficiency of the frackers/drillers and the cost of shipping. FF prices are volatile in the extreme. Even an idiot like Putin can affect world prices. Renewables seem to avoid volatility, a trait important to business and investing.
• 1
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So anybody done a study on the nat gas consumption of creating electricity vrs refining with nat gas. Oil Demand will start dropping soon if not already. Say per 5 million electric cars, how much nat gas demand from refining is saved vrs demand needed for electricity generated.
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5 hours ago, Ecocharger said:
If you declare war on 85% of your energy supply, energy prices will rise dramatically and standards of living will be massively reduced.
There is no way to dance around that eventuality.
Totally agree Eco
I'm for all types of energy as long as its economical.
I dont think any subsidies should be given to any energy sector whether its FF, nuclear, renewable or whatever.
There is no need to be on one side or the other as the world needs ALL of them. Renewables in the UK are keeping 100's of thousands in jobs that previously were in the oil and gas business as many skill sets are transferrable, I'm all for that!
I also think the current situation in Ukraine is a tradegy not only for the Ukrainian and Russian people but potentially globally due to the misguided energy policies of so many countries.
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On 8/18/2022 at 7:10 PM, Ecocharger said:
... Calling wind turbines “fans” that harm the environment and cause “visual pollution” without providing much energy,
Mexican President Andrés Manuel López Obrador said the government will end the subsidies and stop issuing permits for new wind projects.
Israel is also set to pull the plug on the country’s wind industry, its environmental protection minister arguing that wind provides a “negligible contribution” to the country’s power system “compared to the potential for harm to nature, which is high.”
Because neither mexico nor israel have wind... Especially when both have great solar even in the winter. Both countries could live on a battery of no more than 2 days where only in extreme weather events would supplementary power have to be added. A 2 day battery is doable. VERY expensive, yes, but doable. Even using lead acid. Vast majority of their power is required during the day as well.
Who knew... LOCATION LOCATION LOCATION... it is almost as if Geography is king regarding Wind/Solar just as it is for geothermal, lithium reserves, coal reserves, oil reserves, iron reserves etc etc etc.
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On 8/23/2022 at 11:56 AM, Ron Wagner said:
America needs to produce its own products and mine its own minerals in environmentally safe ways. Not pretend that it is OK if we just buy them from China who does not care about the environment. Buying from allies is a second choice but where do you think they get their "rare" minerals from.
America mines most of its own REE, but due to MORONIC environmental laws labeling them the same as URANIUM and nuclear materials, we ship them to china to be processed... I kid you not. In fact, the USA in several REE's produce enough to supply the entire world, but the USA processes NONE of them even though it was the worlds leader in processing them before 1980. After that moronic environmental bill relabeling them nuclear materials was based back in 1980, the industry had to move overseas to survive.
Can always count on government to Fuck things up.
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(edited)
14 hours ago, Boat said:
For the same money it takes more workers to do renewables. Thanks to the efficiency of the frackers/drillers and the cost of shipping. FF prices are volatile in the extreme. Even an idiot like Putin can affect world prices. Renewables seem to avoid volatility, a trait important to business and investing.
Lithium prices are out of control and will get worse going forward. The electric future will not be an individual vehicle but mass transport. Fossil fuel cars will continue to be the affordable option, so governments will have to ban fossil fuel vehicles by fiat to get rid of them.
However, that doomsday future will never come... the climate science of Green Dreams is too feeble to support the transition.
Edited by Ecocharger
• 1
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14 hours ago, Boat said:
For the same money it takes more workers to do renewables. Thanks to the efficiency of the frackers/drillers and the cost of shipping. FF prices are volatile in the extreme. Even an idiot like Putin can affect world prices. Renewables seem to avoid volatility, a trait important to business and investing.
Only commodity exchange prices are volatile. People who are interested in the actual FFs got themselves long-term contracts, which are significantly less volatile.
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(edited)
On 8/23/2022 at 2:54 AM, Rob Plant said:
Ron in one breath you complain that wind and solar are sourced from China and Europe, and then in the next breath you moan about cost and competitiveness. Guess what, the reason USA is buying from China and Europe for wind and solar is because they are cheaper and superior products. You cant have it both ways unless the US invests into renewables to the same extent as Europe and China have done.
# Renewable Power Remains Cost-Competitive amid Fossil Fuel Crisis
Well no, as Europe has given GARGANTUAN subsidies to the wind industry(as they should as they have no oil/gas/solar), same with China and its solar panel assembly while the USA has allowed these MASSIVELY subsidized products ENTRY into our country without massive tariffs.
The problem, once again, is government policy.. or in the case of the USA, LACK of policy tied with bottom basement cost of NG which no one else has.
You might notice, USA has the highest efficiency solar panels on the planet... just not mass production. Also, wind sighting in USA was paused due to bird death strikes for decades and why I initially lost my job in said industry going on 2 decades ago now and I had to move on. This is still a gargantuan problem in the USA. Apparently either Europeans have no protected big birds already and therefore no bird deaths or do not care as they have to worry more about keeping the lights on. In the USA we do not have the problem with the later but do have a big problem with the former with large birds everywhere it is windy other than a few select desert locations.
Yes, one more reason West Texas and West Oklahoma have seen explosive growth in wind turbines in USA(40GW currently and climbing quickly with an average capacity factor of 44% and going up with all newer birds hitting an average of +50%)... NO BIRDS as it is effect a desert. Likewise California's early wind turbine parks also did not have bird problems as they were in desert location. Maybe no one gives a damn about sea birds in Europe so when they get smashed and fall in the water no one ever knows as most of Europe's early adopters of wind turbines are right next to water or in the water. Just an FYI, Germany with a capacity of ~60GW(onshore+offshore), has CF of 38% in its OFFSHORE birds all under 5 years of age. https://energynumbers.info/germanys-offshore-wind-capacity-factors
In otherwords, TX/OK with 40GW get roughly same power as Germany with 60GW of sunk cost
Who knew, LOCATION matters. Government policy MATTERS.
You can SAY you wish to go wind/solar, does not make it a viable option just because you SAY it is so. Pesky things like birds, tariffs, corruption allowing an effective dictatorial slave nation state to be able to import into your country tariff free.... MATTERS.
Edited by footeab@yahoo.com
## Join the conversation
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2022-10-01 08:28:19
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https://www.physicsforums.com/threads/electric-field-equation-hollow-cylinder.291525/
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# Electric Field Equation Hollow Cylinder
## Main Question or Discussion Point
Hello,
Does anyone know of (or have a link to) an equation for the electric field at any point inside a a hollow cylinder shell of finite length?
thanks,
## Answers and Replies
Related Classical Physics News on Phys.org
jtbell
Mentor
I've never seen one. I suspect that it's not possible to get a closed formula for all points, and that you'd have to calculate it via numerical integration or using a series approximation of some kind.
Meir Achuz
Science Advisor
Homework Helper
Gold Member
More detail please. Is it a conducting cylinder kept at a given potential?
Are the ends open or closed?
Okay, let's simplify.
Suppose the cylinder is of finite length, and the point is inside the cylinder midway between the two ends. The ends are open. The charge is uniform and kept constant. The cylinder is made of conducting material.
Meir Achuz
Science Advisor
Homework Helper
Gold Member
That is impossible. A conducting cylinder will not have a uniform charge.
True that.
Suppose it is made of non-conducting material such that the charge is uniformly distributed.
Meir Achuz
Science Advisor
Homework Helper
Gold Member
That problem can be solved by taking the field or potential on the axis of a uniformly charged ring and integrating along the axis.
jtbell
Mentor
Right, on the axis you can get an equation for the field as a function of position fairly easily. Off the axis it's much more difficult, maybe even impossible, using "common" functions.
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2020-08-14 20:51:19
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https://codegolf.stackexchange.com/questions/23481/partially-solve-the-halting-problem-for-brainf
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# Partially Solve the halting problem for brainf***
To solve the Halting Problem you are given a description of a program, and must determine whether or not it will ever finish. You can never do this for all programs. Yet for programs like (in brainf***):
>
It obviously will halt, and for programs like:
+[]
It obviously will not. Your challenge is to "solve" the halting problem for as many programs as possible. These programs will not use . or ,, and will not have input or output. You will be given a description of the program and must output either "Halts", "Does not halt", or "Unknown". When your program outputs "Halts" or "Does not halt", you have solved the input program. Here are some requirements.
1. It must solve at least an infinite amount of programs.
2. For every program it solves, its solution must be correct.
3. You may only output 1 of the 3 above choices.
4. You may assume that the running computer has infinite time and memory, so XKCD 1266 would not work (the tape is unlimited).
5. No external resources.
6. You may not use a programming language that can actually solve the halting problem.
You may have a non-code-golfed side program that takes a string that is a program, and generates some sort of abstract syntax tree of it if you like. Note, that isn't really scoring per se, but how to determine if one program beats another.
1. If program A solves an infinite number of programs that B doesn't, but B only solves finite or no programs that A solves, A automatically wins.
2. Otherwise, the program with the fewest characters wins. Do not count white space or comments, so do not obfuscate your code.
Tip: Timers won't work. You see, for any time T and given machine, there is an N, such that all programs longer than that have to take more than T time. This means that a timer can only achieve the solution of a finite number of programs, and, as you can see above, solving a finite number of programs doesn't help.
• I don't think the scoring system will work. Given any solution, it is easy to construct a better one as follows: Find any program P on which the solution S outputs "Unknown", create a new solution which outputs the correct answer on input P, the same answer on P with any number of >s added to the end (since these halt iff P halts), and outputs S's answer on all other inputs. This new solution solves infinitely more problems than S. Mar 8, 2014 at 17:03
• These made not add any solutions though. For example, the original P could just say "if the last thing is >, ignore it." Then your thing would be redundant. Mar 8, 2014 at 17:06
• Right, so first create a solution S' which answers the same as S but ignores >s after the end of the program, then find a program P on which S' answers "Unknown", then create a new solution that answers correctly on P with >s appended and gives the answer of S' otherwise. Since S' ignores >s then P with any number of >s appended will also not be solved by S'. Mar 8, 2014 at 17:12
• "At least an infinite amount of programs"? Is there a bonus for solving more? ;-) Mar 8, 2014 at 17:44
• Since you're apparently not following the reference implementation, you should probably clarify all of the other implementation differences: cell size, behaviour on underflow and overflow, whether the tape is infinite in both directions or only one, and if only one what happens when you try to move past it. It's not the most tightly specified language... Mar 8, 2014 at 18:40
## Python, ungolfed spaghetti code
Oh dear.
def will_it_halt(instructions):
tape_length = 1
LOOP_BOUND = 1000
registry = [0] * tape_length
pos = 0
jumpbacks = []
reached_states = set()
pos_instructions = 0
while True:
letter = instructions[pos_instructions]
if letter == "+":
registry[pos] = (registry[pos] + 1) % 256
elif letter == "-":
registry[pos] = (registry[pos] - 1) % 256
elif letter == ">":
pos += 1
if pos >= tape_length:
registry += [0]*tape_length
tape_length = len(registry)
elif letter == "<":
pos -= 1
if pos <= 0:
registry = [0]*tape_length+registry
tape_length = len(registry)
pos += tape_length
elif letter == "[":
if registry[pos] == 0:
nests = 1
while nests:
pos_instructions += 1
if instructions[pos_instructions] == "[": nests += 1
elif instructions[pos_instructions] == "]": nests -= 1
if jumpbacks == []:
reached_states.clear()
else:
jumpbacks.append(pos_instructions-1)
elif letter == "]":
stripped_registry = [str(x) for x in registry if x != 0]
translated_pos = pos - (len(registry) - len(stripped_registry))
state = (translated_pos, pos_instructions, ".".join(stripped_registry))
if state in reached_states: return "Does not halt"
elif len(reached_states) > LOOP_BOUND: return "Unknown"
else:
pos_instructions = jumpbacks.pop()
pos_instructions += 1
if pos_instructions >= len(instructions): break
return "Halts"
Pretty brute-forcey solution to the problem: just run the bf code. We assume the tape length is arbitrarily long and that individual cells wrap at 256. At the end of every loop, we store the state of the tape with a set. States are of the form (our position on the tape, our position on the instructions, what the tape looks like with leading 0's stripped).
If we store the same state twice, then we're somewhere in an infinite loop, so the program does not halt. If we store over 1,000 states, then cut losses and return unknown. Once we leave a loop we check to see if we aren't in any larger loops. If not, we're never seeing any of the previous states ever again (at the very least, the instruction position will always be different!) so we can clear the set of states.
This should accurately determine any BF program who's loops aren't longer than 1,000 iterations, as well as many programs that repeat a state before 1,000 iterations in a loop. Not all of them, though: something like "{1 million +'s here}[-]>+[+-]" eventually repeats a state, but the [-] loop passes 1,000 iterations first.
Some examples:
>+>->+>-
No loops, so it reaches the end and halts.
+[+]
Loop ends after 256 iterations, so it reaches the end and halts.
+[+-]
Eventually repeats the state (0,5,"1"), so it does not halt.
+[->+]
This doesn't repeat any states but the loop never ends, so it should print "unknown". But the program kind of cheats here. Instead of storing the position on the tape, it adds an offset between the original registry and the stripped one. If all a loop does is translate the tape by some spaces, then it will continue translating it indefinitely (like a life glider), so we can say it does not halt.
+[>+]
Doesn't translate, doesn't repeat any states, prints unknown.
+++++++++++[-]
This does halt, but it would print "unknown" if LOOP_BOUND was 10.
There's a couple of ways to make this smarter. You could obviously increase LOOP_BOUND to reduce the number of unknowns. You could have smarter handling of nested loops. You could probably do something fancy with BB numbers and the size of loops to better detect if something should halt, but I'm not good enough at CS nor at Python to be able to do that yet.
## GolfScript (23 chars, infinite correct answers)
'[]'&!
# 0 if there are brackets, so Unknown
# 1 if there are no brackets, so no looping, so definitely halts
'UnknownHalts'7/=
• Saying infinite correct answers is unnecessary, as it was a requirement. Mar 8, 2014 at 19:00
• Rules abuse... Lol Feb 2, 2015 at 20:52
## Awk
A small extension in power from the two examples. If a program contains no loops at all, hence no decisions, it is still obviously determined to halt. Since we're assuming validity of the program, we also assume brackets are balanced and thus need only search for one or the other of the brackets.
BEGIN{RS=""}
!/\[/{print "Halts"; exit}
END{print "Unknown"}
For the second, it must check first if the loop runs at all, so we must simulate the straight-line code preceding the loop. Then, if the loop returns to the same cell (ie. number of >s is equal to the number of <s within the loop), and it performs no incs or decs at this cell (ie. for any position-balanced prefix of the balanced loop body, there are no instances of + or - before the next < or >, then the cell is unmodified). Implementing this part may take me more time. Ooh, wait, for the first part of checking if the loop runs at all, we can take this same idea and search the pre-loop program for balanced suffixes and insist that there be a + or - (unbalanced).
main=do
It basically sees if there is a loop in the beginning. If that exact loop doesn't occur in the beginning, it just gives up. It doesn't even work for ++[]. It does solve an infinite number of programs though, and it is always correct when it solves it.
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2022-10-02 18:45:55
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http://openstudy.com/updates/4de45a834c0e8b0b9c17aed8
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## anonymous 5 years ago simplify log4 81^-2 help me please
1. anonymous
are you sure its log base 4 ?
2. anonymous
I think its possibly 3
3. anonymous
if it is $log_3(81^{-2})$ then you get $-2log_3(81)$ and since $3^4=81$ you know $log_3(81)=4$ so your answer will be $-2\times 4=-8$
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2017-01-18 12:49:25
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https://repo.scoap3.org/record/30468
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# New Phase Transition Related to the Black Hole’s Topological Charge
Lan, Shan-Quan (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China) ; Li, Gu-Qiang (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China) ; Mo, Jie-Xiong (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China) ; Xu, Xiao-Bao (Department of Physics, Lingnan Normal University, Zhanjiang, Guangdong 524048, China)
23 January 2019
Abstract: The topological charge $ϵ$ of AdS black hole is introduced by Tian et al. in their papers, where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat ${C}_{ϵ}$ and determine the phase transition critical point. Secondly, the $T-r$ curve and $T-S$ curve are investigated and they exhibit an interesting van der Waals system’s behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system’s swallow tail behavior is observed when $ϵ>{ϵ}_{c}$ in the $F-T$ graph. What is more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other.
Published in: Advances in High Energy Physics 2019 (2019) 8270265
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2019-02-21 17:32:30
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http://blog.csdn.net/xingcpp/article/details/1603679
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# 0.0.3 致谢
613人阅读 评论(0)
Acknowledgments
We would like to thank the many people who have helped us develop this book and this curriculum.
Our subject is a clear intellectual descendant of 6.231,'' a wonderful subject on programming linguistics and the lambda calculus taught at MIT in the late 1960s by Jack Wozencraft and Arthur Evans, Jr.
We owe a great debt to Robert Fano, who reorganized MIT's introductory curriculum in electrical engineering and computer science to emphasize the principles of engineering design. He led us in starting out on this enterprise and wrote the first set of subject notes from which this book evolved.
Much of the style and aesthetics of programming that we try to teach were developed in conjunction with Guy Lewis Steele Jr., who collaborated with Gerald Jay Sussman in the initial development of the Scheme language. In addition, David Turner, Peter Henderson, Dan Friedman, David Wise, and Will Clinger have taught us many of the techniques of the functional programming community that appear in this book.
Joel Moses taught us about structuring large systems. His experience with the Macsyma system for symbolic computation provided the insight that one should avoid complexities of control and concentrate on organizing the data to reflect the real structure of the world being modeled.
Joel Moses 教我们如何考虑大型系统的构造。他在 Macsyma 符号计算系统上的经验中得到的真知灼见是，应该避免控制中的复杂性，将精力集中到数据的组织上，以反映所模拟世界里的真实结构。
Marvin Minsky and Seymour Papert formed many of our attitudes about programming and its place in our intellectual lives. To them we owe the understanding that computation provides a means of expression for exploring ideas that would otherwise be too complex to deal with precisely. They emphasize that a student's ability to write and modify programs provides a powerful medium in which exploring becomes a natural activity.
We also strongly agree with Alan Perlis that programming is lots of fun and we had better be careful to support the joy of programming. Part of this joy derives from observing great masters at work. We are fortunate to have been apprentice programmers at the feet of Bill Gosper and Richard Greenblatt.
It is difficult to identify all the people who have contributed to the development of our curriculum. We thank all the lecturers, recitation instructors, and tutors who have worked with us over the past fifteen years and put in many extra hours on our subject, especially Bill Siebert, Albert Meyer, Joe Stoy, Randy Davis, Louis Braida, Eric Grimson, Rod Brooks, Lynn Stein, and Peter Szolovits. We would like to specially acknowledge the outstanding teaching contributions of Franklyn Turbak, now at Wellesley; his work in undergraduate instruction set a standard that we can all aspire to. We are grateful to Jerry Saltzer and Jim Miller for helping us grapple with the mysteries of concurrency, and to Peter Szolovits and David McAllester for their contributions to the exposition of nondeterministic evaluation in chapter 4.
Many people have put in significant effort presenting this material at other universities. Some of the people we have worked closely with are Jacob Katzenelson at the Technion, Hardy Mayer at the University of California at Irvine, Joe Stoy at Oxford, Elisha Sacks at Purdue, and Jan Komorowski at the Norwegian University of Science and Technology. We are exceptionally proud of our colleagues who have received major teaching awards for their adaptations of this subject at other universities, including Kenneth Yip at Yale, Brian Harvey at the University of California at Berkeley, and Dan Huttenlocher at Cornell.
Al Moyé arranged for us to teach this material to engineers at Hewlett-Packard, and for the production of videotapes of these lectures. We would like to thank the talented instructors -- in particular Jim Miller, Bill Siebert, and Mike Eisenberg -- who have designed continuing education courses incorporating these tapes and taught them at universities and industry all over the world.
Al Moy&ecute; 安排我们到惠普公司为工程师教授这一课程，并为这些课程制作了录像带。我们感谢有些才干的教师——特别是 Jim Miller、Bill Siebert 和 Mike Eisenberg——他们设计了结合这些录像带的继续教育课程，并在全世界的许多大学和企业讲授。
Many educators in other countries have put in significant work translating the first edition. Michel Briand, Pierre Chamard, and André Pic produced a French edition; Susanne Daniels-Herold produced a German edition; and Fumio Motoyoshi produced a Japanese edition. We do not know who produced the Chinese edition, but we consider it an honor to have been selected as the subject of an unauthorized'' translation.
It is hard to enumerate all the people who have made technical contributions to the development of the Scheme systems we use for instructional purposes. In addition to Guy Steele, principal wizards have included Chris Hanson, Joe Bowbeer, Jim Miller, Guillermo Rozas, and Stephen Adams. Others who have put in significant time are Richard Stallman, Alan Bawden, Kent Pitman, Jon Taft, Neil Mayle, John Lamping, Gwyn Osnos, Tracy Larrabee, George Carrette, Soma Chaudhuri, Bill Chiarchiaro, Steven Kirsch, Leigh Klotz, Wayne Noss, Todd Cass, Patrick O'Donnell, Kevin Theobald, Daniel Weise, Kenneth Sinclair, Anthony Courtemanche, Henry M. Wu, Andrew Berlin, and Ruth Shyu.
Beyond the MIT implementation, we would like to thank the many people who worked on the IEEE Scheme standard, including William Clinger and Jonathan Rees, who edited the R4RS, and Chris Haynes, David Bartley, Chris Hanson, and Jim Miller, who prepared the IEEE standard.
Dan Friedman has been a long-time leader of the Scheme community. The community's broader work goes beyond issues of language design to encompass significant educational innovations, such as the high-school curriculum based on EdScheme by Schemer's Inc., and the wonderful books by Mike Eisenberg and by Brian Harvey and Matthew Wright.
Dan Friedman 多年以来一直是 SCheme 社团的领袖。这一社团的工作范围已经从语言设计问题，扩展到围绕着重要的教育创新问题，例如基于 Schemer's Inc. 的 EdScheme 的高中教学计划，以及由 Mike Eisenberg 和由 Brian Harvey 和 Matthew Wright 撰写的绝妙著作。
We appreciate the work of those who contributed to making this a real book, especially Terry Ehling, Larry Cohen, and Paul Bethge at the MIT Press. Ella Mazel found the wonderful cover image. For the second edition we are particularly grateful to Bernard and Ella Mazel for help with the book design, and to David Jones, TEX wizard extraordinaire. We also are indebted to those readers who made penetrating comments on the new draft: Jacob Katzenelson, Hardy Mayer, Jim Miller, and especially Brian Harvey, who did unto this book as Julie did unto his book Simply Scheme.
Finally, we would like to acknowledge the support of the organizations that have encouraged this work over the years, including support from Hewlett-Packard, made possible by Ira Goldstein and Joel Birnbaum, and support from DARPA, made possible by Bob Kahn.
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2017-06-28 00:05:47
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http://mathhelpforum.com/algebra/219847-algebra-percentages-need-helpful-hints-2.html
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Math Help - Algebra and percentages - In need of helpful hints
1. Re: Algebra and percentages - In need of helpful hints
Keep in mind that $.6$ is $10$% of $6$
2. Re: Algebra and percentages - In need of helpful hints
Thank you both for all your help
Page 2 of 2 First 12
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2015-03-27 03:50:28
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https://mathoverflow.net/questions/191147/strong-morita-equivalence-and-representation-theory
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# Strong Morita equivalence and representation theory
In the context of pure algebra we say that two algebras (in general: rings) $A,B$ are Morita equivalence when there are bimodules $_AP_B,_BQ_A$ such that $P \otimes_B Q \cong _AA_A$ and $Q \otimes_A P \cong _BB_B$. The remarkable theorem states that this condition is equivalent to the following fact: the categories of (for example) left modules over $A$ and over $B$ are naturally equivalent. There is a notion of so called strong Morita equivalence due to Rieffel: this notion is for the $C^*$-algebra context. I saw the following remark: two Morita equivalent $C^*$-algebras have the same representation theory. I wonder what exactly does it mean: I'm interested in $*$-representations. In particular, is it true that $*$-representations of the $C^*$-algebra somehow form the category and the notion of strong Morita equivalence is the natural equivalence of these categories?
Let $A$ and $B$ be two $C^{*}$ algebras. Then the category of $*$-representation of $A$ on Hilbert space is equivalent to that of $B$ if and only if their enveloping von Neumann algebra are morita equivalent (note that the notion of morita equivalence is slightly more restrictive for Von Neumann algebras because we expect the bi-modules to be self dual as module).
In particular, two commutative algebras with the same enveloping von Neuman algebras are going to have the same representations categories but are not Morita equivalent (unless they are isomorphic of course)
The good notion of module to have a similar result for $C^*$-algebra are the Hilbert Modules : two $C^*$-algebra are Morita equivalent if and only if they have equivalent categories of Hilbert modules (equivalent as C* categories).
Oh, but the converse holds: two Morita equivalent $C^*$ algebras do have the same category of representations (for exemple, because the equivalence bi-module between them can be completed into a self-dual equivalence bi-module between their enveloping algebras)
Some references:
The first references are I think the two papers of Rieffel:
Morita equivalence for C* algebras and W* algebras
Morita equivalence for operator algebras
In the first paper (and contrary to what the title suggest) he deals with morita equivalence for von Neumann algebras (what he calls morita equivalence of C* algebra in this paper corresponds to the weak notion and hence to morita equivalences of the enveloping W*-algebras) In the second paper he talks about strong morita equivalence of C* algebras. He didn't explicitly proves that it the same as the equivalence of the categories of Hilbert modules but He makes some remarks that essentially explain how it works.
Bruce Blackadar's "Operator Algebras" give a nice and modern acount of the basic theory of Morita equivalence (section II.7) but didn't seems to prove that it is equivalent to the equivalence of the categories of C* module neither...
Unfortunately, I haven't been able to find an actual complete and explicit proof in the literature of this last results. (I will edit again if I found one)
• Thank you, could you give me some references to these results? I would be grateful Dec 21 '14 at 1:18
• I have edited my answer. Dec 22 '14 at 17:41
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2021-09-25 22:35:10
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https://www.pololu.com/blog/732/new-adjustable-voltage-regulators-with-multi-turn-fine-adjustment
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# New adjustable voltage regulators with multi-turn fine adjustment
Posted by Jan on 4 December 2017
I am excited to announce our first voltage regulators with multi-turn trimmer potentiometers! I have wanted to add multi-turn pots to our products for a long time, but the problem has been that they are really expensive. They also tend to be quite big, at least compared to many of our boards, which we try to keep compact, and the smaller, surface-mounted ones are especially expensive. My latest round of looking for lower-cost options did not pan out, but I decided to just give it a try with the expensive parts.
The new S9V11x regulators that feature these potentiometers are buck-boost regulators that can output a voltage that is lower, the same, or higher than the input voltage. There are also versions with a multi-turn pot for adjusting the undervoltage cutoff threshold, so that if you use these with batteries, you can prevent overdischarging them. With twelve turns of adjustment available, it’s much easier to precisely set the voltages on the modules than with the single-turn potentiometers we have used on other adjustable regulators.
While I have been talking mostly about the potentiometers, the main regulator is pretty magical, too, giving you quite a bit of power over a broad operating input range in a small size.
Our stock products are available in several combinations of adjustable and fixed output voltage and cutoff. If you have a higher-volume application, we can make them with fixed voltages wherever you need them. You could initially prototype your design with the adjustable version and then get fixed ones made once you know exactly what voltage you need.
Regulator Input (V) Output (V) Low-voltage cutoff Size Price
#2868 S9V11MACMA 2* – 16 2.5 – 9 (fine-adjust) fine-adjust 0.50″ × 0.60″ × 0.25″ $11.95 #2869 S9V11MA 2.5 – 9 (fine-adjust)$8.95
#2870 S9V11F5S6CMA 5 (6 V selectable) fine-adjust $8.95 #2871 S9V11F3S5CMA 3.3 (5 V selectable) fine-adjust$8.95
#2872 S9V11F3S5 3.3 (5 V selectable) 0.50″ × 0.60″ × 0.17″ $5.95 #2873 S9V11F3S5C3 3.3 (5 V selectable) 3 V (fixed)$5.95
#2836 S9V11F5 5 0.30″ × 0.45″ × 0.17″ \$5.95
* The regulator has a minimum start-up voltage of 3 V, but it can operate down to 2 V after startup. It is disabled when the input voltage is below the low-voltage cutoff.
I am very interested to see what people think of the multi-turn adjustment feature. If these new regulators sell decently or customers ask for it, we will add the multi-turn potentiometers to our other regulator offerings. Is the extra expense worth it? Or do you know of a good, low-cost, multi-turn potentiometer we could consider for future products like this?
Like this device. Would like to see it in a 2.5 to 15 volt output version.
Thanks for the feedback. That higher output range you are asking for is not feasible on this particular design. Do you need the 3-16V input range in the same device, or are you wanting the higher output voltage for an application where the input voltage range would be smaller? (I'm asking because it's much easier to make just a step-up converter for low input voltage applications, and the step down/step up (or even straight step down) functionality would be easier to achieve if it did not have to operate at so low of a voltage.)
- Jan
It would be nice if there was a low voltage led tied to the lvc. Set up 0.5v above the cutoff would be perfect. Maybe even adjustable
Hi, Patrick.
Thanks for your feedback! Adding a low voltage indicator LED and circuit would add to the current draw and size of the board, so I am not sure the trade offs would be worth it for a general-purpose regulator, but we will keep it in mind. You could also add a circuit like that externally to the regulator's VIN or EN pins. If you have a high-volume application for such a regulator, please let us know, and we can probably make it for you.
-Claire
Hello,
Is it a problem if there's 5v applied on the output pin? From another power source? Is there a diode on the output pin? I tried googling, but haven't found the answer.
Thanks!
Costyn.
Hi, Costyn.
You definitely should never connect the output of this regulator to another source when the regulator is on. The board does not include any protection from power flowing back into the regulator, and in generally two regulated power sources will likely fight each other if directly connected. If you need to do something like that, I recommend looking into ORing circuits.
-Claire
HI Claire,
Thanks for the response. I definitely won't be applying 5v to the output pin when the regulator is itself live. Just when I'm programming the attached microcontroller there'll be power on the 5v rail. When my project is installed it will be just the microcontroller.
Regards.
What controller is this converter using? Would be useful to know other parameters like soft start, current impulse response, etc...
Hello, Jose.
We do not disclose the regulator chip on those boards, but the soft start time is typically 850μs while boosting and 400μs while bucking. For information about other specific parameters please email us.
-Tony
Hi,
I'd like to know some details about the low-voltage-cutoff function:
-how do you reset it? (I guess removing input voltage and putting in back on resets it, which would be just what I want)
-if the battery voltage goes above a certain level, will the regulator switched on again automatically?
Best regards,
Simon
Hello, Simon.
Please refer to the "Setting the cutoff voltage" section of the product page, which answers both of your questions.
- Patrick
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2020-07-13 15:09:51
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https://msdn.microsoft.com/en-us/library/ff542432.aspx
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# Build Utility Environment Variables
The values of the following environment variables can be set in the build environment window. For an overview of how these environment variables are used, see Using Macros and Environment Variables.
The following environment variables are automatically set through the SetEnv.bat file when the build environment is created:
_BUILDARCH
BASEDIR
BUILD_ALT_DIR
BUILD_DEFAULT
BUILD_DEFAULT_TARGETS
BUILD_MAKE_PROGRAM
BUILD_MULTIPROCESSOR
DDK_TARGET_OS
DDKBUILDENV
DEPRECATE_DDK_FUNCTIONS
NO_BINPLACE
NO_BROWSER_FILE
NTDEBUG
The following environment variables are not automatically set by using the SetEnv.bat file when the build environment is created, but can be created by using the set command:
AMD64_FLAGS
BINPLACE_LOG
BUILD_OPTIONS
CHECKED_ALT_DIR
PREFAST_ROOT
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2015-03-04 12:22:18
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https://mathoverflow.net/questions/185042/obscure-names-in-mathematics
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# Obscure Names in Mathematics [closed]
I recently stumbled over the "Happy Ending Problem" (cf e.g. http://en.wikipedia.org/wiki/Happy_Ending_problem), which made we wonder, if there are other conjectures, theorems or problems, whose names do not give any indication to what they are about or, to which person it is related;
the "kissing number" would not qualify here, because it is a definition, but neither a problem nor a theorem.
Besides the "Happy Ending Theorem", I also found
## closed as off-topic by Yemon Choi, Boris Bukh, Chris Godsil, Suvrit, Mariano Suárez-ÁlvarezOct 22 '14 at 22:28
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Yemon Choi, Boris Bukh, Chris Godsil, Suvrit, Mariano Suárez-Álvarez
If this question can be reworded to fit the rules in the help center, please edit the question.
• I thought Happy Ending referred to something completely different. – Will Jagy Oct 22 '14 at 4:35
• voted to close because it's nowhere near research level. I'm not sure whether or not this is on-topic at math.SE because I don't know enough about that site. – Peter McNamara Oct 22 '14 at 7:42
• @WillJagy: See also the Going Down Theorem. – Nate Eldredge Oct 22 '14 at 18:38
• Yes, I believe that's known as Yemon's Observation. – Gerry Myerson Oct 22 '14 at 22:05
• I propose Myerson's Observation: "If we are going to add theorems named after the wrong people then we will be here all day." – Joel Reyes Noche Oct 23 '14 at 5:16
I'm not sure if all these give "no clue", but they are somewhat obscure clues:
The Law of the Unconscious Statistician.
The Chinese Postman Problem
The Googol Game (aka the Secretary Problem)
The Art Gallery Theorem (or Problem)
and for those who know some Latin:
• as this is a soft question, all of these are acceptable to me – Manfred Weis Oct 22 '14 at 5:12
• The Tomato Can principle. – Robert Israel Oct 22 '14 at 7:03
• @RobertIsrael: Gauß has a theorema aureum, too. André Weil even wrote once something like, "he [the Princeps Mathematicorum] was very fond of this type of names"... – José Hdz. Stgo. Oct 23 '14 at 0:18
The Ten Martini Problem was a conjecture posed by Kac and Simon and answered by Avila and Jitomirskaya.
The ugly duckling theorem.
The no free lunch theorem.
• For a layman hearing ‘Cox-Zucker’ for the first time, it might take on a whole different meaning. – Transcendental Oct 22 '14 at 19:41
• "problems, whose names do not give any indication to what they are about or, to which person it is related...." Do Killing-Hopf and Cox-Zucker qualify? – Gerry Myerson Oct 22 '14 at 22:07
• In the strict sense: no, but let's be generous – Manfred Weis Oct 23 '14 at 0:17
• Similar to the Killing-Hopf theorem, the Italian name for the Gaussian elimination method sounds like someone is debating on the best way to kill poor C.F. Gauss. – Federico Poloni Nov 15 '14 at 10:02
The Busy Beaver Problem.
The Beer Glass Theorem.
The Garden of Eden Theorem.
• After posting this, I tried to StartPage "beer glass theorem" and couldn't find anything, so maybe it's not so well known by that name. Too bad, it would be a nice accompaniment to the Ham Sandwich Theorem. – bof Oct 22 '14 at 6:42
• The Beer Glass Theorem says that, if three congruent circles in the plane intersect at one point, then the circle determined by the other three intersections is congruent to the original circle. Is there another name for this theorem? – bof Oct 23 '14 at 3:47
• I mentioned the Byzantine Generals in an earlier comment on the original post. – Gerry Myerson Oct 23 '14 at 4:42
• @GerryMyerson Dagnabbit! I searched the page for "Byzantine" but I forgot to click on "show more comments". I will delete the generals from my answer. – bof Oct 23 '14 at 4:52
Pigeonhole (or Box) Principle. (Note that "rational box problem" is very different from "Box principle".)
Jugendtraum (as with Dirichlet for the Pigeonhole Principle, the name of Kronecker is sometimes omitted).
Hauptvermutung
Technically this is a conjecture, but there are results about whether it is true or not under various circumstances.
• That meets the kriterion of obscurity and not being a definition (if the conjecture were proven, it would be a theorem). – Manfred Weis Oct 22 '14 at 7:14
• Speaking of tropical geometry: the Aztec diamond and the arctic circle theorem ( en.wikipedia.org/wiki/Aztec_diamond ). – darij grinberg Oct 22 '14 at 21:13
• And speaking of Aztec diamond, Cairo pentagonal tilings. – Yoav Kallus Oct 22 '14 at 21:26
• "problems, whose names do not give any indication to what they are about or, to which person it is related...." Does the Margulis napkin problem qualify? – Gerry Myerson Oct 22 '14 at 22:06
• @GerryMyerson : Maybe I should use the Wikipedia name, "napkin folding problem." But then maybe the objection is that "folding" is a clue to what it is about. – Timothy Chow Oct 23 '14 at 17:40
The master theorem. ${}{}{}{}{}{}{}{}{}$
For a theorem whose name is actually misleading about its actual content, check out the case of the Diversity trumps ability theorem, as described by Abigail Thompson in a recent Notices: http://www.ams.org/notices/201409/index.html
The Hauptsatz (due to Gentzen).
The Stable marriage problem.
• The Stable Marriage problem (or theorem) is about the stability of marriage, isn't it? – bof Oct 23 '14 at 3:42
• I guess, though that sort of objection applies to lots of other answers here too (e.g., the Traveling Salesman problem is about a traveling salesman). – dfan Oct 23 '14 at 12:37
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2019-04-18 17:19:38
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https://webwork.libretexts.org/webwork2/html2xml?answersSubmitted=0&sourceFilePath=Library/272/setStewart13_2/problem_4.pg&problemSeed=123567&courseID=anonymous&userID=anonymous&course_password=anonymous&showSummary=1&displayMode=MathJax&problemIdentifierPrefix=102&language=en&outputformat=sticky
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Find parametric equations for line that is tangent to the curve $x=\cos t,\ y=\sin t, \ z=t$ at the point
$(\cos(\frac{5\pi}{6}) ,\sin(\frac{5\pi}{6}) ,\frac{5\pi}{6} )$ .
Parametrize the line so that it passes through the given point at t=0. All three answers are required for credit.
$x(t)$ =
$y(t)$ =
$z(t)$ =
Your overall score for this problem is
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2020-03-29 22:18:22
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https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/10%3A_Rotational_Motion_and_Angular_Momentum/10.0%3A_Prelude_to_Rotational_Motion_and_Angular_Momentum
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$$\require{cancel}$$
# 10.0: Prelude to Rotational Motion and Angular Momentum
Why do tornadoes spin at all (Figure $$\PageIndex{1}$$)? And why do tornados spin so rapidly? The answer is that air masses that produce tornadoes are themselves rotating, and when the radii of the air masses decrease, their rate of rotation increases. An ice skater increases her spin in an exactly analogous manner as seen in Figure $$\PageIndex{2}$$. The skater starts her rotation with outstretched limbs and increases her spin by pulling them in toward her body. The same physics describes the exhilarating spin of a skater and the wrenching force of a tornado.
Figure $$\PageIndex{1}$$: The mention of a tornado conjures up images of raw destructive power. Tornadoes blow houses away as if they were made of paper and have been known to pierce tree trunks with pieces of straw. They descend from clouds in funnel-like shapes that spin violently, particularly at the bottom where they are most narrow, producing winds as high as 500 km/h. (credit: Daphne Zaras, U.S. National Oceanic and Atmospheric Administration)
Clearly, force, energy, and power are associated with rotational motion. These and other aspects of rotational motion are covered in this chapter. We shall see that all important aspects of rotational motion either have already been defined for linear motion or have exact analogs in linear motion. First, we look at angular acceleration—the rotational analog of linear acceleration.
Figure $$\PageIndex{2}$$: This figure skater increases her rate of spin by pulling her arms and her extended leg closer to her axis of rotation. (credit: Luu, Wikimedia Commons)
# Contributors
• Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).
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2019-11-12 18:13:39
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https://hackage.haskell.org/package/twee-lib-2.4.2/docs/Twee-Rule-Index.html
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twee-lib-2.4.2: An equational theorem prover
Twee.Rule.Index
Synopsis
# Documentation
data RuleIndex f a Source #
Constructors
RuleIndex Fieldsindex_oriented :: !(Index f a) index_all :: !(Index f a)
#### Instances
Instances details
(Labelled f, Show f, Show a) => Show (RuleIndex f a) Source # Instance detailsDefined in Twee.Rule.Index MethodsshowsPrec :: Int -> RuleIndex f a -> ShowS #show :: RuleIndex f a -> String #showList :: [RuleIndex f a] -> ShowS #
insert :: forall f a. (Symbolic a, ConstantOf a ~ f, Has a (Rule f)) => Term f -> a -> RuleIndex f a -> RuleIndex f a Source #
delete :: forall f a. (Symbolic a, ConstantOf a ~ f, Eq a, Has a (Rule f)) => Term f -> a -> RuleIndex f a -> RuleIndex f a Source #
matches :: Term f -> Index f a -> [(Subst f, a)] Source #
Look up a term in the index. Like lookup, but returns the exact value that was inserted into the index, not an instance. Also returns a substitution which when applied to the value gives you the matching instance.
lookup :: (Has a b, Symbolic b, Has b (TermOf b)) => TermOf b -> Index (ConstantOf b) a -> [b] Source #
Look up a term in the index. Finds all key-value such that the search term is an instance of the key, and returns an instance of the the value which makes the search term exactly equal to the key.
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2023-02-02 15:02:37
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https://tinynet.autoai.org/en/latest/optims.html
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# Optimizers¶
class tinynet.optims.SGDOptimizer(lr, momentum=None)
In this class, we implement the stochastic gradient descent algorithm, which is used to update the parameters in a neural network. The algorithm is simple:
$w^{new} = w^{old}-\lambda \nabla$
where $$\lambda$$ is the preset learning rate, and $$\nabla$$ is the gradient.
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2020-10-26 19:19:46
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https://testbook.com/objective-questions/mcq-on-project-management--5f3af34f9db84b2091264f0e
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Crashing is
1. Abandoning the project
2. Completing the project with all possible haste
3. Reduction of duration for a few of the activities
4. Reducing the cost of the project with all needful modifications
Option 3 : Reduction of duration for a few of the activities
Project Management MCQ Question 1 Detailed Solution
Explanation:
Crashing is the method for shortening the project duration by reducing the time of one or more critical activities to less than their normal time. In crashing if cost increases then time decreases.
With reference to problem solving, fixation refers to
1. Focused approach to problem solving
2. Planned approach to problem solving
3. An ability to see a problem from a fresh perspective
4. An ability to comprehend the goals to be achieved
Option 3 : An ability to see a problem from a fresh perspective
Project Management MCQ Question 2 Detailed Solution
Problem-solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.
There are 4 steps to solve the problem:
Step 1: Understand the problem.
Step 2: Devise a plan (translate).
Step 3: Carry out the plan (solve).
Step 4: Look back (check and interpret).
Fixation - An ability to see a problem from a fresh perspective. This impedes problem-solving, Two examples of fixation are mental set and functional fixedness.
CPM method of network analysis is1. Ideally suited for linearly extending works2. Meant essentially for research and development activities.3. Activity-oriented4. Used for planning, scheduling and controlling purposes
1. 1 and 2 only
2. 2 and 3 only
3. 3 and 4 only
4. 1 and 4 only
Option 3 : 3 and 4 only
Project Management MCQ Question 3 Detailed Solution
Explanation:
• Critical Path Method (CPM) have been used for planning scheduling and controlling in the construction project management.
• It is activity oriented method.
CPM PERT I. Critical path method Programme valuation and review technique II. Deterministic Probabilistic III. Control time and cost Control only time IV. Activity oriented Event oriented V. One time estimate Three time estimate VI. Use-Non Research Research
Which term refers to a single person having authority to oversee all aspects of a product's production scheduling, inventory, dislocation and sales?
1. Project management
2. Product management
3. Commercial management
4. Venture management
Option 2 : Product management
Project Management MCQ Question 4 Detailed Solution
Explanation:
• Project Management is the process which includes initiating the project, developing a plan, executing the project as per approved plan, monitoring and controlling the project, handing over the output of the project to the client and finally closing the project.
• Product Management is responsible to oversee all the aspects of product's production is set a product vision and strategy that is differentiated and delivers unique value based on customer demand, define what product will deliver and timeline for implementation, provide cross functional leadership, most notably between engineering team, stores, distribution, sales, marketing and support.
• Commercial Management is identification and development of business opportunities and profitable management of projects and contracts from in option to completion.
• Venture management is a discipline that focuses on being both innovative and challenging in the realm of introducing what could be a completely new product or entering a promising new emerging market.
• After the project has been successfully completed, production is undertaken. Product Managers look after the aspects of products production, production scheduling, and inventory requirement of location and sales of the project.
The application of Special purpose material handling equipment is:
1. Both 'Process layout' and ' Line layout'
2. Process layout
3. Line layout
4. None of these
Option 3 : Line layout
Project Management MCQ Question 5 Detailed Solution
The special-purpose material handling equipment is used in the line layout. Line layout is also known as product layout.
Process Layout:
The process layout is recommended for batch production. All machines performing a similar type of operation are grouped at one location in the process layout e.g., all lathes, milling machines, etc. are grouped in the shop will be clustered in like groups.
Process layout is normally used when the production volume is not sufficient to justify a product layout.
Product Layout:
It is also known as line layout. In implies that various operations on raw material are performed in a sequence and the machines are placed along the product flow line i.e. machines are arranged in the sequence in which the raw material will be operated upon.
This type of layout is preferred for continuous production i.e. involving a continuous flow of in-process material towards the finished product stage.
Which one of the following schedules shows the specific activities necessary to complete an activity or work package?
1. Project schedule
2. Master schedule
4. Internal schedule
Project Management MCQ Question 6 Detailed Solution
Explanation:
Work break down structure
Work break down (WBD) defines each deliverable and the decomposition of the deliverable into work packages.
• Task schedule deals with allocation of resources related to work package as well activity.
• When the project activities have been defined, they are broken down into tasks and after time & resource allocation, task schedules are prepared which is specified activities necessary to complete a work package.
An individual investor who invests in the e-project usually during an early stage is
1. corporate strategic investor
2. founder capital
3. angel investor
4. venture capital
Option 3 : angel investor
Project Management MCQ Question 7 Detailed Solution
Explanation:
• An angel investor (also known as a private investor, seed investor or angel investor) is a high net worth individual who provides financial backing for small startups or entrepreneurs, typically in exchange for ownership equity in the company.
• The funds that angel investors provide may be a one-time investment to help the business get off the ground or an ongoing injection to support and carry the company through its difficult early stages.
• Angel investors vary widely, but they are typically willing to accept risk and demand little or no control in return for the chance to own.
The market price per share of a company is Rs. 125. The dividend per share (DPS) is Rs 12 and DPS is expected to grow at a constant rate of 8% per annum. The cost of the equity capital to company will be
1. 17.6%
2. 15.4%
3. 13.2%
4. 11.8%
Option 1 : 17.6%
Project Management MCQ Question 8 Detailed Solution
Concept:
$$Cost\;of\;equity = \frac{{DP}}{{MPS}} + r$$
Calculation:
Given:
Market price per share = Rs 125, Dividend per share = Rs 12, Rate = 8 % = 0.08
Now,
$$Cost\;of\;equity = \frac{{DP}}{{MPS}} + r$$
$$\therefore Cost\;of\;equity = \frac{{12}}{{125}} + 0.08$$
Cost of equity = 0.096 + 0.08 = 0.176
Thus, the cost of equity = 17.6%
The best tool to ensure that there is neither piling up of stocks nor shortage of materials in a project to run it economically is
1. Economic Order Quantity
2. ABC Analysis
3. Inventory Control and Management
4. Gantt Chart Method
Option 3 : Inventory Control and Management
Project Management MCQ Question 9 Detailed Solution
Explanation:
• Inventory control with optimum stock level to minimize annual cost by controlling inventory.
• The purpose of inventory management is to ensure availability of materials in sufficient quantity as when required and also to minimize investment in inventories.
• EOQ is the order size at which the sum of carrying cost and ordering cost is minimum.
_______ is a manufacturing philosophy that emphasizes careful scheduling of work, on-time delivery of zero-defect supplies, and a highly-skilled workforce.
1. PERT
2. MRP
3. EOQ
4. JIT
Option 4 : JIT
Project Management MCQ Question 10 Detailed Solution
Explanation:
JIT is associated with Japanese management techniques. It is known as just-in-time production (JIT) is a set of principles and practices based on the philosophy that firms should hold little or no inventory beyond that required for immediate production or distribution.
JIT consists of different operations such as,
• Carefully scheduling
• on-time delivery
• Zero defects
• Skilled workforce
Other Manufacturing phylosophies
PERT stands for Program Evaluation and Review Technique and was developed to address the needs of projects for which the time and cost estimates tend to be quite uncertain.
• It has a probabilistic approach and hence suitable for the projects which are to be conducted for the first time or projects related to research and development.
• PERT uses 3 cases:
• Optimistic time estimates the shortest possible time required for the completion of the activity
• Most likely time estimates the time required for the completion of activity under normal circumstances
• Pessimistic time estimates the longest possible time required for the completion of the activity
EOQ:
The ordering quantity Q* at which holding cost becomes equal to ordering cost and the total inventory cost is minimum is known as Economic Order Quantity (EOQ).
At EOQ, Ordering cost = Holding cost
$$\frac{D}{{{Q^*}}}{C_o} = \frac{{{Q^*}}}{2}{C_h} \Rightarrow {Q^*} = \sqrt {\frac{{2D{C_o}}}{{{C_h}}}}$$
where D = Annual or yearly demand for inventory (unit/year), Q = Quantity to be ordered at each order point (unit/order), Co = Cost of placing one order [Rs/order], Ch = Cost of holding one unit in inventory for one complete year [Rs/unit/year]
Materials requirements planning (MRP)
• It is a simple system of calculating arithmetically the requirements of the input materials at different points of time based on the actual production plan.
• It can be seen from the figure that an MRP system has three major input components:
In a project life cycle, the maximum percentage of effort is done in
1. Concept phase
2. Definition phase
3. Planning and organizing phase
4. Implementation phase
Option 4 : Implementation phase
Project Management MCQ Question 11 Detailed Solution
Explanation:
A standard project typically has the following four major phases (each with its own agenda of tasks and issues): initiation, planning, implementation, and closure. Taken together, these phases represent the path a project takes from the beginning to its end and are generally referred to as the project "life cycle."
Initiation Phase
• During the first of these phases, the initiation phase, the project objective or need is identified; this can be a business problem or opportunity.
• An appropriate response to the need is documented in a business case with recommended solution options.
• A feasibility study is conducted to investigate whether each option addresses the project objective and a final recommended solution is determined. Issues of feasibility ("can we do the project?") and justification ("should we do the project?") are addressed.
Planning Phase
• The next phase, the planning phase, is where the project solution is further developed in as much detail as possible and the steps necessary to meet the project's objective are planned.
• In this step, the team identifies all of the work to be done. T
• The project's tasks and resource requirements are identified along with the strategy for producing them. This is also referred to as "scope management."
Implementation (Execution) Phase
• During the third phase, the implementation phase, the project plan is put into motion and the work of the project is performed.
• It is important to maintain control and communicate as needed during implementation. Progress is continuously monitored and appropriate adjustments are made and recorded as variances from the original plan. In any project, a project manager spends most of the time in this step.
• During project implementation, people are carrying out the tasks, and progress information is being reported through regular team meetings. The project manager uses this information to maintain control over the direction of
Closing Phase
• During the final closure or completion phase, the emphasis is on releasing the final deliverables to the customer, handing over project documentation to the business, terminating supplier contracts, releasing project resources, and communicating the closure of the project to all stakeholders.
• The last remaining step is to conduct lessons-learned studies to examine what went well and what didn't. Through this type of analysis, the wisdom of experience is transferred back to the project organization, which will help future project teams.
The intensity of activities (% of work done) is highest in the implementation phase of PLC.
From the above graph it is clear that in a project life cycle, the maximum percentage of effort is done in the implementation phase.
In which method we can calculate net annual return as percentage of capital investment.
1. Net percent value method
2. Return on investment method
3. Cost benefit method
4. Payback method
Option 2 : Return on investment method
Project Management MCQ Question 12 Detailed Solution
Explanation:
Return on investment (ROI):
• It is a financial metric that is widely used to measure the probability of gaining a return from a capital investment.
• It is a ratio that compares the gain or loss from an investment relative to its cost.
• It can be used to measure the profitability of a stock investment, when deciding whether or not to invest in the purchase of a business, or evaluate the results of a real estate transaction.
Net present value (NPV):
It is a method used to determine the current value of all future cash flows generated by a project, including the initial capital investment. It is widely used in capital budgeting to establish which projects are likely to turn the greatest profit.
$$NPV = \frac{{{R_t}}}{{{{\left( {1 + i} \right)}^t}}}$$
NPV = net present value
Rt = net cash flow at time t
i = discount rate
t = time of the cash flow
Cost-benefit analysis (CBA): It is a technique used to compare the total costs of a program/project with its benefits, using a common metric (most commonly monetary units).
Payback method:
• It is a method of evaluating a project by measuring the time it will take to recover the initial investment.
• The payback period is the number of months or years it takes to return the initial investment.
• To calculate a more exact payback period: payback period = amount to be invested/estimated annual net cash flow.
• The payback method also ignores the cash flows beyond the payback period; thus, it ignores the long-term profitability of a project.
The information to be made available for certain heavy purchases through the newspaper is called:
1. Guideline
2. Terms and condition
3. Purchased notice
4. Tender Notice
Option 4 : Tender Notice
Project Management MCQ Question 13 Detailed Solution
Call of Quotations:
After receiving requisition from various departments, the purchase department issues letters to several registered suppliers for calling rate list.
Issuing registered postal letters to various reputed suppliers for their competitive rates is called calling of quotations.
The quotations are called in two ways.
• By issuing individual letters by register post letters to suppliers which is called Limited Tender.
• By newspaper advertisement which is called Tender Notice or a Public Tender or Open Tender.
Tender: It is an offer made by the supplier or manufacturer in reply to a quotation letter for the supply of material on the basis of some terms & condition.
What is an optimizing strategy?
1. Strategy of choosing the best possible solution considering all parameters
2. Strategy of choosing a compromise solution
3. Strategy of choosing the least cost solution
4. Strategy of choosing a solution on the basis of precedents
Option 1 : Strategy of choosing the best possible solution considering all parameters
Project Management MCQ Question 14 Detailed Solution
Explanation:
• Finding an alternative with the most cost-effective or highest achievable performance under the given constraints, by maximizing desired factors and minimizing undesired one.
• In comparison, maximization means trying to attain the highest or maximum result or outcome without regard to cast or expense.
A simple project comprises of two start-to-end parallel paths, each with three activities in series, with no interpath dependencies. The a, m, b data (in days) for each activity are shown in the diagram. Assuming that three activities in series are enough for further computations, what will be the total project duration and its standard deviation?
1. 35 1 / 2 days and 14 / 3 days
2. 34 1 / 2 days and 5 / 2 days
3. 35 1 / 2 days and 13 / 6 days
4. 34 1 / 2 days and 11 / 6 days
Option 4 : 34 1 / 2 days and 11 / 6 days
Project Management MCQ Question 15 Detailed Solution
Explanation:
Here two path – (I) ⇒ 1 – 2 – 4 – 6
(II) ⇒ 1 – 3 – 5 – 6
Calculation of expected time for both path –
$${T_e} = \frac{{{T_0} + 4{T_m} + {T_p}}}{6}$$
For I
$$\Rightarrow \frac{{2 + 4 \times 3 + 4}}{6} + \frac{{4 + 4 \times 6 + 8}}{6} + \frac{{5 \times 4 \times 8 + 11}}{6}$$
= 3 + 6 + 8
= 17 days
For II
$$\Rightarrow \frac{{6 + 4 \times 7 + 8}}{6} + \frac{{12 + 4 \times 12 + 18}}{6} + \frac{{9 + 4 \times 15 + 18}}{6}$$
= 7 + 13 + 14.5
$$= 34\frac{1}{2}{\rm{\;days}}$$
Hence longest path II so it is critical standard deviation.
$$\delta d = \sqrt {\sum {{\left( {\frac{{{T_p} - {T_0}}}{6}} \right)}^2}}$$
$$\sigma = \sqrt {{{\left( {\frac{{8 - 6}}{6}} \right)}^2} + {{\left( {\frac{{18 - 12}}{6}} \right)}^2} + {{\left( {\frac{{18 - 9}}{6}} \right)}^2}}$$
$$\sigma = \sqrt {{{\left( {\frac{1}{3}} \right)}^2} + 1 + {{\left( {\frac{3}{2}} \right)}^2}} = \sqrt {\frac{1}{9} + 1 + \frac{9}{4}} = \sqrt {\frac{{121}}{{36}}}$$
$$\therefore \;\left[ {\sigma = \frac{{11}}{6}\;days} \right]$$
If the EOQ is 360 units, order cost is Rs. 5 per order and carrying cost is Rs. 0.20 per unit, what is the usage?
1. 2654 units
2. 2592 units
3. 1875 units
4. 1574 units
Option 2 : 2592 units
Project Management MCQ Question 16 Detailed Solution
explanation:
EOQ = 360
(Co) ordering cost per unit = Rs. 5 per order
(Cc) carrying cost per unit = Rs. 0.20
So,
$$EOQ = \sqrt {\frac{{22R{C_o}}}{{{C_c}}}}$$
$$EOQ = 360 = \sqrt {\frac{{2 \times R \times 5}}{{0.20}}} \;$$
$${\left( {360} \right)^2} = \frac{{2 \times R \times 5}}{{0.20}}$$
$$R = \frac{{{{\left( {360} \right)}^2} \times 0.20}}{{2 \times 5}}$$
R = 2592 Unit
[Demand = 2592 Unit]
ABC analysis in materials management is a method of classifying the inventories based on the
1. Economic order quanitity
2. Value of annual usage of the items
3. Volume of material consumption
4. Quantity of materials used
Option 2 : Value of annual usage of the items
Project Management MCQ Question 17 Detailed Solution
Explanation:
ABC Analysis – Always better control.
• It is a method of inventory control that involves a system that controls inventory is used for the material throughout distribution.
• It is also known as selective inventory control SIC.
• This method divides the subject/inventory into three categories.
A ⇒ Most valuable product or customer and less quantity.
B ⇒ Middle valuable second-highest in No.
C ⇒ Less value and a no. of inventory.
Which one of the following risks can be reduced by investing in project or acquiring other firms that have a negative correlation with the earnings of the firm?
1. Investment risk
3. Financial risk
4. Portfolio risk
Option 4 : Portfolio risk
Project Management MCQ Question 18 Detailed Solution
Explanation:
• When two variables are negatively correlated, one variable decreases as the other increases, and vice versa. Negative correlations between two investments are used in risk management to diversify, or mitigate, the risk associated with a portfolio.
• Business risk refers to the basic viability of a business—the question of whether a company will be able to make sufficient sales and generate sufficient revenues to cover its operational expenses and turn a profit.
• While financial risk is concerned with the costs of financing, business risk is concerned with all the other expenses a business must cover to remain operational and functioning. These expenses include salaries, production costs, facility rent, office, and administrative expenses.
• Interest rate risk is the risk that an investment's value will change due to a change in the absolute level of interest rates, the spread between two rates, in the shape of the yield curve, or in any other interest rate relationship.
• This type of risk affects the value of bonds more directly than stocks and is a significant risk to all bondholders. As interest rates rise, bond prices in the secondary market fall and vice versa.
During an assessment of economic viability of the project, the ratio of average annual earnings after tax to the average book investment after depreciation is called
1. Benefit-Cost Ratio (BCR)
2. Net Present Value (NPV)
3. Pay-Back Period PBP)
4. Return on Investment (ROI)
Option 4 : Return on Investment (ROI)
Project Management MCQ Question 19 Detailed Solution
Explanation:
• Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment or compare the efficiency of a number of different investments. (Average rate of return is also called as return on investment).
• ROI tries to directly measure the amount of return on a particular investment, relative to the investment’s cost.
• It calculates the profitability of the company by measuring the earnings related to the amount of capital invested.
• To calculate ROI, the benefit (or return) of an investment is divided by the cost of the investment. The result is expressed as a percentage or a ratio.
$$Return\;on\;investment\;\left( {ROI} \right) = \frac{{{\rm{Annual\;average\;profit\;after\;tax\;}}}}{{{\rm{Average\;investment}} \times 100}}$$
Points to remember:
1. A benefit-cost ratio (BCR) is an indicator showing the relationship between the relative costs and benefits of a proposed project, expressed in monetary or qualitative terms. If a project has a BCR greater than 1.0, the project is expected to deliver a positive net present value to a firm and its investors.
2. Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.
3. Payback Period (PBP) is one of the simplest capital budgeting techniques. It calculates the number of years a project takes in recovering the initial investment based on the future expected cash inflows.
Direction: It consists of two statements, one labelled as ‘Statement (I)’ and the others as ‘Statement (II)’. You are to examine these two statements carefully and select the answer using the codes given below:Statement (I): All projects have constraints or limitations that inhibit their ability to reach goals and objectives.Statement (ll): Time and money are universal constraints in projects.
1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
2. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
3. Statement (I) is true but Statement (II) is false
4. Statement (I) is false but Statement (II) is true
Option 2 : Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
Project Management MCQ Question 20 Detailed Solution
Explanation:
Projects are subject to several constraints including time, money, quality, resources and risks.
Constraints tend to inhibit project management ability to reach the goals of the project. Besides time and money often vital constraints like quality and risks are constantly working throughout the project life cycle.
Three constraints –
• Time – The amount of time it takes to perform the projects.
• Scope – The amount of work to be performed and deliverable to be provided.
• Cost – The amount of money it takes to perform the work.
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2021-11-27 11:22:04
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http://mattwhipple.com/site_generation.html
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# Site Generation - Matt Whipple
This site is generated with pandoc(1). Each html file can be produced by the corresponding source markdown(2). The source files can be collected using a wildcard/glob which can then be used to derive the output files. The pattern itself can be used to call pandoc with the desired invocation.
To support execution in CI or on any system without a haskell environment, this will also support execution through a container.
# gen_site
Here a script will be defined which drives building the site from the relevant source files.
## Set Some Flags
To enforce stricter bash behavior we’ll abort on unhandled failures and require variables to be defined.
set -euo pipefail
## Transform a File
The site itself will be generated by producing individual files with pandoc. If this function is called with a source and an output file it will invoke pandoc with some standard options.
Here the call to pandoc is abstracted so that the presence of pandoc can be validated or alternative execution methods can be provided.
gen_site::xform_file() {
local -r source=${1:?'Source file must be specified!'} local -r output=${2:?'Output file must be specified!'}
gen_site::call_pandoc --defaults pandoc.defaults --standalone --output ${output}${source}
}
## Call Pandoc
The pandoc indirection introduced above can now be defined. The initial implementation to match the development system will call Pandoc through Docker and it will relay any provided parameters.
TODO Detect options or die trying
gen_site::call_pandoc() {
docker run --rm --volume $(pwd):/host -w /host pandoc/core:2.14.0.1${@}
}
## Main
The main build process will consist locating all of the source files and transofming each. This will expect a directory where *.md source files exist and a directory to which output will be written.
gen_site::main() {
local -r src_dir=${1:?'Source directory must be specified!'} local -r out_dir=${2:?'Output directory must be specified!'}
mkdir -p "${out_dir}" for src in "${src_dir}"/*md; do
gen_site::xform_file "${src}" "${out_dir}/${src%.md}.html" done } gen_site::main${@}
## Required Commands
This section will define some of the invoked commands using the required command Make recipe. For the time being this will just be copied around.
missing-command = $(error$(or ${${1}_INSTALL}, '${1}; is missing; please install${1}))
required-command = $(or${_${1}_which}, \$(eval _${1}_which=$(shell which ${1})), \${_${1}_which}, \$(call missing-command,${1})) DOCKER =$(call required-command,docker)
## Basic Project Structure
Next to define some basic project structure with inputs and outputs. A site PHONY target will be defined to enable building of all of the outputs.
OUT_DIR := public/
SOURCES = $(wildcard *.md) OUTPUTS =$(addprefix ${OUT_DIR},${SOURCES:%.md=%.html})
else
PANDOC = $(call required-command,pandoc) endif ## Store Commands in File While it seems somewhat heavy, this project will also support a third means of execution. The pandoc image used above does not include make and therefore cannot readily use the invocations derived by the rules within this file. Since these steps can be done independently I’d rather go that route than introduce a customized image when wanting to use a pipeline of containers (for CI). It seems likely I’ll find a one-stop image at some point which will render this unnecessary, but for now this file will also support generation of a shell script containing what it would otherwise do. Generation of such a file is fairly straightforward as it can amount to overriding the already defined PANDOC variable to echo to the specified file rather than call the produced command. The final functionality is very simple but is built on top of a fairly high level of comfort with the underlying tools. GEN_SCRIPT:= gen_site clean-script: ; rm -f${GEN_SCRIPT}
.PHONY: clean_script
${GEN_SCRIPT}: PANDOC = >>${GEN_SCRIPT} echo pandoc
${GEN_SCRIPT}: clean-script site chmod +x${@}
## Define Conversion Rule
With all of the building blocks defined, the rule to pass the sourcefiles through pandoc to produce the HTML output can be defined.
${OUT_DIR}%.html: %.md${PANDOC} --defaults pandoc.defaults -s -o ${@}${<}
# Pandoc defaults file
Pandoc will be configured through the use of the defaults file (1 sec. #default-files). supports which is pointed to above.
## Define input and output formats
I’ll be using Pandoc enhanced Markdown as input and generating modern HTML. At some point in the future I may want to swap the output over to something more component/React based but that’s not particularly likely to actually happen and if so not for a bit yet.
from: markdown
to: html5
## Configure Citations
I want to use citations with a global bibliography. The link-citations metadata field (1 sec. #other-relevant-metadata-fields) is helpful to provide appropriate hyperlinking. With the linking I also prefer more of a footnote citation style so this uses the numeric ISO 690 CSL style retrieved from the Zotero Style Repository(4). Without an appropriate background, sticking to an ISO standard seemed a safe choice.
citeproc: true
bibliography:
- sources.bib
citation-style: iso690-numeric-en.csl
link-citations: true
## Configure Math Rendering
At some point I’ll likely be incorporating some interesting path but in the short term I’ve already run up against the limits of the raw rendering so I’ll start with what seems like the default better option of mathjax.
html-math-method:
method: mathjax
1.
Pandoc - pandoc user’s guide [online]. June 2021. Available from: https://pandoc.org/MANUAL.html
2.
Daring fireball: markdown [online]. 17 April 2021. Available from: https://daringfireball.net/projects/markdown
3.
Pandoc/dockerfiles: Dockerfiles for various pandoc images [online]. May 2021. Available from: https://github.com/pandoc/dockerfiles
4.
Zotero style repository [online]. Available from: https://zotero.org/styles
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2021-09-19 07:22:56
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https://czgdp1807.github.io/2021/05/21/week_1.html
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# Week 1 - Declaring, Initialising and Passing Fortran Arrays
Hi, welcome to another blog of mine. I am back with GSoC, Season 2, this time with LFortran, an awesome compiler project for Fortran, an underappreciated but beautiful programming language. I am working on adding support for arrays under the mentorship of Ondřej Čertík, who is also the founder of LFortran. In this and upcoming blogs I will be discussing weekly progress of my GSoC project. Let’s get started with the first week.
During the first week, I worked on three things, first one being extending support for declaring any type of static array, the second one involves making initialiser expressions work for static arrays and the last one is about passing arrays to intrinsic functions such as size. I have provided details on each of the three in the following subsections.
Declaring Static Arrays
In Fortran, arrays are declared by providing dimensions to the type or variable in either of the following ways, real, dimension(2,3,4) :: h or real :: h(2, 3, 4). This code was getting parsed for integer and LLVM IR was successfully generated. However, for other types such as real, logical, complex and derived types, the support was only available till Abstract Semantic Representation (ASR) level. Note that LFortran has three levels of abstraction, Abstract Syntax Representation (AST) which extracts all the syntactic information directly available from the Fortran program; ASR, which makes out the meaning from ASR and checks whether the program is making sense and Backend (such as LLVM) generates target code (binary, C++, etc) depending upon the user input. Now coming back to the blog. So, in this week I extended support for generating LLVM IR for declarations of real, complex, logical and derived types.
Merge Request - !931
Initialising Static Arrays
After completing declaration, I headed towards providing support for initialzer expressions for arrays. One example is, x = [(i+1, i*2, i = 1, 3)], where x is the array variable. First I added ImpliedDoLoop node at ASR level and then I introduced an ASR pass to convert the overall assignment operation with array variable on the LHS and an ArrayInitializer wrapping an ImpliedDoLoop to a DoLoop. Basically the pass performs the following task,
Converts:
x = [(i*2, i = 1, 6)]
to:
do i = 1, 6
x(i) = i*2
end do
This allows us to generate LLVM IR without even touching the backend algorithm as the resulting do loop has all the logic already implemented in the LLVM backend to generate LLVM IR. I learnt the trick of writing ASR passes from Ondřej before GSoC and that worked beautifully here.
Merge Request - !932
Passing Fortran Arrays To Intrinsic Functions
I would say this was the most challenging part of the first week. It required a hell lot of brainstorming. The main problem was to decide the interface of size intrinsic function in LLVM IR. The LLVM IR considers static arrays of different sizes as different types altogether. Hence, we may need to define different size functions for different sized arrays doing exactly the same thing again and again. So, in the end I finally decided to extract the dimension information (lower bound, upper bound) and pass it to the interface. Since, dimension descriptor is of a single unique type we will be needing just one definition of size function at LLVM level. However, the game is not over yet. Ondřej highlighted some important points today. One of them is the issue of overshadowing of user defined size function with the intrinsic function but the opposite should happen. I am working on it and will let you know in the next week’s update. Until then stay tuned…
Merge Request - !918
### Email
singh.23@iitj.ac.in
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2022-01-18 22:20:50
|
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|
http://materialstechnology.asmedigitalcollection.asme.org/article.aspx?articleid=2667148&journalid=121
|
0
Research Papers
# Ab Initio Study of Iodine-Doped Carbon Nanotube ConductorsPUBLIC ACCESS
[+] Author and Article Information
Yangchuan Li
Department of Mechanical Engineering,
University of Texas,
Austin, TX 78712
e-mail: liyangchuan@utmail.utexas.edu
Eric Fahrenthold
Department of Mechanical Engineering,
University of Texas,
Austin, TX 78712
e-mail: epfahren@mail.utexas.edu
Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 8, 2017; final manuscript received December 13, 2017; published online January 19, 2018. Assoc. Editor: Peter W. Chung.
J. Eng. Mater. Technol 140(2), 021008 (Jan 19, 2018) (9 pages) Paper No: MATS-17-1132; doi: 10.1115/1.4038780 History: Received May 08, 2017; Revised December 13, 2017
## Abstract
The widespread use of copper in power and data cabling for aircraft, ships, and ground vehicles imposes significant mass penalties and limits cable ampacity. Experimental research has suggested that iodine-doped carbon nanotubes (CNTs) can serve as energy efficient replacements for copper in mass sensitive cabling applications. The high computational costs of ab initio modeling have limited complimentary modeling research on the development of high specific conductance materials. In recent research, the authors have applied two modeling assumptions, single zeta basis sets and approximate geometric models of the CNT junction structures, to allow an order of magnitude increase in the atom count used to model iodine-doped CNT conductors. This permits the ab initio study of dopant concentration and dopant distribution effects, and the development of a fully quantum based nanowire model which may be compared directly with the results of macroscale experiments. The accuracy of the modeling assumptions is supported by comparisons of ballistic conductance calculations with known quantum solutions and by comparison of the nanowire performance predictions with published experimental data. The validated formulation offers important insights on dopant distribution effects and conduction mechanisms not amenable to direct experimental measurement.
<>
## Introduction
The widespread use of copper in power and data cabling for aircraft, ships, and ground vehicles imposes significant mass penalties and can limit system electrical performance. Carbon nanotube (CNT) [1,2] based electrical conductors have attracted considerable attention, as potential replacements for pure copper, since they may offer improved specific conductivity [3] and higher ampacity [4,5]. CNT-based conductors have been studied both experimentally and computationally, as a promising new cable technology. Their relatively low electrical conductivity [6], as compared to copper, has encouraged the consideration of doped nanotubes as mass efficient replacements in weight-sensitive applications. Tables 1 and 2 compare published data on the electrical conductivity and the mass-specific electrical conductivity of doped CNT with the corresponding properties of copper.
Over the course of the last two decades, considerable experimental research has investigated the conduction performance of single wall carbon nanotubes [7], multiwall carbon nanotubes ([8], doped CNT [3,912], CNT composites [13,14], CNT junctions [15], and CNT networks [16]. Complimentary computational research on these topics has also been performed, although the ab initio computational literature has modeled rather simple systems [11], due in large part to high computational cost. Given the substantial basic knowledge base, recent experimental and computational research has increasingly focused on the most promising material candidates to replace copper in weight-sensitive engineering applications [17,18]. An example application is the development of high specific conductivity power and data cabling for civilian and military aircraft.
The most widely used approach to ballistic conductance modeling employs density functional theory and nonequilibrium Green's function methods to study the electrical transport properties of nanoscale conductors [1921]. Since a macroscopic CNT cable is necessarily composed of many nanoscale CNT conductors and junctions, modeling work on the ballistic conductance of both CNT conductors and CNT junctions is of major interest.
The previous work on CNT conductors has included studies of (1) defects (e.g., vacancies [22]), (2) chemical doping (e.g., F [23], I2, ICl, IBr [11], MoO3 [24], and AuCl3 [25]), (3) multiwall CNT systems (e.g., a double wall CNT in which each tube has different electrical properties [26] or a double wall CNT with variations in the interwall spacing [8]), and (4) the performance of nanocomposite wires (e.g., copper-CNT conductors [27] and sulfur chains positioned inside CNT [28]). Some research has investigated such parameters acting in combination. For example, Lopez-Bezanilla [29] investigated chemically doped double wall CNT, examining the effects of both interwall spacing and outer wall modification [by monovalent phenyl (-C6H5) and divalent dichlorocarbene (>CCl2) dopants] on conductor performance. Note that doping can also have negative effects on conductivity. The last cited research suggested that monovalent dopants have a stronger negative (for metallic CNT) effects on conductance than do divalent dopants. They noted that large interwall spacing can prevent the negative effects of outer tube doping from affecting the inner tube.
In the case of CNT junctions, modeling research has focused on: (1) structural effects (e.g., variations in junction overlap [30,31] or tube intersection angles [32,33]) and (2) chemical doping effects (including transition metals [34], gold nanoparticles [35], or O2 and N2 [36]) on junction performance. The computational results indicate that the junction conductance “oscillates” with the extent of tube overlap, which may explained by “quantum interference” effects [30,31]. With respect to tube intersection angles, the highest conductance has been reported to occur when the junction structure is “commensurate” [33]. In the case of transition metal doping, it appears that the best junction conductance results from chromium doping [34].
In the case of CNT network modeling, most modeling work has employed percolation theory, which accounts for both conductor and junction performance. For example, Refs. [16], [37], and [38] combine the macroscale conductance properties of the conductor with the ballistic conductance properties of the junctions to predict the overall performance of CNT composites. In this paper, the overall CNT network performance is estimated by developing a transmission line model, parametrized by the ballistic conductance properties of both the CNT conductors and the CNT junctions. Hence, in all cases, the results presented in this paper are based on electronic structure calculations.
The succeeding sections of this paper are organized as follows: Section 2 describes the computational methods employed. Section 3 presents modeling results on polyiodide-doped CNT conductors and junctions. The effects of iodine doping on both metallic [CNT(M)] and semiconducting [CNT(S)] carbon nanotubes are included in the analysis. As compared to the previous work [11,39] on iodine dopants, this section considers atom counts as high as 616, an approximate order of magnitude increase over the last cited works. The combination of high atom counts, complex junction structures, and complex dopant distributions resulted in very high computational costs. Hence, this section also describes certain modeling approximations introduced in order to perform ballistic conductance analyses at models sizes sufficient to allow for the study of nanotube interaction, dopant concentration, and dopant distribution effects. The study of these effects is a critical part of any attempt to compare ab initio performance predictions with macroscale experimental results.
Section 4 formulates a transmission line model, used to estimate nanowire performance, applying conductor and junction analysis data presented in the preceding section. The transmission line is represented as series combination [16] of CNT conductors and CNT junctions (alternative methods might be used [40]), in order to estimate nanowire performance. Using room temperature copper conductor properties as a reference, the expected performance of various CNT-based conductors are compared on a specific conductivity basis.
Section 5 discusses conclusions suggested by the computational results presented in the paper.
## Computational Methods
The computational package used in this paper is the open source code SIESTA [41], which is based on density functional theory and employs atomic orbitals as a basis set. The electrical transport properties are computed using a nonequilibrium Green's function method [42], implemented in the TranSIESTA module [43] of the SIESTA package. The electrical conductance ($G$) is calculated using the Landauer formula [44] Display Formula
(1)$G=2e2h∫−∂fE∂ETEdE,TE=Trt†EtE$
where $e$ is the electron charge, $h$ is Planck's constant, $fE$ is the Fermi–Dirac distribution function, $E$ is the wave energy, $TE$ is the transmission function, $†$ denotes the conjugate transpose, and $tE$ is a matrix of transmission coefficients for waves propagating along the conductor. The calculations presented in this paper are made for zero temperature conditions, in which case [45] Display Formula
(2)$−∂fE∂E=δE−Ef$
with $Ef$ being the Fermi energy and $δ$ a Dirac delta function, so that Display Formula
(3)$G=G0TEf,G0=2e2h=7.75×10−5S$
where $G0$ is the standard quantum conductance unit. For an ideal metallic carbon nanotube, $TEf=2$ and $G=2G0$ [7].
All calculations were performed using the generalized gradient approximation for the exchange-correlation functional parameterized by Perdew et al. [46]. A single-zeta basis set was employed for all atoms to reduce computational cost. The accuracy of the single-zeta basis calculations was evaluated by comparing the computed ballistic conductance results for single and dual parallel metallic nanotubes to the “exact” conductance solutions for those systems. The integration k-points in the Brillouin zone were chosen using a Monkhorst–Pack mesh [47]. The model parameters used in the calculations are discussed in the sections which follow.
The junction conductance calculations presented in this paper were performed on atom sets obtained by removing atoms from “relaxed” models of dual, parallel, doped, and undoped nanotubes. This approximation was adopted in part due to difficulties encountered in obtaining converged equilibrium solutions for junction structures using the default SIESTA force convergence criterion (0.04 eV/Å). Note that the published work has employed force convergence criteria that vary by two orders of magnitude (0.001 eV/Å [48] to 0.1 eV/Å [36]).
The accuracy of the approximate junction models was evaluated by comparing the predictions of a nanowire performance model (which incorporates the approximate junction models) with the published experimental data on iodine-doped CNT fibers, as detailed in Sec. 4. Such indirect validation of the approximate junction models is necessitated by the absence of nanoscale experimental data measuring directly junction ballistic conduction as a function of junction geometry, nanotube type, doping concentration, and dopant distribution. The consistency of the nanowire modeling results with the published macroscale experimental data suggests that the conductance calculations presented in this paper are in general representative of the modeled physical systems. The conclusions presented in Sec. 5, which discuss junction geometry, doping mass fraction, doping distribution, and other characteristics of the system not amenable to direct experimental measurement are intended to assist experimental research on the development of new high specific conductivity cabling.
## Polyiodide-Doped Carbon Nanotube
In general, the performance of iodine-doped CNT systems may be affected by iodine atom interactions. An example is the presence of iodine in polyiodide form, as described in experimental papers on both CNT [3,49] and graphene [50], which suggest that $I3−$ and $I5−$ polyiodide chains may be formed during the doping process. An iodine chain structure located inside CNT's was also observed in experiments performed by Fan et al. [51].
Transmission electron microscope images of iodine-doped CNT [3] suggest that the iodine distribution in doped CNT cables consists of (1) interstitial dopant atoms concentrated near CNT “contacts” and (2) randomly distributed dopant atoms scattered across CNT surfaces. To better understand the effects of polyiodide doping, the analysis which follows considers CNT's doped with polyiodide (note that the present model is formulated at the electronic structure level and no molecular structure is imposed). The interaction of both metallic and semiconducting CNT's with polyiodides is investigated.
The following iodine-doped system configurations were modeled, for both metallic and semiconducting CNT (in some configurations, dopant weighting was also varied):
• CNT conductors with “aligned” doping
• CNT conductors with “random” doping
• CNT conductors with “interstitial” doping
• CNT junctions with “interstitial” doping
The modeled CNTs are metallic with chirality (5,5) [CNT(5,5)] and semiconducting with chirality (8,0) [CNT(8,0)], which have diameters 7.1 Å and 6.4 Å, respectively. Note that the smallest energetically stable CNT has diameter of 4 Å [52]. The calculations employed k-points chosen using a Monkhorst–Pack mesh [47]. It is important to note that previous work has employed k-grid dimensions which varied widely. Published conductance calculations have employed k-point dimensions that range from $1×1×4$ [29,34] to $1×1×50$ [53,54]. Since the models presented here are computationally quite expensive, a relatively coarse k-grid was selected. For the relaxation calculations, the k-grid has dimensions $1×1×4$ [34]. For the conductance calculations, the k-grid has dimensions $1×1×9$. The fineness of the real space mesh was controlled by setting the energy cutoff to 200 Ry [5557].
###### Polyiodide-Doped Carbon Nanotube Conductors.
The polyiodide-doped conductor models investigated single nanotube and dual nanotube configurations. In the single nanotube configurations, both aligned and random doping patterns were modeled. In the dual nanotube configuration, only interstitial doping patterns were modeled. These three doping geometries are illustrated in the figures which follow.
Figure 1 shows the doped single metallic nanotube configurations considered. The first and second models assume aligned dopant atoms, with 0.7 iodine atoms per CNT unit cell (0.7/u.c.) and 1.0 iodine atoms per CNT unit cell (1.0/u.c.), respectively. The third model depicts the random doping pattern. In the case of the randomly doped CNT, the electrodes were not doped.
Figure 2 shows the computed conductance for the modeled metallic CNT's. The calculation made here for an undoped metallic CNT (shown by the bar labeled “none”) correctly returns the exact solution of 2.0 quantum conductance units. Note that Ref. [11], which employs a double zeta basis set, returns a conductance 25% lower, perhaps due to electrode effects. The present work employs an electrode whose structure matches that of the modeled device, in order to represent a segment of a much longer (as long as the material's mean free path (MFP)) conductor. The remaining three bars in Fig. 2 show conductance results for the doped metallic nanotubes. They indicate that the conductance of the doped tube is affected by both the dopant concentration and the dopant distribution. At the lowest dopant concentration, the iodine converts the metallic tube into a semiconducting tube, as reported in previous experimental and computational work [39]. At the highest doping concentration, the distribution of the modeled dopant is random and the semiconducting conversion is maintained. At the intermediate doping concentration, the dopant distribution is aligned and the metallic conductance of the system is restored. This restoration may be due to the formation of polyiodide structures, and two consequent effects: (1) the creation of p-doped conduction “pathways” (axially asymmetric doping) in the nanotubes, and (2) conduction in the polyiodide chains, via a Grothuss mechanisim [5860]. Given the highly ordered structure of the conduction paths in metallic CNT's [61], conductance sensitivity to dopant distribution is certainly plausible.
Figure 3 shows the doped single semiconducting nanotube configurations considered. The first and second models assume aligned dopant atoms, with 1.0 iodine atoms per CNT unit cell and 1.5 iodine atoms per CNT unit cell, respectively. The third model depicts the random doping pattern. In the case of the semiconducting CNT's, the electrodes were doped.
Figure 4 shows the computed conductance for the modeled semiconducting CNT's. The calculation made here for an undoped semiconducting CNT (shown by the bar labeled none) returns (as expected) negligible conductance. Note that Ref. [11], which employs a double zeta basis set, returns a conductance fully 70% of that computed (in that work) for a metallic tube, in a copper electrode configuration. The remaining three bars in Fig. 4 show conductance results for the doped semiconducting nanotubes. As in the metallic case, they indicate that the conductance of the doped tube is affected by both the dopant concentration and the dopant distribution. At the lowest dopant concentration, application of the iodine does not improve conductance. At the highest doping concentration, the distribution of the modeled dopant is random and the conductance is again negligible. At the intermediate doping concentration, the dopant distribution is aligned and a small but nonzero conductance is computed. The modeling results might again be explained by the formation of polyiodide structures: (1) the creation of p-doped conduction pathways (axially asymmetric doping) in the nanotubes and (2) the conduction in the polyiodide chains.
Although the preceding calculations on isolated nanotubes are of great interest, experimental studies of iodine-doped CNT conductors emphasize that macroscale cables are composed of nanotube bundles, and that such bundles will give rise to more complex doping patterns. The simplest doping pattern associated with interacting tubes (a pattern depicted in Ref. [3]) is the interstitial doping configuration shown in Fig. 5. The latter figure depicts dual parallel metallic nanotubes, interstitially doped at two different iodine concentrations. Figure 6 shows the computed conductance results for the modeled dual metallic CNT's. The calculation for the undoped system (shown by the bar labeled none) correctly returns the exact solution of 4.0 quantum conductance units. The remaining two bars in Fig. 6 show computed conductance results for the doped dual tubes. As in the single metallic nanotube case, low levels of iodine doping significantly reduce metallic system conductance. Note that for multinanotube bundles, alignment of the dopant atoms along the intersticial crevice might be encouraged by some manufacturing processes (e.g., extrusion). Consistent with the arguments made for the isolated tube models, the creation of p-doped conduction pathways (axially asymmetric doping) in the nanotubes and possible conduction within the polyiodide chains may be responsible for the nonmonotonic variation in conductance.
Figure 7 depicts dual parallel semiconducting nanotube configurations, interstitially doped at two different iodine concentrations. Figure 8 shows the computed conductance results for the modeled dual semiconducting CNT's. The calculation for the undoped system (shown by the bar labeled none) correctly returns a result indicating negligible conductance. The remaining two bars in Fig. 8 show computed conductance results for the doped dual tubes. Interstitial iodine doping improves system conductance, and the system conductance increases with dopant concentration. As in the metallic case, the dual nanotube geometry appears to promote the formation of polyiodides and the formation of p-doped conduction pathways. At the higher of the two modeled dopant concentrations, the computed system conductance reaches 75% of that expected for dual undoped metallic nanotubes.
###### Polyiodide-Doped Carbon Nanotube Junctions.
The polyiodide-doped CNT junction models investigated dual nanotube configurations, at various overlaps, in interstitial doping configurations. The dopant per unit length was varied, and both metallic and semiconducting tubes were analyzed. In general, relaxation calculations for the doped CNT junctions failed to converge. The junction models were constructed by removing carbon atoms from the relaxed models of the interstitially doped CNT's depicted in Figs. 5 and 7.
It is important to note that the junctions of interest in this paper are intended to be representative of nanotube bundles contained in macroscale cables, typically manufactured by pressure rolling [18], extrusion [62], or other mechanically intrusive processes. Given these circumstances, the junction models analyzed in this paper are perhaps far more likely to be representative of those in macroscale cables than any junction models obtained by “re-relaxation” of isolated atomic configurations of the type depicted in Fig. 9. The authors are not aware of any previous work which has performed ab initio relaxation or conductance calculations for interstitially doped junctions like those depicted in Fig. 9.
The metallic nanotube junction shown in Fig. 9 was analyzed at five different overlaps, ranging from 2 to 10 unit cells, without doping and at two different doping concentrations. Figure 10 shows the computed conductance results. As indicated in the previous work [30,31], junction conduction does not in general vary monotonically with overlap. In the undoped configuration modeled here, the junction conductance is (at best) half of that expected for an undoped metallic nanotube, emphasizing the importance of “contact resistance” in determining the performance of nanotube-based cabling. The reduced conductance computed (for all overlaps) at the low doping concentration mimics the previously discussed response of isolated metallic nanotubes to low dopant concentrations. Only at the highest levels of dopant concentration and overlap considered in the analysis does the junction conductance approach 75% of the conductance of a pristine nanotube: that result, indicated by the highlighted square in Fig. 10, is used in the nanowire performance calculations discussed in Sec. 4.
The semiconducting nanotube junction shown in Fig. 11 was also analyzed at five different overlaps, in this case ranging from 0.7 to 4.7 unit cells. Since the undoped semiconducting tubes analyzed previously performed as insulators, junction performance was modeled only with doping applied, at two concentrations. Figure 12 shows the computed conductance results. At the low doping concentration, the junction conductance was negligible at all overlaps. At the high doping concentration, junction performance was very good, peaking at an overlap of 3.7 unit cells, where the doped junction performance approached that of a pristine metallic nanotube. That result, indicated by the highlighted square in Fig. 12, is used in the nanowire performance calculations discussed in Sec. 4.
###### Summary.
The precise effects of polyiodide doping vary significantly with nanotube type (metallic or semiconducting) and dopant distribution (aligned, random, or interstitial). The results presented in this section suggest several conclusions:
1. (1)At low dopant levels, metallic nanotubes are adversely affected by iodine doping. However if the dopant is properly distributed, the performance of metallic nanotubes can be recovered (at least in part) by increasing the dopant concentration. In the case of the semiconducting nanotubes, conductance improves with iodine dopant concentration, as long as the dopant is properly distributed.
2. (2)At low dopant levels, metallic nanotube junctions are adversely affected by iodine doping. However if the dopant is interstitially distributed, the performance of metallic junctions can be recovered by increasing the dopant concentration and junction overlap. In the case of the semiconducting nanotube junctions, conductance improves with iodine dopant concentration, if the dopant is interstitially distributed.
3. (3)In the CNT configurations modeled here: interstitial doping is broadly beneficial, aligned doping offers some benefits, and random doping is ineffective.
4. (4)Current explanations of the effects of iodine doping on CNT conductance focus broadly on iodine as p-type dopant for the CNT [11,63]. However, the enhanced conductance offered by interstitial doping may more specifically be due to asymmetric p-doping of the nanotubes.
5. (5)Conduction within polyiodide structures (charge transfer without mass transport [5860]) may contribute to the doped system's performance. The formation of interstitial polyiodides might be encouraged by particular fabrication processes, such as pressure rolling or extrusion.
Section 4 of the paper applies the results of the ballistic conduction calculations just discussed, in order to estimate the measured performance of iodine-doped CNT cables studied in macroscale experiments. Comparison with experiment serves to critique the assumptions made in formulating the nanoscale model, evaluating its usefulness in assisting engineering design.
## Transmission Line Model
In this section, a nanowire is modeled as a transmission line consisting of a set of conductors, each with a length no greater than the electron MFP for the conductor material, joined by discrete “junction” resistors. The mass and conductivity properties of the transmission line components are taken from the ballistic conductance analysis described in Sec. 3. The assumed model, shown in Fig. 13, is inspired by experimental measurements on CNT networks [16]. Estimates of the mean free path for the nanotube-based conductors are taken from the literature [64,65].
The mass per unit length and the resistance per unit length of the transmission line are determined by the conductor resistance $Rc$, junction resistance $Rj$, conductor mass per unit length $m̂c$, and added mass per junction $mjadd$, all determined from the models described in Sec. 3, and by the mean free path ($Lm$) of an electron in the conductor. Adopting the product of mass ($m$) per unit length and resistance ($R$) per unit length as performance measures for a nanowire, one may define a performance metric ($M$) using Display Formula
(7)$1M=ρσ=mL×RL=m̂c+mjaddLmn̂Rc+RjLmn̂$
where the number of junctions per mean free path is Display Formula
(8)$n̂=nL/Lm$
and $n$ is the number of junctions in a transmission line of length $L$ (composed of segments of length $Ls$). Note that in the case of a continuum conductor, the performance metric is the mass specific conductance, defined as the ratio of electrical conductivity (σ) to mass density (ρ).
The plots which follow employ the metric $M$ to estimate the performance of nanowires fabricated using the material systems considered in Secs. 3.1 and 3.2. Specifically, they plot the relative specific conductivity $M/Mref$ versus the number of junctions per unit mean free path $(n̂)$ for each material system, where $Mref$is a reference value for the chosen metric (the specific conductivity of pure copper). Note that for the minimum value of $n̂=1$ indicated in the plots, the number of junctions is just sufficient to permit ballistic conductance. Additional junctions add parasitic mass and resistance, reducing nanowire performance. The plots which follow assume a mean free path of either 500 nm or 1000 nm for the CNT's [64,65]. The high performance combinations of polyiodide-doped CNT conductors and junctions selected for the nanowire analysis presented in this section are shown in Table 3. The junction conductance data used in the analysis are indicated by the highlighted squares shown in Figs. 10 and 12.
The upper plot in Fig. 14 shows that for the minimum junction count ($n̂=1$) and a CNT MFP of 500 nm, the relative specific conductance ($M/Mref$) for the iodine-doped CNT nanowires ranges from one to three: the estimated specific conductance of the CNT nanowire is as much three times that of pure copper. This range matches that described by published experimental data [3] on the performance of iodine-doped CNT cables. The transmission line (nanowire) model also suggests that the number of junctions per mean free path ($n̂$) should be limited, in order to obtain high performance. As indicated in the lower plot of Fig. 14, for the range of parameters considered in this analysis, performance varies approximately linearly with mean free path.
## Conclusions
This section presents general conclusions on the polyiodide-doped CNT systems analyzed in this paper and offers suggestions for future research. The ballistic conductance and transmission line analysis results for the polyiodide-doped CNT nanowires suggest a number of conclusions:
• The analysis results are consistent with the published experimental data [3], which indicate that iodine-doped CNT conductors can offer specific conductivity in the range of one to three times that of copper.
• The analyses presented here considered smaller diameter nanotubes (by a factor of four) and higher dopant to carbon mass ratios (by a factor of three) than those described in published experiments [3,17]. Since the model and the experiments indicate similar mass specific conductivity, mass specific performance does not appear to depend strongly on nanotube diameter.
• Estimated CNT nanowire performance varies approximately linearly with CNT mean free path; published experimental data indicate that mean free path is reduced as temperature is increased [66].
• In the case of iodine doping, realizing high specific conductivity appears to require very mass efficient use of the dopant.
• Doping distribution is highly important and might be influenced by cable fabrication processes.
• Charge transport in within polyiodides may contribute to conductor performance.
The computational research described in this paper, and the corresponding experimental research literature, suggest many opportunities for future research. Of immediate interest are: (1) the modeling of more complex dopants, including ICl [12] and KAuBr4 [9]; (2) consideration of longer junction overlaps; (3) the modeling of multitube interactions (as computational costs permit), based on the experimentally observed complexity [67] of CNT cable architectures; (4) application of the modeling approach to graphene [50]; and (5) the development of improved computational methods for both equilibrium calculations and ballistic conduction calculations, an essential enabler if computational research is to keep pace with experimental work on the increasingly complex cable nanostructures, doping systems, and fabrication processes of interest.
## Acknowledgements
Computer time support was provided by the Texas Advanced Computing Center at the University of Texas at Austin.
## Funding Data
• Office of Naval Research Global (Grant No. N00014-15-1-2693).
## References
Volder, M. F. L. D. , Tawfick, S. H. , Baughman, R. H. , and Hart, A. J. , 2013, “ Carbon Nanotubes: Present and Future Commercial Applications,” Science, 339(6119), pp. 535–539. [PubMed]
Wernik, J. M. , and Meguid, S. A. , 2010, “ Recent Developments in Multifunctional Nanocomposites Using Carbon Nanotubes,” ASME Appl. Mech. Rev., 63(5), p. 050801.
Zhao, Y. , Wei, J. , Vajtai, R. , Ajayan, P. M. , and Barrera, E. V. , 2011, “ Iodine Doped Carbon Nanotube Cables Exceeding Specific Electrical Conductivity of Metals,” Sci. Rep., 1, p. 83. [PubMed]
Subramaniam, C. , Yamada, T. , Kobashi, K. , Sekiguchi, A. , Futaba, D. N. , Yumura, M. , and Hata, K. , 2013, “ One Hundred Fold Increase in Current Carrying Capacity in a Carbon Nanotube-Copper Composite,” Nat. Commun., 4, p. 2202. [PubMed]
Wang, X. , Behabtu, N. , Young, C. C. , Tsentalovich, D. E. , Pasquali, M. , and Kono, J. , 2014, “ High-Ampacity Power Cables of Tightly-Packed and Aligned Carbon Nanotubes,” Adv. Funct. Mater, 24(21), pp. 3241–3249.
Harvey, S. E. , 2012, “ Carbon Conductor: A Pragmatic View,” International Wire Cable Connectivity Symposium (IWCS), Providence, RI, Nov. 11–14, p. 558.
Kong, J. , Yenilmez, E. , Tombler, T. W. , Kim, W. , and Dai, H. , 2001, “ Quantum Interference and Ballistic Transmission in Nanotube Electron Waveguides,” Phys. Rev. Lett., 87(10), p. 106801. [PubMed]
Soto, M. , Boyer, T. A. , Biradar, S. , Ge, L. , Vajtai, R. , Elías-Zúñiga, A. , Ajayan, P. M. , and Barrera, E. V. , 2015, “ Effect of Interwall Interaction on the Electronic Structure of Double-Walled Carbon Nanotubes,” Nanotechnology, 26(16), p. 165201. [PubMed]
Alvarenga, J. , Jarosz, P. R. , Schauerman, C. M. , Moses, B. T. , Landi, B. J. , Cress, C. D. , and Raffaelle, R. P. , 2010, “ High Conductivity Carbon Nanotube Wires From Radial Densification and Ionic Doping,” Appl. Phys. Lett., 97(18), pp. 19–22.
Puchades, I. , Lawlor, C. C. , Schauerman, C. M. , Bucossi, A. R. , Rossi, J. E. , Cox, N. D. , and Landi, B. J. , 2015, “ Mechanism of Chemical Doping in Electronic-Type-Separated Single Wall Carbon Nanotubes Towardshigh Electrical Conductivity,” J. Mater. Chem. C, 3(39), pp. 10256–10266.
Janas, D. , Milowska, K. Z. , Bristowe, P. , and Koziol, K. , 2017, “ Improving the Electrical Properties of Carbon Nanotubes With Interhalogen Compounds,” Nanoscale, 44(27), pp. 3212–3221.
Janas, D. , Herman, A. P. , Boncel, S. , and Koziol, K. K. K. , 2014, “ Iodine Monochloride as a Powerful Enhancer of Electrical Conductivity of Carbon Nanotube Wires,” Carbon, 73, pp. 225–233.
Fan, L. , and Xu, X. , 2015, “ A Stable Iodine-Doped Multi-Walled Carbon Nanotube-Polypyrrole Composite With Improved Electrical Property,” Compos. Sci. Technol., 118, pp. 264–268.
Wescott, J. T. , Kung, P. , and Maiti, A. , 2007, “ Conductivity of Carbon Nanotube Polymer Composites,” Appl. Phys. Lett., 90(3), p. 33116.
Fuhrer, P. L. M. S. , Nygård, J. , Shih, L. , Forero, M. , Yoon, Y.-G. , Mazzoni, M. S. C. , Choi, H. J. , Ihm, J. , Louie, S. G. , and Zettl, McEuen, A. , 2000, “ Crossed Nanotube Junctions,” Science, 288(5465), pp. 494–497. [PubMed]
Nirmalraj, P. N. , Lyons, P. E. , De, S. , Coleman, J. N. , and Boland, J. J. , 2009, “ Electrical Connectivity in Single-Walled Carbon Nanotube Networks,” Nano Lett., 9(11), pp. 3890–3895. [PubMed]
Behabtu, N. , Young, C. C. , Tsentalovich, D. E. , Kleinerman, O. , Wang, X. , Ma, A. W. K. , Bengio, E. A. , ter Waarbeek, R. F. , de Jong, J. J. , Hoogerwerf, R. E. , Fairchild, S. B. , Ferguson, J. B. , Maruyama, B. , Kono, J. , Talmon, Y. , Cohen, Y. , Otto, M. J. , and Pasquali, M. , 2013, “ Strong, Light, Multifunctional Fibers of Carbon Nanotubes With Ultrahigh Conductivity,” Science, 339(6116), pp. 182–186. [PubMed]
Wang, J. N. , Luo, X. G. , Wu, T. , and Chen, Y. , 2014, “ High-Strength Carbon Nanotube Fibre-like Ribbon With High Ductility and High Electrical Conductivity,” Nat. Commun., 5, p. 3848. [PubMed]
Stokbro, K. , 2008, “ First-Principles Modeling of Electron Transport,” J. Phys: Condens. Matter, 20(6), p. 64216.
Qian, Z. , Li, R. , Hou, S. , Xue, Z. , and Sanvito, S. , 2007, “ An Efficient Nonequilibrium Green's Function Formalism Combined With Density Functional Theory Approach for Calculating Electron Transport Properties of Molecular Devices With Quasi-One-Dimensional Electrodes,” J. Chem. Phys., 127(19), p. 194710.
Li, R. , Zhang, J. , Hou, S. , Qian, Z. , Shen, Z. , Zhao, X. , and Xue, Z. , 2007, “ A Corrected NEGF + DFT Approach for Calculating Electronic Transport Through Molecular Devices: Filling Bound States and Patching the Non-Equilibrium Integration,” Chem. Phys., 336(2–3), pp. 127–135.
Biel, B. , Garcia-Vidal, F. J. , Rubio, A. , and Flores, F. , 2008, “ Ab Initio Study of Transport Properties in Defected Carbon Nanotubes: An O(N) Approach,” J. Phys: Condens. Matter, 20(29), p. 15.
Park, H. , Zhao, J. , and Lu, J. P. , 2006, “ Effects of Sidewall Functionalization on Conducting Properties of Single Wall Carbon Nanotubes,” Nano Lett., 6(5), pp. 916–919. [PubMed]
Esconjauregui, S. , D'Arsié, L. , Guo, Y. , Yang, J. , Sugime, H. , Caneva, S. , Cepek, C. , and Robertson, J. , 2015, “ Efficient Transfer Doping of Carbon Nanotube Forests by MoO3,” ACS Nano, 9(10), pp. 10422–10430. [PubMed]
Kim, K. K. , Bae, J. J. , Park, H. K. , Kim, S. M. , Geng, H.-Z. , Park, K. A. , Shin, H.-J. , Yoon, S.-M. , Benayad, A. , Choi, J.-Y. , and Lee, Y. H. , 2008, “ Fermi Level Engineering of Single-Walled Carbon Nanotubes by AuCl3 Doping,” J. Am. Chem. Soc., 130(38), pp. 12757–12761. [PubMed]
Moradian, R. , Azadi, S. , and Refii-Tabar, H. , 2007, “ When Double-Wall Carbon Nanotubes Can Become Metallic or Semiconducting,” J. Phys: Condens. Matter, 19(17), p. 176209. [PubMed]
Du, X. J. , Chen, Z. , Zhang, J. , Yao, C. S. , Chen, C. , and Fan, X. L. , 2012, “ Structural and Electronic Properties of Conducting Cu Nanowire Encapsulated in Semiconducting Zigzag Carbon Nanotubes: A First-Principles Study,” Phys. Status Solidi Basic Res., 249(5), pp. 1033–1038.
Fujimori, T. , Morelos-Gómez, A. , Zhu, Z. , Muramatsu, H. , Futamura, R. , Urita, K. , Terrones, M. , Hayashi, T. , Endo, M. , Hong, S. Y. , Choi, Y. C. , Tománek, D. , and Kaneko, K. , 2013, “ Conducting Linear Chains of Sulphur Inside Carbon Nanotubes,” Nat. Commun., 4, p. 2162. [PubMed]
Lopez-Bezanilla, A. , 2013, “ Electronic Transport Properties of Chemically Modified Double-Walled Carbon Nanotubes,” J. Phys. Chem. C, 117(29), pp. 15266–15271.
Buia, C. , Buldum, A. , and Lu, J. P. , 2003, “ Quantum Interference Effects in Electronic Transport Through Nanotube Contacts,” Phys. Rev. B, 67(11), pp. 113409–113412.
Xu, F. , Sadrzadeh, A. , Xu, Z. , and Yakobson, B. I. , 2013, “ Can Carbon Nanotube Fibers Achieve the Ultimate Conductivity?—Coupled-Mode Analysis for Electron Transport Through the Carbon Nanotube Contact,” J. Appl. Phys., 114(6), p. 063714.
Buldum, A. , and Lu, J. P. , 2001, “ Contact Resistance Between Carbon Nanotubes,” Phys. Rev. B Condens. Matter, 63(16), p. 161403.
Ciraci, S. , Buldum, A. , and Batra, I. , 2001, “ Quantum Effects in Electrical and Thermal Transport Through Nanowires,” J. Phys: Condens. Matter, 13, pp. 537–568.
Li, E. Y. , and Marzari, N. , 2011, “ Improving the Electrical Conductivity of Carbon Nanotube Networks: A First-Principles Study,” ACS Nano, 5(12), pp. 9726–9736. [PubMed]
Khoo, K. H. , and Chelikowsky, J. R. , 2009, “ Electron Transport Across Carbon Nanotube Junctions Decorated With Au Nanoparticles: Density Functional Calculations,” Phys. Rev. B-Condens. Matter Mater. Phys., 79(20), p. 205422.
Mowbray, D. J. , Morgan, C. , and Thygesen, K. S. , 2009, “ Influence of O2 and N2 on the Conductivity of Carbon Nanotube Networks,” Phys. Rev. B-Condens. Matter Mater. Phys., 79(19), pp. 1–6.
Meguid, W. S. B. , Meguid, S. A. , Zhu, Z. H. , and Meguid, M. J. , 2011, “ Modeling Electrical Conductivities of Nanocomposites With Aligned Carbon Nanotubes,” Nanotechnology, 22(48), p. 485704. [PubMed]
Gong, S. , Zhu, Z. H. , and Haddad, E. I. , 2013, “ Modeling Electrical Conductivity of Nanocomposites by Considering Carbon Nanotube Deformation at Nanotube Junctions,” J. Appl. Phys., 114(7), p. 74303.
Ghosh, S. , Yamijala, S. , Pati, S. , and Rao, C. , 2012, “ The Interaction of Halogen Molecules With SWNTs and Graphene,” RSC Adv., 2(3), pp. 1181–1188.
Datta, S. , 1995, Electronic Transport in Mesoscopic Systems, Cambridge University Press, Cambridge, UK.
Soler, J. M. , Artacho, E. , Gale, J. D. , García, A. , Junquera, J. , Ordejón, P. , and Sánchez-Portal, D. , 2002, “ The SIESTA Method for Ab Initio Order-N Materials Simulation,” J. Phys: Condens. Matter, 14(11), p. 2745.
Datta, S. , 2000, “ Nanoscale Device Modeling: The Green's Function Method,” Superlattices Microstruct., 28(4), pp. 253–278.
Stokbro, K. , Taylor, J. , Brandbyge, M. , and Ordejón, P. , 2003, “ TranSIESTA: A Spice for Molecular Electronics,” Ann. New York Acad. Sci., 1006, pp. 212–226.
Imry, Y. , and Landauer, R. , 1999, “ Conductance Viewed as Transmission,” Rev. Mod. Phys., 71(2), pp. S306–S312.
Band, Y. B. , and Avishai, Y. , 2012, Quantum Mechanics With Applications to Nanotechnology and Information Science, 1st ed., Elsevier, Oxford, UK.
Perdew, J. P. , Burke, K. , and Ernzerhof, M. , 1996, “ Generalized Gradient Approximation Made Simple,” Phys. Rev. Lett., 77(18), pp. 3865–3868. [PubMed]
Pack, J. D. , and Monkhorst, H. J. , 1976, “ Special Points for Brillouin-Zone Integrations,” Phys. Rev. B, 13(4), pp. 5188–5192.
Hashim, D. P. , Narayanan, N. T. , Romo-Herrera, J. M. , Cullen, D. A. , Hahm, M. G. , Lezzi, P. , Suttle, J. R. , Kelkhoff, D. , Muñoz-Sandoval, E. , Ganguli, S. , Roy, A. K. , Smith, D. J. , Vajtai, R. , Sumpter, B. G. , Meunier, V. , Terrones, H. , Terrones, M. , and Ajayan, P. M. , 2012, “ Covalently Bonded Three-Dimensional Carbon Nanotube Solids Via Boron Induced Nanojunctions,” Sci. Rep., 2, p. 363. [PubMed]
Wu, Z. , Han, Y. , Huang, R. , Chen, X. , Guo, Y. , He, Y. , Li, W. , Caia, Y. , and Wang, N. , 2014, “ Semimetallic-to-Metallic Transition and Mobility Enhancement Enabled by Reversible Iodine Doping of Graphene,” Nanoscale, 6(21), pp. 13196–13202. [PubMed]
Hoyt, R. A. , Remillard, E. M. , Cubuk, E. D. , Vecitis, C. D. , and Kaxiras, E. , 2017, “ Polyiodide-Doped Graphene,” J. Phys. Chem. C, 121(1), pp. 609–615.
Fan, X. , Dickey, E. C. , Eklund, P. C. , Williams, K. A. , Grigorian, L. , Buczko, R. , Pantelides, S. T. , and Pennycook, S. J. , 2000, “ Atomic Arrangement of Iodine Atoms Inside Single-Walled Carbon Nanotubes,” Phys. Rev. Lett., 84(20), pp. 4621–4624. [PubMed]
Ci, L. , Rao, Z. , Zhou, Z. , Tang, D. , Yan, X. , Liang, Y. , Liu, D. , Yuan, H. , Zhou, W. , Wang, G. , Liu, W. , and Xie, S. , 2002, “ Double Wall Carbon Nanotubes Promoted by Sulfur in a Floating Iron Catalyst CVD System,” Chem. Phys. Lett., 359(1–2), pp. 63–67.
Liu, S. , Nurbawono, A. , and Zhang, C. , 2015, “ Density Functional Theory for Steady-State Nonequilibrium Molecular Junctions,” Sci. Rep., 5, p. 15386. [PubMed]
Yan, Q. , Wu, J. , Zhou, G. , Duan, W. , and Gu, B.-L. , 2005, “ Ab Initio Study of Transport Properties of Multiwalled Carbon Nanotubes,” Phys. Rev. B, 72(15), p. 155425.
Foti, G. , 2014, “ Elastic and Inelastic Electron Transport Through Alkane-Based Molecular Junctions,” Ph.D. thesis, CSIC-UPV−Centro de Física de Materiales (CFM), Madrid, Spain.
Frederiksen, T. , 2007, “ Inelastic Transport Theory for Nanoscale Systems,” Ph.D. thesis, Technical University of Denmark, Lyngby, Denmark.
Yu, J. X. , Cheng, Y. , Sanvito, S. , and Chen, X. R. , 2012, “ Bias-Dependent Oscillatory Electron Transport of Monatomic Sulfur Chains,” Appl. Phys. Lett., 100(10), p. 103110.
Svensson, P. H. , and Kloo, L. , 2003, “ Synthesis, Structure, and Bonding in Polyiodide and Metal Iodide-Iodine Systems,” Chem. Rev., 103(5), pp. 1649–1684. [PubMed]
Rubinstein, I. , and Gileadi, E. , 1980, “ Measurements of Electrical Conductivity in Solid Bromine and Iodine,” J. Electroanal. Chem, 108(2), pp. 191–201.
Tatsuo, K. , 2014, Iodine Chemistry and Applications, Wiley, Hoboken, NJ.
Fugita, S. , and Suzuki, A. , 2013, Electrical Conduction in Graphene and Nanotubes, Wiley-VCH, Weinheim, Germany, p. 306.
Bucossi, A. R. , Cress, C. D. , Schauerman, C. M. , Rossi, J. E. , Puchades, I. , and Landi, B. J. , 2015, “ Enhanced Electrical Conductivity in Extruded Single-Wall Carbon Nanotube Wires From Modified Coagulation Parameters and Mechanical Processing,” Appl. Mater. Interfaces, 7(49), pp. 27299–27305.
Sankapal, B. R. , Setyowati, K. , Chen, J. , and Liu, H. , 2007, “ Electrical Properties of Air-Stable, Iodine-Doped Carbon-Nanotube-Polymer Composites,” Appl. Phys. Lett., 91(17), pp. 10–13.
Park, J.-Y. , Rosenblatt, S. , Yaish, Y. , Sazonova, V. , Üstünel, H. , Braig, S. , Arias, T. A. , Brouwer, P. W. , and McEuen, P. L. , 2004, “ Electron-Phonon Scattering in Metallic Single-Walled Carbon Nanotubes,” Nano Lett., 4(3), pp. 517–520.
Mann, D. , Javey, A. , Kong, J. , Wang, Q. , and Dai, H. , 2003, “ Ballistic Transport in Metallic Nanotubes With Reliable Pd Ohmic Contacts,” Nano Lett., 3(11), pp. 1541–1544.
Fuller, E. J. , Pan, D. , Corso, B. L. , Gul, O. T. , and Collins, P. G. , 2014, “ Mean Free Paths in Single-Walled Carbon Nanotubes Measured by Kelvin Probe Force Microscopy,” Phys. Rev. B, 89(24), p. 245450.
Wang, T. , Hu, X. , and Dong, S. , 2007, “ Construction of Metal Nanoparticle/Multiwalled Carbon Nanotube Hybrid Nanostructures Providing the Most Accessible Reaction Sites,” J. Mater. Chem., 17(39), pp. 4189–4195.
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## References
Volder, M. F. L. D. , Tawfick, S. H. , Baughman, R. H. , and Hart, A. J. , 2013, “ Carbon Nanotubes: Present and Future Commercial Applications,” Science, 339(6119), pp. 535–539. [PubMed]
Wernik, J. M. , and Meguid, S. A. , 2010, “ Recent Developments in Multifunctional Nanocomposites Using Carbon Nanotubes,” ASME Appl. Mech. Rev., 63(5), p. 050801.
Zhao, Y. , Wei, J. , Vajtai, R. , Ajayan, P. M. , and Barrera, E. V. , 2011, “ Iodine Doped Carbon Nanotube Cables Exceeding Specific Electrical Conductivity of Metals,” Sci. Rep., 1, p. 83. [PubMed]
Subramaniam, C. , Yamada, T. , Kobashi, K. , Sekiguchi, A. , Futaba, D. N. , Yumura, M. , and Hata, K. , 2013, “ One Hundred Fold Increase in Current Carrying Capacity in a Carbon Nanotube-Copper Composite,” Nat. Commun., 4, p. 2202. [PubMed]
Wang, X. , Behabtu, N. , Young, C. C. , Tsentalovich, D. E. , Pasquali, M. , and Kono, J. , 2014, “ High-Ampacity Power Cables of Tightly-Packed and Aligned Carbon Nanotubes,” Adv. Funct. Mater, 24(21), pp. 3241–3249.
Harvey, S. E. , 2012, “ Carbon Conductor: A Pragmatic View,” International Wire Cable Connectivity Symposium (IWCS), Providence, RI, Nov. 11–14, p. 558.
Kong, J. , Yenilmez, E. , Tombler, T. W. , Kim, W. , and Dai, H. , 2001, “ Quantum Interference and Ballistic Transmission in Nanotube Electron Waveguides,” Phys. Rev. Lett., 87(10), p. 106801. [PubMed]
Soto, M. , Boyer, T. A. , Biradar, S. , Ge, L. , Vajtai, R. , Elías-Zúñiga, A. , Ajayan, P. M. , and Barrera, E. V. , 2015, “ Effect of Interwall Interaction on the Electronic Structure of Double-Walled Carbon Nanotubes,” Nanotechnology, 26(16), p. 165201. [PubMed]
Alvarenga, J. , Jarosz, P. R. , Schauerman, C. M. , Moses, B. T. , Landi, B. J. , Cress, C. D. , and Raffaelle, R. P. , 2010, “ High Conductivity Carbon Nanotube Wires From Radial Densification and Ionic Doping,” Appl. Phys. Lett., 97(18), pp. 19–22.
Puchades, I. , Lawlor, C. C. , Schauerman, C. M. , Bucossi, A. R. , Rossi, J. E. , Cox, N. D. , and Landi, B. J. , 2015, “ Mechanism of Chemical Doping in Electronic-Type-Separated Single Wall Carbon Nanotubes Towardshigh Electrical Conductivity,” J. Mater. Chem. C, 3(39), pp. 10256–10266.
Janas, D. , Milowska, K. Z. , Bristowe, P. , and Koziol, K. , 2017, “ Improving the Electrical Properties of Carbon Nanotubes With Interhalogen Compounds,” Nanoscale, 44(27), pp. 3212–3221.
Janas, D. , Herman, A. P. , Boncel, S. , and Koziol, K. K. K. , 2014, “ Iodine Monochloride as a Powerful Enhancer of Electrical Conductivity of Carbon Nanotube Wires,” Carbon, 73, pp. 225–233.
Fan, L. , and Xu, X. , 2015, “ A Stable Iodine-Doped Multi-Walled Carbon Nanotube-Polypyrrole Composite With Improved Electrical Property,” Compos. Sci. Technol., 118, pp. 264–268.
Wescott, J. T. , Kung, P. , and Maiti, A. , 2007, “ Conductivity of Carbon Nanotube Polymer Composites,” Appl. Phys. Lett., 90(3), p. 33116.
Fuhrer, P. L. M. S. , Nygård, J. , Shih, L. , Forero, M. , Yoon, Y.-G. , Mazzoni, M. S. C. , Choi, H. J. , Ihm, J. , Louie, S. G. , and Zettl, McEuen, A. , 2000, “ Crossed Nanotube Junctions,” Science, 288(5465), pp. 494–497. [PubMed]
Nirmalraj, P. N. , Lyons, P. E. , De, S. , Coleman, J. N. , and Boland, J. J. , 2009, “ Electrical Connectivity in Single-Walled Carbon Nanotube Networks,” Nano Lett., 9(11), pp. 3890–3895. [PubMed]
Behabtu, N. , Young, C. C. , Tsentalovich, D. E. , Kleinerman, O. , Wang, X. , Ma, A. W. K. , Bengio, E. A. , ter Waarbeek, R. F. , de Jong, J. J. , Hoogerwerf, R. E. , Fairchild, S. B. , Ferguson, J. B. , Maruyama, B. , Kono, J. , Talmon, Y. , Cohen, Y. , Otto, M. J. , and Pasquali, M. , 2013, “ Strong, Light, Multifunctional Fibers of Carbon Nanotubes With Ultrahigh Conductivity,” Science, 339(6116), pp. 182–186. [PubMed]
Wang, J. N. , Luo, X. G. , Wu, T. , and Chen, Y. , 2014, “ High-Strength Carbon Nanotube Fibre-like Ribbon With High Ductility and High Electrical Conductivity,” Nat. Commun., 5, p. 3848. [PubMed]
Stokbro, K. , 2008, “ First-Principles Modeling of Electron Transport,” J. Phys: Condens. Matter, 20(6), p. 64216.
Qian, Z. , Li, R. , Hou, S. , Xue, Z. , and Sanvito, S. , 2007, “ An Efficient Nonequilibrium Green's Function Formalism Combined With Density Functional Theory Approach for Calculating Electron Transport Properties of Molecular Devices With Quasi-One-Dimensional Electrodes,” J. Chem. Phys., 127(19), p. 194710.
Li, R. , Zhang, J. , Hou, S. , Qian, Z. , Shen, Z. , Zhao, X. , and Xue, Z. , 2007, “ A Corrected NEGF + DFT Approach for Calculating Electronic Transport Through Molecular Devices: Filling Bound States and Patching the Non-Equilibrium Integration,” Chem. Phys., 336(2–3), pp. 127–135.
Biel, B. , Garcia-Vidal, F. J. , Rubio, A. , and Flores, F. , 2008, “ Ab Initio Study of Transport Properties in Defected Carbon Nanotubes: An O(N) Approach,” J. Phys: Condens. Matter, 20(29), p. 15.
Park, H. , Zhao, J. , and Lu, J. P. , 2006, “ Effects of Sidewall Functionalization on Conducting Properties of Single Wall Carbon Nanotubes,” Nano Lett., 6(5), pp. 916–919. [PubMed]
Esconjauregui, S. , D'Arsié, L. , Guo, Y. , Yang, J. , Sugime, H. , Caneva, S. , Cepek, C. , and Robertson, J. , 2015, “ Efficient Transfer Doping of Carbon Nanotube Forests by MoO3,” ACS Nano, 9(10), pp. 10422–10430. [PubMed]
Kim, K. K. , Bae, J. J. , Park, H. K. , Kim, S. M. , Geng, H.-Z. , Park, K. A. , Shin, H.-J. , Yoon, S.-M. , Benayad, A. , Choi, J.-Y. , and Lee, Y. H. , 2008, “ Fermi Level Engineering of Single-Walled Carbon Nanotubes by AuCl3 Doping,” J. Am. Chem. Soc., 130(38), pp. 12757–12761. [PubMed]
Moradian, R. , Azadi, S. , and Refii-Tabar, H. , 2007, “ When Double-Wall Carbon Nanotubes Can Become Metallic or Semiconducting,” J. Phys: Condens. Matter, 19(17), p. 176209. [PubMed]
Du, X. J. , Chen, Z. , Zhang, J. , Yao, C. S. , Chen, C. , and Fan, X. L. , 2012, “ Structural and Electronic Properties of Conducting Cu Nanowire Encapsulated in Semiconducting Zigzag Carbon Nanotubes: A First-Principles Study,” Phys. Status Solidi Basic Res., 249(5), pp. 1033–1038.
Fujimori, T. , Morelos-Gómez, A. , Zhu, Z. , Muramatsu, H. , Futamura, R. , Urita, K. , Terrones, M. , Hayashi, T. , Endo, M. , Hong, S. Y. , Choi, Y. C. , Tománek, D. , and Kaneko, K. , 2013, “ Conducting Linear Chains of Sulphur Inside Carbon Nanotubes,” Nat. Commun., 4, p. 2162. [PubMed]
Lopez-Bezanilla, A. , 2013, “ Electronic Transport Properties of Chemically Modified Double-Walled Carbon Nanotubes,” J. Phys. Chem. C, 117(29), pp. 15266–15271.
Buia, C. , Buldum, A. , and Lu, J. P. , 2003, “ Quantum Interference Effects in Electronic Transport Through Nanotube Contacts,” Phys. Rev. B, 67(11), pp. 113409–113412.
Xu, F. , Sadrzadeh, A. , Xu, Z. , and Yakobson, B. I. , 2013, “ Can Carbon Nanotube Fibers Achieve the Ultimate Conductivity?—Coupled-Mode Analysis for Electron Transport Through the Carbon Nanotube Contact,” J. Appl. Phys., 114(6), p. 063714.
Buldum, A. , and Lu, J. P. , 2001, “ Contact Resistance Between Carbon Nanotubes,” Phys. Rev. B Condens. Matter, 63(16), p. 161403.
Ciraci, S. , Buldum, A. , and Batra, I. , 2001, “ Quantum Effects in Electrical and Thermal Transport Through Nanowires,” J. Phys: Condens. Matter, 13, pp. 537–568.
Li, E. Y. , and Marzari, N. , 2011, “ Improving the Electrical Conductivity of Carbon Nanotube Networks: A First-Principles Study,” ACS Nano, 5(12), pp. 9726–9736. [PubMed]
Khoo, K. H. , and Chelikowsky, J. R. , 2009, “ Electron Transport Across Carbon Nanotube Junctions Decorated With Au Nanoparticles: Density Functional Calculations,” Phys. Rev. B-Condens. Matter Mater. Phys., 79(20), p. 205422.
Mowbray, D. J. , Morgan, C. , and Thygesen, K. S. , 2009, “ Influence of O2 and N2 on the Conductivity of Carbon Nanotube Networks,” Phys. Rev. B-Condens. Matter Mater. Phys., 79(19), pp. 1–6.
Meguid, W. S. B. , Meguid, S. A. , Zhu, Z. H. , and Meguid, M. J. , 2011, “ Modeling Electrical Conductivities of Nanocomposites With Aligned Carbon Nanotubes,” Nanotechnology, 22(48), p. 485704. [PubMed]
Gong, S. , Zhu, Z. H. , and Haddad, E. I. , 2013, “ Modeling Electrical Conductivity of Nanocomposites by Considering Carbon Nanotube Deformation at Nanotube Junctions,” J. Appl. Phys., 114(7), p. 74303.
Ghosh, S. , Yamijala, S. , Pati, S. , and Rao, C. , 2012, “ The Interaction of Halogen Molecules With SWNTs and Graphene,” RSC Adv., 2(3), pp. 1181–1188.
Datta, S. , 1995, Electronic Transport in Mesoscopic Systems, Cambridge University Press, Cambridge, UK.
Soler, J. M. , Artacho, E. , Gale, J. D. , García, A. , Junquera, J. , Ordejón, P. , and Sánchez-Portal, D. , 2002, “ The SIESTA Method for Ab Initio Order-N Materials Simulation,” J. Phys: Condens. Matter, 14(11), p. 2745.
Datta, S. , 2000, “ Nanoscale Device Modeling: The Green's Function Method,” Superlattices Microstruct., 28(4), pp. 253–278.
Stokbro, K. , Taylor, J. , Brandbyge, M. , and Ordejón, P. , 2003, “ TranSIESTA: A Spice for Molecular Electronics,” Ann. New York Acad. Sci., 1006, pp. 212–226.
Imry, Y. , and Landauer, R. , 1999, “ Conductance Viewed as Transmission,” Rev. Mod. Phys., 71(2), pp. S306–S312.
Band, Y. B. , and Avishai, Y. , 2012, Quantum Mechanics With Applications to Nanotechnology and Information Science, 1st ed., Elsevier, Oxford, UK.
Perdew, J. P. , Burke, K. , and Ernzerhof, M. , 1996, “ Generalized Gradient Approximation Made Simple,” Phys. Rev. Lett., 77(18), pp. 3865–3868. [PubMed]
Pack, J. D. , and Monkhorst, H. J. , 1976, “ Special Points for Brillouin-Zone Integrations,” Phys. Rev. B, 13(4), pp. 5188–5192.
Hashim, D. P. , Narayanan, N. T. , Romo-Herrera, J. M. , Cullen, D. A. , Hahm, M. G. , Lezzi, P. , Suttle, J. R. , Kelkhoff, D. , Muñoz-Sandoval, E. , Ganguli, S. , Roy, A. K. , Smith, D. J. , Vajtai, R. , Sumpter, B. G. , Meunier, V. , Terrones, H. , Terrones, M. , and Ajayan, P. M. , 2012, “ Covalently Bonded Three-Dimensional Carbon Nanotube Solids Via Boron Induced Nanojunctions,” Sci. Rep., 2, p. 363. [PubMed]
Wu, Z. , Han, Y. , Huang, R. , Chen, X. , Guo, Y. , He, Y. , Li, W. , Caia, Y. , and Wang, N. , 2014, “ Semimetallic-to-Metallic Transition and Mobility Enhancement Enabled by Reversible Iodine Doping of Graphene,” Nanoscale, 6(21), pp. 13196–13202. [PubMed]
Hoyt, R. A. , Remillard, E. M. , Cubuk, E. D. , Vecitis, C. D. , and Kaxiras, E. , 2017, “ Polyiodide-Doped Graphene,” J. Phys. Chem. C, 121(1), pp. 609–615.
Fan, X. , Dickey, E. C. , Eklund, P. C. , Williams, K. A. , Grigorian, L. , Buczko, R. , Pantelides, S. T. , and Pennycook, S. J. , 2000, “ Atomic Arrangement of Iodine Atoms Inside Single-Walled Carbon Nanotubes,” Phys. Rev. Lett., 84(20), pp. 4621–4624. [PubMed]
Ci, L. , Rao, Z. , Zhou, Z. , Tang, D. , Yan, X. , Liang, Y. , Liu, D. , Yuan, H. , Zhou, W. , Wang, G. , Liu, W. , and Xie, S. , 2002, “ Double Wall Carbon Nanotubes Promoted by Sulfur in a Floating Iron Catalyst CVD System,” Chem. Phys. Lett., 359(1–2), pp. 63–67.
Liu, S. , Nurbawono, A. , and Zhang, C. , 2015, “ Density Functional Theory for Steady-State Nonequilibrium Molecular Junctions,” Sci. Rep., 5, p. 15386. [PubMed]
Yan, Q. , Wu, J. , Zhou, G. , Duan, W. , and Gu, B.-L. , 2005, “ Ab Initio Study of Transport Properties of Multiwalled Carbon Nanotubes,” Phys. Rev. B, 72(15), p. 155425.
Foti, G. , 2014, “ Elastic and Inelastic Electron Transport Through Alkane-Based Molecular Junctions,” Ph.D. thesis, CSIC-UPV−Centro de Física de Materiales (CFM), Madrid, Spain.
Frederiksen, T. , 2007, “ Inelastic Transport Theory for Nanoscale Systems,” Ph.D. thesis, Technical University of Denmark, Lyngby, Denmark.
Yu, J. X. , Cheng, Y. , Sanvito, S. , and Chen, X. R. , 2012, “ Bias-Dependent Oscillatory Electron Transport of Monatomic Sulfur Chains,” Appl. Phys. Lett., 100(10), p. 103110.
Svensson, P. H. , and Kloo, L. , 2003, “ Synthesis, Structure, and Bonding in Polyiodide and Metal Iodide-Iodine Systems,” Chem. Rev., 103(5), pp. 1649–1684. [PubMed]
Rubinstein, I. , and Gileadi, E. , 1980, “ Measurements of Electrical Conductivity in Solid Bromine and Iodine,” J. Electroanal. Chem, 108(2), pp. 191–201.
Tatsuo, K. , 2014, Iodine Chemistry and Applications, Wiley, Hoboken, NJ.
Fugita, S. , and Suzuki, A. , 2013, Electrical Conduction in Graphene and Nanotubes, Wiley-VCH, Weinheim, Germany, p. 306.
Bucossi, A. R. , Cress, C. D. , Schauerman, C. M. , Rossi, J. E. , Puchades, I. , and Landi, B. J. , 2015, “ Enhanced Electrical Conductivity in Extruded Single-Wall Carbon Nanotube Wires From Modified Coagulation Parameters and Mechanical Processing,” Appl. Mater. Interfaces, 7(49), pp. 27299–27305.
Sankapal, B. R. , Setyowati, K. , Chen, J. , and Liu, H. , 2007, “ Electrical Properties of Air-Stable, Iodine-Doped Carbon-Nanotube-Polymer Composites,” Appl. Phys. Lett., 91(17), pp. 10–13.
Park, J.-Y. , Rosenblatt, S. , Yaish, Y. , Sazonova, V. , Üstünel, H. , Braig, S. , Arias, T. A. , Brouwer, P. W. , and McEuen, P. L. , 2004, “ Electron-Phonon Scattering in Metallic Single-Walled Carbon Nanotubes,” Nano Lett., 4(3), pp. 517–520.
Mann, D. , Javey, A. , Kong, J. , Wang, Q. , and Dai, H. , 2003, “ Ballistic Transport in Metallic Nanotubes With Reliable Pd Ohmic Contacts,” Nano Lett., 3(11), pp. 1541–1544.
Fuller, E. J. , Pan, D. , Corso, B. L. , Gul, O. T. , and Collins, P. G. , 2014, “ Mean Free Paths in Single-Walled Carbon Nanotubes Measured by Kelvin Probe Force Microscopy,” Phys. Rev. B, 89(24), p. 245450.
Wang, T. , Hu, X. , and Dong, S. , 2007, “ Construction of Metal Nanoparticle/Multiwalled Carbon Nanotube Hybrid Nanostructures Providing the Most Accessible Reaction Sites,” J. Mater. Chem., 17(39), pp. 4189–4195.
## Figures
Fig. 1
CNT(5,5) models: aligned 0.7/u.c. (left), aligned 1.0/u.c. (center), and random 2.3/u.c. (right) doping
Fig. 2
Conductance of the metallic CNT models
Fig. 3
CNTs (8,0) models: aligned 1.0/u.c. (left), aligned 1.5/u.c. (middle), and random 4.9/u.c. (right) doping
Fig. 4
Conductance of the semiconducting CNT models
Fig. 5
Doped metallic CNT(5,5): 1.3/u.c. (left) and 2.0/u.c. (right)
Fig. 6
Conductance of the interstitially doped dual CNT(5,5) models
Fig. 7
Doped CNT(8,0): 2.0/u.c. (left), and 3.0/u.c. (right)
Fig. 8
Conductance of the interstitially doped dual CNT(8,0) models
Fig. 9
Doped CNT(5,5) junction: overlaps of 2 unit cells (left) and 10 unit cells (right)
Fig. 10
Conductance of a metallic CNT(5,5) junction
Fig. 11
Doped CNT(8,0) junction: overlaps of 0.7 unit cells (left) and 4.7 unit cells (right)
Fig. 12
Conductance of a semiconducting CNT(8,0) junction
Fig. 13
Transmission line model
Fig. 14
Performance of the polyiodide-doped CNT nanowires (MFP = 1000 nm, top, and 500 nm, bottom)
## Tables
Table 1 Electrical conductivities
Table 2 Mass-specific electrical conductivities
Table 3 High performance combinations of iodine-doped CNT conductors and junctions
## Errata
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2019-05-20 02:43:19
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https://www.dronstudy.com/book/squares-and-square-roots-exercise-6-3-mathematics-ncert-class-8th/
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# Squares And Square Roots : Exercise 6.3 (Mathematics NCERT Class 8th)
Q.1 What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 9801 (ii) 99856 (iii) 998001 (iv) 657666025
Sol. (i) 9801 - The digit 9801 ends with ‘1’ then the one’s digit of the square root of that number may be 1 or 9.
Hence, the one’s digit of square root of 9801 is either 1 or 9.
(ii) 99856 - The digit 99856 ends with ‘6’ then the one’s digit of the square root of that number may be 4 or 6.
Hence, the one’s digit of square root of 99856 is either 4 or 6.
(iii) 998001 - The digit 998001 ends with ‘1’ then the one’s digit of the square root of that number may be 1 or 9.
Hence, the one’s digit of square root of 998001 is either 1 or 9.
(iv) 657666025 - The digit 657666025 ends with ‘5’ then the one’s digit of the square root of that number will be 5.
Hence, the one’s digit of square root of 657666025 is 5.
Q.2 Without doing any calculation, find the numbers which are surely not perfect squares.
(i) 153 (ii) 257 (iii) 408 (iv) 441
Sol. We know that the perfect square of a number can end only with 0, 1, 4, 5, 6, 9 or even number of zeros.
(i) 153
Since, 153 ends with ‘3’ it cannot be a perfect square number.
(ii) 257
Since, 257 ends with ‘7’ it cannot be a perfect square number.
(iii) 408
Since, 408 ends with ‘8’ it cannot be a perfect square number.
(iv) 441
Since, 441 ends with ‘1’ it can be a perfect square number.
Q.3 Find the square roots of 100 and 169 by the method of repeated subtraction.
Sol. We know that the sum of first n odd natural numbers is n2.
Finding square root of 100 by using repeated subtraction:
(i) 100 – 1 = 99 (ii) 99 – 3 = 96 (iii) 96 – 5 = 91 (iv) 91 – 7 = 84
(v) 84 – 9 = 75 (vi) 75 – 11 = 64 (vii) 64 – 13 = 51 (viii) 51 – 15 = 36
(ix) 36 – 17 = 19 (x) 19 – 19 = 0
We obtained zero at the 10th step. Hence, $\sqrt{100}$= 10.
Finding square root of 169 by using repeated subtraction:
(i) 169 – 1 = 168 (ii) 168 – 3 = 165 (iii) 165 – 5 = 160 (iv) 160 – 7 = 153
(v) 153 – 9 = 144 (vi) 144 – 11 = 133 (vii) 133 – 13 = 120 (viii) 120 – 15 = 105
(ix) 105 – 17 = 88 (x) 88 – 19 = 69 (xi) 69 – 21 = 48 (xii) 48 – 23 = 25
(xii) 25 – 25 = 0
We obtained zero at the 13th step. Hence, $\sqrt{169}$= 13.
Q.4 Find the square roots of the following numbers by the Prime Factorisation Method.
(i) 729 (ii) 400 (iii) 1764 (iv) 4096
(v) 7744 (vi) 9604 (vii) 5929 (viii) 9216
(ix) 529 (x) 8100
Sol. (i) 729
3 729 3 243 3 81 3 27 3 9 3 3 Â 1
Here, 729 = 3 x 3 x 3 x 3 x 3 x 3
Therefore, $\sqrt{729}$= 3 x 3 x 3 = 27.
(ii) 400
2 400 2 200 2 100 2 50 5 25 5 5 Â 1
Here, 400 = 2 x 2 x 2 x 2 x 5 x 5
Therefore, $\sqrt{400}$= 2 x 2 x 5 = 20
(iii) 1764
2 1764 2 882 3 441 3 147 7 49 7 7 Â 1
Here, 1764 = 2 x 2 x 3 x 3 x 7 x 7
Therefore, $\sqrt{1764}$= 2 x 3 x 7 = 42
(iv) 4096
2 4096 2 2048 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 2 Â 1
Here, 4096 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Therefore, $\sqrt{4096}$= 2 x 2 x 2 x 2 x 2 x 2 = 64
(v) 7744
2 7744 2 3872 2 1936 2 968 2 484 2 242 11 121 11 11 Â 1
Here, 7744 = 2 x 2 x 2 x 2 x 2 x 2 x 11 x 11
Therefore, $\sqrt{7744}$= 2 x 2 x 2 x 11 = 88
(vi) 9604
2 9604 2 4802 7 2401 7 343 7 49 7 7 Â 1
Here, 9604 = 2 x 2 x 7 x 7 x 7 x 7
Therefore, $\sqrt{9604}$= 2 x 7 x 7 = 98
(vii) 5929
7 5929 7 847 11 121 11 11 Â 1
Here, 5929 = 7 x 7 x 11 x 11
Therefore, $\sqrt{5929}$= 7 x 11 = 77
(viii) 9216
2 9216 2 4608 2 2304 2 1152 2 576 2 288 2 144 2 72 2 36 2 18 3 9 3 3 Â 1
Here, 9216 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3
Therefore, $\sqrt{9216}$= 2 x 2 x 2 x 2 x 2 x 3 = 96
(ix) 529
23 529 23 23 Â 1
Here, 529 = 23 x 23
Therefore, $\sqrt{529}$= 23
(x) 8100
2 8100 2 4050 3 2025 3 675 3 225 3 75 5 25 5 5 Â 1
Here, 8100 = 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5
Therefore, $\sqrt{8100}$= 2 x 3 x 3 x 5 = 90
Q.5 For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
(i) 252 (ii) 180 (iii) 1008 (iv) 2028Â Â (v) 1458 (vi) 768
Sol. (i) 252
2 252 2 126 3 63 3 21 7 7 Â 1
Here, 252 = 2 x 2 x 3 x 3 x 7
Here, prime factor 7 has no pair. Therefore 252 must be multiplied by 7 to make it a perfect square.
Therefore, 252 x 7 = 1764
Therefore, $\sqrt{1764}$= 2 x 3 x 7 = 42
(ii) 180
2 180 2 90 3 45 3 15 5 5 Â 1
Here, 180 = 2 x 2 x 3 x 3 x 5
Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.
Therefore, 180 x 5 = 900
Therefore,$\sqrt{900}$ = 2 x 3 x 5 = 30
(iii) 1008
2 1008 2 504 2 252 2 126 3 63 3 21 7 7 Â 1
Here, 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square.
Therefore, 1008 x7 = 7056
Therefore, $\sqrt{7056}$= 2 x 2 x 3 x 7 = 84
(iv) 2028
2 2028 2 1014 3 507 13 169 13 13 Â 1
Here, 2028 = 2 x 2 x 3 x 13 x 13
Here, prime factor 3 has no pair. Therefore 2028 must be multiplied by 7 to make it a perfect square.
Therefore, 2028 x3 = 6084
Therefore, $\sqrt{6084}$= 2 x 3 x 13 = 78
(v) 1458
2 1458 3 729 3 243 3 81 3 27 3 9 3 3 Â 1
Here, 1458 = 2 x 3 x 3 x 3 x 3 x 3 x 3
Here, prime factor 2 has no pair. Therefore 1458 must be multiplied by 2 to make it a perfect square.
Therefore, 1458 x2 = 2916
Therefore,$\sqrt{2916&space;}$ = 2 x 3 x 3 x 3 = 54
(vi) 768
2 768 2 384 2 192 2 96 2 48 2 24 2 12 2 6 3 3 Â 1
Here, 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
Here, prime factor 3 has no pair. Therefore 768 must be multiplied by 3 to make it a perfect square.
Therefore, 768 x3 = 2304
Therefore, $\sqrt{2304}$= 2 x 2 x 2 x 2 x 3 = 48
Q.6 For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.
(i) 252 (ii) 2925 (iii) 396 (iv) 2645Â Â (v) 2800 (vi) 1620
Sol. (i) 252
2 252 2 126 3 63 3 21 7 7 Â 1
Here, 252 = 2 x 2 x 3 x 3 x 7
Here, prime factor 7 has no pair. Therefore 252 must be multiplied by 7 to make it a perfect square.
Therefore, 252 ÷7 = 36
Therefore, $\sqrt{36}$= 2 x 3 = 6
(ii) 2925
3 2925 3 975 5 325 5 65 13 13 Â 1
Here, 2925 = 3 x 3 x 5 x 5 x 13
Here, prime factor 13 has no pair. Therefore 2925 must be multiplied by 13 to make it a perfect square.
Therefore, 2925 ÷13 = 225
Therefore, $\sqrt{225}$= 3 x 5 = 15
(iii) 396
2 396 2 198 3 99 3 33 11 11 Â 1
Here, 396 = 2 x 2 x 3 x 3 x 11
Here, prime factor 11 has no pair. Therefore 396 must be multiplied by 11 to make it a perfect square.
Therefore, 396 ÷11 = 36
Therefore, $\sqrt{36}$= 2 x 3 = 6
(vi) 2645
5 2645 23 198 23 99 Â 1
Here, 2645 = 5 x 23 x 23
Here, prime factor 5 has no pair. Therefore 396 must be multiplied by 5 to make it a perfect square.
Therefore, 2645 ÷5 = 529
Therefore, $\sqrt{529}$= 23 x 23 = 23
(v) 2800
2 2800 2 1400 2 700 2 350 5 175 5 35 1 7 Â 1
Here, 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7
Here, prime factor 7 has no pair. Therefore 396 must be multiplied by 7 to make it a perfect square.
Therefore, 2800 ÷7 = 400
Therefore, $\sqrt{400}$= 2 x 2 x 5 = 20
(vi) 1620
2 1620 2 810 3 405 3 135 3 45 3 15 5 5 Â 1
Here, 1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5
Here, prime factor 5 has no pair. Therefore 1620 must be multiplied by 5 to make it a perfect square.
Therefore, 1620 ÷5 = 324
Therefore, $\sqrt{324}$= 2 x 3 x 3 = 18
Q.7 The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
Sol. Given, each student donated as many rupees as the number of students in the class. Therefore, number of students in class will be the square root of the amount donated by the students of the class.
Now, total amount donated is Rs 2401.
Hence, number of students in class =$\sqrt{2401}$
Here, 2401 = 7 x 7 x 7 x 7
$\sqrt{2401}$= 7 x 7 = 49.
Therefore, number of students in the class is 49.
Q.8 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Sol. Given, each row contains as many plants as the number of rows.
Therefore, number of rows = number of plants in each row
Here, Total number of plants = number of rows x number of plants in each row
Number of rows x number of plants in each row = 2025
(Number of rows)2 = 2025
Number of rows =$\sqrt{2025}$
Now, 2025 = 5 x 5 x 3 x 3 x 3 x 3
Therefore, = 5 x 3 x 3 = 45
Hence, the number of rows and the number of plants in each row is 45.
Q.9 Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
Sol. The LCM of 4, 9 and 10 is 180.
2 180 2 90 3 45 3 15 5 5 Â 1
Prime factors of 180 = 2 x 2 x 3 x 3 x 5
Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.
Therefore, 180 x 5 = 900
Therefore, the smallest square number which is divisible by 4, 9 and 10 is 900.
Q.10 Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
Sol. The LCM of 8, 15 and 20 is 120.
2 120 2 60 2 30 3 15 5 5 Â 1
Prime factors of 120 = 2 x 2 x 2 x 3 x 5
Here, prime factor 2, 3 & 5 has no pair. Therefore 120 must be multiplied by 2 x 3 x 5 to make it a perfect square.
Therefore, 120 x 2 x 3 x 5 = 3600
Therefore, the smallest square number which is divisible by 8, 15 and 20 is 3600.
• Naik aayan
Goòdddd
• Anonymous
very nice brother and thank you
• all questions helps me to under stand problems
• Pratham Gupta
its very big answer
• Jogender
Nice site . All que are correct but one mistake in que 5 you write multipied instead of divide and the roman number in same question point v is uncorrect u write 6th
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2019-04-21 09:12:07
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https://www.physicsforums.com/threads/area-between-polar-curves.709464/
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# Area between Polar curves
PsychonautQQ
## Homework Statement
Find the area inside r = 9sinθ but outside r = 2
## Homework Equations
Area = 1/2(Integral of (f(θ)^2 - g(θ)^2)dθ
## The Attempt at a Solution
f(θ)^2 =
81sin^2θ = 81((1-cos(2θ))/2)
g(θ)^2 = 4
f(θ)^2 - g(θ)^2 = 36.5 - cos(2θ)/2
integral of (36.5 - cos(2θ)/2)
[36.5θ - sin(2θ)/4]
Area = 1/2[36.5θ - sin(2θ)/4]
If I integrate from 0 to ∏/2 then multiply that area times two I get 114.6681319
Where did I go wrong ;-(
Gold Member
How did you get the limits 0 to π/2? Have you sketched the two circles?
PsychonautQQ
Should I integrate from the intersection point to pi/2?
9sin(theta) = 2
theta = arcsin(2/9)
theta = .224093
If I do that that is half of the area and then I can multiply that by two to get the full area. Does that look better to you?
Gold Member
Should I integrate from the intersection point to pi/2?
Yes, that is valid because the shaded region is symmetric wrt the y axis.
9sin(theta) = 2
theta = arcsin(2/9)
theta = .224093
I would suggest subbing in arcsin(2/9). The range of this function is [-pi/2,pi/2] so subbing this in will give you the required theta.
If I do that that is half of the area and then I can multiply that by two to get the full area. Does that look better to you?
Yes.
PsychonautQQ
I would suggest subbing in arcsin(2/9). The range of this function is [-pi/2,pi/2] so subbing this in will give you the required theta.
Yes.
I plug these in for theta and then get a required theta? I'm confused by what you mean here. Do you mean that the limits of integration are [-∏/2,∏/2]?
Gold Member
I plug these in for theta and then get a required theta? I'm confused by what you mean here. Do you mean that the limits of integration are [-∏/2,∏/2]?
No, just sub in arcsin(2/9) instead of subbing in 0.224... to avoid rounding errors. The principal solution of arcsin(2/9) is the one that appears in [-pi/2,pi/2] which is the theta that the two curves intersect at in the first quadrant.
You could find the other theta corresponding to the other intersection and integrate between these two values, but your method is also good, perhaps more elegant given you have noticed the symmetry.
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2022-10-06 04:41:16
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https://askdev.io/questions/108561/how-to-make-screen-zoom-little-much-less-dreadful
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# How to make screen zoom little much less dreadful?
You recognize just how you zoom - in entire screen with your magic - trackpad+ctrl+2fingers in snow leopard?
The outcome is not - so - wonderful - looking screen. You can see pixels and also primarily the resolution is crapy ... just how do I deal with that?
0
2019-12-02 03:08:34
Source Share
There is no other way of dealing with that. It is multiplying the screen, not a real resolution independent zoom, so as points multiply they will certainly show up heavyset.
0
2019-12-03 04:57:54
Source
You can make display little smooth in Pref panes > Universal Access > Seeing tab > Zoom options… > Check Smooth images (or type ⌥⌘\) yet RobZolkos right.
0
2019-12-03 04:57:41
Source
I do not assume it is dreadful!
I periodically do some visuals and also website design job, and also I do a great deal of digital photography, and also when I respect pixels the convenience with which I can focus and also see plainly what is taking place down there is wonderful.
Additionally, as a little a typography geek, I such as to look at the below - pixel antialiasing that is taking place :B
0
2019-12-03 04:57:11
Source
As kept in mind in the previous solutions, the os does not re - provide the details at a finer degree of information - it resembles holding a magnifying glass on a published web page simply reveals bigger information as opposed to making the printing finer.
The only means to "fix" the zoom is to make the Mac draw points bigger and also allow you scroll around to see a window of the bigger details.
What you desire is called an Oversized Desktop. Primarily you fool the system right into sending out information to the graphics card to provide a 2000x1024 sized desktop. After that your computer mouse or various other commands control and also a viewport of 1440x900 with several of the information attracted offscreen.
I do not recognize of a solitary program that collaborates with 10.5 or later on - yet at the very least you recognize what to seek and also this could trigger somebody else with a referral.
0
2019-12-03 04:55:37
Source
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2022-05-23 05:55:57
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http://yhysuxev.ga/binary-call-option-13776.html
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### Binary call option example ⭐ 2020's Best Trading Brokers
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2021-10-28 13:30:30
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https://admin.clutchprep.com/organic-chemistry/practice-problems/30204/draw-the-mirror-image-160-of-the-following-molecule-160-2
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# Problem: Draw the mirror image of the following molecule.
###### Problem Details
Draw the mirror image of the following molecule.
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2020-07-13 05:04:29
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http://www.scienceforums.com/topic/11349-super-nova-voyager/?p=174498
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# Super Nova Voyager
9 replies to this topic
### #1 The Transhumanist
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Posted 20 May 2007 - 12:07 PM
The Unlimited Voyager is a shuttle that is propelled by growing explosions, it has unlimited fuel, and unlimited speed.
The first explosion is created by curving a micro inch of space time into a hundredth of a micro inch of space time using countless amounts of energy created from curve less space time (You will see what I mean later), and then shooting particles of matter and antimatter at the opposite sides of the curved space time, this causes them to collide and annihilate at astronomical speeds, which causes the curved space time to bounce back and uncurve, which releases tons of energy, this energy pushes the shuttle at great speeds, the shuttle has a machine that holds hot atoms together that are extremely firmly held together themselves, the energy splits the atoms, and because they are so firmly held together, they recover and trap tons of energy, and then a machine annihilates the atoms to the point in which they can't recover and release the energy, and uses the energy from that to curve more space time into less and repeat the process on and on, and each time it repeats, the explosions get bigger, and the shuttle accelerates even faster until it reaches the cosmic speed limit.
The energy to produce the hot atoms, and to curve space time, and anti matter, come from extremely fast collisions of matter and anti matter, from negative charge using dark matter.
With unlimited fuel we can travel around our galaxy. This shuttle has the same design as the Orion shuttle, and has two shock absorbers instead of one, and encase it passes a planet that can sustain life, it can launch a probe or a smaller shuttle out of itself. The only thing that I designed is the object in between the two shock absorbers, which is the over unity device.
### #2 Jay-qu
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Posted 21 May 2007 - 02:12 AM
Even if your crazy cool firing mechinism worked, you ship would sadly still be limited to the cosmic speed limit of c..
### #3 The Transhumanist
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Posted 21 May 2007 - 11:17 AM
By c you mean that if it goes to fast it will go slower, right?
Space Time pressure will send signals to the shuttle causing the explosions to stop at that point. And the shuttle will keep going at the very edge of the cosmic speed limit. The shuttle doesn't stop, but it holds multiple probes that can land on an object and absorb particles or take samples from it. And then the shuttle will turn around using orbit of a heavy object and then the probe will magnetically attach to it, and go flying back to earth for research.
Imagine what we could find out there?
My next space ship design is going to be a war ship that has lasers powered by the same thing that is used to propel this shuttle, in other words, some very powerful ****.
### #4 CraigD
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Posted 21 May 2007 - 01:56 PM
The Unlimited Voyager is a shuttle that is propelled by growing explosions, it has unlimited fuel, and unlimited speed.
The first explosion is created by curving a micro inch of space time into a hundredth of a micro inch of space time using lots of energy …
This first step is pretty tricky one. The only think known to curve space-time is gravity. The only thing known to produce gravity is mass. To curve (compress) 1 cm of space by a factor of 100, requires the mass-energy equivalent of about 10$^{29}$ kg (about 5% the mass of the sun), concentrated somehow within that centimeter of space. (For a look at the math behind these numbers, check out the wikipedia article “gravitational time dilation”) This is way beyond the usual meaning of “using lots of energy”, requiring matter denser greater than even exotic theoretical stuff like quarkium.
A more serious problem is that such a region of space doesn’t result in an explosion – just a region of space gravitationally similar to near the event horizon of a black hole.
… and then shooting particles of matter and antimatter at the opposite sides of the curved space time so they go through more space in less time, this causes them to collide and annihilate at astronomical speeds…
You don’t need to go to any unusual lengths to get matter and antimatter to annihilate – in its ionized form – the way the little bit that’s been created and observed comes – it’s magnetically attracted to its ordinary matter counterpart particles, rapidly annihilating with them. Preventing antimatter from annihilating before researchers have had a chance to observe or do interesting things with it is the current focus of research.
Though colliding anti-particles at relativistic speed will result in more energy being released, matter/antimatter annihilation is already not only a tremendously high-energy event, but the theoretically highest energy event there can be for a given mass.
Though I’m not sure why you’d want to, space-time “curved” into less distance as described above would result in particles taking more time to go through the same space, as observed by someone outside the curved space-time, not less. To get the opposite effect, you need a sort of negative-mass Exotic matter, something nobody has more than the slightest idea can even exist, yet alone how to make.
None of this is of much concern, however, because the next claim,
… which causes the curved space time to bounce back and uncurve, which releases tons of energy, this energy pushes the shuttle at great speeds, the shuttle takes some of that energy by absorbing it, and uses it to curve more space time into less space time and repeat the process on and on, and each time it repeats, the explosions get bigger, and the shuttle accelerates even faster forever.
just isn’t predicted by any theory, or suggested by any experimental observation. What’s being described is, in essence, a perpetual motion machine “of the first kind”, or, if you prefer a newer name, an “over unity device”. Though a popular subject with inventors and science enthusiasts, such devices simply can’t, by any of the known rules of nature, exist.
A note on word usage: As in your previous exotic spacecraft propulsion thread, ”The Explorer Shuttle”, you call your proposed spacecraft a “shuttle”. That word, which comes from an old one for the device used to carry thread back and forth when weaving, is normally used to refer to vehicles that make short, frequent trips between regular destinations. For example, http://en.wikipedia....huttle_program'>NASA’s STS is called a “shuttle” not because it is powerful, fast, or cool (which it is), but because it was intended to routinely travel between the Earth’s surface and low orbit (which its proven not-so-successful at ).
The sorts of spacecraft you appear to be most interested in, Gardamorg, though none actually yet exist, are more commonly called “interstellar vessels”, “starships”, or other names conveying “ultra-long-range”.
A note on source citations. Gardamorg, your illustration looks suspiciously like a couple of copies of a 1977 NASA archives illustration of the proposed Project Orion spacecraft (such as the one at the preceding wikipedia link), stuck together only one copy of the nose on that end. The tubes for ejecting little fission bombs are still visible – and the one in the middle of the craft makes very little sense!
Though you do note that they are “same design as the Orion shuttle”, and I’m certain neither NASA, wikipedia, nor any of the Orion designers would be in the least offended by you using these images, its customary, polite, and technically a hypography site rule to mention where you get images from, unless you make them yourself. The image in question is, as are most NASA archive images, in the public domain, but it’s still a good idea not to give the impression they’re you own work.
Gardamorg, I admire you enthusiasm for and dedication to spacecraft design and space exploration. I recommend, though, that you put at least as much effort into learning the fundamental of physics well. Without a grasp of these basics, you’ll likely be doomed to chase after impossible design ideas, without being able to figure out what’s wrong with them.
### #5 The Transhumanist
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Posted 21 May 2007 - 02:37 PM
I called it a shuttle because it doesn't have nice accommodating rooms, and artificial gravity, en fact its not supposed to hold any life at all, just machines.
Would it take more energy to curve and unkink a microscopic worm hole than it would release?
The shuttle has a machine that holds hot atoms that are extremely firmly held together, that absorb energy, and then a machine splits the atoms and uses the energy from that to curve more space time into less, even though curved space time doesn't speed up two particals, would the annihilation even with out as much kinetic energy (or force) from a faster impact still be powerful enough to unkink one hundredth of a micro inch of the curved space time?
How does an over unity device break the laws of physics, or as you call it, "the rules of nature"
I edited the topic, it is more feasible now.
### #6 Jay-qu
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Posted 21 May 2007 - 03:53 PM
No it wouldnt produce enough energy. What craig was saying is you have to produce a certian density of matter/energy to curve space time - releasing a whole lot of energy from the nucleus of a hot atom will actually decrease this density and space time would in effect be curved less..
I dont know of any processes that can 'unkink' curved space time - you must understand know one has much of a clue how one ould create and use a wormhole, this is all highly theoretical physics.
Over unity means its efficiency is greater than one, or greater than 100%. That means that you get more energy out than you put in. This violates the conservation of mass/energy in the universe - which we believe to hold true everywhere/when in the universe.
### #7 The Transhumanist
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Posted 21 May 2007 - 06:50 PM
Yeah, I thought that their might be a way to break E=MC2, and I swear that I will find a way!
JK, so if it breaks E=MC2, then how would the theorized big bang occur, how would all of the mass of the universe be condensed into such a small ball with out creating a HUGE black hole? What you are saying disproves the big bang theory, and our exp;anding universe disproves String Theory, so MY theory (And I have heard this theory before some were) that both the string theory and the big bang theory exist, I believe that their are an infinite number of universes, and that two of these universes collided, creating a new type of universe, one of matter, anti mater, and dark energy, I believe that the collision of the two universes created the big bang!
Its a new theory made by two scientists, or something. Anyway, back on topic, if a collision could create an explosion so big, that the center of the fireball would expand faster than the cosmic speed limit, or "Faster than light" Then imagine what we could do with further research.
Negative charge. And the laws of physics, I'll learn them both!
I recommend, though, that you put at least as much effort into learning the fundamental of physics well. Without a grasp of these basics, you’ll likely be doomed to chase after impossible design ideas, without being able to figure out what’s wrong with them.
If I ever become a scientist, I will have a group of people like you helping me out, chances are, 4 our 5 scientists will find out sooner than 1.
Although I would have to get them to help me first, and thats where propaganda comes in handy.
### #8 Jay-qu
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Posted 22 May 2007 - 05:52 AM
No, what I say doesnt dissprove big bang theory - it is accepted that our current laws of physics break down at the extremes on the universe. That is when singularities are considered, such as a big bang singularity.
### #9 The Transhumanist
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Posted 23 May 2007 - 11:59 AM
Here are two ideas, one is something that produces the energy to do the other.
### #10 TheFaithfulStone
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Posted 31 May 2007 - 10:39 AM
As long as we're making stuff up willy-nilly, can I have talking dog?
I'd say if these are for a sci-fi story or something, you've got just the right amount of plausible sounding bs. If you actually expect to build them someday, you've got some studying to do.
It doesn't seem particularly clear to me what the aim is.
TFS
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2014-09-03 04:35:42
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https://code.bioconductor.org/browse/MBttest/master/
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Name Mode Size
R 040000
data 040000
inst 040000
man 040000
vignettes 040000
DESCRIPTION 100644 1 kb
NAMESPACE 100755 0 kb
NEWS 100644 0 kb
# MBttest MBttest, also called mBetat test, uses new beta t-test method to identify differential expression for each gene or RNA isoform. This approach introduces a gene- or isoform-specific variable, called rho, into t-statistic based on beta distribution. It outperforms the existing statistical methods for identifying differential expressions of genes or isoforms either by inflating t-values with rho > omega (a null rho) or by shrinking those with rho < omega when number of replicate libraries in each condition is smaller. ## Installation You can install MBttest from GitHub using devtools in R Console or Rstudio: library(devtools) install_github("yuande/MBttest") or if (!requireNamespace("BiocManager", quietly=TRUE)) install.packages("BiocManager") BiocManager::install("MBttest", dependencies = TRUE)l library(MBttest) ## Data preparation When RNA-seq data have been produced from RNA sequecing experiments, user should first perform pipeline analysis of the RNA sequence read data and map the short RNA sequences to a reference genome. Currently many pipeline tools such as BWA, Bowtie2, tophat2, star and galaxy can be used to map and annotate RNA sequences on a reference genome. The pipeline analysis generates count matrix. The count matrix contains two parts: Annotation information and count data. Information may contain tagid, geneid, gene name, chromosome, DNA strand, etc columns, depending on a pipeline tool that user used. Information columns are in the left side of the matrix. It has at least one column for geneid or tagid (isoformid). The count data contain two conditions each having several replicate libraries and must be in the right side. Here is an example: data(jkttcell) jkttcell[1:10,] or using head to display the data jkttcell: head(jkttcell) jkttcell is matrix count data generated from RNA sequences due to differential polyadenylation in Jurkat T-cell betweem resting and stimulating statuses using BWA. Data jkttcell contains 7 columns for information of poly(A) sites in the left side and 10 columns for count data. ## Simulation for calculation of omega Before performing *mbetattest* on the real data, user needs simulation to determine $$\omega$$ value. There are three steps for doing so: Step1: Use the following function to generate null simulation data: sjknull<-simulat(yy=jkttcell, nci=7, r1=3, r2=3, q=0.2) where yy is real data. r1 and r2 are replicate numbers in conditions 1 and 2. q is proportion of genes artificial noise. nci = column number of information of data. Step2: Perform multiple beta t-tests on simulated null data sjknull: mysim<-smbetattest(X=sjknull, na=3, nb=3, alpha=0.05) Figure1 in vignettes fold shows the results. In symbol column, *mbetattest* gives test result: "-" means that a gene or a tag or isoform is not chosen, while "+" indicates that the gene or isoform is found to be differentially expressed between two statuses (see Figure2 in vignettes folder. In this example, 12 genes would be detected to be falsely positive. Step3: Calculate omega: Here is a demo for calculating omega (since we can not use greek letter omega in R function, we use W to represent omega. In Figure 3 in vignettes, red highlighted column is rho column. We copied the rho values of these 12 genes into another empty column and sorted them from the smallest to the largest. Then we gave sequence number (k) from 1 to 12 corresponding to rho-values and calculate q=k/12 for each ordered rho value. Then we chose rho with q >= 0.85. Repeat this process for about 5 times (depends on number of genes or isofroms in the real data that user uses) and give average the rho values as W. ## Normalize the count data As a second processing step, we need to estimate the effective library size. This step is also called "normalization of data", even though it may not make the count data be of normal distribution. If the counts of expressed genes in one condition are, on average, twice as high as in another (because the library was sequenced twice as deeply), the size factor for the first condition should be twice higher than the second one, then differential analysis would give error results. For this reason, we must make all libraries have the same size before performing any statistical method. For doing so, user can use the following simple method to normalize the the count data: In excel sheet, use function sum to calculate sizes of all libraries, and then use excel function average to calculate averaged library size. The last step is to use the following equation to convert the original count data to new count data with the same library size: xij = yij*bar(N)/Nj where i = 2, ..., n(number of genes or isofoms) in rows in a sheet, j = 1, ..., c where c=na+nb; Nj is size of library j and bar(N) is mean of sizes over all libraries; yij is the original count of **RNA** reads in row i and column j. ## Perform multiple beta t-tests on the real data Suppose the data have been normalized so that all libraries have the same size. After obtaining W value, user can use the function and the real data to perform MBttest: res<-mbetattest(X=jkttcell, na=3, nb=3, W=1, alpha=0.05, file= "jurkat_result.csv") Function *mbetattest* has two output results: one is saved in .csv file and the other is res for making heatmap. Function *myheatmap* has multiple options: both-side, row and column cluster trees with distance methods: "euclidean", "pearson", "spearman", and "kendall" correlation coefficients and color label with "redgreen", "greenred", "redblue", "bluered" or "heat.colors" and angles for genes or isoforms in row and cases (conditions) in column. User can use default without any choice, like myheatmap(dat=res, r1=3,r2=3,maptitle="Jurkat T-cell heatmap") ## Author Yuande Tan tanyuande@gmail.com
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2023-03-21 15:32:38
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https://www.vedantu.com/question-answer/if-a789-then-the-relation-r89-in-a-is-a-class-11-maths-cbse-5edb78d04ec09b71530f7eb3
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Question
If A={7,8,9} then the relation R={(8,9)} in A is${\text{A}}{\text{.}}$ Symmetric only${\text{B}}{\text{.}}$ Symmetric and transitive only${\text{C}}{\text{.}}$ Transitive only${\text{D}}{\text{.}}$ Equivalence
Hint- Here, we will proceed by checking whether the given relation is symmetric or not, transitive or not, equivalence or not with the help of the general conditions which are used.
Given, set A={7,8,9} and relation R={(8,9)} in A
Any relation is said to be equivalence relation when that relation is reflexive, symmetric as well as transitive.
For a relation in set A to be reflexive, if $\left( {a,a} \right) \in R$ for every $a \in R$
For a relation R in set A to be symmetric, if $\left( {a,b} \right) \in R$ then $\left( {b,a} \right) \in R$
For a relation R in set A to be transitive, if $\left( {a,b} \right) \in R$ and $\left( {b,c} \right) \in R$ then $\left( {a,c} \right) \in R$
Clearly $\left( {8,9} \right) \in R$ but $\left( {9,8} \right) \notin R$, so the given relation R in set A does not satisfy the necessary condition for symmetric relation. Hence, relation R is not symmetric.
Since for the relation R in set A to be an equivalence relation, it is necessary for that relation to be symmetric also. Hence, the given relation R is not an equivalence relation.
The given relation R in set A contains only one element i.e., (8,9) so it is said to be transitive.
Therefore, the given relation R in set A is only transitive.
Hence, option C is correct.
Note- In this particular problem, we haven’t checked whether the given relation R in set A is reflexive or not because only reflexive is not anywhere there in the options and it has already proved that the given relation isn’t an equivalence relation. The above given transitive condition can only be applied if there is more than one element in the given relation but here there is only one element.
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2021-04-12 05:48:02
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http://mathhelpforum.com/calculus/31326-please-help-find-area-bounded-two-curves.html
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Please find the value of the definite integral thanks.
x=100000(9√y-1)
x=100000((9√y-1)/(8√y))
2. Originally Posted by waite3
Please find the value of the definite integral thanks.
x=100000(9√y-1)
x=100000((9√y-1)/(8√y))
First, find out for what values of y, that these two equations equal.
$9\sqrt{y}-1=\frac{(9\sqrt{y}-1)}{8\sqrt{y}}$
$1=8\sqrt{y}$
$y=\frac{1}{64}$
Also, note that when $y=\frac{1}{81}$, the equations are both equal to zero. We now have our limits, so let's continue to integration...
Graphs are positive, so take the difference between the equations to get: $100000(9\sqrt{y}-1)(\frac{1}{8\sqrt{y}}-1) = 100000(\frac{9}{8}-9\sqrt{y}-\frac{1}{8\sqrt{y}}+1)$
Now, integrate it...
$\int _{\frac{1}{81}}^{\frac{1}{64}} 100000(\frac{9}{8}-9\sqrt{y}-\frac{1}{8\sqrt{y}}+1) dy$
Can you finish this?
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2017-08-17 07:05:08
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https://tex.stackexchange.com/questions/linked/10684?sort=newest
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27 questions linked to/from Vertical space in lists
39 views
### How to reduce the vertical empty space height/space of the center environment with huge text?
This famous question explains how you can reduce the empty useless spacing between listings or so, but now I'd like to do the same with center, which also has a big space here: \documentclass{scrartcl}...
52 views
### enumerate* - indent issue with next line item
I am trying to create a list that would look like: Awards: 1. Award A 2. Award B I have used the \usepackage[inline]{enumitem} but the result I am getting is the following: Awards: 1. Award ...
60 views
### Remove the spacing before the itemized list
Anybody knows how I can remove the spacing before my itemized list? \begin{document} {\bf main text }\hfill{year}\\ {title}\\ \renewcommand\labelitemii{$\square$} \begin{itemize} ...
264 views
### Suppress item numbers specifically in enumerate environment as modified by the package enumitem
I'm trying to create a list or listlike structure that has the following characteristics: no extra vertical space between items no leading line numbers "looking nice" when surrounded by \begin{...
114 views
### Enumitem settings have no effect on enumerate environment
I've read this question: Vertical space in lists but neither solution offered there works for me. When I add this: \usepackage{enumitem} \setitemize{itemsep=-10pt,parsep=-10pt,topsep=-10pt,partopsep=...
2k views
### Spacing after Enumerate [duplicate]
How can I remove the space after enumerated item and the next line in text ? I use following: \begin{enumerate} \setlength{\itemsep}{0pt} \item bi-axial etc. etc. \item uni-axial etc. ...
559 views
### List of items at normal line spacing [duplicate]
It's been a while, but in TeXWorks I'm making a list of items. The long way: \textbullet\hspace*{0.2cm} Jam \textbullet\hspace*{0.2cm} Custard \textbullet\hspace*{0.2cm} Beef \textbullet\hspace*{0....
16k views
### Math book: how to write Exercise and Answers
EDIT within \documentclass[12pt]{book}I want to create chapter-wise exercises and put all the solutions (with or without hints) at the end of the book. I want to do this in simple and non-tedious way ...
2k views
### Diagram with LaTeX (Smart Art)
I would like to create the following diagram: I have tried with the following code: \begin{figure} \begin{tikzpicture}[scale=1, transform shape] %\draw[step=0.5cm,gray,very thin] (0,0) grid (12,6);...
86 views
### How do I change the vertical separation of questions in a questions environment in exam class?
How do I change the vertical separation of questions in a questions environment? I need to know how to do it because there are times a vertical separation is not needed, and there are times it is more ...
2k views
### Vertical Spacing (with enumitem) with Various Levels of Itemize
I am currently working around verstical space in lists and changig a bit the spacing. I have come up around this answer: Vertical space in lists That has worked fine for me with enumitem package. ...
62k views
### \topsep, \itemsep, \partopsep, \parsep - what do they each mean (and what about the bottom)?
The enumitem package documentation says: \topsep, \itemsep, \partopsep, \parsep? Ok, it doesn't quite say that, but it also doesn't illustrate what these dimensions mean. Can I get a diagram with ...
241 views
### Aesthetics of enumerations [closed]
I am currently writing my master's thesis and I try to avoid using enumerations as much as I can, as they look rather ugly/unprofessional to me. However, sometimes I can't escape using some them and I'...
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2021-03-04 22:28:40
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http://physiology.med.cornell.edu/people/banfelder/qbio/exams/
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Old exams from qBio are available, and collected here for your convenience.
qBio Midterm exams: 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
qBio Final exams: 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015
qBio I Final exams: 2015
Answers are not posted. Study, and discuss among yourselves!
Note that as the curriculum has evolved, material from some questions on older exams may not have been covered in more recent years. In particular, as of Fall 2015, qBio has been split into two separate courses; qBio I nominally tracks the content of the Midterm exams posted here, and qBio II tracks the content of the Final exams posted here.
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2018-05-28 01:12:55
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http://new-contents.com/New-York/estimate-error.html
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Address 945 E Henrietta Rd, Rochester, NY 14623 (585) 427-7880
estimate error Bergen, New York
Therefore, the predictions in Graph A are more accurate than in Graph B. A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample. As will be shown, the mean of all possible sample means is equal to the population mean. Kind regards, Nicholas Name: Himanshu • Saturday, July 5, 2014 Hi Jim!
Please help. Frost, Can you kindly tell me what data can I obtain from the below information. Loss function Squared error loss is one of the most widely used loss functions in statistics, though its widespread use stems more from mathematical convenience than considerations of actual loss in These authors apparently have a very similar textbook specifically for regression that sounds like it has content that is identical to the above book but only the content related to regression
For a value that is sampled with an unbiased normally distributed error, the above depicts the proportion of samples that would fall between 0, 1, 2, and 3 standard deviations above Thank you once again. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Next: Dispersion Variance Up: Variances and Regularization Previous: Variances and Regularization Contents Estimation Error, Estimation Variance Every estimation In case of the assumption of second-order stationarity of the random function we have (i) the mathematical expectation, (ii) a variance, called the estimation variance'', The expectation characterizes the mean error,
For each sample, the mean age of the 16 runners in the sample can be calculated. Thanks for the beautiful and enlightening blog posts. This definition for a known, computed quantity differs from the above definition for the computed MSE of a predictor in that a different denominator is used. The next graph shows the sampling distribution of the mean (the distribution of the 20,000 sample means) superimposed on the distribution of ages for the 9,732 women.
The reason N-2 is used rather than N-1 is that two parameters (the slope and the intercept) were estimated in order to estimate the sum of squares. Recall that the regression line is the line that minimizes the sum of squared deviations of prediction (also called the sum of squares error). Probability and Statistics (2nd ed.). Examples Mean Suppose we have a random sample of size n from a population, X 1 , … , X n {\displaystyle X_{1},\dots ,X_{n}} .
The sample proportion of 52% is an estimate of the true proportion who will vote for candidate A in the actual election. The fourth central moment is an upper bound for the square of variance, so that the least value for their ratio is one, therefore, the least value for the excess kurtosis I think it should answer your questions. Mathematical Statistics with Applications (7 ed.).
Applications Minimizing MSE is a key criterion in selecting estimators: see minimum mean-square error. Experimental observation has shown that the arithmetic mean of these six holes, , can be taken as the true grade of block . However, one can use other estimators for σ 2 {\displaystyle \sigma ^{2}} which are proportional to S n − 1 2 {\displaystyle S_{n-1}^{2}} , and an appropriate choice can always give However, S must be <= 2.5 to produce a sufficiently narrow 95% prediction interval.
But, since the two most important characteristics of this function-its expectation and variance-can be calculated, we shall refer to a standard two-parameter ( and ) function which will provide an order Assume the data in Table 1 are the data from a population of five X, Y pairs. How can an estimator look like, which produces such estimated values of a particular realization. In this scenario, the 2000 voters are a sample from all the actual voters.
Errors when Reading Scales > 2.2. Of course, T / n {\displaystyle T/n} is the sample mean x ¯ {\displaystyle {\bar {x}}} . A quantitative measure of uncertainty is reported: a margin of error of 2%, or a confidence interval of 18 to 22. Ignore any minus sign.
For example, the U.S. Similar formulas are used when the standard error of the estimate is computed from a sample rather than a population. Being out of school for "a few years", I find that I tend to read scholarly articles to keep up with the latest developments. Unlike R-squared, you can use the standard error of the regression to assess the precision of the predictions.
The answer to this question is in this chapter. Jim Name: Nicholas Azzopardi • Wednesday, July 2, 2014 Dear Mr. Mini-slump R2 = 0.98 DF SS F value Model 14 42070.4 20.8s Error 4 203.5 Total 20 42937.8 Name: Jim Frost • Thursday, July 3, 2014 Hi Nicholas, It appears like Retrieved from "https://en.wikipedia.org/w/index.php?title=Mean_squared_error&oldid=741744824" Categories: Estimation theoryPoint estimation performanceStatistical deviation and dispersionLoss functionsLeast squares Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history
The sample mean will very rarely be equal to the population mean. This estimate may be compared with the formula for the true standard deviation of the sample mean: SD x ¯ = σ n {\displaystyle {\text{SD}}_{\bar {x}}\ ={\frac {\sigma }{\sqrt {n}}}} What is the Standard Error of the Regression (S)? If the estimator is derived from a sample statistic and is used to estimate some population statistic, then the expectation is with respect to the sampling distribution of the sample statistic.
The last column, (Y-Y')², contains the squared errors of prediction. Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma } This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall
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2018-12-12 17:13:17
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http://math.wikia.com/wiki/Limit
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## FANDOM
1,022 Pages
If a variable $x$ takes values which are more and more close to a finite number $a$ , then we say that $x$ approaches $a$ written as $x\to a$).
• If values of $x$ come closer to $a$ but are always greater than $a$ , then we say that $x$ approaches $a$ form right ($x\to a^+$).
• If values of $x$ come closer to $a$ but are always less than $a$ , then $x$ approaches $a$ from left ($x\to a^-$) .
The concept of a limit is essentially what separates the field of calculus, and analysis in general, from other fields of mathematics such as geometry or algebra.
The concept of a limit may apply to:
## Examples
If $x\to2$ , then $x$ can approach to '2' from two sides:
• From right side: In notation we write $x\to2^+$ means $x$ is coming closer to '2' from right i.e. it is more than '2'.
\begin{align}&x=2.1\\&x=2.01\\&x=2.0001\\&\vdots\end{align}
• From left side: In notation we write $x\to2^-$ mean $x$ is coming closer to 2 from left i.e. it is less than '2'.
\begin{align}&x=1.9\\&x=1.99\\&x=1.9999\\&\vdots\end{align}
## Meaning of a limiting value
Let $f(x)$ be function of $x$ . If the expression $f(x)$ comes close to $L$ as $x$ approaches $a$ then we say that $L$ is the limit of $f(x)$ as $x$ approaches $a$ .
In notation, it is written as $\lim_{x\to a}f(x)=L$ .
## Right Hand Limit
If $f(x)$ approaches $L_1$ as $x$ approaches $a$ from right, then $L_1$ is called as the right hand limit of $f(x)$ .
Right hand limit can be expressed in two ways:-
• $\lim_{x\to a^+}f(x)=L_1$
• $\lim_{h\to0}f(a+h)\text{ Put }x=a+h\text{ in the above result}$
## Light Hand Limit
If $f(x)$ approaches a form left, then $L_2$ is called as the left hand limit of $f(x)$ . Left hand limit can be expressed in two ways:-
• $\lim_{x\to a^-}f(x)=L_2$
• $\lim_{h\to0}f(a-h)\text{ Put }x=a-h\text{ in the above result}$
Note that $h$ is an infinitely small positive number approaching to 0.
## Existence of Limit
For existence of limit at $x=a$
\begin{align}&\Rightarrow LHL=RHL\\ &\Rightarrow L_1=L_2\\ &\Rightarrow\lim_{x\to a^-}f(x)=\lim_{x\to a^+}f(x)\end{align}
### Illustrating the concept
If $f(x)=\frac{x^2-4}{x-2}$ , then evaluate $\lim_{x\to2}f(x)$ .
L.H.L. = $\lim_{x\to2^-}\frac{x^2-4}{x-2}$ i.e. $x$ is coming closer to 2 but it is less than '2'. So, observe the situation in table below:
$x$ $2-x$ $f(x)$
1.9 0.1 3.9
1.99 0.01 3.99
1.999 0.001 3.999
$\vdots$ $\vdots$ $\vdots$
Coming closer to 2 but less than 2 Coming closer to 4 but less than 4
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2017-07-23 06:37:14
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https://artofproblemsolving.com/wiki/index.php?title=2010_AMC_10B_Problems/Problem_11&diff=prev&oldid=44453
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# Difference between revisions of "2010 AMC 10B Problems/Problem 11"
## Problem
A shopper plans to purchase an item that has a listed price greater than $\textdollar 100$ and can use any one of the three coupons. Coupon A gives $15\%$ off the listed price, Coupon B gives $\textdollar 30$ off the listed price, and Coupon C gives $25\%$ off the amount by which the listed price exceeds $\textdollar 100$.
Let $x$ and $y$ be the smallest and largest prices, respectively, for which Coupon A saves at least as many dollars as Coupon B or C. What is $y - x$?
$\textbf{(A)}\ 50 \qquad \textbf{(B)}\ 60 \qquad \textbf{(C)}\ 75 \qquad \textbf{(D)}\ 80 \qquad \textbf{(E)}\ 100$
## Solution
Let the listed price be $(100 + p)$, where $p > 0$
Coupon A saves us: $0.15(100+p) = (0.15p + 15)$
Coupon B saves us: $30$
Coupon C saves us: $0.25p$
Now, the condition is that A has to be greater than or equal to either B or C which give us the following inequalities:
$A \geq B \Rightarrow 0.15p + 15 \geq 30 \Rightarrow p \geq 100$
$A \geq C \Rightarrow 0.15p + 15 \geq 0.25p \Rightarrow p \leq 150$
We see here that the greatest possible value for $p$ is $150$, thus $y = 100 + 150 = 250$ and the smallest value for p is $100$ so $x = 100 + 100 = 200$.
The difference between $y$ and $x$ is $y - x = 250 - 200 = \boxed{\textbf{(A)}\ 50}$
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2021-05-14 01:44:45
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https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/review-synthesis-chapters-1-5-review-exercises-page-192/4
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## College Physics (4th Edition)
We can convert $3/4~tsp$ to units of $mL$: $3/4~tsp \times \frac{4.9~mL}{1~tsp} = 3.675~mL$ We can find the factor that the baby was overmedicated: $\frac{3.675~mL}{0.75~mL} = 4.9$ The baby was overmedicated by a factor of 4.9, which is the conversion factor from units of $tsp$ to units of $mL$
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2020-04-04 03:45:40
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