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http://www.reference.com/browse/Dimensionless+unit
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Definitions
# Thomson (unit)
The unit Thomson is a unit that has appeared infrequently in scientific literature relating to the field of mass spectrometry as a unit of mass-to-charge ratio. The name refers to J. J. Thomson who measured the mass-to-charge ratio of electrons and ions.
## Definition
Cooks and Rockwood proposed the unit thomson (Th) for the physical quantity mass-to-charge ratio.
$1~Th equiv 1~frac\left\{u\right\}\left\{e\right\} equiv 1~frac\left\{Da\right\}\left\{e\right\}$
where u represents the atomic mass unit, Da represents the unit dalton, and e represents the elementary charge which is the electric charge unit in the atomic unit system.
For example, for the ion C7H72+ has an exact mass of 91.0 Da and a charge number of +2, the the ion will be observed at 45.5 Th in a mass spectrum.
An interesting part of their proposal allowed for negative values for negatively charged ions. For example, the benzoate anion would be observed at m/z 121, but at -121 Th since the charge number is -1.
Unfortunately, the article proposing the unit of the thomson contains an ambiguity relating to the specification of charge. In one place the article refers to "charge number," as noted above, but in another place the article specifies charge in terms of actual units of charge: "Using standard rules for abbreviation, we have 1 Th = 1 u/ atomic charge." Or in other words the units of the thomson are units of mass (unified atomic mass units) divided by units of charge (atomic or elementary charge). This unfortunate ambiguity may have contributed to the controversey over the unit. The ambiguity about specification of charge does not affect the numerical value assigned to the mass-to-charge ratio of an ion, but instead relates to the dimensionality to be associated with the quantity. Clarification of the original intent of the authors has not appeared in the literature, although in private communications Rockwood states that the intended dimensionality was mass/charge with the specific units being unified atomic mass units per elementary charge.
## Use
The thomson has been used by some mass spectrometrists, for example by the inventor of the Orbi Trap in a scientific posters,. papers, and (notably) one book. The journal Rapid Communications in Mass Spectrometry (in which the original article appeared) states that "the Thomson (Th) may be used for such purposes as a unit of mass-to-charge ratio although it is not currently approved by IUPAP or IUPAC. Even so, the term has been called "controversial" by RCM's former Editor-in Chief (in a review the Hoffman text cited above). The Editor-in-chief of the Journal of the Mass Spectrometry Society of Japan has written an editorial in support of the thomson unit.
In his book, Mass Spectrometry Desk Reference, Sparkman argues strongly against the use of the thomson,. However, his arguments were against a dimensionless unit because of the possible confusion with the Thomson number in fluid dynamics, Thomson scattering, and the Thomson coefficient (the latter named after Lord Kelvin). He seems not to have realized that the unit "thomson" is not dimensionless but actually of dimension mass/charge and that therefore the possibility of confusion is minimal.
The thomson is not a SI unit, nor is it currently accepted by IUPAC; however, it can be argued that the thomson complies better to the international standards about quantities and units as described in ISO 31 and the IUPAC green book than the "unitless" m/z that is widely used for labeling mass spectra.
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2014-09-01 15:03:07
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https://lists.matroska.org/pipermail/matroska-devel/2006-April/002959.html
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# [Matroska-devel] EBML Namespaces
Steve Lhomme steve.lhomme at free.fr
Sun Apr 30 17:51:43 CEST 2006
HAESSIG Jean-Christophe wrote:
> The lowlevel EBML parser's job will be to demultiplex the
> elements from different vocabularies and feed them to the
> correct application. Since the namespace information is only
> a means to multiplexing, it is not forwarded to the application
> and therefore "removed".
Technically I think an application should "register" itself as capable
of understanding namespace X. This way this application gets the element
in the order they appear, while separating the namespaces could mean a
'desynchronisation' of the level where the ID was found.
Then if the "host" app wants to handle namespace separately in the code,
it's its responsability.
> Below is a schematic of my idealized vision of the EBML logical
> infrastructure :
> _____
> Lowlevel / \
> parser --------->| | X application
> ______ __ /elements | |
> | | / \ / in NS X \_____/
> | |----->| |---- _____
> | | | |---- elements / \
> |______| \__/ \in NS Y | | Y application
> EBML File ^| ---------->| |
> ||elements \_____/
> registration|| _____ |EBML API
> &state after|| / \ |e.g. seeking
> seeking |*-->| |<--------*
> *----| | EBML application
> \_____/
>
> A plain old EBML application (e.g. Matroska) without namespaces
> Would extend the EBML application.
> A new one (with namespace support) would implement a new
> application module and register to the lowlevel parser.
Yes, we probably meant the same thing then ;)
> Now where do I see the NS IDs precisely ?
>
> [Class-ID][Size][Data ****]
> / \_______________________________
> / \
> [Length Descriptor][Namespace][Class Value]
>
> The lowlevel parser reads the length descriptor and extracts
> the value bits (NS+CLASS). In these bits are the namespace of
> the element and the class ID value. Before the parser tries
> to decode the NS, all the possible NS values that this element
> may use must be known to the parser (that's somewhat obvious,
> but it doesn't mean that NS definitions have to physically be
> written before the element using them -- think XML ;).
>
> The possible NS values must be prefix codes, this allows the
> parser to scan the values bits from left to right and exactly
> know when the NS ID ends. The rest of the value bits are the
> Class-ID value which is forwarded to the corresponding
> application.
>
> Examples with 3 namespaces :
> 0 : EBML
> 10 : NSX
> 11 : NSY
Would you have a variable length size or use 00, 01, 10, 11 ?
The number of namespaces in the file is written in the EBML which is
mandatory to read. So it's known beforehand how many bits will be needed
to read the namespace. And therefore I think it's better to have a fixed
length, it will use less space. The impact on backward compatibility
(matroska) is about the same as some Class-ID will need to be extended
by 1 octet to remain valid.
Now as we're probably heading for this compatibility issue (only for
files including more than 1 namespace) I'd also like to introduce the
EbmlMaster bit in the ID header. So that it's possible for an EBML
parser to parse the whole tree without knowing anything about the semantic.
> 0x8F = 0b10001111 Namespace : EBML
> LNVVVVVV Class-ID value : 15(dec)
>
> 0xDB = 0b11011011 Namespace : NSX
> LNNVVVVV Class-ID value : 27(dec)
>
> 0x7D09 = 0b01111101 00001001 Namespace : NSY
> LLNNVVVV VVVVVVVV Class-ID value : 3337(dec)
>
>>> EBML is supposed to be a byte-aligned format and it would
>>> require at least 1 extra byte for each element. This is not
>>> bad in itself, but it would waste a great amount of bits,
>>> since I do not expect files with more than 5 mixed namespaces
>>> to be frequent. Therefore, I expect the namespace value to take
>>> up to 3 bits in most cases, this is why I try to pack it into
>>> an existing field.
>> Well, what happens when you need 6 or 7 ? You don't have any
>> more bits left. Adding another byte or 2 gives room for
>
> When I say that I do not expect files using more than 5 namespaces
> to be frequent it doesn't mean that I want to disallow files which
> need to use more... It only means that we should be able to encode
> the NS on less than 1 byte (preferably only 2 or 3 bits) for the most
> frequent case. Cases requiring 300+ simultaneous namespaces will
> still be allowed, but they will use more bits (8,9,10,more) to
> express the namespace of the various contained elements.
OK that's fine. Unfortunately the matroska IDs were designed to make use
of as many different bits as possible (less false alarm in case of
errors). And we needed as varied elements as possible in a format where
all tags would be global. Now with namespaces that constraint will fall.
> Moreover, even if we have files using many namespaces, I really
> doubt they will massively mix them -- a localized use of some
> namespace is more likely. Therefore we should definitely have
> some namespace switching feature, and namespace IDs should not
> be globally fixed for a given file.
Yes, there is no point at a level X to use different namespaces in
random order as their semantic is orthogonal. So the elements will
probably end up being grouped by namespace. Given that it means
Atamido's proposition for a new special tag might be enough ! But it
should be a Class-A tag to avoid overhead. In this case it would be 3
octets for each added namespace: the ID, the size of the namespace
(could be more than one if that element is an EbmlMaster), the namespace
value. Another option would be to use a new EBML type, similar to
EbmlMaster but with a namespace ID before the other elements.
Using such an element/type could be problematic though. It can keep
matroska compatibility easily only if we revert to the default/main
namespace in absence of that container element. That means, as proposed
before, we always assume, in the absence of a namespace, that we use the
default. That proposition also allow to chain namespaces (like
std::iterator::int).
Seeking anywhere in the file (at the EBML level) is still a problem (in
all cases proposed) as we are unable to recover the complete namespace
context. It could only work for 0 or 1 namespace in the chain.
Another problem if we don't have the notion of default namespace is to
seek in matroska (semantic level) because that means the level 0 would
need to be contained in the default namespace, and therefore would need
to be prepended with that new ID. That means it's not backward
compatible at all.
Now chaining namespaces may not be so clean. Imagine you have a
namespace for "comments" and a namespace for "signature". You can put
signature anywhere in the file. But if what you add a comment in a
signature or a signature in a comment ? How to interpret
"signature::comment" or "comment::signature" IDs ? In that case we only
need to use "comment" or "signature"... So is namespace chaining a
feature we want ? Or we always revert to the last seen namespace ? (in
which case seeking becomes easy)
>> I'm not too concerned about the overhead because right now if
>> you need a lot of IDs you need to use 2 octets long ones.
>> While with a namespace most IDs for each namespace won't need
>> a lot of room (127 possibilities for Class A IDs). So in the
>> end there should be a good balance.
>
> EBML is a wonderful structured format. I don't mean to restrain
> format writers from defining the format they like, but using a
> lot of IDs in some flat space is not what I would call good
> engineering. As for XML, I think the tree-like encapsulating
You're right. Even matroska could do with a better element mapping.
Especially to show how matroska is modular. We could easily see if a
parser supports a module and not the others... (like tags or chapters)
>> Using 3 bits in the ID header would reduce the number of
>> possible Class A IDs of a format to 2^4-1 = 15 ! That's too
>> small IMO. So I think adding another bit will give us more
>> freedom and space and almost no cost.
>
> With a variable-width NS-ID embedded in the ID header, a
> separation in classes is less relevant. In cases where only 2
> namespaces are used, only 1 bit is needed, thus 6 bits are left
> to encode the element ID value. Format writers should be aware
> that element IDs ranging from 0 to 63(dec) use at least 1 byte,
> maybe more, depending on the number of namespaces actually in
> use. For example, if the namespace ID for one element uses 2
> bits, element ID values ranging from 32 to 4095 will need 2
> bytes. If the namespace ID 3 bits, element ID values ranging
> from 16 to 2047 will need 2 bytes, and element ID values
> ranging from 2048 to 262143 will need 3 bytes, etc...
>
> The following chart summarizes how much bytes are required to
> encode an element ID assuming various NS ID lengths. In fact
> it could be a little smarter than that (there are still some
> wasted bits but for the moment I don't know what to do with
> them).
>
> |NS ID Length Bytes Required ------->
> v 1 2 3 4 5
> 0 0-127 128-16383 16384-2097151 2097152-268435455 268435456-34359738367
> 1 0-63 64-8191 8192-1048575 1048576-134217727 134217728-17179869183
> 2 0-31 32-4095 4096-524287 524288-67108863 67108864-8589934591
> 3 0-15 16-2047 2048-262143 262144-33554431 33554432-4294967295
> 4 0-7 8-1023 1024-131071 131072-16777215 16777216-2147483647
> 5 0-3 4-511 512-65535 65536-8388607 8388608-1073741823
> 6 0-1 2-255 256-32767 32768-4194303 4194304-536870911
> 7 * 1-127 128-16383 16384-2097151 2097152-268435455
> 8 * 1-63 64-8191 8192-1048575 1048576-134217727
>
> Also, I don't intend to change the Reserved Values : these are still
> 127,16383,2097151,268435455,34359738367, etc, regardless of the
> inserted NS ID.
>
>>> You seem to be prepared to make big changes to the format,
>> but I don't
>>> know to what extent whe should break compatibility...
>> Again, for current Matroska files it shouldn't be a problem
>> as matroska would be the default namespace. In that case the
>> namespace shouldn't be used for such IDs. That means older
>> files will play without any problem in namespace-aware
>> parsers. Only newer files containing some namespace will not
>> be usable by older parsers. Which AFAIK is the same with what
>> you propose.
>>
>> BTW, we still haven't discussed how to define the namespace
>> in the EBML header, but the DocType existing today will
>> remain. And that is the way to define the special namespace
>> that will be used as default... The other namespaces will
>> probably fall back in an list. It's like the DocType in XML
>> (like html). At least we got the right name for that field ;)
>
> I understand that you are referring to a "default" namespace as
> in XML. Well, that's not how I see it. If there is some kind of
> default namespace i.e. not expressed for elements in this
> namespace we still need a way to tell that the namespace value
> is present or absent. I intend to have two kinds of files :
> * Files without namespaces, i.e. NS length = 0. This
> mathematically forbids the presence of namespaces since the
> empty code is a prefix for all codes.
> * Files using namespaces, i.e. NS length >= 1. There can be
> only 2 namespaces (0 & 1, each using one bit), or more, as
> seen in the previous examples, but each element holds a
> namespace ID.
This is only necessary for your proposal (and mine). As seen above
having multiple namespaces nested might not be a problem. And we need to
have a default fall back value (when we're out of the new element/type).
>> Yes that would be a limit but seeking in a file format is a
>> very special feature not used a lot for most formats. It
>> makes sense in A/V formats where there is a timeline, but
>> then you need to know the semantic to know what you're
>> looking for when seeking.
>
> A good seeking feature could be quite useful in applications
> without a timeline : large images can be tiled and zooming to
> a precise position can be sped up by seeking info indexed by
> (x,y) coordinates. Databases using EBML would clearly benefit
> from seeking features. I think I could find many other
> examples...
Yes, I've been dreaming about a DB that would be EBML based or a file
system. And given custom attributes are present in modern file systems
it could be an option. Seeking in a file system would also be very
important.
Steve (thinks we're getting somewhere)
--
robUx4 on blog <http://robux4.blogspot.com/>
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2021-04-12 12:06:22
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http://www.physicsforums.com/showthread.php?t=304110
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Artificial Gravity Field Generator Possible?
by earamsey
Tags: artificial, field, generator, gravity
P: 34 I read about an equation; $$E = mc^2$$ and concluded that $$m=\frac{E}{c^2}$$. Therefore, I assume that one can create earth gravity by emitting energy equivalent to mass of earth. I also read that, simply put, that a stars gravity can be amplified when it's core collapses, or compresses creating intense gravity field. I put everything together and assume that you can create earth gravity by compressing a fractional amount of E equivalent to mass of earth. You can compress it using magnetic fields similar to what they use in experimental fusion generators. And one would already have such a thing because I would assume it would require lots of energy to compress E of size $$n \% M$$ to size some size $$m$$. Why would this not work, I assume it would not since NASA is not researching any thing like because they are proposing spinning people like a spinning top to get earth gravity.
P: 51 I really would know nothing about this, but my first guess would be E=mc^2 is saying that a certain amount of mass is equivalent to a certain about of energy proportionate to 1/c^2, and that they can be transferred back and forth between the two. Not that they act in the same way (energy can't act as mass, and vice versa, until they are transformed into the other one). But like I said, I don't really know anything about it. I would be curious to see what someone who really knows their stuff would say.
Emeritus Sci Advisor PF Gold P: 6,238 In general relativity, "mass" is not the (only) source of gravity. In fact, there is something called the stress-energy tensor (for some basic information about it, you can consult the wiki entry on it http://en.wikipedia.org/wiki/Stress-energy_tensor). That tensor contains energy (including the mass-equivalent) but also motion, pressure and things like that. All that generates "gravity".
P: 51
Artificial Gravity Field Generator Possible?
Ha, showed me :P. Cool.
That helps a theory of mine actually. haha
Mentor P: 15,398 I'm not quite sure what you mean by compressing energy, but the most "compressed" form of energy we have is mass. To get the mass of the earth requires a body about the size of the earth. The worldwide total energy production corresponds to about 100 pounds, which has virtually no perceptible gravitational force.
P: 534 .... are you talking relativistically here....? Or otherwise.
PF Gold
P: 8,961
Quote by Vanadium 50 To get the mass of the earth requires a body about the size of the earth.
That is incorrect. The mass is an intrinsic quality of matter independent of size. This might also be the basis of Earamsey's error regarding the amplification of a gravitational field. If a supermassive star spews its guts and becomes a black hole, its gravitational field is actually less than that of the original, since there is less mass remaining. The critical factor is that the gravitational attraction is based upon the distance between the centres of the involved masses, not the diameters. If our sun were to somehow be compressed into a neutron star or a black hole (not possible by natural methods), the orbits of the planets would not be altered.
Mentor
P: 15,398
Quote by Danger The mass is an intrinsic quality of matter independent of size.
True...but. Bodies that weigh as much as planets are the size of planets. (I'm ignoring exotic things like neutron stars and black holes, which are even less realistic) Sure, we could make something that weighs as much of the earth but out of tungsten instead - it's radius would be 2/3 the radius of the earth.
PF Gold P: 8,961 Ah... gotcha. Sorry for the intrusion.
Related Discussions General Physics 7 Astrophysics 9 Introductory Physics Homework 1 Introductory Physics Homework 4 Special & General Relativity 13
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2014-03-10 10:43:00
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https://xmphysics.com/2023/01/10/18-4-2-beta-decay/
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18.4.2 Beta Decay
A beta particle is basically a very energetic electron. A beta decay is represented by the equation
$\displaystyle {}_{Z}^{A}X\to {}_{{Z+1}}^{A}Y+{}_{{-1}}^{0}e$
If you compare the A and the Z numbers of the parent and daughter nuclei carefully, you will realize that the nucleus has lost one neutron, gained one proton and thrown out one electron. What the heck happened? Well, a neutron has decided to split itself into a proton and an electron. The electron is ejected at high speed (as the beta particle), while the proton stays behind in the nucleus.
Why Beta-Decay has an Energy Spectrum
Let’s use the beta-decay of bismuth-210 as an example. After one of its neutrons has changed into a proton, bismuth transmuted into polonium.
$\displaystyle {}_{{83}}^{{210}}Bi\to {}_{{84}}^{{210}}Po+{}_{{-1}}^{0}e$
The total mass of a polonium-210 and an electron is smaller than the mass of a bismuth-210. From the mass difference, the total energy released can be calculated to be a 1.16 MeV.
If Po-210 and the beta particle are the only two product nuclei, then they must have equal but opposite momentum (as dictated by PCOM). This translates to a fixed KE ratio between them which is equal to the inverse of their mass-ratio. Since Po-210 is almost 400,000 times as massive as the electron, we would expect the daughter nucleus to show negligible recoil and carry negligible KE. This means that all the beta particles should have KE of 1.16 MeV.
However, it was observed that the beta particles produced by bismuth-210 have a continuous energy spectrum (unlike alpha radiation, which are mono-energetic). Furthermore, the recoil of the polonium-210 nucleus is not always in opposite direction to the beta particle.
OMG, what happened to the principles of conservation of energy and momentum? Physicists were so stumped that Niels Bohr actually believed that the time had come for us to dump these most fundamental conservation laws.
In 1931, Wolfgang Pauli suggested humorously that there was probably an as yet unobserved particle emitted during a beta decay. He gave this particle a very cute sounding name, neutrino, which means the little neutral one. Having no charge and almost negligible mass, the neutrino is practically undetectable. However, having this “imagined” particle to carry some of the “missing” energy and momentum does provide an answer to the beta decay conundrum and a lifeline for PCOM and PCOE.
So the beta process was updated to include the emission of a neutrino.
Beta-minus decay: $\displaystyle {}_{Z}^{A}X\to {}_{{Z+1}}^{A}Y+{}_{{-1}}^{0}e+\bar{\upsilon }$
The symbol $\displaystyle \bar{\upsilon }$denotes an anti-neutrino. They had to do this because they have given the neutrino to the positive beta decay.
Beta-positive decay: $\displaystyle {}_{Z}^{A}X\to {}_{{Z-1}}^{A}Y+{}_{1}^{0}e+\upsilon$
The symbol $\displaystyle \upsilon$ denotes a neutrino, and $\displaystyle {}_{1}^{0}e$ is a positron.
The beta-decay in the H2 syllabus refers to the negative beta decay only. You are also not required to know anything about the neutrino, other than the context in which its existence was predicted. By the way, the elusive neutrino evaded experimental detection until 1956, a remarkable 26 years after its “discovery”.
Concept Test
3621
Comics
Beta Boy
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2023-01-30 11:16:26
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https://civilengineering.blog/2017/10/01/ordinary-portland-cement-and-its-composition/
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# Ordinary portland cement and its composition
## Ordinary portland cement and its composition
Cement, commonly used for normal construction work, is known as Ordinary Portland Cement. However, for use under specific conditions a variety of Ordinary portland cement and its composition are available these days.
Its quick setting property, strength and case with which it can be used under variety of conditions has revolutionized the concept of construction and made it the most popular cementing material. It was first of all introduced in 1824 by Joseph Aspdin, a brick layer of Leeds, England. On setting, the colour of cement resembles the colour of rocks near Portland in England and hence the name of this cement. Below are discussed the composition, manufacture and tests etc. of Ordinary Portland Cement.
### 2. COMPOSITION
Approximate composition of raw materials used for manufacturing Ordinary Portland Cement is :
Calcium Oxide (CaO) = 60 to 65%
Silica (S1O2) = 20 to 25%
Aluminium Oxide (Al2O3) = 4 to 8%
Ferrous Oxide (Fe2O3) = 2 to 4%
Magnesium Oxide (MgO) = 1 to 3%
All the above compounds undergo some chemical combinations during the process of burning and fusion. Main constituents of cement are Tri-Calcium Silicate (3 CaO.SiO2). Di-Calcium Silicate (2 CaO.SiO2) and Tri-Calcium Aluminate (3 CaO.Al2O3). Tri-Calcium Silicate is the best cementing material and the more it is present in cement the better the cement is. In a properly burnt clinker Tri-Calcium Silicate should be about 40%. In case the burning is not done properly then the clinker shall have less of Tri-calcium Silicate and more of free lime. After the addition of water to cement it sets and hardens due to the hydration and hydrolysis of the above three compounds which act as a glue. The aluminate is the first to set and harden. Tri-Silicate is slower and the Di-Silicate is the slowest. As such the initial setting of cement is due to the action of aluminate. Further early gain in strength is due to Tri-Silicate. Di-Silicate takes 14 to 28 days to add to the strength. All the three compounds in their action with water give out heat. Maximum heat giving compounds is the aluminate which is responsible for most of the undesirable properties of concrete. A cement having lesser aluminate shall have lesser initial strength but higher ultimate strength. Also there shall be lesser generation of heat, more volumetric stability, lesser cracking and more resistance to acid attacks. Incomplete burning of clinker leaves free lime in it. This free lime causes expansion and disruption of concrete after use. The silicates form a gel with water. The gel later on crystallises and firmly binds the particles.
#### According to IS 269-1975 composition of ordinary Portland cement
According to IS 269-1975 composition of ordinary Portland cement shall satisfy the following conditions:
(1) Ratio of the percentage of lime to that of silica, alumina and iron oxide when calculated by the formula,
$\frac{CaO-0.75O_{3}}{2.8SiO_{2}+1.2Al_{2}O_{3}+0.65Fe_{2}O_{3}}$
shall not be less than 0.66 and not more than 1.02.
(2) Ratio of percentage of alumina to that of iron oxide shall not be less than 0.66.
(3) Weight of insoluble residue shall not be less than two per cent.
(4) Weight of magnesia shall not be more than six per cent.
(5) Total sulphur content calculated as sulphuric anhydride (SO2) shall not be more than 2.75 per cent.
(6) Total loss on ignition shall not be more than four per cent.
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2018-06-24 06:51:26
|
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https://www.tug.org/pipermail/tex4ht/2015q3/001230.html
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# [tex4ht] graphics Images no longer resize in TL 2015 with tex4ht, need help finding why
Nasser M. Abbasi nma at 12000.org
Wed Jul 22 10:21:44 CEST 2015
Spend 6 hrs on this and I gave up. For some reason, the images
no longer resize in the web pages as before. This
used to work.
I made earlier a small document that describes this
resizing method here (layout)
http://12000.org/my_notes/faq/LATEX/layout/index.htm
But when I tried this method now, I found that the images
do not resize anymore ! Something changed and I can't find
what. I used to use 32 bit TL 2014 before. Now I am on
64 bit Linux and TL 2015.
I show the steps I did below, which is the same as in the layout
document, and I also put everything in one zip file at :
http://12000.org/tmp/072215/image_do_not_resize.zip
Here is MWE:
-------------------------------------
\documentclass[11pt,notitlepage]{article}%
\usepackage{graphicx}
\begin{document}
\includegraphics[width=0.1\paperwidth]{1_pic}
\includegraphics[width=0.2\paperwidth]{1_pic}
\includegraphics[width=0.3\paperwidth]{1_pic}
\includegraphics[width=0.4\paperwidth]{1_pic}
\end{document}
--------------------------------------
The folder contains 1_pic.pdf and 1_pic.svg. The SVG image
was obtained _from_ the pdf file using
pdfcrop --margins 10 --clip 1_pic.pdf 1_pic.pdf
pdf2svg 1_pic.pdf 1_pic.svg
The command used to compile is:
make4ht -u -c nma.cfg foo.tex "htm,pic-align,notoc*"
I also tried
htlatex foo.tex "nma,htm,pic-align,notoc*"
the nma.cfg is :
-----------------
\Preamble{ext=htm,charset="utf-8",p-width,pic-align}
\Configure{VERSION}{}
\Configure{DOCTYPE}{\HCode{<!DOCTYPE html>\Hnewline}}
\Configure{HTML}{\HCode{<html>\Hnewline}}{\HCode{\Hnewline</html>}}
\begin{document}
\DeclareGraphicsExtensions{.svg,.png}
\Configure{Picture}{.svg}
\makeatletter
% Various helper functions
% default font size
\newcommand\emwidth{16}
\let\emwidth\f at size
% convert pt to rem
\newcommand\CalcRem[1]{\strip at pt\dimexpr(#1)/\emwidth}
\Configure{graphics*}
{svg}
{\Picture[pict]{\csname Gin at base\endcsname.svg
\space style="width:\CalcRem{\Gin at req@width}em;"
}%
\special{t4ht+ at File: \csname Gin at base\endcsname.svg}%
}
\makeatother
\EndPreamble
------------------------------
All of the above, is exactly what is described in my layout document.
But the images come out all the same size. Which is not what is supposed
to happen. I do not want to use natural sizes. I use [width=0.7\paperwidth]{image}
and such for all the images.
Could someone please try this and see if they get different image sizes?
Simply unzip the folder, and just type the compile command and see if
you get different size images.
I am using TL 2015, 64 bit, on Linux mint 7.2, 64 bits.
thank you,
--Nasser
|
2022-08-11 03:08:05
|
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https://dwwiki.mooo.com/w/index.php?title=Silver_rat_ring&oldid=61991&printable=yes
|
# Silver rat ring
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
## What is it?
It is a magical piece of jewellery, an artifact. It's description reads:
This is a thick silver band, embossed with a circle of three rats biting on each other's tails. Each rat has two tiny red rubies for eyes.
<number> of its eyes glow a dull red.
It emits a slight octarine glow.
It is in excellent condition.
## What does it do?
You can wear the ring, and if you twist it and have sufficient skills (ma.it.wo.ring?), you will summon a rat that will protect you. This rat is a lot tougher than normal rats, though.
The number of charges seem to be equal to the number of glowing eyes on the ring.
## How do I get one?
In the Rat Farm you will sometimes encounter a rat king. Once the rat king is defeated, the rats that scatter leave behind a ring. The ring always has the same amount of glowing eyes as the number of tails that the rat king had. This seems to always be between 4-6.
|
2022-01-29 02:34:30
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|
https://socratic.org/questions/what-is-the-temperature-of-sirius
|
# What is the temperature of Sirius?
Sirius A have a surface temperature of ${9940}^{0} K$.
Sirius B have a surface temperature of ${25200}^{0} K$.
|
2018-10-23 11:51:51
|
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|
http://tiku.21cnjy.com/?mod=quest&channel=4&xd=3&catid=11358
|
## 牛津译林版 试题
• 文中共有10处语言错误，每句中最多有两处。错误涉及一个单词的增加、删除或修改。增加：在缺词处下加一个漏子符号（/\），并在其下面写出该加的词。删除：把多余的词用斜线（\）划掉。修改：在错的词下划一横线，并在该词下面写出修改后的词。
注意：1. 每处错误仅限1词；2. 只允许修改10处，多者（从第11处起）不计分。
Mobile phones are being more wide used. They’re light in weight and easy to carry, offer fast and convenient service for communication. The users use them for making phone call, sending short messages and Internet-surfing. In recently years, mobile phones have become popular to middle school students. Quite few use them to keep in touch with their families and friends, what, of course, was of great convenience. However, I don’t think it’s good to do so. In spite of the advantages mentioned above, student users often waste a lot of time chat on the phone in their spare time. Some even cheat in exams. In addition to, mobile phone bills cost their parents lots of money.
• 书面表达（满分20分）
目前，许多学校对学生采取封闭式管理，学生对此看法不一。请根据下表所提供的信息，写一篇短文，谈谈自己的看法。
有的同学认为: V" H/ d- h- a' O7 W. j* G 有的同学认为+ I. C+ : R# C9 ?( Q% J2 Y) h 学校限制学生的自由学生和社会接触少学生的兴趣和爱好不能得到充分的发展，因此……* Q8 g1 D/ i2 E: U 学校是学习知识的地方学生应该安心在学校学习学生缺乏自觉性，离开了老师，可能会…．．2 _% j) \& R% O0 K! a* O2 Y: @0 H 你的看法: ……．．, T# S9 ?' W3 a! D5 K
注意：1 词数100---120左右；
2 短文开头已给出，不计入总词数。
Nowadays a lot of schools keep their students in school all day long．___________________
• ______ frightened us ______ a tiger turned up suddenly in front of us. A． What; was that B．What; was C．It; that was D．It was; that
• To improve their oral English, everyone in the class is supposed to ______ actively in these discussions. A．participate# E4 c! F( X- 2 E( ^" N B．attend+ c& Z3 e" f! S0 L C．enter6 c" P6 @0 a [5 Z+ M( h D．take' j5 M* h! A! L" M$I# \7 e • Some say everyday miracles (奇迹) are predestined (注定的)----the right time for the appointed meeting. And it can happen anywhere. In 2001, 11-year-old Kevin Stephan was a bat boy for his younger brother’s Little League team in Lancaster, New York. It was an early evening in late July. Kevin was standing on the grass away from the plate, where another youngster was warming up for the next game. Swinging his bat back and forth, giving it all the power an elementary school kid could give. The boy brought the bat back hard and hit Kevin in the chest. His heart stopped. When Kevin fell to the ground, the mother of one of the players rushed out of the stands to his aid. Penny Brown hadn’t planned to be there that day, but at the last minute, her shift (换班) at the hospital had been changed to see her son’s performance. She was given the night off. Penny bent over the senseless boy, his face already starting to turn blue, and giving CPR, breathing into his mouth and giving chest compressions. And he revived in the end. After his recovery, he became a volunteer junior firefighter, learning some of the emergency first-aid techniques that had saved his life. He studied hard in school and was saving money for college by working as a dishwasher in a local restaurant in his spare time. Kevin, now 18, was working in the kitchen when he heard people screaming, customers in confusion, employees rushing toward a table. He hurried into the main room and saw a woman there, her face turning blue, her hands at her throat. She was choking. Quickly Kevin stepped behind her, wrapped his arms around her and clasped his hands. Then, using skills he’d first learned in Scouts. The food that was trapped in the woman’s throat was freed. The color began to return to her face. "The food was stuck. I couldn’t breathe," she said. She thought she was dying. "I was very frightened." Who was the woman? Penny Brown. 【小题1】The author wrote the passage to show us that __________. A．miracles are predestined and they can happen anywhere# g j3 ]6 R' % e/ F B．whoever helps you in trouble will get a reward one day# ^, i& c1 F- I$ a C．God will help those who give others a helping hand. G2 R" Q4 i7 X% ?- _4 g D．miracles won’t come without any difficulty sometimes8 S* ^) Y7 d: L& K6 g
【小题2】Which of the following statements is True of Kevin Stephan? A．He was hit on the face by a boy and almost lost his life9 M' J- g' h8 d. B B．He was a volunteer junior firefighter, teaching the players first-aid skills 9 h( O9 W' d2 j8 S( W+ G: X( P C．He worked part-time in a local restaurant to save money for college ! j3 U! @) X9 b; P. @ D．He saved Penny Brown though he didn’t really know how to deal with food choke& K- U& M9 ^, [' h7 Y
【小题3】The underlined word “revived” (paragraph3) most likely means __________. A．came back to life4 [# I* X# _- O! O0 f5 c+ E0 K B．became worse( L8 @& A. E5 K2 S9 H3 F C．failed2 D1 f h" H: G& ^# f8 F D．moved6 _* e0 Z7 X! G- [. T
【小题4】Why did Penny Brown change her shift and was given the night off that night? A．She was invited to give the players directions/ M5 V: _; I- O+ E B．She volunteered to give medical services8 E+ c a! G9 T6 V! N C．She was a little worried about his son’s safety & I" a- [( S Q2 c8 \ D．She came to watch her son’s game and cheered him" @; H5 E; d! ]; e
• 此题要求改正所给短文的错误。对标有题号的每一行作出判断：如无错误，在该行右边横线上画一个勾（√）；如有错误（每行只有一个错误），则按下列情况改正：
此行多一个词：把多余的词用斜线（＼）划掉，在该行右边横线上写出该词，并也用斜线划掉。
此行缺一个词：在缺词处加一个漏字符号（∧），在该行右边横线上写出该加的词。
此行错一个词：在错的词下画一横线，在该行右边横线上写出改正后的词。
注意：原行没有错的不要改。
Dear Bill,
Thank you very much for your letter. I pleased to hear【小题1】 ________
about your holiday and the people you meet in Rome. It 【小题2】________
sounded great fun and how I wish I had been with 【小题3】________
you. Thank you also for the stamps you sent them to me 【小题4】 ________
for my collection. Most of their were those I had 【小题5】 ________
been expecting for long. You said by your letter that 【小题6】 ________
you wish to have some photos of me. Sorry to tell you, 【小题7】________
I have little photos good enough to send to others. Yet I 【小题8】_______
will send you a photo of your family. Please write soon 【小题9】 ________
and tell me what you are getting on with your college life. 【小题10】________
Best wishes!
Yours,
Jason
• 书面表达 (满分25分)
当前不少文学作品被改编成电影。有人选择看电影，有人则喜欢读原著。请你以“Film or book, which do you prefer?”为题，按照下列要点写一篇短文
要点：1、 看电影：省时、有趣、易懂
2、 读原著：细节更多、语言优美
3、 自己的看法及理由
注意：1、词数：100词左右，文章题目和开头已给出（不计入词数）。
2、参考词汇： original work 或 book in the original （原著）
Film or book, which do you prefer?
Some of us think that it is better to see the film than to read the book in the original.
• 书面表达（满分30分）
高中阶段学习比较紧张，正确的学习方法尤为重要。下表显示了两位同学不同的学习方法，请简述并发表你的观点。 字数在100---120之间。文章开头已经给出。
学习方法3 j% H3 ^/ h2 @; I+ D" Q 李 华, a* # U! F' C+ d( L 王 海1 ^0 b. H( S' \* D V+ @ 你的观点. f$^" B. M, I0 F$ M 白天6 [1 Z7 T: D( ?0 J; e- ?0 I 上课专心听讲，尽可能经常向老师请教疑难问题。9 Y/ g+ O5 M$?0 e# F 上课打瞌睡，漏掉了许多要点。8 P6 D3 X. L+ T8 P. ?6 c$ ]5 G ) c1 C\$ X6 f) b8 d; D1 U 晚上4 D! h( [ V& Q% \, a: h 花较少时间完成作业，早点休息，上课经常保持旺盛的精力. Y, H2 b/ P0 A0 ^1 K3 R0 c2 K 花较多的时间完成作业，熬夜学习，导致注意力无法集中。( X; Y8 j% J4 L 9 O1 S& V3 S* G" _
文章开头：
Li Hua and Wang Hai are two students of Senior high school．Both of them work hard but they have different learning methods．
• 短文改错（共10小题，每小题1分，满分10分）
假如英语课上老师要求同学们交换修改作文，请你修改你同桌写的一下作文。文中共有10处语言错误，要求你在错误的地方增加、删除或修改某个单词。
增加：在缺词处加一个漏字符号（/\），并在其下面写上该加的词。
删除：把多余的词用斜线(\)划掉。 修改：在错的词下划一横线，并在该辞词下面写上修改后的词。
注意：1．每处错误及其修改均限一词； 2．只允许修改10处，多者（从第11处起）不计分。
Welcome to the Polynesian Cultural Centre! You are entering a world of funs! My name is called Tera, a Polynesian name which mean “the sun”. I’m very glad you can come today and learn about some of the amazing Polynesian way. As you can see, here behind myself is one of their boats. To build a boat like this, you needed a very tall, straight tree. You first cut down the tree and remove the branch. Then you cut the tree in half so you have two long pieces of woods. You use one piece to make the boat. Remove the inside for a person to sit. Take the bark off the outside of the boat and puts oil on it so it will easily go through the sea.
• 书面表达（共1小题；满分20分）
假定你是李华，第一天到英国就遇到了可怕的大雾，找不到去学校的路。你站在雾中吓呆了。幸亏一个叫John的英国人帮助了你。他拉着你的手给你带路并且鼓励你，消除了你的恐惧。现在你已安定下来，请写一封信表达你对他的感激之情。
注意：1. 信的开头已经写好，但不计入总词数；2.语句通顺，要点齐全；3.词数：150左右。
Dear John,
I’d like to thank you for your kind help in the terrible fog on my first day in London.
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
Sincerely yours,
Li Hua
|
2018-07-16 18:03:32
|
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|
https://too-meta.neocities.org/anki/analysis/1575499995541/
|
Math and science::Analysis::Tao::08. Infinite sets
# Count all the things (countability propositions)
A number of propositions related to countable sets:
• All subsets of the natural numbers are at most countable.
• Let $$Y$$ be a set, and let $$f: \mathbb{N} \rightarrow Y$$ be a function. Then the image $$f(\mathbb{N})$$ is [...].
• Let $$X$$ be a countable set, and let $$f : X \rightarrow Y$$ be a function. Then $$f(X)$$ is [...].
• Let $$X$$ and $$Y$$ be countable sets. Then $$X \cup Y$$ is [...].
• The integers $$\mathbb{Z}$$ are [...].
• The set $$A := \{(n, m)\ \in \mathbb{N} \times \mathbb{N} : 0 \le m \le n\}$$ is [...].
• The set $$\mathbb{N} \times \mathbb{N}$$ is [...].
• The rationals $$Q$$ are [...].
• The set of all functions from $${0, 1}$$ to $$\mathbb{N}$$ is [...].
• The set of all functions from $$\mathbb{N}$$ to $${0, 1}$$ is [...].
Maybe some of these should be split up and their proofs outlined.
|
2023-02-06 02:57:51
|
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|
https://email.esm.psu.edu/pipermail/macosx-tex/2016-June/054834.html
|
[OS X TeX] Chapter proof outputs
Alan Litchfield alan at alphabyte.co.nz
Fri Jun 17 20:48:32 EDT 2016
Hmm, interesting. I'll give that a go.
Thanks. I'll let you know.
Alan
On 18/06/16 9:36 am, Giovanni Dore wrote:
> Please try the following modifications.
>
> Add the following lines to the file autthesis.cls:
>
> \newcommand{\ChapterProof}[1]{
> \renewcommand{\beforeabstract}{\relax}
> \renewcommand{\afterabstract}{\relax}
> \renewcommand{\afterpreface}{\relax}
> \def\myChapter##1{\title{Draft chapter \\ ##1}
> \date{\today}
> \maketitle
> \chapter{##1}}
> \includeonly{#1}
> }
>
> In the file AUTThesis.tex change every command \input{includes/name} in \include{includes/name}.
>
> If you want a chapter proof for the chapter contained in the file intro.tex add the line
>
> \ChapterProof{includes/intro}
>
> to the file AUTThesis.tex, somewhere between \documenteclass and \begin{document}.
>
> I hope this solves your problem.
>
> Giovanni Dore
> ________________________________________
> Da: MacOSX-TeX <macosx-tex-bounces at email.esm.psu.edu> per conto di Alan Litchfield <alan at alphabyte.co.nz>
> Inviato: venerdì 17 giugno 2016 21:12
> A: macosx-tex at email.esm.psu.edu
> Oggetto: Re: [OS X TeX] Chapter proof outputs
>
> Hi,
>
> I use include now for all the chapters.
>
> The objective of the chapter proof is that it does not provide all the
> front matter, ToC's, etc. Just a one page coversheet with the
> appropriate details on it.
>
> The structure is all provided in a class file, so a function that
> provides one structure (full thesis) or the other (chapter proof) might
> work. However a simplistic A or B option loses all the aux data (cross
> refs, counters, etc.) that would make a chapter proof more useful.
>
> I have looked at splitting the pdf, but frankly, I would get various
> results if students were left to do this.
>
> Alan
>
>
>
> On 18/06/16 4:51 am, Giovanni Dore wrote:
>> You can use \include and \includeonly.
>> See https://en.wikibooks.org/wiki/TeX/includeonly or http://www.tex.ac.uk/FAQ-conditional.html.
>>
>> Giovanni Dore
>>
>>
>> Il giorno 16/giu/2016, alle ore 23.19, Alan Litchfield ha scritto:
>>
>>> Hi,
>>>
>>> I know this is a question that comes up from time to time, but I have yet to find a satisfactory answer. I just hoping for some suggestions for improvement.
>>>
>>> Several (many) years ago I developed a thesis template while doing my master thesis based on the report class. I further adapted it for my PhD and some folk saw what I'd done and asked to use it. Since then, it has become the defacto template for the university where I work. That means I have had to spend a lot of time cleaning it up, simplifying parts and writing documentation on how to use it. Now I am at a stage where I need to resolve an annoyance, which is *how to generate chapter proofs* for supervisors to check.
>>>
>>> Presently, I have two template headers: one for the whole thesis that generates all the front matter, chapters (as includes), ToCs, etc.; the other is for chapter proofs that produces a front page with the student name, chapter title, etc and then the chapter as an include (the person changes the chapter file to be included for each proof).
>>>
>>> The downside of the present situation is that chapter numbers have to be replaced with a preset counter ("X" in this case) and cross references to other chapters are broken.
>>>
>>> What I would like is to present the option of a chapter proof as an option declared such as this for a full thesis:
>>> \documentclass[12pt,AK1324,thesis,doublespace]{autthesis}
>>>
>>> and this for a chapter proof:
>>> \documentclass[12pt,AK1324,thesis,doublespace,proof="includes/LitReview"]{autthesis}
>>>
>>> In other words, that unless "proof=[some file name]" is declared as an option, the whole thesis is generated. It would be really nice if the thesis aux file were used to maintain the integrity of counters and labels.
>>>
>>> As I said, suggestions are very welcome. The template lives at:
>>> http://aut.ac.nz.libguides.com/computer/LaTeX
>>>
>>> Alan
>>> --
>>> Dr Alan Litchfield
>>> AlphaByte
>>> PO Box 1941
>>> Auckland, New Zealand 1140
>>>
>>> ----------- Please Consult the Following Before Posting -----------
>>> TeX FAQ: http://www.tex.ac.uk/faq
>>> List Reminders and Etiquette: https://www.esm.psu.edu/~gray/tex/
>>> List Archives: http://dir.gmane.org/gmane.comp.tex.macosx
>>> https://email.esm.psu.edu/pipermail/macosx-tex/
>>> TeX on Mac OS X Website: http://mactex-wiki.tug.org/
>>> List Info: https://email.esm.psu.edu/mailman/listinfo/macosx-tex
>>
>>
>> 5x1000 AI GIOVANI RICERCATORI
>> DELL'UNIVERSITÀ DI BOLOGNA
>> Codice Fiscale: 80007010376
>> ----------- Please Consult the Following Before Posting -----------
>> TeX FAQ: http://www.tex.ac.uk/faq
>> List Reminders and Etiquette: https://www.esm.psu.edu/~gray/tex/
>> List Archives: http://dir.gmane.org/gmane.comp.tex.macosx
>> https://email.esm.psu.edu/pipermail/macosx-tex/
>> TeX on Mac OS X Website: http://mactex-wiki.tug.org/
>> List Info: https://email.esm.psu.edu/mailman/listinfo/macosx-tex
>>
>
> --
> Dr Alan Litchfield
> AlphaByte
> PO Box 1941
> Auckland, New Zealand 1140
>
> ----------- Please Consult the Following Before Posting -----------
> TeX FAQ: http://www.tex.ac.uk/faq
> List Reminders and Etiquette: https://www.esm.psu.edu/~gray/tex/
> List Archives: http://dir.gmane.org/gmane.comp.tex.macosx
> https://email.esm.psu.edu/pipermail/macosx-tex/
> TeX on Mac OS X Website: http://mactex-wiki.tug.org/
> List Info: https://email.esm.psu.edu/mailman/listinfo/macosx-tex
>
> 5x1000 AI GIOVANI RICERCATORI
> DELL'UNIVERSITÀ DI BOLOGNA
> Codice Fiscale: 80007010376
>
> ----------- Please Consult the Following Before Posting -----------
> TeX FAQ: http://www.tex.ac.uk/faq
> List Reminders and Etiquette: https://www.esm.psu.edu/~gray/tex/
> List Archives: http://dir.gmane.org/gmane.comp.tex.macosx
> https://email.esm.psu.edu/pipermail/macosx-tex/
> TeX on Mac OS X Website: http://mactex-wiki.tug.org/
> List Info: https://email.esm.psu.edu/mailman/listinfo/macosx-tex
>
--
Dr Alan Litchfield
AlphaByte
PO Box 1941
Auckland, New Zealand 1140
|
2017-11-23 22:05:50
|
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|
https://byjus.com/step-function-calculator/
|
# Step Function Calculator
nullnull
The Step Function an online tool which shows Step Function for the given input. Byju's Step Function is a tool
which makes calculations very simple and interesting. If an input is given then it can easily show the result for the given number. Step function equation | Step function differential equations
#### Practise This Question
A calorimeter contains 0.2kg of water at 30C. 0.1 kg of water at 60C is added to it, the mixture is well stirred
and the resulting temperature is found to be 35C. The thermal capacity of the calorimeter is
|
2019-06-25 11:30:17
|
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|
https://indico.desy.de/indico/event/8648/contributions
|
# PANIC 2014 - Particles and Nuclei International Conference 2014
24-29 August 2014
Hamburg University
Europe/Berlin timezone
Home > Contribution List
## Contribution List
Displaying 282 contributions out of 282
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Suppression of $J/\psi$ production in heavy-ion collisions due to color screening of quark and antiquark potential in the deconfined medium has been proposed as a signature of quark-gluon plasma (QGP) formation. However, there are other effects that may alter the observed $J/\psi$ yields, such as cold nuclear matter effects, and statistical coalescence of c-$\bar{\mathrm{c}}$ pairs. Indeed, recent ... More
Presented by Dr. Petr CHALOUPKA on 25 Aug 2014 at 4:30 PM
Type: Poster Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
We study the effects of the decuplet-octet mass difference for the baryon axial vector current at one-loop order in large-Nc baryon chiral perturbation theory, where Nc is the number of color. The baryon axial vector current is considered within the combined framework of large-Nc baryon chiral perturbation theory and the baryon axial vector couplings are extracted. We extend the g_A analysis by in ... More
Presented by Dr. MARIA DE LOS ANGELES HERNANDEZ-RUIZ
Type: Talk Session: Beyond Standard Model
Track: 7) Energy frontier physics beyond the standard model
In this talk, the latest results from CMS on searches for stop and sbottom squarks are presented. Searches for direct squark production and indirect production through gluino cascades in a variety of decay channels are reviewed. The results are based on 20 fb-1 of data collected during the 8 TeV LHC run.
Presented by Mr. Florent Sylvain LACROIX on 25 Aug 2014 at 2:20 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Pb nuclei, accelerated at LHC, are sources of strong electromagnetic fields that can be used to measure photon-induced interactions in a new kinematic regime. These interactions can be studied in ultra-peripheral p-Pb and Pb-Pb collisions where impact parameters are larger than the sum of nuclear radii and hadronic interactions are strongly suppressed. Heavy quarkonium photoproduction is of pa ... More
Presented by E. KRYSHEN on 28 Aug 2014 at 3:00 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
After the successful LHC operation at the center-of-mass energies of 7 and 8 TeV in 2010 - 2012, plans are actively advancing for a series of upgrades of the accelerator, culminating roughly ten years from now in the high luminosity LHC (HL-LHC) project, delivering of the order of five times the LHC nominal instantaneous luminosity along with luminosity leveling. The final goal is to extend the da ... More
Presented by Dr. Ingrid-Maria GREGOR on 25 Aug 2014 at 4:55 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
The production of jets in association with a W or a Z boson is an important process to study QCD in a multi≠scale environment in p≠p collisions at the LHC. The cross sections, differential in several kinematics variables, and their ratios (W+jets)/(Z+jets), have been measured up to high jet multiplicities and high jet transverse momenta, and compared to state≠of≠the≠art QCD cal ... More
Presented by Mr. Mark James TIBBETTS on 28 Aug 2014 at 2:20 PM
Type: Talk Session: String theory
I will describe a chiral infinite tension limit of the RNS superstring, known as ambitwistor string theory, which provides a powerful point of view on tree-level Yang-Mills and gravity amplitudes in arbitrary dimensions. In four dimensions, ambitwistor string theory gives rise to new formulae for tree-level Yang-Mills and gravity amplitudes with arbitrary amounts of supersymmetry, which are suppor ... More
Presented by Dr. Arthur LIPSTEIN on 28 Aug 2014 at 4:30 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Anisotropies of the azimuthal hadron distributions measured in nuclear collisions at highest energies carry information about the anisotropies of collective transverse expansion. Through a comparison of these data with hydrodynamic simulations one hopes to extract transport coefficients of the hot nuclear matter. It is widely accepted that the flow anisotropies have their root in strong inhomogene ... More
Presented by Dr. Boris TOMASIK on 28 Aug 2014 at 3:30 PM
Session: Plenary
on 26 Aug 2014 at 10:30 AM
We present evidence of associated vector boson+prompt J/psi production and measure its production rate. This is a key observable to further the understanding of quarkonium production mechanisms. We estimate the relative contributions to the signal from single and double parton scattering (DPS) and discuss possible implications of this novel final state for study of multiple parton intera ... More
Presented by Mr. Soeren PRELL on 28 Aug 2014 at 5:10 PM
Type: Talk Session: Beyond Standard Model
Track: 7) Energy frontier physics beyond the standard model
The discovery of a Higgs boson with a mass of about 125 GeV has prompted the question of whether or not this particle is part of a larger and more complex Higgs sector than that envisioned in the Standard Model. In this talk, the current results from the ATLAS experiment on Beyond-the-Standard Model (BSM) Higgs searches are outlined. Searches for additional Higgs bosons are presented and i ... More
Presented by Mr. Gunar ERNIS on 26 Aug 2014 at 2:20 PM
Type: Poster
We study the Higgs boson production in the minimal B-L model at future linear colliders ILC and CLIC, with the reaction e+e- ->(Z, Z’)->ffh, W+W-h including both the resonant and non-resonant effects. We evaluate the total cross section of ffh, W+W-h and calculate the total number of events considering the complete set of Feynman diagrams at the tree level.
Presented by Dr. Alejandro GUTIERREZ-RODRIGUEZ, Dr. Maria de los Angeles HERNANDEZ-RUIZ
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
CANDLES is the project to search for neutrino-less double beta decay (0$\nu\beta\beta$) of $^{48}$Ca. 0$\nu\beta\beta$ is acquiring great interest after the confirmation of neutrino oscillation which demonstrated nonzero neutrino mass. Measurement of 0$\nu\beta\beta$ provides a test for the Majorana nature of neutrinos and gives an absolute scale of the effective neutrino mass. In ord ... More
Presented by Dr. Saori UMEHARA on 25 Aug 2014 at 2:40 PM
The Drell-Yan (DY) process is considered to be a powerful tool to study hadron structure. A new generation of polarized DY measurements using unpolarized pion beam and polarized target is under the preparation at COMPASS experiment at CERN. One of the key experimental tasks here is the modification of the unique COMPASS low temperature polarized target for Drell-Yan experiment which is the prerequ ... More
Presented by Mr. Jan MATOUSEK on 25 Aug 2014 at 3:20 PM
We present recent COMPASS results on the longitudinal spin structure of the nucleon. Results from measurements of the gluon helicity Delta G (x) from various channels are shown. We recently analysed longitudinal double spin asymmetry A_LL(pT) for single hadron production with high-pT hadrons in the low Q2 regime using all COMPASS data. LiD and NH3 were used as polarized deuteron and proton targ ... More
Presented by Mr. Hiroki MATSUDA on 25 Aug 2014 at 5:50 PM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
The LHCb experiment has a great potential for precise measurements of the CP violating phase in the standard model, and for searches of new phases. We report on recent measurements of the CP violating angle angle γ which is the least constrained parameter in the CKM unitarity triangle, the phase in B mixing, and direct CP violation in B decays.
Presented by Ms. Shu-Faye CHEUNG on 26 Aug 2014 at 3:15 PM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
We study the meson-baryon interaction in S-wave in the strangeness S=-1 sector using a chiral SU(3) Lagrangian extended to next-to-leading order (NLO). Our model has 7 new parameters, which have to do with NLO terms in the chiral Lagrangian, and which are fitted to the large set of experimental data available for different two-body channels. We pay particular attention to the K- p --> K Cascade re ... More
Presented by Prof. Volodymyr MAGAS on 25 Aug 2014 at 4:55 PM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
New final results from an analysis of about 400 K+- --> pi+- gamma gamma rare decay candidates collected by the NA48/2 and NA62 experiments at CERN during low intensity runs with minimum bias trigger configurations are presented. The results include a model-independent decay rate measurement and fits to Chiral Perturbation Theory (ChPT) description. The data support the ChPT prediction for a cusp ... More
Presented by Mr. Flavio COSTANTINI on 25 Aug 2014 at 4:55 PM
Type: Poster Track: 9) Tests of symmetries and conservation laws
In addition to a chiral N 3LO two-nucleon potential V2N , we include an in-medium three-nucleon (NNN) force V3N as the input elementary interaction in the ring diagram calculation for the binding energy of 4He. The low momentum Vlowk effective interaction matrix elements of V2N and V3N are calculated for the uses in this study. Parameters cD and cE in V3N are taken from the cD − cE curve in ... More
Presented by Prof. YIHARN TZENG
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
A review of the combination of the coupling and spin CP properties measurements of the recently discovered Higgs boson using the ATLAS detector and up to 25 fb-1 of 7 TeV and 8 TeV pp collision data collected in 2011 and 2012 will be presented.
Presented by Mr. Peter KLUIT on 25 Aug 2014 at 4:50 PM
Type: Poster Track: 9) Tests of symmetries and conservation laws
The foundations of the modern quantum theory of electro-magnetic radiation and its interaction with medium are constituted by the Einstein's theory of photo-effect and the theory of the Compton effect. However, in the theory proposed by Compton and subsequent refinements, the medium features in explicit form are not generally accounted at all. This theory is based on the relationship between the p ... More
Presented by Prof. Sergey CHEFRANOV
Session: Plenary
on 29 Aug 2014 at 11:20 AM
Session: Plenary
Presented by Mr. Peter SCHLEPER, Mr. Matthias KASEMANN on 25 Aug 2014 at 9:00 AM
Type: Poster Track: 6) Standard model physics at the TeV scale
We study the connection between the inclusive spectra of hadrons produced in $pp$ collision at LHC energies at low transverse momenta and the unintegrated gluon distribution (u.g.d.) at small $x$ at the starting scale $Q_0^2$. This gluon distribution [1] is obtained from the best description of the LHC data in the soft kinematical region and it does not contradict to the asymptotic behavi ... More
Presented by Prof. Gennady LYKASOV, Dr. Nikolay ZOTOV
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
With the advent of low-threshold detectors that look for neutrino scattering at sub-keV energy deposition, the sensitivity to possible neutrino electromagnetic moments can be further increased. As such low energies start to overlap with atomic scales, it is necessary to take atomic binding effects into account so that detector responses can be understood more reliably. In this talk, we present our ... More
Presented by Mr. Cheng-Pang LIU on 28 Aug 2014 at 5:10 PM
A complete picture of collinear nucleon spin structure, at leading twist, requires knowledge of three types of parton distribution functions (PDFs): the unpolarized PDFs; the helicity PDFs; and the transversity PDF, the net transverse polarization of quarks within a transversely polarized nucleon. Of the three, transversity is the most difficult to probe due to its chiral-odd nature. Current knowl ... More
Presented by Dr. James DRACHENBERG on 25 Aug 2014 at 2:20 PM
Type: Talk Session: Beyond Standard Model
Track: 7) Energy frontier physics beyond the standard model
The discovery of the Higgs boson opens many perspectives to explore physics beyond the Standard Model. This talk describes constraints of new physics in a number of models using the combined measurements of the coupling strength of the 125 GeV Higgs particle using the entire ATLAS run-I data. The various models presented include an additional real electroweak singlet, two Higgs doublet m ... More
Presented by Ms. Camilla MAIANI on 26 Aug 2014 at 3:20 PM
Type: Talk Session: Dark matter and cosmology
Track: 4) Dark matter and cosmology
CRESST is a cryogenic direct Dark Matter search experiment based on phonon-light technique. It is aiming for the detection of weakly interacting massive particles (WIMPs) via their elastic scattering off nuclei in CaWO4 target crystals. Significant improvements have been achieved with respect to previous measuring campaigns in terms of the intrinsic radiopurity of CaWO4 crystals and the rejection ... More
Presented by Mr. Holger KLUCK on 25 Aug 2014 at 4:30 PM
Type: Talk Session: Dark matter and cosmology
Track: 4) Dark matter and cosmology
DarkSide-50 (DS-50) at Gran Sasso underground laboratory, Italy, is a direct dark matter search experiment based on a TPC with liquid argon from underground sources. The DS-50 TPC, with 50 kg of active argon and a projected fiducial mass of >33 kg, is installed inside an active neutron veto based on a boron-loaded organic scintillator. The neutron veto is built inside a water cherenkov m ... More
Presented by Mr. Davide D'ANGELO on 25 Aug 2014 at 3:15 PM
A longstanding goal in nuclear and particle physics has been to describe the three dimensional structure of the nucleon in terms of the quarks and gluon fields. In this regard, exclusive electron scattering experiments, in which all final state particles are measured, are important contributors. Examples are electron elastic scattering, deeply virtual Compton scattering (DVCS), and deeply virtual ... More
Presented by Prof. Michel GUIDAL on 26 Aug 2014 at 3:00 PM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
The results of analysis for SERP-E-184 (SVD-2 Collaboration) experiment data (5*10^7 inelastic events) obtained with 70 GeV proton beam irradiation of active target with carbon, silicon and lead plates are presented. For two-prongs neutral and three-prongs charged charmed mesons decays, event selection criteria were developed and detection efficiencies were calculated with detailed modeling using ... More
Type: Talk Session: Dark matter and cosmology
Track: 4) Dark matter and cosmology
The XENON100 detector, which is being operated at the Gran Sasso Underground Laboratory, is a dual phase (liquid-gas) xenon time-projection chamber for particle detection. The total amount of liquid xenon is 161 kg, of which 62 kg are in the active target enclosed in a Teflon/copper structure, the rest being in the surrounding active veto. The direct and proportional UV light signal produced by pa ... More
Presented by Mr. Gaudenz KESSLER on 25 Aug 2014 at 4:55 PM
Type: Talk Session: Plenary
Presented by Dr. Marco CIRELLI on 26 Aug 2014 at 12:00 PM
Type: Talk Session: Dark matter and cosmology
Track: 4) Dark matter and cosmology
Gravitational accretion of dark matter in neutron stars may constitute a mechanism to check for further indirect effects of its existence. In this way, dark matter annihilations taking place within such compact astrophysical objects may prevent the appearance of additional particle population of hadrons inside the neutron star core. We discuss on the experimental consequences of this possibility.
Presented by Dr. M. Angeles PEREZ-GARCIA on 25 Aug 2014 at 5:20 PM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
The NA48/2 Collaboration at CERN has accumulated unprecedented statistics of rare kaon decays in the Ke4 modes Ke4(+-) to pi+ pi- e nu and Ke4(00) to pi0 pi0 e nu with ~one percent background contamination. The detailed study of form factors is sensitive to small isospin symmetry breaking effects. This brings new inputs to low energy QCD description and crucial tests of predictions from Chiral P ... More
Presented by Dr. Patrizia CENCI on 25 Aug 2014 at 5:20 PM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
We study the X(3872) to D bar{D} pi^0 decay within a molecular D bar{D}^* picture for the X(3872) state. This mode is more sensitive to the long-distance structure of the X(3872) resonance than its J/\psi\pi\pi and J/\psi 3pi$decays, which are mainly controlled by the details of the X(3872) wave function at short distances. We show that the D bar{D} final state interaction can be important, an ... More Presented by Mr. Carlos HIDALGO-DUQUE on 28 Aug 2014 at 4:30 PM Type: Poster Track: 12) New concepts and techniques for accelerators and particle detectors Gadolinium (Gd) loaded liquid scintillator used to detect neutrino. For a neutrino experiment to be successful, it is very important for the Gd-loased LAB-based liquid scintillator to know several parameters. Also, feasiblity study on a new type of liquid scintillator based on water-based scintillator have been performed. In order to make a liquid scintillator based on water, a surfactant that con ... More Presented by Ms. sunheang SO Type: Poster Introduction Measurement of optical properties Summary Future Plan References about liquid sintillator for detecting neutrino. Presented by Mr. sunheang SO Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale Recent CMS measurements of di ffractive and exclusive processes will be pre- sented, based on p-p and p-Pb data from Run 1 of the LHC. These include measurements of single and double di ffractive cross sections, photon-induced pro- cesses, and low-mass Central Exclusive Production. These results are compared to other measurements and to theoretical predictions implemented in various Monte Car ... More Presented by Mr. Sandro Fonseca DE SOUZA Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum Recent CMS measurements of diffractive and exclusive processes will be presented, based on p-p and p-Pb data from Run 1 of the LHC. These include measurements of single and double diffractive cross sections, photon-induced processes, and low-mass Central Exclusive Production. These results are compared to other measurements and to theoretical predictions implemented in various Monte Carlo simulati ... More Presented by Dr. Sandro FONSECA DE SOUZA on 28 Aug 2014 at 5:50 PM Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter We investigate dilepton production at SIS and SPS energies in transport-based approaches and show that the baryon couplings of the rho meson represent the most important ingredient for understanding the measured dilepton spectra. At lower energies, the baryon resonances naturally play a larger role and affect already the vacuum spectra via Dalitz-like contributions, which can be captured well in a ... More Presented by Dr. Janus WEIL on 26 Aug 2014 at 2:48 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum see submitted pdf file Presented by Prof. Aparajita BHATTACHARYA on 28 Aug 2014 at 3:20 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum While consistent results for the charge radius of the proton have been extracted from elastic electron-scattering data and through the spectroscopy of atomic hydrogen, recent high-precision studies of muonic hydrogen found notably smaller values for the charge radius. This so-called proton-radius puzzle raises questions ranging from experimental and methodological issues to physics beyond the sta ... More Presented by Mr. Steffen STRAUCH on 28 Aug 2014 at 5:30 PM Type: Poster Track: 2) Quarks and gluons in hadrons, the hadron spectrum We study electromagnetic couplings of baryons in an extension of the quark model, called the Unquenched Quark Model (UQM), in which the contributions of the quark-antiquark pairs are taken into account explicitly. The interaction Hamiltonian is obtained from quantum field theory in the nonrelativistic limit and includes electromagnetic transitions between quarks and antiquarks, as well as cre ... More Presented by Mr. Hugo GARCIA-TECOCOATZI Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale The LHCb forward acceptance covers a range of rapidities not accessible by the other LHC experiments, allowing for complementary measurements. We report recent measurements of electroweak boson production, either inclusive, or in association with a jet or a D meson. Presented by Ms. Mueller KATHARINA on 28 Aug 2014 at 5:50 PM Type: Talk Session: Plenary Presented by Dr. Pushpalatha BHAT on 27 Aug 2014 at 9:00 AM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter Heavy-ion collisions provide unique opportunities to explore the phenomenology of the quark-gluon plasma (QGP), a deconfined phase of QCD. The hot medium is considered to be a strongly-coupled system because the hadronic elliptic flow -- azimuthal anisotropy in momentum space -- is large and in quantitative agreement with the hydrodynamic models with very small viscosity. The elliptic flow of dire ... More Presented by Dr. Akihiko MONNAI on 25 Aug 2014 at 3:20 PM Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter We analyze the$\bar{K}N$and$\eta N$interactions using an effective separable potential coupled channels model that implements chiral symmetry [1], [2]. The energy dependence of both the$\bar{K}N$and$\eta N$scattering amplitudes is strongly affected by dynamically generated resonances close to the meson-baryon thresholds, the$\Lambda(1405)$and$N^{\star}(1535)$, respectively. We discuss t ... More Presented by Dr. Ales CIEPLY on 26 Aug 2014 at 2:24 PM Type: Talk Session: Nuclear and particle astrophysics Track: 5) Nuclear and particle astrophysics The equation of state (EoS) of hot and dense matter plays a fundamental role in the understanding of core-collapse supernova. A phase transition from hadronic to exotic phases might occur in the early post-bounce phase of a core collapse supernova. We generate a full tabular equation of state of dense matter with$\Lambda$hyperons. The$\beta$-equilibrated EoS involving hyperon-hyperon in ... More Presented by Dr. sarmistha BANIK on 25 Aug 2014 at 2:00 PM Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter We plan a missing-mass spectroscopy experiment of eta’ mesic nuclei to study in-medium properties of the eta' meson. The large mass of the eta’ meson compared to the other pseudoscalar mesons is explained by the axial anomaly effect. Since this effect on the eta’ mass is associated with spontaneous breaking of chiral symmetry, in the nuclear medium, where chiral symmetry is partially resto ... More Presented by Yoshiki K. TANAKA on 25 Aug 2014 at 5:20 PM Type: Talk Session: New concepts and techniques for accelerators and particle detectors Track: 12) New concepts and techniques for accelerators and particle detectors Hyperons could provide essential signatures of the excited and compressed baryonic matter. Their identification and reconstruction should be one of the most important tasks of any experiment with heavy ions. The MPD/NICA start version's characteristics for measuring hyperons (\Lambda, \bar\Lambda, \Xi^-, \Omega^-) obtained on Monte Carlo simulated event samples of gold-gold collisions ... More Presented by Veronika VASENDINA on 28 Aug 2014 at 2:00 PM Type: Talk Session: New concepts and techniques for accelerators and particle detectors Track: 12) New concepts and techniques for accelerators and particle detectors High-Luminosity running at the LHC, which is planned for 2022 and beyond, will imply an order of magnitude increase in radiation levels and particle fluences with respect to the present LHC running conditions. The performance evolution of the CMS electromagnetic calorimeter (ECAL), comprising 75,848 scintillating lead tungstate crystals, indicates that an upgrade of its endcaps will be needed ... More Presented by Mr. Marco PERUZZI on 25 Aug 2014 at 5:45 PM Type: Talk Session: Tests of symmetries and conservation laws Track: 9) Tests of symmetries and conservation laws The study of the Hadronic Weak Interaction, and particularly of the stangeness-conserving HWI between nucleons, is of interest for several reasons: Some of the phenomena observed in the strangeness-changing HWI cannot be explained in terms of the symmetries of QCD, which opens the possibility for a non-trivial QCD dynamical process that is either related to the presence of the strange quark, or is ... More Presented by Dr. Libertad BARRON-PALOS on 25 Aug 2014 at 5:40 PM Type: Talk Session: Tests of symmetries and conservation laws Track: 9) Tests of symmetries and conservation laws Experimental search for an electric dipole moment of the neutron The existence of a permanent non-zero electric dipole moment of the neutron (nEDM) would be unambiguous evidence for a violation of time reversal symmetry (T). The Standard Model (SM) contribution to the nEDM is of order 10^(-32) e*cm while the current experimental limit is dn < 2.9 * 10^(-26) e*cm. The search for an nEDM is one ... More Presented by Dr. Malgorzata KASPRZAK on 28 Aug 2014 at 4:30 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model Although the LHC experiments have put strong limits on coloured supersymmetric states, it is still possible that electroweakly interacting supersymmetric particles have masses in the range 100-200 GeV. Even outside of supersymmetry, candidates for the particle of dark matter may have masses in this range unconstrained by LHC data. In e+e- annihilation, the low backgrounds, precise knowledge of the ... More Presented by Juergen REUTER on 28 Aug 2014 at 5:10 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum The STAR Collaboration is performing a wide range of measurements to determine the gluon and antiquark helicity distributions in the proton. The longitudinal double-spin asymmetries,$A_{LL}$, for inclusive jet and dijet production provide direct access to the gluon polarization. The parity-violating single-spin asymmetries,$A_L$, for$W^{+/-}$production are sensitive to the$\bar{u}$and$\ba ... More
Presented by Mr. Carl GAGLIARDI on 25 Aug 2014 at 5:10 PM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
The standard model of particle physics contains three generations of quarks, whereas most of the matter is built out of quarks from the first generation, the up- and down-quarks. Nevertheless, strange quarks confined in hyperons can play an important role for example in compact astrophysical objects. Calculations show, that it is likely that hyperons appear at large nuclear densities which are r ... More
Presented by Dr. Kirill LAPIDUS on 25 Aug 2014 at 5:45 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
The MINOS and MINOS+ experiments are long-baseline neutrino oscillation experiments using the MINOS detectors in two incarnations of the Fermilab NuMI neutrino beam. The first combined MINOS and MINOS+ results, which yield the most precise measurement of the mass-splitting dm2_32, will be presented. The data are also used to probe the theta23 octant degeneracy, the mass hierarchy and the CP violat ... More
Presented by Dr. Leigh WHITEHEAD on 28 Aug 2014 at 3:20 PM
Type: Poster
The magnitude of the correlations between multiplicities in two separated rapidity windows, proposed as a signature of the string fusion and percolation phenomena, is studied in the framework of the Monte Carlo string-parton model. The model is based on the picture of strings formation in elementary collisions of color dipoles. The hardness of the elementary collisions is defined by a transverse s ... More
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
ALPHA is an international project at CERN, whose ultimate goal is to test symmetry between matter and antimatter at highest possible precision via comparisons of the properties of atomic hydrogen with its antimatter counter-part, antihydrogen. After several years of development, we recently achieved significant milestones, including the first stable confinement of antihydrogen [1] for as long as 1 ... More
Presented by Mr. Makoto FUJIWARA on 25 Aug 2014 at 6:00 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The China JinPing underground Laboratory (CJPL) is the deepest underground laboratory in operation in the world. It is located under the Jinping mountain, in the southwestern Chinese province of Sichuan. The experimental hall has an overburden of about 2400 m of rock. The measured muon flux in CJPL is around 60 muons per squaremeter per year. This extremely small muon flux make CJPL a perfect ... More
Presented by Mrs. Lucia GARBINI on 28 Aug 2014 at 3:12 PM
Generalized Parton Distribution (GPDs) functions describe the correlation between the spatial distribution of the quarks and its longitudinal momentum fraction. Their definition in the mid 1990’s has revolutionized our approach to the description of the internal structure of the nucleon. Deeply Virtual Compton Scattering (DVCS) off the nucleon (γ ∗ N → γ N ) is the simplest process which i ... More
Presented by Dr. Julie ROCHE on 26 Aug 2014 at 3:20 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
The Germanium Detector Array (GERDA) experiment, located underground in the Gran Sasso National Laboratory of INFN, Italy, is searching for the neutrinoless double beta decay (0nbb) of Ge-76. It uses a new shielding concept by operating bare Ge diodes enriched in Ge-76 in 64 m^3 of liquid argon supplemented by a 3m thick layer of water. The experiment aims at exploring the 0nbb decay up to a half ... More
Presented by Ms. Anne WEGMANN on 25 Aug 2014 at 6:00 PM
Type: Talk Session: Plenary
Presented by Prof. Werner HOFMANN on 27 Aug 2014 at 11:30 AM
Type: Talk Session: Plenary
Presented by Dr. Ties BEHNKE on 29 Aug 2014 at 9:40 AM
The GlueX experiment at Jefferson Lab will use a linearly polarized photon beam to explore the light quark meson spectrum, with emphasis on mesons with exotic quantum numbers. These exotic mesons cannot be formed by a simple quark-antiquark pair and could indicate the excitation of gluonic degrees of freedom. The GlueX detector is nearly complete and first beam is expected later in the year. ... More
Presented by Mr. Will LEVINE on 28 Aug 2014 at 3:40 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The HADES spectrometer installed at GSI Darmstadt is a second generation experiment designed to measure e+e- pairs (dielectrons) in the SIS∕BEVALAC energy regime. The main goal of the experiment is to measure electromagnetic emissivity of a compressed baryonic matter formed in course of heavy ion collisions and ultimately learn about in-medium hadron properties. For this purpose a dedicated ... More
Presented by Mr. Andrej KUGLER on 28 Aug 2014 at 2:24 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
We present the HERAFitter project which provides a framework for Quantum Chromodynamics (QCD) analyses related to the proton structure in the context of multi-processes and multi-experiments. Based on the concept of factorisable nature of the cross sections into universal parton distribution functions (PDFs) and process dependent partonic scattering cross sections, HERAFitter allows determina ... More
Presented by Mr. Volodymyr MYRONENKO on 28 Aug 2014 at 5:30 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
New combined H1 and ZEUS data on neutral and charged current inclusive cross sections at HERA from all running periods 1994-2007, are used as the sole input to NLO and NNLO QCD analyses to determine new sets of parton distributions, HERAPDF2.0, with small experimental uncertainties and an estimate of model and parametrisation uncertainties. A HERAPDF fit, evolved in leading order (LO) in alpha_s ... More
Presented by Mrs. Amanda COOPER-SARKA on 26 Aug 2014 at 3:20 PM
Type: Talk Session: Plenary
Presented by Prof. Nicole D'HOSE on 28 Aug 2014 at 11:30 AM
Type: Talk Session: Plenary
Presented by Ralf ULRICH on 27 Aug 2014 at 11:00 AM
Type: Poster Track: 6) Standard model physics at the TeV scale
If studies of electroweak gauge boson final states at the Large Hadron Collider, for Standard Model physics and beyond, are sensitive to effects of the initial state's transverse momentum distribution, appropriate generalizations of QCD shower evolution are required. We propose a method to do this based on QCD transverse momentum dependent (TMD) factorization at high energy. The method incorpo ... More
Presented by Ms. Dooling SAMANTHA
Hard exclusive leptoproduction of real photons (deeply virtual Compton scattering, DVCS) or mesons on nucleons is widely considered to be one of the most promising reactions that can provide information about the structure of the nucleon in the framework of generalized parton distributions (GPDs). During last years, DVCS has been extensively studied at the HERMES experiment through measurements of ... More
Presented by Dr. Sergey YASHCHENKO on 26 Aug 2014 at 2:20 PM
Type: Talk Session: Plenary
Presented by Dr. Andrzej OLSZEWSKI on 25 Aug 2014 at 11:00 AM
Type: Talk Session: Plenary
Presented by Dr. Thomas Edward LATHAM on 27 Aug 2014 at 9:30 AM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
ATLAS has performed searches for heavy hadrons, with results including the first observation of the chi_b(3P) Bottomonium states. New results in this program are discussed, including searches for excited b-hadrons and new decay modes of b-hadrons as well as the bottomonium counterpart of X(3872). We also review ATLAS studies of B-hadron decays, including the measurement of the parity v ... More
Presented by Mr. Andreas KORN on 28 Aug 2014 at 5:45 PM
Its forward acceptance puts the LHCb in a unique position at the LHC to measure QCD phenomena at large rapidities and low transverse momenta, where theoretical models often fail to describe the data accurately. We present studies of the production and polarisation of the J/ψ, ψ(2S) and χc charmonium states as well as those of ϒ and χb bottomonia.
Presented by TBA
ATLAS has a wide programme to study the production cross section and decay properties of particles with beauty, as well as charmonium and bottomonium states. This presentation will cover ATLAS results in the domain of charmonium production, including J/psi, psi(2s) and chi_c states, B+ production, and updates on the D(*) meson cross-section analysis. The analyses discussed include doub ... More
Presented by Mr. Roger JONES on 28 Aug 2014 at 4:50 PM
The identification of the relevant effective degrees of freedom of QCD is the most important step in order to understand the structure of the nucleon. Since the resonance contributions to the excitation spectrum are often broad and overlapping, the comparison of experimental data and theoretical models is rather difficult. Single and double polarization observables allow the determination of the ... More
Presented by Ms. Lilian WITTHAUER on 28 Aug 2014 at 2:40 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
The results on the Standard Model Higgs Boson in lepton decay channels with pp collision data at 7 and 8 TeV center-of-mass energies collected by the CMS detector at the LHC will be summarized. A direct evidence of the Higgs-fermion coupling is established with the tau pair decay mode. Searches for Higgs Bosons decaying to leptons in scenarios Beyond the Standard Model such as supersymmetry will a ... More
Presented by Dr. Somnath CHOUDHURY on 25 Aug 2014 at 2:00 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
The Compact Linear Collider (CLIC) is an attractive option for a future multi-TeV linear electron-positron collider, offering the potential for a rich precision physics programme, combined with sensitivity to a wide range of new phenomena. The physics reach of CLIC has been studied in the context of three distinct centre-of-mass energy stages, 350 GeV, 1.4 TeV and 3.0 TeV. This staged scenario pro ... More
Presented by Dr. Frank SIMON on 28 Aug 2014 at 3:40 PM
Type: Poster Track: 6) Standard model physics at the TeV scale
In the forthcoming high-luminosity phase of the LHC many of the most interesting measurements for precision QCD studies are hampered by large pile-up conditions, especially at not very high transverse momenta. However, with the recently discovered Higgs boson, which couples in the heavy top limit directly to gluons, we have access to a novel production process to probe QCD by a colour-singlet curr ... More
Presented by Dr. Hans VAN HAEVERMAET
Type: Talk Session: Plenary
Presented by David ROUSSEAU on 25 Aug 2014 at 9:15 AM
Type: Talk Session: Plenary
Presented by Prof. Kara HOFFMAN on 27 Aug 2014 at 12:00 PM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
High-resolution x-ray spectroscopies of hadronic atoms will be performed with an x-ray spectrometer based on an array of superconducting transition-edge-sensor (TES) microcalorimeters which have achieved remarkable development in recent years [1]. The instrument offers unprecedented full-width-at-half-maximum energy resolutions of 2 - 3 eV at 6 keV being two order of magnitude improved resolution ... More
Presented by Dr. Shinji OKADA on 26 Aug 2014 at 2:00 PM
Type: Talk Session: Plenary
Presented by Prof. Eugenio SCAPPARONE on 25 Aug 2014 at 11:30 AM
Type: Talk Session: Plenary
Presented by Prof. Hirokazu TAMURA on 29 Aug 2014 at 10:50 AM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
Recently, a hyperon-nucleon (YN) interaction has been derived up to next-to-leading order in chiral effective field theory by the Jülich-Bonn-Munich group. At that order there are contributions from one- and two-pseudoscalar-meson exchange diagrams and from four-baryon contact terms without and with two derivatives. SU(3) flavor symmetry is imposed for constructing the YN interaction i ... More
Presented by J. HAIDENBAUER on 25 Aug 2014 at 2:25 PM
Type: Poster Track: 6) Standard model physics at the TeV scale
The algorithm used for reconstruction and identi cation of hadronic tau decays by the CMS experiment at the LHC is presented. The tau reconstruction in CMS takes advantage of the particle-flow algorithm which allows to reconstruct individual hadronic decay modes. The performance of the algorithm in terms of tau ID eciency, rate of jet -> tau, e -> tau and mu -> tau fakes and in terms of tau ... More
Presented by Mr. Raman KHURANA
Type: Talk Session: Beyond Standard Model
Track: 7) Energy frontier physics beyond the standard model
In this talk, the latest results from CMS on inclusive searches for squark and gluino production at the LHC are reviewed. A variety of complementary fi nal state signatures and methods are presented using 20 fb-1 of data from the 8 TeV LHC run.
Presented by Lukas VANELDEREN on 25 Aug 2014 at 3:00 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
Recent results on deep-inelastic scattering at HERA are presented. The H1 and ZEUS experiments each have determined new measurements of the proton longitudinal structure function FL, making use of the HERA data recorded at reduced centre-of-mass energies. The results are in agreement with each other and with predictions derived from QCD fits. The region of high x is explored in a dedicated me ... More
Presented by Mr. Zhiqing ZHANG on 26 Aug 2014 at 3:00 PM
Type: Talk Session: Beyond Standard Model
Track: 7) Energy frontier physics beyond the standard model
Despite the absence of experimental evidence, weak scale supersymmetry remains one of the best motivated and studied Standard Model extensions. This talk summarises recent ATLAS results on inclusive searches for supersymmetric squarks and gluinos, including third generation squarks produced in the decay of gluinos. The searches involved final states containing jets, missing transverse mo ... More
Presented by Mr. Bertrand MARTIN DIT LATOUR on 25 Aug 2014 at 2:40 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
T2K is a long-baseline neutrino oscillation experiment in which a muon neutrino beam is produced at the J-PARC facility and detected by Super-Kamiokande, a water Cherenkov detector with a 22.5 kton fiducial mass, after traveling 295 km. Since 2010, T2K has accumulated 6.57e20 protons on target, which is 8% of the experimental goal. T2K has observed 120 numu event candidates, which show a clear dis ... More
Presented by Ms. Helen O'KEEFFE on 26 Aug 2014 at 2:50 PM
Type: Talk Session: Plenary
Presented by Prof. Akira YAMAMOTO on 26 Aug 2014 at 9:00 AM
Type: Talk Session: Nuclear and particle astrophysics
Track: 5) Nuclear and particle astrophysics
The equation of state (EOS) for the high density matter is still not clear and recent several observations indicate the restrictions of the EOSs, therefore theoretical studies should try to elucidate the EOSs in the high density and/or temperature. As there are many rapidly rotating neutron stars (pulsars), many theoretical studies try to take into account the effect of rotation[1]. We accordingly ... More
Presented by Prof. Tomoki ENDO on 26 Aug 2014 at 3:20 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
IsoDAR is an innovative experimental concept to use a high power, low energy cyclotron to produce a source of electron antineutrinos. Such an intense source, when combined with a liquid scintillator based detector, can provide a direct probe of the reactor antineutrino anomaly and, in general, a definitive test of the sterile neutrino. Further, IsoDAR can distinguish between one and two sterile ne ... More
Presented by Prof. Janet CONRAD on 26 Aug 2014 at 3:30 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
The production of J/ψ and Υ-mesons decaying into dimuon final state is studied at the LHCb experiment, with rapidity 1.5 < y < 4.0 or -5.0 < y < -2.5 and transverse momentum pT < 15 GeV/c, in proton-lead collisions at a proton-nucleon centre-of-mass energy of 5 TeV. The analysis is based on a data sample corresponding to an integrated luminosity of 1.6/nb. The forward-backward production ratio a ... More
Presented by Ms. Mueller KATHARINA on 28 Aug 2014 at 2:30 PM
Type: Talk Session: Nuclear and particle astrophysics
Track: 5) Nuclear and particle astrophysics
The LHCf experiment is one of the forward experiments at the LHC. The purpose is to provide critical calibration data for hadronic interaction model which are used for MC simulations of air shower generated by very high energy cosmic-rays. The LHCf has two independent detectors which are installed at +/-140m from a LHC interaction point, IP1. The detectors are sampling and imaging calorimeters and ... More
Presented by Dr. Hiroaki MENJO on 25 Aug 2014 at 2:40 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The future Electron Ion Colliders (EIC) LHeC and eRHIC will be able to collide electrons with ions in the LHeC case, or polarized electrons with polarized protons/He+3 or heavy ions in eRHIC. Ions have been already used in both colliders in the existing complex of accelerators of Large Hadron Collider (LHC) and Relativistic Heavy Ion Colliders (RHIC). Electron acceleration in both EIC's are based ... More
Presented by Dr. DEJAN TRBOJEVIC on 28 Aug 2014 at 2:48 PM
Type: Poster Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
Momentum distributions of hydrogen and helium isotopes from 12C fragmentation at 3.5o were measured in FRAGM experiment at ITEP TWA heavy ion accelerator on Be target. At energies 0.3, 0.6, 0.95 and 2.0 GeV/nucleon the momentum spectra of fragments span the region of fragmentation peak as well as the cumulative region. The differential cross sections cover 6 orders of its magnitude. The spectra ... More
Presented by Mr. Viacheslav KULIKOV V.V.
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
We are planning to measure the ground-state hyperfine splitting energy of muonic hydrogen by laser spectroscopy techniques at the RIKEN-RAL Muon facility. The hyperfine splitting energy is about 0.182 eV, which corresponds to the laser wavelength of 6.7 μm. The experiment has become feasible by a narrow-bandwidth tunable mid-infrared laser recently developed in RIKEN [1]. The expected precision f ... More
Presented by Dr. Masaharu SATO on 25 Aug 2014 at 5:20 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
Within the Standard Model (SM), in spite of neutrino oscillations, the flavor of charged leptons is conserved in very good approximation, and therefore charged Lepton Flavor Violation (cLFV) is expected to be unobservable. On the other hand, most new physics models predict cLFV within the experimental reach, and processes like the mu -> e gamma decay became standard probes for physics beyond the S ... More
Presented by Dr. Francesco RENGA on 28 Aug 2014 at 3:10 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
The aSPECT retardation spectrometer measures the electron antineutrino angular correlation coefficient a in free neutron beta decay. This measurement can be used to determine the ratio of g_A/g_V of the weak coupling constants, as well as to search for physics beyond the Standard Model. In spring/summer 2013 aSPECT had a successful beamtime at the Institut Laue-Langevin/Grenoble (France). The goa ... More
Presented by Mr. Alexander WUNDERLE on 25 Aug 2014 at 2:00 PM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
Decays of b-hadrons to light quarks allow spectroscopy measurements with a well defined initial state. The decay B(s)→J/ψππ gives insight on the quark content of the f0(500) and f0(980) mesons, while the decays B→pph and Λb→J/ψph allow for baryon spectroscopy. This talk also includes results on exotic charmonium resonances.
Presented by Mr. Antonio Augusto ALVES JR on 28 Aug 2014 at 6:10 PM
Type: Talk Session: Plenary
Presented by Prof. Constantia ALEXANDROU on 28 Aug 2014 at 12:00 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Thanks to its excellent particle identification and momentum measurement capabilities, the ALICE detector allows for the identification of deuterons, tritons, $\rm ^{3}{He}$ and $\rm ^{4}{He}$ and and their corresponding antinuclei. This is achieved via their specific energy loss in the Time Projection Chamber and the velocity measurement by the Time-Of-Flight detector. Moreover, thanks ... More
Presented by Ramona LEA on 28 Aug 2014 at 5:20 PM
Type: Talk Session: Nuclear and particle astrophysics
Track: 5) Nuclear and particle astrophysics
Experimental nuclear astrophysics has to use often extrapolation procedures to access the relevant Gamow energy peak for astrophysically relevant burning reactions. Thanks to its recent developments, the Trojan Horse Method (THM) allows the experimentalist to investigate astrophysical energies by means of surrogate experiment in which a proper selection of the quasi-free reaction mechanism is perf ... More
Presented by Dr. Livio LAMIA
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
A possible solution to the strong CP problem is a light pseudoscalar boson, the so-called axion. The axion would cause a new spin-dependent short-range interaction. Of interest here is the search for an axion mediated short range interaction between a fermion and the spin of another fermion. To search for this effect, co-located, nuclear spin polarized 3He and 129Xe gas is used to become independe ... More
Presented by Dr. Kathlynne TULLNEY on 28 Aug 2014 at 6:10 PM
Type: Poster Track: 3) Neutrinos and related astrophysical implications
Daya Bay Reactor Neutrino Experiment is designed to measure the mixing angle θ13 using 8 identical Anti-neutrino detectors (AD). Each AD contains 20-ton Gadolinium-loaded liquid scintillator (Gd-LS) as the target for catching neutrino. Optical properties and stability of Gd-LS are of great important for the experiment. Here we report the choice of Gd-LS recipe and the preparation procedures of 18 ... More
Presented by Dr. Yayun DING
Type: Talk Session: Nuclear and particle astrophysics
Track: 5) Nuclear and particle astrophysics
The origin, composition and mechanisms of acceleration the Ultra-High Energy Cosmic Rays (UHECRs) are not yet fully understood. The trajectories of these particles can be affected by cosmic magnetic fields. Depending on the strength and properties of these fields, charged cosmic rays can diffuse and have propagation times comparable to the age of the universe, causing a suppression in the measure ... More
Presented by Mr. Rafael ALVES BATISTA on 26 Aug 2014 at 2:20 PM
Type: Poster Track: 2) Quarks and gluons in hadrons, the hadron spectrum
Magnetic Moments of The Baryon Anti-decuplet and Octet pentaquark States R. Ghosh Department of Physics, Jadavpur University, Calcutta – 700032, India e-mail : rismita.ghosh@gmail.com The baryons built of four quarks and an antiquark as the lowest Fock component, referred to as ... More
Presented by Ms. Rismita GHOSH
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
Mass and lifetime predictions of b-flavoured hadrons are an impmortant probe of QCD models. We report the world's best measurements of lifetimes of many b-flavoured mesons and baryons. We also report on observations of excited states of the B, Bs and Λb hadrons and measurements of their masses and decay widths.
Presented by Mr. Stefano GALLORINI on 26 Aug 2014 at 2:50 PM
Meson photoproduction offers unique possibilities to investigate the nucleon and its excited states. Double meson photoproduction has the great advantage of enabling access to higher lying nucleon resonances that have no significant decay mode to the nucleon ground state via photoproduction of single mesons. Among the different meson pairs $2\pi^{0}$ is in particular interesting as non-resonant ba ... More
Presented by Mr. Manuel DIETERLE on 28 Aug 2014 at 2:20 PM
Type: Poster Track: 6) Standard model physics at the TeV scale
The first measurement of the Drell-Yan and associated jet cross section as a function of the Drell-Yan mass is presented using an integrated luminosity of 4.9 fb-1 in the dimuon channel of proton-proton collisions recorded with the CMS detector. Cross Sections as a function of the Drell-Yan transverse momentum are measured differentially in the Drell-Yan mass. The pt spectrum of the Drell-Yan allo ... More
Presented by Ms. Dooling SAMANTHA
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
A detailed review of the results on the main properties of the Higgs boson in the diphoton, ZZ (with subsequent decays to four leptons), WW (with subsequent decays to lvlv) and Z-photon channels, with the ATLAS detector using approximately 25 fb-1 of pp collision data collected at 7 TeV and 8 TeV in 2011 and 2012, will be given. The measurements discussed will be the mass, couplings prop ... More
Presented by Mr. Peter KLUIT, Mrs. Eleonora BENHAR NOCCIOLI on 25 Aug 2014 at 3:20 PM
The photoproduction reaction $\gamma p \to K^+ \Lambda(1520)$ is a topic of interest due to possible interference with the $\gamma p \to \phi p$ reaction and possible heavy excited nucleon decay to $K^+ \Lambda(1520)$. In particular, an unexplained bump has been seen in measurements of the differential cross-section and provoked theoretical work. Information about the production mechanism of this ... More
Presented by Mr. William LEVINE on 28 Aug 2014 at 2:00 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
The latest results on the measurement of the Higgs boson mass in the diphoton and ZZ decay channels with the ATLAS detector is presented, using approximately 25 fb-1 of pp collision data collected at 7 TeV and 8 TeV in 2011 and 2012.
Presented by Mr. Oliver KORTNER on 25 Aug 2014 at 3:00 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
We present the measurement of the forward-backward asymmetry in top antitop quark pair production in proton antiproton collisions in the lepton plus jets and dilepton final state. Measurements use the full data set collected by D0 in Run II corresponding to an integrated luminosity of 9.7/fb. We present the most recent measurement of the lepton-based asymmetries both in lepton+jets and dilepton fi ... More
Presented by Kamil AUGSTEN on 25 Aug 2014 at 5:50 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
The precise determination of the mass, couplings and other properties of the particle discovered in 2012 around 125 GeV is important to establish precisely if it is a Standard Model Higgs boson. CMS experiment has collected lot more data since the discovery of this particle in July 2012 and has performed many of its properties measurements. In this talk, I will present some of these mea- sure ... More
Presented by Ms. Shivali MALHOTRA on 25 Aug 2014 at 2:20 PM
Type: Poster Track: 6) Standard model physics at the TeV scale
The mass of the top quark is measured using a sample of ttbar candidate events with one electron or muon and at least four jets in the final state, collected by CMS in pp collisions at √s=8 TeV at the LHC. The candidate events are selected from data corresponding to an integrated luminosity of 19.7/fb. For each event the mass is reconstructed from a kinematic fit of the decay products to a ttbar ... More
Presented by Mr. Markus SEIDEL
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
LHCb has collected the world's largest sample of charmed hadrons. This sample is used to search for direct and indirect CP violation in charm, and to measure D0 mixing parameters. New updated measurements from several decay modes are presented, with complementary time-dependent and time-integrated analyses.
Presented by Mr. Michael ALEXANDER on 26 Aug 2014 at 2:25 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
Electric Dipole Moments (EDM) of elementary particles are considered to be one of the most powerful tools to investigate CP violation beyond the Standard Model and to find an explanation for the dominance of matter over anti-matter in our Universe. Up to now experiments concentrated on neutral systems (neutrons, atoms, molecules). Storage rings offer the possibility to measure EDMs of charged par ... More
Presented by Dr. Volker HEJNY on 28 Aug 2014 at 4:50 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
We provide a summary of the latest measurements of the WV production cross- sections, where V=W or Z. The data sample(s) correspond to proton-proton collision events collected with the CMS detector at the center of mass energy of 7 and 8 TeV. Subsequent searches for Anomalous Triple Gauge Couplings, which allow us to probe the non-Abelian structure in the Electroweak Sector, and corresponding ... More
Presented by Mr. Ilya OSIPENKOV on 28 Aug 2014 at 5:10 PM
The KLOE experiment has collected 2.5 fb-1 at the peak of the phi resonance at the e+e- collider DAPHNE in Frascati. A new beam crossing scheme, allowing for a reduced beam size and increased luminosity, is operating at DAPHNE. The upgraded KLOE-2 detector is successfully rolled in inside this new interaction region and is ready to acquire collision data. The V-->Pgamma Dalitz decay ... More
Presented by Ms. Li BALKESTAHL on 28 Aug 2014 at 3:20 PM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
The interest in low energy antiprotons annihilating on nuclei covers several physics topics. Some fundamental cosmology models assume the existence of distinct regions of matter and antimatter in the universe where the process of annihilation is of interest at the boundaries. Nuclear physics puts a great relevance on the annihilation process at low energy as a probe of the external region of ... More
Presented by Mr. Valerio MASCAGNA
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
Vector boson production in p≠p collisions in LHC Run≠1 has been extensively studied by ATLAS and CMS. Charged and neutral current Drell Yan cross sections are sensitive to the parton distribution functions of the proton and electroweak corrections. The measurements of the neutral current Drell≠Yan process in three distinct kinematic regions, i.e. at the Z boson mass peak, below and ... More
Presented by Ms. Manuella VINCTER on 28 Aug 2014 at 2:00 PM
The OLYMPUS experiment seeks to provide a high-precision measurement (<1% error) of the positron-proton versus electron-proton elastic scattering cross section ratio. This requires fi ne control of all systematic uncertainties, including the calculation of the luminosity. For this purpose, multiple independent subsystems were operated alongside the main spectrometer during data taking to allow for ... More
Presented by Mr. Dmitry KHANEFT on 28 Aug 2014 at 4:50 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Despite the successes of the HERA collider, where much information was gained on the structure of the nucleon, data on the structure of the nucleus at moderate-to-small \x remains elusive, as only fixed-target high-\x data currently exist. The small-\x region, however, is of great interest. The nucleon structure in this region is dominated by gluons which show a rapid rise with decreasing \x. A ... More
Presented by Dr. Matthew LAMONT on 26 Aug 2014 at 3:30 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
Recent measurements of the neutron lifetime have individually reported uncertainties of about 1 s but disagree by as much 7 s, resulting in a shift of about 6.5 sigma in the accepted value over recent years. Measurements based on the decay in flight of cold neutron beams appear to yield longer lifetimes than those based on counting surviving ultracold neutrons after storage in material-walled tra ... More
Presented by Dr. Alexander SAUNDERS on 25 Aug 2014 at 3:00 PM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
PANDA is a key experiment of the FAIR facility in Darmstadt. It will study fundamental questions of hadron physics and QCD by exploring interactions between an antiproton beam and a fixed proton or nuclear target. Because of the relative large production cross section of hyperon-antihyperon pairs in antiproton-nucleus collisions, PANDA will be an ideal instrument to study hyperons and antihyperon ... More
Presented by Dr. Alicia SANCHEZ-LORENTE on 25 Aug 2014 at 2:50 PM
Mass and structure of 16^O and 40^Ca are studied on the basis of quantum chromodynamics (QCD), the fundamental theory of the strong interaction. We derive two-nucleon potentials from lattice QCD simulations by the recently developed HAL QCD method. Then we apply the results to the structure of medium-heavy nuclei (16^O and 40^Ca) using the Brueckner-Hartree-Fock theory. We find that these two n ... More
Presented by Prof. Takashi INOUE on 28 Aug 2014 at 3:00 PM
Type: Poster Track: 12) New concepts and techniques for accelerators and particle detectors
The development of a reliable monitoring system was a key element in the successful consolidation and upgrade of the cabling infrastructure of the CERN accelerator complex. The work undertaken consisted of a large number of installations, distributed over a wide area and carried out to a tight schedule, sometimes in highly radioactive environment, requiring precise and efficient monitoring of all ... More
Presented by Stefano MEROLI
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
The Precision IceCube Next Generation Upgrade (PINGU) is a proposed low-energy extension to the IceCube Neutrino Observatory, located at the geographic South Pole. PINGU will increase IceCube’s sensitivity to neutrinos with energies down to a few GeV with a multi-megaton effective volume. For every year of PINGU detector operation, tens of thousands of atmospheric neutrinos will be collected. Th ... More
Presented by Dr. Tomasz PALCZEWSKI on 28 Aug 2014 at 2:40 PM
Type: Talk Session: Plenary
Presented by Prof. Janet CONRAD on 28 Aug 2014 at 9:00 AM
Type: Talk Session: Plenary
Presented by Prof. Stephen PARKE on 28 Aug 2014 at 10:00 AM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
EXO-200 is one of the most sensitive searches for neutrinoless double beta decay in the world. The experiment uses 175 kg of enriched liquid xenon in an ultralow background time projection chamber installed at the Waste Isolation Pilot Plant, a salt mine with a 1600 m water equivalent overburden. This detector has demonstrated excellent energy resolution and background rejection capabilities. Usin ... More
Presented by Dr. Dave MOORE on 25 Aug 2014 at 2:00 PM
Type: Talk Session: Plenary
Presented by Robert D. MCKEOWN on 28 Aug 2014 at 11:00 AM
The normalization studies performed for the DVCS 2010 experiment in Jefferson Lab Hall A lead to a re-analysis of the published 2004 results. In addition to the updated results for the published kinematics, we will also show new data points for the unpolarized DVCS cross section at $Q^2$=1.9 GeV$^2$ and $x_B$=0.36. Moreover, using the same data set, we analyzed the $x_B$-dependence of the helici ... More
Presented by Mr. Maxime DEFURNE on 26 Aug 2014 at 2:00 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
We performed a search for a Lorentz-invariance- and CPT-violating coupling of the 3He and 129Xe nuclear spins (each largely determined by a valence neutron) to posited background tensor fields that permeate the Universe. Our experimental approach is to measure the free precession of nuclear spin polarized 3He and 129Xe atoms in a homogeneous magnetic guiding field of about 400 nT using LTC SQUIDs ... More
Presented by Mr. Fabian ALLMENDINGER on 28 Aug 2014 at 5:50 PM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
Flavour changing neutral currents and precision measurements of CP violation are investigated in ATLAS as probes to new physics beyond the standard model. This talk presents the most recent results on the search for the rare decay Bs (B0) -> mu+mu-, as well as providing the latest update on the study of the different angular amplitudes contributing to flavour tagged Bs -> J/psi phi (mu+m ... More
Presented by Ms. Lidia SMIRNOVA on 28 Aug 2014 at 2:00 PM
Type: Talk Session: Plenary
Presented by Dr. Thomas ROSER on 26 Aug 2014 at 9:30 AM
Type: Talk Session: Plenary
Presented by Dr. Jens OSTERHOFF on 26 Aug 2014 at 10:00 AM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
Cosmology and particle physics come across a tight connection in the attempt to reproduce quantitatively the results of experimental findings. Indeed, the dark matter relic abundance and the amount of baryon asymmetry in the universe are accurately determined by the recent analysis of the cosmic microwave background. The Standard Model can not account for none of these evidences. Majorana fermi ... More
Presented by Mr. Simone BIONDINI on 28 Aug 2014 at 5:30 PM
Type: Poster Track: 1) Quarks and gluons in hot and dense matter
We propose to benefit from a concept of the enthalpy in order to include volume corrections to a nucleon rest energy, which are proportional to pressure and absent in a standard Relativistic Mean Field (RMF) with point-like nucleons. As a result a nucleon mass can decrease with Nuclear Matter (NM) density, making an Equation of State (EoS) softer. It is shown, how the EOS depends from nucleon siz ... More
Presented by Dr. Jacek ROZYNEK
Type: Talk Session: Plenary
Presented by Prof. Hendrik SCHATZ on 28 Aug 2014 at 9:30 AM
Type: Talk Session: Nuclear and particle astrophysics
Track: 5) Nuclear and particle astrophysics
Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process. Purpose: We plan to study the behaviour of the pairing gaps as a function of the Fermi momentum for neutron and nuclear matter in all relevant angular momentum channels where superflu ... More
Presented by Dr. Paolo FINELLI on 26 Aug 2014 at 3:00 PM
Type: Poster Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
At the Mainz Microtron MAMI the first high-resolution spectroscopy of pionic decays of strange systems was performed in electron scattering. Kaons were detected with the short-orbit spectrometer Kaos making use of a broad momentum acceptance at zero degree with respect to the beam. Reactions of strangeness production were efficiently tagged. In coincidence about 1000 decay-pions were detected with ... More
Presented by Dr. Patrick ACHENBACH
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
We propose a pure four-dimensional formulation (FDF) of the d-dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are rep- resented by massive internal states regulating the divergences. The latter obey Feynman rules containing multiplicative selection rules which automatically account for the effects of the extra- dimensional ... More
Presented by Angelo Raffaele FAZIO on 26 Aug 2014 at 3:40 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Starting with the interpretation of parton evolution with rapidity as a branching-diffusion process, we describe the different kinds of fluctuations of the density of partons which affect the properties of QCD scattering amplitudes at moderately high energies. We then derive some of these properties as direct consequences of the stochastic picture. We get new results on the expression of the satur ... More
Presented by Dr. Stephane MUNIER on 26 Aug 2014 at 2:30 PM
Session: Plenary
Presented by Mr. Matthias KASEMANN on 27 Aug 2014 at 10:30 AM
Session: Plenary
on 28 Aug 2014 at 10:30 AM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
The study of strong interactions and hadron matter in the process of antiproton-proton annihilation seems to be a challenge nowadays. The research of charmonium cc\bar , charmed hybrid cc\bar g and tetraquark cq(cq\prime)\bar ( q, and q\prime = u, d, s) spectra and their main characteristics (mass, width, branching ratio) in experiments using high quality antiproton beam with momentum up to 15 Ge ... More
Presented by Dr. Barabanov MIKHAIL on 28 Aug 2014 at 4:55 PM
Type: Talk Session: Dark matter and cosmology
Track: 4) Dark matter and cosmology
The recently formed PICO collaboration, a merger of COUPP and PICASSO, is designing a 250L bubble chamber to search for dark matter in the form of Weakly Interacting Massive Particles (WIMPs). This experiment will have nearly four orders of magnitude greater sensitivity to spin-dependent WIMP-nucleon interactions as compared to our existing world-best results. We operate bubble chambers with thr ... More
Presented by Mr. Alan ROBINSON on 25 Aug 2014 at 5:45 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
We report on the measurement of parity-violating (PV) asymmetries in the deep inelastic scattering (DIS) and nucleon resonance regions using inclusive scattering of longitudinally polarized electrons off an unpolarized deuterium target. The effective weak couplings C_2q are accessible through the DIS measurements. Here we report a measurement of the PV asymmetry, which yields a determinatio ... More
Presented by Dr. Vince SULKOSKY on 28 Aug 2014 at 2:50 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
The technique of measuring tiny single-spin asymmetries in the scattering of longitudinally polarized relativistic electrons off unpolarized fixed targets is well-established. These measurements, which exploit the non-conservation of parity symmetry by the neutral weak interaction, are being used in a variety of applications to address fundamental questions in nuclear and particle physics. One thr ... More
Presented by Mr. Krishna KUMAR on 28 Aug 2014 at 2:00 PM
Partial Wave Analysis of the $\pi^+\pi^-\pi^-$ system produced by 28 GeV/c $\pi^-$ beam on berillium target is presented. About $30\cdot10^6$ events in the wide $|t|$-prime range $0\ldots1~GeV^2/c^2$ are collected with upgraded VES setup. The size of the data sample is 2.5 times larger than that previously analyzed by VES. Data are analyzed using formalism of density matrix with unlimited ran ... More
Presented by Mr. Igor KATCHAEV on 28 Aug 2014 at 2:40 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The LHC phase-II upgrade will provide considerably higher annual luminosities leading to a total of 3000 fb-1. This data will allow precision measurements of Higgs properties, vector boson scattering and substantially higher sensitivities in searches for new physics in particular for rare processes. Detectors will need to be upgraded in order to operate in such a high rate and high radiation e ... More
Presented by Mr. David Anthony PETYT on 25 Aug 2014 at 5:20 PM
Our understanding of the structure of nucleons is described by the properties and dynamics of quarks and gluons in the theory of quantum chromodynamics. With advancements in theory and the development of phenomenological tools we are preparing for the next step in subnuclear tomographic imaging at a future electron-ion collider. A large range of center-of-mass energies ($\sqrt{s}\approx 77 - 141$ ... More
Presented by Dr. Salvatore FAZIO on 28 Aug 2014 at 6:10 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The ability to correct jets and jet shapes for the contributions of multiple uncorrelated proton-proton interactions (pileup) largely determines the ability to identify new physics via highly boosted hadronic decays of W, Z, and Higgs bosons, or top quarks. We present a new method that operates at the level of the jet constituents and provides both a performance improvement and a simplification ... More
Presented by Dr. Spousta MARTIN on 25 Aug 2014 at 4:30 PM
The COMPASS experiment at CERN has been contributing to the description of the nucleon spin structure, namely the transverse momentum dependent parton distribution functions (TMDs), through the Semi-Inclusive Deep Inelastic Scattering (SIDIS) using a muon beam impinging on polarised targets. These TMD functions are also accessible via the transversely polarised Drell-Yan (DY) process, which will b ... More
Presented by Mrs. Márcia QUARESMA on 25 Aug 2014 at 3:00 PM
Meson photoproduction has developed into a powerful tool to study the nucleons excitation spectrum and test effective quark models which operate in the non-perturbative regime of QCD. An insight into the $J^P$ configurations and isospin decompositions of the contributing resonances is gained by measuring a minimal set of polarization observables on both the proton and the neutron. Single $\pi^ ... More Presented by Mr. Thomas STRUB on 28 Aug 2014 at 3:00 PM Type: Talk Session: Plenary Presented by Dr. Thomas SCHOERNER-SADENIUS on 29 Aug 2014 at 9:00 AM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications T2K is a long-baseline neutrino oscillation experiment, where a muon neutrino beam is produced at the J-PARC facility and detected by Super-Kamiokande, a water Cherenkov detector with a 22.5 kton fiducial mass, after traveling 295 km. One aim of the experiment is to precisely determine the mixing angle theta_23 and the mass squared difference Delta m^2_23 using a measurement of muon neutrino disap ... More Presented by Mr. Erez REINHERZ-ARONIS on 26 Aug 2014 at 2:30 PM Type: Poster Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications To study the properties of elusive atmospheric neutrinos, the India-based Neutrino Observatory (INO) has been planned to be set up at Theni (Tamilnadu), South India. INO will host a 50 kt magnetized Iron CALorimeter (ICAL) detector for determination of neutrino mass and mixing parameters which is one of the important issues for the leptonic sector in today's particle physics. The detector will ... More Presented by Mr. D. KAUR Type: Talk Session: Tests of symmetries and conservation laws Track: 9) Tests of symmetries and conservation laws Recent results and prospects for precision tests of the Standard Model in kaon decay in flight experiments at CERN are presented. A measurement of the ratio of leptonic decay rates of the charged kaon at a 0.4% precision constrains the parameter space of new physics models with extended Higgs sector, a fourth generation of quarks and leptons or sterile neutrinos. Searches for heavy neutrino mass ... More Presented by Mr. Tommaso SPADARO on 25 Aug 2014 at 3:40 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum One of the major goals of the proton spin physics program at RHIC at BNL is to constrain the gluon polarization distribution$\Delta g(x)$and thus determine the contribution of gluons to the spin of the proton. Measurements of spin asymmetries with jets and neutral pions at central pseudorapidities at STAR and PHENIX have been critical to this effort. A recent global analysis has, for the first ... More Presented by Mr. Adam GIBSON on 25 Aug 2014 at 5:30 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum Inclusive baryon production in the jet events from e+e- collision was studied at ¥Upsilon(4S) energy by ARGUS and CLEO collaborations. The production rates divided by spin multiplicity showed a clear dependence on the exponential of baryon masses. Among them, ¥Lambda(1116) and ¥Lambda(1520) seemed to have higher production rates. Some theorists suggested diquark correlation in ¥Lambda may ex ... More Presented by Dr. Masayuki NIIYAMA on 28 Aug 2014 at 4:30 PM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications Project 8 aims to determine the neutrino mass from the beta-decay of tritium (Q = 18.6 keV). Since the cyclotron frequency of a charged particle traveling in a homogeneous magnetic field is inversely proportional to its total energy, a measurement of this frequency provides accurate knowledge of the particle's total energy. This allows the reconstruction of the electron energy spectrum from a fr ... More Presented by Dr. Martin FERTL on 25 Aug 2014 at 4:30 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model The Compact Linear Collider (CLIC) is an attractive option for a future multi-TeV linear electron-positron collider. A staged construction in several centre-of-mass energy steps from a few hundred GeV up to 3 TeV is foreseen. At high energies, CLIC provides sensitivity to a wide range of phenomena beyond the Standard Model through direct observation of new particles and precision measurements. An ... More Presented by Lucie LINSSEN on 28 Aug 2014 at 5:30 PM Type: Talk Session: Flavour physics - CKM and beyond Track: 8) Flavour physics - CKM and beyond The rare decays K+ ->pi+ nu nu are excellent processes to make tests of new physics at the highest scale complementary to LHC thanks to their theoretically cleaness. The NA62 experiment at CERN SPS aims to collect of the order of 100 events in two years of data taking, keeping the background at the level of 10%. Part of the experimental apparatus has been commissioned during a technical run in 2 ... More Presented by Mr. Giuseppe RUGGIERO on 25 Aug 2014 at 4:30 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter Measurements of soft and hard particle production in proton-lead collisions at the LHC have provided surprising results. Studies of correlations in the production of soft particles have provided results that suggest strong collective behavior similar to that observed in lead-lead collisions. Measurements of jets and high-pT hadrons have shown an unexpected enhancement in the production of high-pT ... More Presented by Mr. Martin SPOUSTA on 28 Aug 2014 at 2:00 PM Presented by Prof. Albrecht WAGNER on 27 Aug 2014 at 7:00 PM Type: Talk Session: String theory Track: 11) String theory: ADS/QCD or more generally, ADS/QFT In this talk I will discuss 1+1-dimensional QCD with fermions in the adjoint representation. In the high density regime, the infrared physics of this theory is described by a constrained free fermion theory with an emergent N=(2,2) superconformal symmetry. I will discuss the partition function and the search for chiral primaries in this model. In view of the construction of a holographic dual, I w ... More Presented by Mr. Ingo KIRSCH on 28 Aug 2014 at 5:00 PM Type: Talk Session: Plenary Presented by Prof. Carsten GREINER on 25 Aug 2014 at 12:00 PM Type: Talk Session: Plenary Presented by Prof. Gagan MOHANTY on 27 Aug 2014 at 10:00 AM Type: Talk Session: Flavour physics - CKM and beyond Track: 8) Flavour physics - CKM and beyond Electroweak penguin b-hadron and c-hadron decays are very sensitive to physics beyond the Standard Model. Recent LHCb measurements have shown indications of large unexpected asymmetries in B→K*μμ, hints of lepton universality violation, and the first observation of the photon polarisation in b→sγ decays. We report the most recent LHCb results in this sector. Presented by Ms. Fatima SOOMRO, Ms. Fatima SOOMRO, Ms. Fatima SOOMRO on 28 Aug 2014 at 3:15 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter Over the last decade it has been established that a quark-gluon plasma (QGP) is formed in ultrarelativistic A+A collisions at RHIC energies. In recent years, detector upgrades have enabled the detailed study of this hot and dense matter. Although the RHIC d+Au program was originally undertaken to study initial state and cold nuclear matter effects, recent measurements at both RHIC (d+Au) and the ... More Presented by Dr. Baldo SAHLMUELLER on 28 Aug 2014 at 6:00 PM Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale The ATLAS collaboration has performed studies of a wide range of QCD phenomena, from soft particle to hard photon and jet production. Recent soft≠QCD measurements include studies of underlying event, vector meson production and quark confinement effects. Differential measurements of inclusive and multi≠jet production provide stringent tests of high≠order QCD predictions and provide ... More Presented by Mr. Zenis TIBOR on 28 Aug 2014 at 4:30 PM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications MINERvA (Main INjector ExpeRiment for v-A) is a few-GeV neutrino nucleus scattering experiment at Fermilab using various nuclei as targets. The experiment provides measurements of neutrino and anti-neutrino cross sections off of nuclear targets which are important for neutrino oscillation experiments and the probing of the nuclear medium. Presented are recent results from MINERvA on quasi-ela ... More Presented by Dr. Jonathan MILLER on 28 Aug 2014 at 4:30 PM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications The ANTARES neutrino telescope is located in the Mediterranean Sea at a water depth of about 2500m, roughly 40km south of the town of Toulon at the French coast. It is detecting neutrinos by measuring the Cherenkov light emitted by relativistic secondary particles generated in neutrino interactions. Its primary goal is the search for astrophysical neutrinos in the TeV/PeV range. The research progr ... More Presented by Dr. Robert LAHMANN on 28 Aug 2014 at 2:20 PM Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale ATLAS measurements of multi≠boson production processes involving combinations of W, Z and isolated photons are summarized. Production processes sensitive to vector≠boson fusion and vector≠boson scattering such as electroweak production of single vector boson associated with two forward jets and the di≠boson production at 8 TeV p≠p collisions are also presented and compared to S ... More Presented by Mr. Jochen MEYER on 28 Aug 2014 at 4:50 PM Type: Talk Session: Flavour physics - CKM and beyond Track: 8) Flavour physics - CKM and beyond Thanks to the excellent tracking and muon identification performance, combined with a flexible trigger system, the CMS experiment at the Large Hadron Collider is conducting a rich and competitive program of measurements in the field of heavy flavor physics. In this talk we review our most recent results on heavy flavour physics, based on a data sample collected by the CMS detector. Presented by Mr. Paolo RONCHESE on 28 Aug 2014 at 2:50 PM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications The T2K near detector complex, ND280, is located at the J-PARC accelerator facility in Tokai, Japan, 280 meters downstream from the target. This talk will summarize recent physics results from ND280. Presented by Mr. Jonathan PERKIN on 26 Aug 2014 at 3:10 PM Type: Talk Session: Nuclear and particle astrophysics Track: 5) Nuclear and particle astrophysics The Telescope Array Experiment (TA) is the northern hemisphere's largest detector of ultra-high-energy cosmic rays (UHECRs). Built to measure the UHECR chemical composition, arrival-direction anisotropy, and energy spectrum for E > 1 EeV, TA's instrumentation includes both an array of scintillator-based particle counters and three fluorescence detector stations overlooking the ground array. This t ... More Presented by Dr. Thomas STROMAN on 25 Aug 2014 at 2:20 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum In the last decade, transverse-momentum distributions (TMD) have been recognized as crucial ingredients for a complete understanding of the nucleon structure. They allow for a three-dimensional description of the nucleon (nucleon tomography) in momentum space and could provide insights into the yet unmeasured quark orbital angular momentum through correlations between the quark transverse momentu ... More Presented by Dr. Ami ROSTOMYAN on 25 Aug 2014 at 4:30 PM Type: Talk Session: Flavour physics - CKM and beyond Track: 8) Flavour physics - CKM and beyond CP violation and mixing in the charm meson system are expected to be very small in the standard model (SM), hence it can be a good probe to search for new physics beyond the SM. With large relative cross-section for charmed hadron production and clean event environment combined with high luminosity, the Belle experiment, with high statistics$e^+ e^-$collision data taken at the KEKB energy-asym ... More Presented by Mr. Changwoo JOO on 26 Aug 2014 at 2:00 PM Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale In this talk I will review recent experimental results on the measurement of top quark mass and their relation to open theoretical questions in the Standard Model and Beyond the Standard Model. I will also present some recent developments and proposals for top quark mass precision measurements that are motivated from the theory stand point for their robustness and their ease of interpretat ... More Presented by Mr. Roberto FRANCESCHINI on 25 Aug 2014 at 6:10 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter The comprehensive heavy-ion program launched recently at JINR (Dubna) is devoted to the study of the properties of strongly interacting matter, including a search for possible signals of deconfinement phase transition, chiral symmetry restoration and the QCD critical endpoint. The future accelerator facility NICA will supply ion species ranging from polarized proton to heavy ions with design lumi ... More Presented by Alexander ZINCHENKO on 25 Aug 2014 at 6:00 PM Type: Talk Session: Nuclear and particle astrophysics Track: 5) Nuclear and particle astrophysics Despite the efforts of numerous experiments with different components of extensive air showers (EAS) in the last decades, the uncertainty in the all nuclei spectrum of primary cosmic rays is still high and the results on chemical composition of primary cosmic rays from different experiments contradict each other. In this study an overview of the SPHERE experiment based on detection of the Vavilov- ... More Presented by Dr. T.A. DZHATDOEV on 26 Aug 2014 at 2:40 PM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications CUORE-0 is a cryogenic detector that uses an array of tellurium dioxide bolometers to search for neutrinoless double-beta decay of 130Te. CUORE-0 is located at the Laboratori Nazionali del Gran Sasso in Italy and has been taking data since March 2013. I will present the analysis of data collected since March 2013. Based on the measurements in the region of interest, the CUORE-0 half-life sensi ... More Presented by Dr. Kyungeun E. LIM on 25 Aug 2014 at 3:00 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter The primary goal of ALICE at the Large Hadron Collider (LHC) is to characterise the state of matter with partonic degrees of freedom, the Quark Gluon Plasma (QGP) produced in nucleus-nucleus collisions. Heavy-quarks are considered efficient probes of the properties of the QGP since they are produced on a short time scale with respect to that of the QGP. Therefore, they are expected to traverse ... More Presented by Dr. Grazia LUPARELLO on 25 Aug 2014 at 5:30 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter We study saturation e ffects in the production of forward dijets in proton-lead collisions at the LHC, using the framework of High Energy Factorization. Such con gurations, with both jets produced in the forward direction, probe the gluon density of the lead nucleus at small longitudinal momentum fraction, and also limit the phase space for emissions of additional jets. We find a signi cant suppr ... More Presented by Dr. Cyrille MARQUET on 26 Aug 2014 at 2:00 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model Searches at the LHC are complementary to direct detection experiments. Very low masses and several DM properties can only be studied at the LHC. In this very recent fi eld at accelerators, several analyses were developed and performed with 2012 data. Final states with Monojet, monophoton, and monolepton are all considered, as well as dark matter particles that are produced in association with ... More Presented by kerstin HOEPFNER on 28 Aug 2014 at 4:30 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model After a Higgs boson with a mass near 125 GeV has been discovered, it is still unclear whether this is the Higgs boson predicted by the Standard Model (SM) or part of a di fferent, possibly extended Higgs sector. Various models with extended Higgs sectors are being considered, such as the minimal and next-to-minimal supersymmetric extensions (MSSM and NMSSM) of the SM. Recent results of search ... More Presented by Mr. Matthias SCHRÖDER on 26 Aug 2014 at 2:40 PM Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale After the discovery of a Higgs boson, the direct observation of the coupling of this particle to top quarks is of particular importance. In this talk, a review of ATLAS results on the search for the Higgs boson produced in association with top quarks, and on the search for flavour-changing neutral currents in top quark decays t -> qH (q = c,u) will be presented. Presented by Mr. Stefan GUINDON on 25 Aug 2014 at 5:30 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter In ultrarelativistic heavy-ion collisions with high particle multiplicities, a produced muon can be bound to a charged hadron (proton, antiproton,$K^{+}$,$K^{-}$,$\pi^{+}$,$\pi^{-}$) by Coulomb force and form a hydrogen-like atom. Among these atoms, the antimatter muonic hydrogen and the$K-\mu$atom have been predicted but not yet been discovered. At the STAR experiment, muon identification a ... More Presented by Mr. Kefeng XIN on 28 Aug 2014 at 5:40 PM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications Several observed anomalies in the neutrino sector could be explained by a fourth (sterile) neutrino with a squared mass difference in the order of 1eV² to the other three standard neutrinos. This hypothesis can be tested with an artificial MCi neutrino (Cr-51) or a kCi antineutrino (Ce-144/Pr-144) source deployed near or inside a large low background detector like Borexino. The SOX project (Short ... More Presented by Mr. Mikko MEYER on 25 Aug 2014 at 5:20 PM Type: Poster Track: 7) Energy frontier physics beyond the standard model A search for Supersymmetry in opposite-sign same-flavour lepton pairs is presented. This final state, in addition with requirements on the number of jets and missing transverse energy, allows for a large reduction as well as a precise estimation of Standard Model backgrounds. In the cascade decays of new heavy particles, correlated production of leptons can lead to distinctive "edges" in the dilep ... More Presented by Mr. Jan-Frederik SCHULTE Type: Talk Session: Tests of symmetries and conservation laws Track: 9) Tests of symmetries and conservation laws Time-reversal invariance will be tested in proton-deuteron scattering via an internal target transmission experiment at COSY[1].The polarization asymmetry Ay,xz will be measured using a polarized proton beam (polarization Py) and polarized deuterium target (tensor polarization Pxz). For P-parity conserving interactions this observable provides a real null test of time-reversal invariance which is ... More Presented by Prof. yury UZIKOV on 25 Aug 2014 at 3:20 PM Type: Poster Track: 6) Standard model physics at the TeV scale A search for a standard model-like Higgs dimuon boson decay is presented based on proton-proton collision data at the centre-of-mass energies of 7 and 8 TeV. The data samples, recorded by the CMS experiment at the LHC, correspond to integrated luminosities of 5.0 +/- 0.1 1/fb at 7 TeV and 19.7 +/- 0.5 1/fb at 8 TeV. To enhance the sensitivity of the search, events are categorised by topolog ... More Presented by Dr. Adrian PERIEANU Type: Talk Session: Plenary Presented by Prof. Kenichi HATAKEYAMA on 26 Aug 2014 at 11:30 AM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model In this talk, the latest results from CMS on searches for supersymmetry produced through electroweak production channels are presented using 20 fb-1 of data from the 8 TeV LHC run. A variety of complementary final state signatures and methods are used, such as searches with Higgs, W, and Z bosons in the fi nal state, to probe gaugino and slepton production. Presented by Mr. Mario MASCIOVECCHIO on 25 Aug 2014 at 3:20 PM Type: Talk Session: Flavour physics - CKM and beyond Track: 8) Flavour physics - CKM and beyond One of the most intriguing puzzles in hadron spectroscopy are the numerous charmonium-like states observed in the last decade, including charged states that are manifestly exotic. Over the years BaBar has extensively studied these states in B meson decays, initial state radiation processes and two photon reactions. We report new and additional studies on some of these states performed using ... More Presented by Elisabetta PRENCIPE on 28 Aug 2014 at 5:20 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model At the LHC, the production of heavy resonances decaying into a pair of particles can be probed at unprecedented centre-of-mass energies. Two-particle resonances are predicted in a variety of BSM models and can be searched for in a largely model-independent fashion. Results from searches for resonances in fi nal states with leptons, jets and photons based on the full dataset of 20 fb-1 taken by ... More Presented by Mr. Andreas GUTH on 28 Aug 2014 at 2:00 PM Type: Poster Track: 12) New concepts and techniques for accelerators and particle detectors Millicharged particles, i.e. particles with charges much smaller than that of an electron, have been predicted by extensions to the Standard Model containing additional weakly-coupled gauge sectors, such as hidden sector dark matter models. If such particles were thermally produced in the early universe, they could have formed stable bound states with atoms and exist in measurable concentrations i ... More Presented by David MOORE Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications The question of the existence of sterile states for neutrinos is addressed since many years. If they exist such states would not be directly detected but could mix with the three ordinary states and would be “seen” as new oscillations in the propagation of the neutrinos. Recently this question arose by the observation of a small deficit of anti-neutrinos with respect to predictions by previous ... More Presented by Dr. Alain LETOURNEAU on 25 Aug 2014 at 5:40 PM Type: Poster Track: 7) Energy frontier physics beyond the standard model A search for beyond the standard model physics with at least one photon, missing transverse energy and jets is presented. The data sample corresponds to an integrated luminosity of 19.7/fb of pp collisions at sqrt(s) = 8 TeV, recorded by the CMS experiment at the LHC. The missing transverse energy distribution in events containing at least one photon and at least two hadronic jets is compared to ... More Presented by Mr. Maximilian Knut KIESEL Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale A search for Higgs bosons has been carried out in the Higgs to two photons decay channel with the CMS detector at the LHC collider. The analysis is based on pp collision data collected in 2011-2012 at centre-of-mass energies of 7 and 8 TeV corresponding to integrated luminosities of 5/fb and 20/fb, respectively. The analysis strategy and measurements of the mass, couplings, and spin-parity are re ... More Presented by Martina MALBERTI on 25 Aug 2014 at 5:10 PM Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale Since the discovery of the Higgs boson by the ATLAS and CMS experiments at the LHC, the emphasis has shifted towards measurements of its properties. Of particular importance is the direct observation of the coupling of the Higgs boson to fermions. In this presentation a comprehensive review of ATLAS results in the search for the Higgs boson in tau, muon, and b-quark pairs will be given. Presented by Mr. Michel TROTTIER-MCDONALD on 25 Aug 2014 at 4:30 PM Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter The investigation of antikaon(Kbar) nuclear bound states is one of the hottest topics in strangeness nuclear physics since observations of such states give quite unique information on the sub-threshold KbarN interaction[1]. However, the existence of Kbar nuclear-states has not been established so far, even for the simplest system, K ̄pp[2]. Our approach is to search for the K ̄pp bound state ... More Presented by Dr. Tadashi HASHIMOTO on 25 Aug 2014 at 3:15 PM Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale A search for the Standard Model (SM) Higgs boson decaying to bottom quarks pairs is presented. Two production channels have been analyzed: vector-boson fusion and associated production with a vector boson decaying to leptons. The search is performed on data collected with the CMS detector at LHC during 2011 and 2012, at center-of-mass energies of 7 and 8 TeV, corresponding to integrated lumin ... More Presented by Mr. Silvio DONATO on 25 Aug 2014 at 2:40 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model Different approaches to finding evidence for dark matter at the LHC are presented. These include searches for events with large missing transverse momentum and a single jet, photon or W/Z boson. Searches for hidden sectors in events with long-lived particles resulting in displaced hadronic vertices or lepton-jet signatures are also reported. Finally, studies sensitive to the presence of ... More Presented by Mr. Christophe CLEMENT on 28 Aug 2014 at 4:50 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model Naturalness arguments for weak-scale supersymmetry favour supersymmetric partners of the third generation quarks with masses not too far from those of their Standard Model counterparts. Top or bottom squarks with masses less than a few hundred GeV can also give rise to direct pair production rates at the LHC that can be observed in the data sample recorded by the ATLAS detector. The talk ... More Presented by Mr. Giulio USAI on 25 Aug 2014 at 2:00 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model This talk presents the latest ATLAS results in the context of electroweak production of SUSY particle, R-Parity violating SUSY scenarios, and scenarios with long-lived SUSY particles. The results presented use the full 20/fb of sqrt(s) = 8 TeV p-p collisions collected by the ATLAS experiment in 2012. The prompt searches consider final states including leptons, jets (including b-jets) and missing e ... More Presented by Mr. Maximilian GOBLIRSCH-KOLB on 28 Aug 2014 at 3:00 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model Events containing several leptons are useful probes of new phenomena due to the low background from Standard Model processes. We look for anomalous production of prompt like-sign leptons or events with three or more leptons, as well as search for excited leptons, heavy leptons and heavy neutrinos. The searches use the data recorded in 2012 at sqrt(s)=8 TeV centre-of-mass energy by the AT ... More Presented by Mr. Rozmin DAYA on 28 Aug 2014 at 2:20 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model A search for Higgs boson invisible decay modes has been carried out in events where the Higgs boson is produced in association with a Z boson or through Vector Boson Fusion. In the associated production search, electron, muon, and b-quark pair decay modes of the Z boson are considered. The analyses are based on proton-proton collision data collected with the CMS detector at the LHC collider at cen ... More Presented by Mr. Patrick James DUNNE on 26 Aug 2014 at 3:00 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model Searches for events containing two Higgs bosons are presented using several decay channels of the h(126) boson. The analyses use pp collision data recorded at centre-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5 fb-1 and 20 fb-1, respectively. Extended Higgs sector scenarios predict the resonant decay of new particles into a pair of h(126) bosons. These resonan ... More Presented by Mr. Souvik DAS on 26 Aug 2014 at 2:00 PM Type: Talk Session: Tests of symmetries and conservation laws Track: 9) Tests of symmetries and conservation laws The existence of a permanent electric dipole moment (EDM) in any non-degenerate system would affirm the presence of Time and (Charge Conjugation-)Parity Violation in fundamental interactions. The discovery of a non-zero EDM in next-generation experiments may point to an explanation of the numerical size of the baryon asymmetry of the Universe. Worldwide multiple ongoing efforts are trying to ... More Presented by Mr. Wolfgang KORSCH on 28 Aug 2014 at 5:20 PM Type: Talk Session: Beyond Standard Model Track: 7) Energy frontier physics beyond the standard model Various extensions of the Standard Model predict the existence of new types of quarks. We report on several search channels such as vector-like quarks decaying to a Higgs boson and a top quark or to a W boson and a b quark. The talk presents results from searches for new resonances decaying to a top-antitop pair and a top-antibottom pair, including the use of boosted top quark reconstructi ... More Presented by Mr. David CALVET on 28 Aug 2014 at 2:40 PM Type: Talk Session: Dark matter and cosmology Track: 4) Dark matter and cosmology The existence of a photon-like massive particle, the gamma' or dark photon, is postulated in several extensions of the Standard Model. Such a particle could indeed help to understand the puzzling behavior of the observed cosmic positron fraction as well as to solve the sofar unexplained deviation between the measured and calculated values of the muon g−2 anomaly. The dark photon, unlike its c ... More Presented by Dr. Romain HOLZMANN on 25 Aug 2014 at 2:50 PM Type: Talk Session: Dark matter and cosmology Track: 4) Dark matter and cosmology First postulated more than 80 years ago to address the 'missing mass' of the Milky Way galaxy Dark Matter remains as one of the best motivations for Physics Beyond the Standard Model. The Large Underground Xenon (LUX) experiment is a 350kg liquid xenon time projection chamber designed to directly detect galactic dark matter. Currently deployed 1 mile underground in the Sanford Underground Research ... More Presented by Dr. James DOBSON on 25 Aug 2014 at 2:25 PM Type: Talk Session: Standard model physics at the TeV scale Track: 6) Standard model physics at the TeV scale Measurements of the single top quark production cross sections in proton-proton collisions with the ATLAS and CMS detectors at the Large Hadron Collider are presented. Measurements of single top-quark production in the t- and Wt-channels are shown and determination of the CKM matrix element |Vtb| is discussed. We also discuss the separate measurement of the top and anti-top quark and the ... More Presented by Mr. James MUELLER on 25 Aug 2014 at 3:40 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum Its forward acceptance puts the LHCb in a unique position at the LHC to measure soft QCD phenomena at large rapidities and low transverse momenta. Recent results on charged particle multiplicity production, energy flow, and inclusive cross-sections are presented. Presented by Mr. Alexandru GRECU on 28 Aug 2014 at 6:10 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter Measurements of low-pT (< 5 GeV) particle production have provided valuable insight on the production and evolution of the quark-gluon plasma in Pb+Pb collisions at the LHC. In particular, measurements of elliptic and higher order collective flow imprinted on the azimuthal angle distributions of low-pT particles directly probe the strongly-coupled dynamics of the quark gluon plasma and test h ... More Presented by Mr. Krzysztof WOZNIAK on 28 Aug 2014 at 4:30 PM Type: Talk Session: Tests of symmetries and conservation laws Track: 9) Tests of symmetries and conservation laws The ASACUSA CUSP collaboration at the Antiproton Decelerator of CERN has recently succeeded in detecting 80 antihydrogen atoms 2.7 meters away from their production trap in a magnetic field free region [1]. This successful detection constitutes a milestone toward precision spectroscopy of antimatter atoms in a beam. The goal of the ASACUSA CUSP collaboration is indeed to measure the ground- state ... More Presented by Dr. Chloé MALBRUNOT on 25 Aug 2014 at 4:50 PM Type: Poster Track: 3) Neutrinos and related astrophysical implications The method of quasi-optimal weights is applied to constructing (quasi-)optimal criteria for various anomalous contributions in experimental spectra [1, 2]. Anomalies in the spectra could indicate physics beyond the Standard model (additional interactions and neutrino flavours, Lorenz violation etc.). In particular the cumulative tritium beta-decay spectrum (for instance, in Troitsk-nu-mass, Mainz ... More Presented by Mr. Aleksei LOKHOV Type: Talk Session: Flavour physics - CKM and beyond Track: 8) Flavour physics - CKM and beyond The anomalous magnetic dipole moment of the muon can be both measured and computed to very high precision, making it a powerful probe to test the standard model and search for new physics such as SUSY. The previous measurement by the Brookhaven E821 experiment found a 3.6 standard deviation discrepancy from the predicted value. The new g-2 experiment at Fermilab will improve the precision by a fac ... More Presented by Prof. Kawall DAVID on 25 Aug 2014 at 5:45 PM Type: Talk Session: Neutrinos and related astrophysical implications Track: 3) Neutrinos and related astrophysical implications Neutrino properties, and in particular the open question regarding the scale of neutrino rest masses, bear fundamental relevance to many current research topics in cosmology, theoretical particle physics, and astroparticle physics. Due to the smallness of neutrino masses, the determination of their absolute scale is a challenging experimental task. Precision measurements of the kinematics of weak ... More Presented by Dr. Kathrin VALERIUS on 25 Aug 2014 at 5:00 PM Type: Talk Session: Quarks and gluons in hot and dense matter Track: 1) Quarks and gluons in hot and dense matter Fluctuations of conserved charges, i.e. baryon number, strangeness and electric charge, are sensitive probes for the transition from the confined hadronic to the deconfined partonic phase of strong interaction matter. Rapid changes of, e.g. quadratic fluctuations of net baryon number, net strangeness as well as correlations between these conserved charges, signal the change of degrees of fre ... More Presented by Frithjof KARSCH on 25 Aug 2014 at 2:00 PM Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter The low-energy QCD in the strangeness sector is still lacking fundamental experimental results in order to achieve a breakthrough in its understanding. Among these experimental results, the low-energy kaon-nucleon/nuclei interaction studies are playing a key-role. Combining the excellent quality kaon beam delivered by the DAFNE collider with new experimental techniques, as fast and very precise X ... More Presented by catalina CIRCEANU on 25 Aug 2014 at 2:00 PM Type: Talk Session: Quarks and gluons in hadrons, the hadron spectrum Track: 2) Quarks and gluons in hadrons, the hadron spectrum COMPASS is a fixed-target experiment at the CERN SPS aimed to study the structure and dynamics of hadrons. Data with negative (mostly$\pi^-$) hadron beams of$190\,\text{GeV}/c$has been taken to study in particular light mesons. Their spectrum is investigated in diffractive dissociation reactions with final-states containing$\pi$and$\eta$. At four-momentum transfers to the target between$0.1 ... More
Presented by Mr. Sebastian UHL on 28 Aug 2014 at 2:00 PM
Type: Talk Session: Flavour physics - CKM and beyond
Track: 8) Flavour physics - CKM and beyond
B meson decays provide various tests in the quark flavor structure of the standard model (SM) of particle physics, e.g. in the CP violation and the CKM quark-mixing structure. With high statistics $B\bar{B}$ event sample collected at the KEKB $e^+ e^-$ energy-asymmetic collider using the Belle detector, Belle has obtained numerous results in the B meson system. In this presentation, we report ... More
Presented by Mr. Bastian KRONENBITTER on 28 Aug 2014 at 2:25 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
For the connection of front-end read-out chips to a silicon sensor of a hybrid pixel detector an in-house flip-chip bump bonding process using precision tin-silver solder balls has been developed at DESY. The electrical testing of the bump connections follows immediately using an automated probe station by sensing a capacitively induced charge. The bump bonding quality and results from thermal str ... More
Presented by Dr. Somnath CHOUDHURY on 26 Aug 2014 at 3:15 PM
PANDA (anti-Proton ANnihilations at DArmstadt) is a next generation hadron physics experiment to be operated at the future Facility for Antiproton and Ion Research (FAIR) at Darmstadt, Germany. It will use intense cooled antiproton beams with a momentum between 1.5 GeV/c and 15 GeV/c. The PANDA detector is a state-of-the-art internal target detector allowing the detection and identification of ne ... More
Presented by Dr. Vasily MOCHALOV on 28 Aug 2014 at 5:50 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
Jet vetoes play a crucial role in the precise measurement of the Higgs properties at the LHC. The vetoes on additional jets introduce sensitivity to soft and collinear radiation and induce logarithms of the jet-veto variable that need to be resummed. In this talk, we consider Higgs production via gluon fusion with a veto on jet beam thrust, Tau_jet, which is a jet-based variable that can be used ... More
Presented by Ms. Shireen GANGAL on 26 Aug 2014 at 2:40 PM
The Okubo-Zweig-Iizuka (OZI) rule states that processes with disconnected quark lines are suppressed. The production of phi mesons from non-strange hadrons is predicted to be suppressed w.r.t. omega by a factor 4.2•10^-3. Violations are often interpreted as gluonic intermediate states or as evidence for hidden strangeness in the nucleon. The reaction pp->pVp (V= omega, phi) has been studied with ... More
Presented by Dr. Karin SCHOENNING on 28 Aug 2014 at 2:20 PM
Type: Talk Session: Plenary
Presented by Prof. Achim DENIG on 26 Aug 2014 at 11:00 AM
The E-906/SeaQuest experiment at Fermilab continues a series of Drell-Yan measurements to explore the antiquark structure of the nucleon and nuclei. To extend existing measurements to larger values of Bjorken-x, a 120 GeV proton beam extracted from Fermilab’s main injector is used, resulting in a factor of 50 more luminosity than previous experiments and enabling access to values of x up to 0.9. ... More
Presented by Dr. Markus DIEFENTHALER on 25 Aug 2014 at 3:40 PM
Type: Talk Session: Dark matter and cosmology
Track: 4) Dark matter and cosmology
EDELWEISS is a direct Dark Matter search program looking for WIMPs in the GeV-TeV mass range. For that purpose, an array of cryogenic Ge mono-crystals read out simultaneously by NTD thermal sensors and by surface electrodes is installed in the Modane underground laboratory. We present a summary of EDELWEISS-II results including limits on axion couplings. For EDELWEISS-III a major upgrade of the se ... More
Presented by Mr. Lukas HEHN on 25 Aug 2014 at 2:00 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
Antihydrogen is the simplest atom made entirely of antimatter, consisting of an antiproton and a positron. The study of its matter counterpart, the hydrogen atom, has produced some of the most precise determinations of physical quantities. High precise measurements of antihydrogen will allow to achieve direct tests of the fundamental symmetries of Nature through the comparison with hydrogen. The A ... More
Presented by Mr. Luca VENTURELLI on 25 Aug 2014 at 4:30 PM
An important component of the physics program at COMPASS (Common Muon Proton Apparatus for Structure and Spectroscopy) is the study of the nucleon structure through generalized parton distributions (GPDs). The GPDs correlate the momentum distributions of the quarks inside the nucleon with a transverse spatial distribution, hence providing a three dimensional imaging of the nucleon. Experimentally, ... More
Presented by Dr. Eric FUCHEY on 26 Aug 2014 at 2:40 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
One of the key topics in the physics program of the ILC is the precision measurement of the couplings of the Higgs boson. The two main production modes, ZH production and W boson fusion, provide access to all major Higgs boson decay modes with relatively small backgrounds. The ZH process provides the possibility for a model-independent tagging of Higgs production, allowing measurement of absolute ... More
Presented by Felix SEFKOW on 28 Aug 2014 at 3:00 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
NEXT (an acronym for Neutrinoless Experiment with a Xenon TPC) will search for the neutrinoless double beta decay of 136Xe using a radiopure high-pressure xenon gas TPC filled with 100 kg of Xe enriched in its 136Xe isotope. A measurement of this hypothetical process would provide direct information on neutrino masses at the same time that would lead to a better understanding of many aspects of th ... More
Presented by Mr. David LORCA GALINDO on 25 Aug 2014 at 3:40 PM
Type: Talk Session: Nuclear and particle astrophysics
Track: 5) Nuclear and particle astrophysics
The NUCLEON apparatus is a low orbit space ray detector positioned on the Resurs-P satellite. The main detector for measuring space ray energy is the kinematic lightweight energy meter (KLEM). The KLEM method is a development of the kinematic calorimeter method proposed by Castagnoli in 1953. The main principle of a basic kinematic calorimeter is to measure primary particle’s energy by measuring ... More
Presented by Mr. Igor KOVALEV on 25 Aug 2014 at 3:00 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The LHCb experiment is a spectrometer dedicated to the study of heavy flavour at the LHC. The current LHCb trigger system consists of a hardware level, which reduces the LHC inelastic collision rate of 13MHz to 1 MHz, at which the entire detector is read out. In a second level, implemented in a farm of 20k parallel-processing CPUs, the event rate is reduced to about 5 kHz. We review the performan ... More
Presented by Mr. Christian LINN on 26 Aug 2014 at 2:25 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
Liquid argon time projection chambers (LArTPC), due to their fine-grained tracking and calorimetric capabilities, provide an unprecedented amount of detail to study neutrino interactions in argon and are quickly becoming the desirable technology choice for future neutrino experiments. Various efforts are ongoing at Fermi National Accelerator Laboratory (Fermilab) to develop this intriguing technol ... More
Presented by Mr. Jonathan ASAADI on 28 Aug 2014 at 4:50 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
The Mu2e Experiment at Fermilab will search for coherent, neutrino-less conversion of muons into electrons in the field of a nucleus with a sensitivity improvement of a factor of 10,000 over existing limits. Such a lepton flavor-violating reaction probes new physics at a scale inaccessible with direct searches at either present or planned high energy colliders. The experiment both compleme ... More
Presented by Mr. Giovanni TASSIELLI on 28 Aug 2014 at 3:40 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
The NOvA experiment is a long base-line accelerator based neutrino oscillation experiment. It uses the upgraded NuMI beam from Fermilab and measures electron neutrino appearance and muon neutrino disappearance at its far detector in Ash River, Minnesota. Goals of the experiment include measurements of theta13, mass hierarchy and the CP violating phase. NOvA has begun to take neutrino data and firs ... More
Presented by Mr. Filip JEDINY on 28 Aug 2014 at 3:00 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
The long-baseline neutrino oscillation experiment OPERA has been designed for the direct observation of tau neutrino appearance in the CNGS muon neutrino beam. The OPERA detector is located at the LNGS underground laboratory, with a distance of 730 km from the neutrino source at CERN. It is built of about 150000 emulsion cloud chamber modules (ECC 'bricks'), providing the micrometric resolution r ... More
Presented by Mrs. Annika HOLLNAGEL on 26 Aug 2014 at 2:00 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
This talk introduces the progress of JUNO (Jiangmen Underground Neutrino Observatory) liquid scintillator(LS) research. JUNO will need 20kt LS, and energy resolution of detector reach to 3%/E. So it needs longer attenuation length and higher light yield LS. The method and results of LS purification and the LS performance measurement are reported.
Presented by Prof. Li ZHOU on 28 Aug 2014 at 3:36 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Presently the study of the phase diagram of QCD is the subject of both theoretical and experimental studies under extreme conditions of density and temperature. In particular, it is expected that the phenomenon of deconfinement occurs in relativistic heavy-ion collisions and in the interior of compact stars, two very different scenarios when isospin asymmetry is considered. While in heavy ion col ... More
Presented by Pedro COSTA on 25 Aug 2014 at 2:30 PM
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
The Qweak experiment, which completed a two-year data taking phase in May 2012 at Jefferson Lab, has made the first determination of the weak charge of the proton. We access the weak charge by measuring the parity-violating asymmetry in the elastic scattering of polarized electrons from protons at a small squared four-momentum transfer of Q^2 = 0.025 (GeV/c)^2. Due to the interference of the photo ... More
Presented by Prof. Paul KING on 28 Aug 2014 at 2:30 PM
Type: Talk Session: Hadrons in medium - hyperons and mesons in nuclear matter
Track: 10) Hadrons in medium - hyperons and mesons in nuclear matter
The understanding of p+p reactions is fundamental for the interpretation of p+A and also heavy-ion collisions, in which in-medium modifications of hadrons are expected with increasing nuclear matter density. Such modifications can be investigated by comparisons of experimental data to transport models [1,2,3]. Hence, the models should be able to reproduce elementary reactions at the first place. I ... More
Presented by Mrs. Jia-Chii BERGER-CHEN on 25 Aug 2014 at 4:30 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The heavy quark hadrons are suggested as a clean probe for studying the early dynamic evolution of the dense and hot medium created in high-energy nuclear collisions. The Heavy Flavor Tracker (HFT) of the STAR experiment, designed to improve the vertex resolution and extend the measurement capabilities in the heavy flavor domain, was installed for the 2014 heavy ion run of RHIC. It is composed of ... More
Presented by Mr. Joachim SCHAMBACH on 26 Aug 2014 at 2:50 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
At the quantum level, an interaction of a neutrino with a graviton may trigger the collapse of the neutrino flavor eigenstate to a neutrino mass eigenstate. I will present that such an essentially quantum gravity effect may have strong consequences for neutrino oscillation phenomena in astrophysics due to the relatively large scattering cross section of relativistic neutrinos off massive ... More
Presented by Mr. Jonathan MILLER on 28 Aug 2014 at 2:00 PM
Type: Talk Session: Nuclear and particle astrophysics
Track: 5) Nuclear and particle astrophysics
The Pierre Auger Observatory is the world's largest cosmic ray observatory. The observatory combines two complementary detection techniques to study the extensive particle showers created by collisions of primary cosmic rays with the atmosphere. Analysis of those showers enables one not only to estimate the energy, direction and most probable mass of the primary cosmic particles, but also to o ... More
Presented by Dr. João DE MELLO NETO on 26 Aug 2014 at 2:00 PM
We obtain a model independent expression for the muonic hydrogen Lamb shift. The hadronic effects are controlled by the chiral theory, which allows for their model independent determination. We give their complete expression including the pion and Delta particles. Out of this analysis and the experimental measurement of the muonic hydrogen Lamb shift we determine the electromagnetic proton radi ... More
Presented by Mr. Pineda ANTONIO on 28 Aug 2014 at 5:10 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
The nEXO Collaboration is designing a very large detector for neutrino-less double beta decay of Xe-136. The nEXO detector is rooted in the the currently-running EXO-200 program, which has reached a sensitivity for the half life of the decay of 1.9 x 10^25 years with and exposure of 99.8 kg-yr. The baseline nEXO design uses 5 tonnes of liquid xenon, enriched in the mass 136 isotope, in a time p ... More
Presented by Dr. Dave MOORE on 25 Aug 2014 at 2:20 PM
Type: Talk Session: Neutrinos and related astrophysical implications
Track: 3) Neutrinos and related astrophysical implications
An observation of neutrinoless double-beta decay ($0\nu\beta\beta$) identifies the neutrino as a Majorana particle and constrains the absolute mass scale of neutrinos. The {\sc Majorana} collaboration is constructing an array of high purity germanium detectors that are isotopically enriched in $^{76}$Ge that will serve as both a source and detector of $0\nu\beta\beta$. In the presence of backgroun ... More
Presented by Mr. Christopher O'SHAUGHNESSY on 25 Aug 2014 at 3:20 PM
Type: Talk Session: Plenary
Presented by Christophe GROJEAN on 25 Aug 2014 at 9:45 AM
We present our studies of the Timelike Compton Scattering (TCS) process off the nucleon (gamma N -> N gamma* -> e+e-). At sufficiently large virtuality of the nal state photon, this reaction provides access, via a QCD factorization theorem, to the Generalized Partons Distributions (GPDs) of the nucleon. GPDs contain, in particular, informations about the correlations between the longitudin ... More
Presented by Mrs. Marie BOER on 26 Aug 2014 at 3:40 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
The future precision studies of the Standard Model require excellent knowledge of the top quark mass, to an accuracy of 100 MeV or better. A threshold scan in e+e- annihilation enables a precise measurement in theoretically well-defined mass schemes. The measurement requires a combination of precise QCD calculations, excellent detection efficiency and recognition of top quark events, and excellent ... More
Presented by Dr. Frank SIMON on 28 Aug 2014 at 3:20 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
Measurements of the top quark production cross sections in proton-proton collisions with the ATLAS detector at the Large Hadron Collider are presented. The measurement require no, one or two electrons or muons in the final state (single lepton, dilepton, hadronic channel). In addition, the decay modes with tau leptons are tested (channels with tau leptons). The main focus are measurement ... More
Presented by Spyridon ARGYROPOULOS on 26 Aug 2014 at 2:00 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
Recent results on top quark properties and interactions are presented, obtained using data collected with the CMS experiment during the years 2011 and 2012 at 7 TeV and 8 TeV center-of-mass energy. Measurements are performed for the inclusive and differential top quark pair production cross sections in several top quark final states. The mass of the top quark is extracted using several methods, in ... More
Presented by Dr. Jeremy ANDREA on 26 Aug 2014 at 2:20 PM
In the past decade, the data from transverse spin p+p from the Relativistic Heavy Ion Collider at Brookhaven National Laboratory and polarized DIS experiments have enabled enormous progress in our understanding of the transverse spin dynamics in the proton. PHENIX Collaboration has carried out a very active program of transverse spin measurements, including transverse spin asymmetries (TSSAs) in t ... More
Presented by Dr. Ming LIU on 25 Aug 2014 at 2:00 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
The transverse momentum distributions (pT) of charged particles and identi ed hadrons in p-Pb collisions at sqrt(sNN) = 5.02 TeV have been measured by ALICE at the LHC. Charged-particle tracks are reconstructed at mid-rapidity over a large momentum range 0.15 < pT < 50 GeV/c. Light-flavoured hadrons and resonances are identi ed in the various momentum ranges from 0.15 GeV/c up to 15 GeV/c by u ... More
Presented by Jacek OTWINOWSKI on 28 Aug 2014 at 5:00 PM
The Sivers function $f^{\perp}_{1T}$ describes the correlation of parton transverse momentum with the transverse spin of the nucleon. There is evidence of a quark Sivers effect in semi-inclusive DIS (SIDIS) measurements. In SIDIS, the quark Sivers function is associated with a final state effect from the gluon exchange between the struck quark and the target nucleon remnants. On the other hand, ... More
Presented by Dr. Salvatore FAZIO on 25 Aug 2014 at 2:40 PM
COMPASS is a fixed target experiment at the CERN SPS M2 beam line, taking data since year 2002. Part of its physics programme is dedicated to study the transverse spin and the transverse momentum structure of the nucleon using semi- inclusive deeply inelastic lepton scattering (SIDIS). For these measurements, data have been collected using transversely polarised proton (NH3) and deuteron (6LiD) ta ... More
Presented by Mr. Nour MAKKE on 25 Aug 2014 at 4:50 PM
Type: Poster
The dependence of the spectra shape of produced charged hadrons on the size of a colliding system is discussed using a two component model. As a result, the hierarchy by the system-size in the spectra shape is observed. Next, the extension of the two component model accounting for the 'collective flow' using recent theoretical calculations is suggested to describe the spectra of charged particles ... More
Type: Poster Track: 12) New concepts and techniques for accelerators and particle detectors
Ultra-slow muons, which are positively charged muons having an energy of a few eV, are useful tools for producing variable-energy muon beams with extraordinarily small energy spread by accelerating them through an electrostatic field. We will apply this new technique to a measurement of the muon anomalous magnetic moment g-2 and electric dipole moment at J-PARC [1], which requires an intense muon ... More
Type: Talk Session: Tests of symmetries and conservation laws
Track: 9) Tests of symmetries and conservation laws
The Ultracold Neutron Facility at the Los Alamos Neutron Science Center has developed one of the highest density sources of UCN in the world to perform precision measurements of neutron decay observables. The UCNA collaboration has recently published a sub-percent measurement of the beta-asymmetry, A0 = -0.11954 ± 55(stat) ± 98(sys), used to extract λ = gA/gV = -1.2756 ± 30, the ratio of the a ... More
Presented by Mrs. Leah BROUSSARD on 25 Aug 2014 at 2:30 PM
Type: Poster Track: 6) Standard model physics at the TeV scale
The $U_L(2)\bigotimes U_R(2)$ gauge model for the unified theory of the electromagnetic and weak interactions which is free from the auxiliary self-interaction scalar field is developed. Due to breaking the initial symmetry, the $SU_L(2)\bigotimes U_R(1)$ Lagrangian is derived\cite{1}. The obtained $SU_L(2)\bigotimes U_R(1)$ Lagrangian contains all the terms corresponding to the free b ... More
Presented by Prof. Andrew KOSHELKIN
OLYMPUS, an experiment designed to quantify the contribution of two-photon exchange to the proton form factor discrepancy, completed data taking in early 2013. About 4 fb-1 of data were collected, running with a 2.01 GeV stored lepton beam of alternating charge impinging on an internal hydrogen gas target. The analysis e ffort has progressed signi cantly with data spanning an accepted kinematic ra ... More
Presented by Prof. Norair AKOPOV on 28 Aug 2014 at 4:30 PM
Type: Talk Session: New concepts and techniques for accelerators and particle detectors
Track: 12) New concepts and techniques for accelerators and particle detectors
The Tile Calorimeter (TileCal) is the central hadronic calorimeter of the ATLAS experiment at LHC. Around 2023, after the upgrade of the LHC (High Luminosity LHC, phase 2) the peak luminosity will increase by a factor of 5 compared to the design value (10^34 cm^-2 s^-1), thus requiring an upgrade of the TileCal readout electronics. Except the 9852 photomultipliers (PMTs), most of the on- and off-d ... More
Presented by Mr. Gabriel POPENECIU on 26 Aug 2014 at 2:00 PM
Type: Talk Session: Quarks and gluons in hot and dense matter
Track: 1) Quarks and gluons in hot and dense matter
Due to color screening, the production of quarkonia in high energy heavy ion collisions is expected to be sensitive to the energy density of the medium. Sequential suppression of different quarkonium states may therefore serve as a thermometer of the medium. Although the suppression of charmonia was anticipated as a key signature of the QGP, the observed energy dependence of $J/\psi$ suppression i ... More
Presented by Robert VERTESI on 25 Aug 2014 at 5:00 PM
Type: Talk Session: Standard model physics at the TeV scale
Track: 6) Standard model physics at the TeV scale
Vector Boson + Jets production measurements are tests of perturbative QCD calculations and PDFs. Hence these measurements provide us chances to veri fied MC generators and the background modeling techniques of many searches. We will present measurements of the vector boson + jet production in pp collisions at sqrt(s) = 7 TeV and 8 TeV, using the data collected with the CMS detector. The resul ... More
Presented by Yun-Ju LU on 28 Aug 2014 at 2:40 PM
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2018-11-19 04:43:01
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https://dougo.info/how-to-retire-early-what-to-do-after-retirement.html
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If you are unfortunate enough to find yourself no longer able to physically work in your chosen position, developing a skill set that will allow for a complete career change is a must. The passive income route as a second career is a great backup allowing you to hire out what you can’t physically do. Early on in my career I found I was unable to physically tolerate exposure to tobacco smoke. At that time, smoking was allowed in all offices, restaurants, etc. I was blindsided; who ever thought? It virtually removed me from most positions I had schooling for. As luck would have it, I had purchased a duplex while working and saved a small sum. When I had to leave my career, I made a down payment on another duplex doing any maintenance I could myself. If a physical setback of another sort should happen, I can hire.
The phrase “passive income” has been so overused that it may provoke somewhat negative feelings. You’ve probably seen Facebook ads portraying the “laptop” lifestyle from entrepreneurs trying to sell you on one of their programs. You see what they’re offering and understand that the way they travel and make an income is through people buying their course.
In expensive cities like San Francisco and New York City, net rental yields can fall as low as 2%. This is a sign that there is a lot of liquidity buying property for property appreciation, and not so much for income generation. This is a riskier proposition than buying property based on rental income. In inexpensive cities, such as those in the Midwest, net rental yields can easily be in the range of 8% – 12%, although appreciation may be slower.
As can be seen from the above table, from the age of 45 onwards you are able to create a big source of additional income by just planning and investing Rs10,000 per month in equity SIP today. That is how simple it is to create a regular stream income by planning early. Of course, we do not know which stocks will give high dividend yields at that point in time so we have considered the quality high dividend stocks at this point in time. Above all, this approach is also tax efficient as you only have to pay 10% tax on dividends above Rs.1 million in a fiscal year.
We have decided to invest in 2 ETFs, a multi asset allocation ETF (Fixed Inc, alts and div paying equities) and a preferred stock ETF. This will cover almost 45 percent of our deficit. We will be extremely diversified, can access the markets at a very low cost and the investments are liquid. On this pool of $, we have no plans to invade principal unless the investment grows by 20 percent, which we think is unlikely given the characteristics of the investments. In the early 18th century, the Mughal Empire declined, as it lost western, central and parts of south and north India to the Maratha Empire, which integrated and continued to administer those regions.[85] The decline of the Mughal Empire led to decreased agricultural productivity, which in turn negatively affected the textile industry.[86] The subcontinent's dominant economic power in the post-Mughal era was the Bengal Subah in the east., which continued to maintain thriving textile industries and relatively high real wages.[87] However, the former was devastated by the Maratha invasions of Bengal[88][89] and then British colonization in the mid-18th century.[87] After the loss at the Third Battle of Panipat, the Maratha Empire disintegrated into several confederate states, and the resulting political instability and armed conflict severely affected economic life in several parts of the country – although this was mitigated by localised prosperity in the new provincial kingdoms.[85] By the late eighteenth century, the British East India Company had entered the Indian political theatre and established its dominance over other European powers. This marked a determinative shift in India's trade, and a less-powerful impact on the rest of the economy.[90] That is a nice list of passive income sources. Actually, the most up-to-date list of dividend growth stocks is the list of dividend champions, maintained by Dave Fish. The list of dividend aristocrats is incomplete at best. For example, the dividend champions list has over 100 companies that have managed to increase dividends each year for at least 25 years in a row. The list of dividend aristocrats has no more than 50 – 60. Liquid Funds are those mutual fund schemes which are ideal for putting money for a very short period of time, preferably not more than three months. Since these funds invest in extremely short term Debt papers, they come with very low volatility and risks. Accrual funds are those funds which invest in Debt papers of short and medium tenures to generate interest income. These funds usually do not take any interest rate/credit risk but stick to earning interest. In 2012, even I wrote a 150-page eBook about severance package negotiations that still regularly sells about ~35 copies a month at$85 each (2nd edition for 2017) without any effort. In order to generate $2,975 a month or$35,700 a year in passive income as I do now, I would need to invest $892,500 in something that generates a 4% yield! To earn$10,000 a year in passive income would therefore need roughly $250,000 in capital. India is the largest producer of milk, jute and pulses, and has the world's second-largest cattle population with 170 million animals in 2011.[161] It is the second-largest producer of rice, wheat, sugarcane, cotton and groundnuts, as well as the second-largest fruit and vegetable producer, accounting for 10.9% and 8.6% of the world fruit and vegetable production, respectively. India is also the second-largest producer and the largest consumer of silk, producing 77,000 tons in 2005.[162] India is the largest exporter of cashew kernels and cashew nut shell liquid (CNSL). Foreign exchange earned by the country through the export of cashew kernels during 2011–12 reached ₹4,390 crore (₹ 43.9 billion) based on statistics from the Cashew Export Promotion Council of India (CEPCI). 131,000 tonnes of kernels were exported during 2011–12.[163] There are about 600 cashew processing units in Kollam, Kerala.[160] India's foodgrain production remained stagnant at approximately 252 million tonnes (MT) during both the 2015–16 and 2014–15 crop years (July–June).[164] India exports several agriculture products, such as Basmati rice, wheat, cereals, spices, fresh fruits, dry fruits, buffalo beef meat, cotton, tea, coffee and other cash crops particularly to the Middle East, Southeast and East Asian countries. About 10 percent of its export earnings come from this trade.[17] Book sales ($36,000 a year): Sales of How to Engineer Your Layoff" continue to be steady. I expect book sales to rise once the economy starts to soften and people get more nervous about their jobs. It's always best to be ahead of the curve when it comes to a layoff by negotiating first. Further, if you are planning to quit your job, then there is no downside in trying to engineer your layoff so you can get WARN Act pay for several months, a severance check, deferred compensation, and healthcare.
This equation implies two things. First buying one more unit of good x implies buying {\displaystyle {\frac {P_{x}}{P_{y}}}} less units of good y. So, {\displaystyle {\frac {P_{x}}{P_{y}}}} is the relative price of a unit of x as to the number of units given up in y. Second, if the price of x falls for a fixed {\displaystyle Y} , then its relative price falls. The usual hypothesis is that the quantity demanded of x would increase at the lower price, the law of demand. The generalization to more than two goods consists of modelling y as a composite good.
"The whole idea of Multiple Streams of Income will be a powerfulparadigm shift for most people. Bob Allen gives practical andbeautifully illustrated knowledge on how to do it. Masteringfinancial principles is an important habit in life because it givesus the freedom to focus on what matters most. A valuable read."—Dr. Stephen R. Covey, author of The 7 Habits of HighlyEffective People
**The information contained herein neither constitutes an offer for nor a solicitation of interest in any securities offering; however, if an indication of interest is provided, it may be withdrawn or revoked, without obligation or commitment of any kind prior to being accepted following the qualification or effectiveness of the applicable offering document, and any offer, solicitation or sale of any securities will be made only by means of an offering circular, private placement memorandum, or prospectus. No money or other consideration is hereby being solicited, and will not be accepted without such potential investor having been provided the applicable offering document. Joining the Fundrise Platform neither constitutes an indication of interest in any offering nor involves any obligation or commitment of any kind.
The original version of Barbara Winter’s book, Making a Living Without a Job, came out in 1993, and in it, she recommended creating multiple "profit centers," as opposed to building a single income stream. Over ten years later, Robert Allen, the real estate entrepreneur, also wrote a couple books promoting the idea of multiple streams of income. Back then, building more than one source of income was difficult, time-consuming, and expensive. Fortunately, things have changed today. The Internet has made it easier, faster, and more affordable to generate multiple income streams.
I have to agree. Our Duplex cost us 200k initially in 1998. Over time and completely refurbishing the property with historically appropriate sensitivity, we invested another 200k or so. We just had a realtor advise us we could ask 700k for it today. It nets us 30k annually after taxes, insurance and maintenance. We still have a loan on it which I have not taken into account, that will be paid off within 5 years if we keep it. My mental drama now is, while I am quite giddy over the prospect of earning a tidy sum of profit if I sell, what then would I do to equal the ROI and monthly income this thing generates? Rents are low, they should be 4k a month and will only go up. Tempted to keep it and not sell. And while I do have some stocks, I basically suck at them. I am much better at doing properties.
Agriculture is an important part of the Indian economy. At around 1,530,000 square kilometres (590,000 sq mi), India has the second-largest amount of arable land, after the US, with 52% of total land under cultivation. Although the total land area of the country is only slightly more than one third of China or the US, India's arable land is marginally smaller than that of the US, and marginally larger than that of China. However, agricultural output lags far behind its potential.[367] The low productivity in India is a result of several factors. According to the World Bank, India's large agricultural subsidies are distorting what farmers grow and hampering productivity-enhancing investment. Over-regulation of agriculture has increased costs, price risks and uncertainty, and governmental intervention in labour, land, and credit are hurting the market. Infrastructure such as rural roads, electricity, ports, food storage, retail markets and services remain inadequate.[368] The average size of land holdings is very small, with 70% of holdings being less than one hectare (2.5 acres) in size.[369] Irrigation facilities are inadequate, as revealed by the fact that only 46% of the total cultivable land was irrigated as of 2016,[158] resulting in farmers still being dependent on rainfall, specifically the monsoon season, which is often inconsistent and unevenly distributed across the country.[370] In an effort to bring an additional two crore hectares (20 million hectares; 50 million acres) of land under irrigation, various schemes have been attempted, including the Accelerated Irrigation Benefit Programme (AIBP) which was provided ₹80,000 crore (₹800 billion) in the union budget.[371] Farming incomes are also hampered by lack of food storage and distribution infrastructure; a third of India's agricultural production is lost from spoilage.[249]
When listing your collectibles online, selling through the right channels is key to ensuring you get the best price; look for specialist websites that are both specific to your niche and offer seller-friendly terms – luxury watch marketplace www.chrono24.com, for example, offers competitive listing fees starting at \$5 US, a 90% sales rate and a money-back guarantee if your item doesn’t sell within six months. If you don’t already have a collection in place, it’s never too late to start – follow these tips on how to start a valuable collection.
Stocks (shares) paying dividends are typically a reliable source of income but they have higher risk of capital losses than cash and bonds. So, it’s wise not to chase yield indiscriminately. The 10 highest yielding stocks on the ASX 200 (the 200 largest companies in Australia) are shown in the table below. But their share price performance on average over the last year has been underwhelming, as shown in the far right column:
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2018-11-15 13:30:25
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https://quomodocumque.wordpress.com/2017/10/05/trace-test/
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## Trace test
Jose Rodriguez gave a great seminar here yesterday about his work on the trace test, a numerical way of identifying irreducible components of varieties. In Jose’s world, you do a lot of work with homotopy; if a variety X intersects a linear subspace V in points p1, p2, .. pk, you can move V a little bit and numerically follow those k points around. If you move V more than a little bit — say in a nice long path in the Grassmannian that loops around and returns to its starting point — you’ll come back to p1, p2, .. pk, but maybe in a different order. In this way you can compute the monodromy of those points; if it’s transitive, and if you’re careful about avoiding some kind of discriminant locus, you’ve proven that p1,p2…pk are all on the same component of V.
But the trace test is another thing; it’s about short paths, not long paths. For somebody like me, who never thinks about numerical methods, this means “oh we should work in the local ring.” And then it says something interesting! It comes down to this. Suppose F(x,y) is a form (not necessarily homogenous) of degree at most d over a field k. Hitting it with a linear transformation if need be, we can assume the x^d term is nonzero. Now think of F as an element of k((y))[x]: namely
$F = x^d + a_1(y) x^{d-1} + \ldots + a_d(y).$
Letting K be the algebraic closure of k((y)), we can then factor F as (x-r_1) … (x-r_d). Each of these roots can be computed as explicitly to any desired precision by Hensel’s lemma. While the r_i may be power series in k((y)) (or in some algebraic extension), the sum of the r_i is -a_1(y), which is a linear function A+by.
Suppose you are wondering whether F factors in k[x,y], and whether, for instance, r_1 and r_2 are the roots of an irreducible factor of F. For that to be true, r_1 + r_2 must be a linear function of y! (In Jose’s world, you grab a set of points, you homotopy them around, and observe that if they lie on an irreducible component, their centroid moves linearly as you translate the plane V.)
Anyway, you can falsify this easily; it’s enough for e.g. the quadratic term of r_1 + r_2 to be nonzero. If you want to prove F is irreducible, you just check that every proper subset of the r_i sums to something nonlinear.
1. Is this something I already know in another guise?
2. Is there a nice way to express the condition (which implies irreducibility) that no proper subset of the r_i sums to something with zero quadratic term?
## 7 thoughts on “Trace test”
1. Jason Starr says:
I think that I misunderstood something. Begin with F(x,y) = (x^3+x^2-y^2)x. The extra x factor is just there to insure that there is a nontrivial factorization, which I believe was part of the setup. There are power series roots r_1 = y + s_1 and r_2 = -y + s_2. These are roots of the first factor for F(x,y). The sum of these roots is not linear in y.
2. JSE says:
Crap, I messed this up somehow, I started writing the post thinking about homogeneous forms and then changed it. Give me a sec and I’ll work this out.
3. JSE says:
Wait now I’m confused again about whether I was confused. The first factor x^3 + x^2 – y^2, considered as a polynomial in x, has three roots, whose sum is -1, right? I don’t know if I get which two roots you mean.
4. Jason Starr says:
@JSE. Maybe I misunderstood your post. I thought that we are to sum up roots in pairs. For the polynomial \$x^3+x^2-y^2\$, the “pair sums” of roots are, to order \$y^3\$, \$y+s_1 + y^2\$, \$-y+s_2+y^2\$, and \$s_1+s_2\$. If we sum up all three roots, we get the coefficient of \$x^2\$, which is \$1\$. In general, if we assume that the polynomial has total degree \$n\$ and that the coefficient of \$x^n\$ is nonzero (so equal to \$1\$ after scaling), then certainly the coefficient of \$x^{n-1}\$ has degree zero or one in \$y\$, or else the degree is strictly larger than \$n\$. Maybe that is the point about root sums being linear.
5. Jason Starr says:
Typo correction: Those first two pair sums should have constant term \$-1\$.
6. Jason Starr says:
Now I believe that I understand. The example in your post is for an irreducible quadratic factor. The analogous result holds for a proper irreducible factor of any degree, but you have to consider a partial sum of roots with more than two summands. Let \$F(x,y)\$ be an (inhomogeneous) polynomial of total degree \$n\$ and such that the coefficient of \$x^n\$ is nonzero. Via Puiseux series, we can factor \$F(x,y)\$ as \$(x-r_1(y))…(x-r_n(y))\$. If \$F(x,y)\$ has a nontrivial factorization in \$k[x,y]\$, then there exists a nonempty proper subset of these roots, say \$r_1(y),…,r_m(y)\$ after reordering, whose partial sum \$r_1(y)+…+r_m(y)\$, as a Puiseux series, is actually an (affine) linear polynomial in \$y\$. Thus, if every nonempty, proper partial sum is not (affine) linear in \$y\$, then \$F(x,y)\$ is irreducible. This is straightforward to prove using elementary algebra via the observation I made in my previous comment: for both \$F(x,y)\$ and every irreducible factor of \$F(x,y)\$, since the \$x\$-degree equals the total degree, the “next-to-leading” coefficient in \$x\$ is an (affine) linear polynomial in \$y\$. Note, this sufficient criterion for irreducibility is not necessary: the polynomial \$(x-y)^4-y^3\$ is irreducible, but there are pair sums that are affine linear in \$y\$.
7. JSE says:
Exactly! It’s about all partial sums, not just pairwise sums. It’s a test for whether a subset of the roots could be the set of roots of an irreducible algebraic factor.
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2017-12-11 20:46:00
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https://unapologetic.wordpress.com/2008/10/23/
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# The Unapologetic Mathematician
## Group Representations
We’ve now got the general linear group $\mathrm{GL}(V)$ of all invertible linear maps from a vector space $V$ to itself. Incidentally this lives inside the endomorphism algebra $\hom_\mathbf{Vect}(V,V)$ of all linear transformations from $V$ to itself. In fact, in ring-theory terms it’s the group of units of that algebra. So what can we do with it?
One of the biggest uses is to provide representations for other algebraic structures. Let’s say we’ve got some abstract group. It’s a set with some binary operation defined on it, sure, but what does it do? We’ve seen groups acting on sets before, where we interpret a group element as a permutation of an actual collection of elements. Alternatively, an action of a group $G$ is a homomorphism from $G$ to the group of permutations of some set $S$$\hom_\mathbf{Set}(S,S)$.
Another concrete representation of a group is as symmetries of some vector space. That is, we’re interested in homomorphisms $\rho:G\rightarrow\mathrm{GL}(V)$. A “representation” of a group $G$ is a vector space $V$ with such a homomorphism.
In fact, this extends the notion of a group acting on a set. Indeed, for any set $S$ we can build the free vector space $\mathbb{F}[S]$ with a basis vector $e_s$ for each $s\in S$. Given a permutation $\pi$ on $S$ we get a linear map $\mathbb{F}[\pi]:\mathbb{F}[S]\rightarrow\mathbb{F}[S]$ defined by setting $\mathbb{F}[\pi](e_s)=e_{\pi(s)}$ and extending by linearity.
We thus get a homomorphism from the group of permutations of $S$ to $\mathrm{GL}(\mathbb{F}[S])$. And then if we have a group action on $S$ we can promote it to a representation on the vector space $\mathbb{F}[S]$. We call such a representation a “permutation representation”.
October 23, 2008
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2015-08-03 08:37:52
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https://www.simscale.com/docs/content/simwiki/numerics/what-are-the-navier-stokes-equations.html
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# What are the Navier-Stokes Equations?¶
The movement of fluid in the physical domain is driven by various properties. For the purpose of bringing the behavior of fluid flow to light and developing a mathematical model, those properties have to be defined precisely as to provide transition between the physical and the numerical domain. Velocity, pressure, temperature, density, and viscosity are the main properties that should be considered simultaneously when conducting a fluid flow examination. In accordance with the physical incidents such as combustion, multiphase flow, turbulent, mass transport, etc., those properties diversify enormously, which can be categorized into kinematic, transport, thermodynamic, and other miscellaneous properties$$^1$$.
Thermo-fluid incidents directed by governing equations are based on the laws of conservation. The Navier-Stokes equations are the broadly applied mathematical model to examine changes on those properties during dynamic and/or thermal interactions. The equations are adjustable regarding the content of the problem and are expressed based on the principles of conservation of mass, momentum, and energy$$^1$$:
• Conservation of Mass: Continuity Equation
• Conservation of Momentum: Momentum Equation of Newton’s Second Law
• Conservation of Energy: First Law of Thermodynamics or Energy Equation
Figure 1: Conservation Equations
Although some sources specify the expression of Navier-Stokes equations merely for conservation of momentum, some of them also use all equations of conservation of the physical properties. Regarding the flow conditions, the Navier-Stokes equations are rearranged to provide affirmative solutions in which the complexity of the problem either increases or decreases. For instance, having a numerical case of turbulence according to the pre-calculated Reynolds number, an appropriate turbulent model has to be applied to obtain credible results.
## History¶
Despite the fact that motion of fluid is an exploratory topic for human beings, the evolution of mathematical models emerged at the end of 19$$^{th}$$ century after the industrial revolution. The initial appropriate description of the viscous fluid motion had been indicated in the paper “Principia” by Sir Isaac Newton (1687) in which dynamic behavior of fluids under constant viscosity was investigated$$^1$$. Later, Daniel Bernoulli (1738) and Leonhard Euler (1755) subsequently derived the equation of inviscid flow which is now expressed as Euler’s inviscid equations. Even though Claude-Louis Navier (1827), Augustin-Louis Cauchy (1828), Siméon Denis Poisson (1829), and Adhémar St.Venant (1843) had carried out studies to explore the mathematical model of fluid flow, they had overlooked the viscous (frictional) force. In 1845, Sir George Stokes had derived the equation of motion of a viscous flow by adding Newtonian viscous terms, thereby the Navier-Stokes Equations had been brought to their final form which has been used to generate numerical solutions for fluid flow ever since$$^{1,2}$$.
Figure 2: Newton$$^{9}$$, Navier$$^{10}$$, and Stokes$$^{11}$$, the mathematicians behind the Navier-Stokes equations
## The Navier-Stokes Equations¶
The observation method of fluid flow based on kinematic properties is a fundamental issue for generating a convenient mathematical model. Movement of fluid can be investigated with either Lagrangian or Eulerian methods$$^3$$. Lagrangian description of fluid motion is based on monitoring a fluid particle which is large enough to detect properties. Between the initial coordinates at time $$t_0$$ and coordinates of the same particle at time $$t_1$$ millions of separate particles have to be examined through the path that is almost impossible to follow. In the Eulerian method, any specific particle across the path is not followed; instead, the velocity field as a function of time and position is examined. The missile example (Figure 3) precisely fits to emphasize these methods.
Figure 3: Observation of fluid motion with the methods Lagrangian and Euler
The Lagrangian formulation of motion is always time dependent. As $$a$$, $$b$$, and $$c$$ are the initial coordinates of a particle; $$x$$, $$y$$, and $$z$$ are coordinates of the same particle at time $$t$$. Description of motion for Lagrangian:
$x=x(a,b,c,\,t),y=y(a,b,c,\,t),z=z(a,b,c,\,t) \tag1$
In the Eulerian method, $$u$$, $$v$$ and $$w$$ are the components of velocity at the point $$(x,y,z)$$ while $$t$$ is the time. The velocity components $$u$$, $$v$$ and $$w$$ are the unknowns which are functions of the independent variables $$x$$, $$y$$, $$z$$ and $$t$$. The description of motion with the Eulerian method for any particular value of $$t$$ is:
$u=u(x,y,z,\,t),v=v(x,y,z,\,t),w=w(x,y,z,\,t) \tag2$
The equations of conservation in the Eulerian system in which fluid motion is described are expressed as Continuity Equation for mass, Navier-Stokes Equations for momentum and Energy Equation for the first law of Thermodynamics. The equations are all considered simultaneously to examine fluid and flow fields.
### Conservation of Mass¶
The mass in the control volume can be neither created nor destroyed in accordance with physical laws. The conservation of mass, also expressed as Continuity Equation, states that the mass flow difference throughout system between inlet- and outlet-section is zero:
$\frac{D_\rho}{D_t}+\rho\left(\nabla\cdot\vec{V}\right)=0 \tag3$
where $$\rho$$ is density, $$V$$ is velocity and gradient operator $$\nabla$$;
$\vec{\nabla}=\vec{i}\frac{\partial}{\partial x}+\vec{j}\frac{\partial}{\partial y}+\vec{k}\frac{\partial}{\partial z} \tag4$
While the density is constant, the flow is assumed incompressible and then continuity is simplified as below, which indicates a steady-state process:
$\frac{D_\rho}{D_t}=0 \longrightarrow \nabla\cdot\vec{V}=\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z} =0 \tag5$
### Conservation of Momentum¶
The momentum in a control volume is kept constant, which implies conservation of momentum that we call ‘The Navier-Stokes Equations’. The description is set up in accordance with the expression of Newton’s Second Law of Motion:
$F=m\cdot a \tag6$
where $$F$$ is the net force applied to any particle, $$a$$ is the acceleration, and $$m$$ is the mass. In case the particle is a fluid, it is convenient to divide the equation to volume of particle to generate a derivation in terms of density as follows:
$\rho\frac{DV}{D_t}=f=f_{body}+f_{surface} \tag7$
in which $$f$$ is the force exerted on the fluid particle per unit volume, and $$f_{body}$$ is the applied force on the whole mass of fluid particles as below:
$f_{body}=p\cdot g \tag8$
where $$\rho$$ is the density of fluid and $$g$$ is the gravitational acceleration. External forces which are deployed through the surface of fluid particles, $$f_{surface}$$ is expressed by pressure and viscous forces as shown below:
$f_{surface}=\nabla\cdot\tau_{ij}=\frac{\partial\tau_{ij}}{\partial x_i}=f_{pressure}+f_{viscous} \tag9$
where $$\tau_{ij}$$ is expressed as stress tensor. According to the general deformation law of Newtonian viscous fluid given by Stokes, $$\tau_{ij}$$ is expressed as$$^2$$:
$\tau_{ij}=-p\delta_{ij}+\mu\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)+\delta_{ij}\lambda\nabla\cdot V \tag{10}$
Hence, Newton’s equation of motion can be specified in the form as follows:
$\rho\frac{DV}{D_t}=\rho\cdot g+\nabla\cdot\tau_{ij} \tag{11}$
Substitution of equation (10) into equation (11) results in the Navier-Stokes equations of Newtonian viscous fluid in one equation:
$\underbrace{\rho\frac{DV}{D_t}}_{I} = \underbrace{\rho\cdot g} _ {II} - \underbrace{\nabla p} _ {III}+\underbrace{\frac{\partial}{\partial x _ i}\left[\mu\left(\frac{\partial v _ i}{\partial x _ j} + \frac{\partial v _ j}{\partial x _ i}\right)+\delta _ {ij} \lambda\nabla\cdot V\right]} \tag{12} _ {IV}$
$$I$$: Momentum convection
$$II$$: Mass force
$$III$$: Surface force
$$IV$$: Viscous force
where static pressure $$\rho$$ and gravitational force $$\rho\vec{g}$$. The equation (12) is convenient for fluid and flow fields both transient and compressible. $$D/D_t$$ indicates the substantial derivative as follows:
$\frac{D(\,)}{D_t}=\frac{\partial(\,)}{\partial t}+u\frac{\partial(\,)}{\partial x}+v\frac{\partial(\,)}{\partial y}+w\frac{\partial(\,)}{\partial z}=\frac{\partial(\,)}{\partial t}+V\cdot\nabla(\,) \tag{13}$
If the density of fluid is accepted to be constant, the equations are greatly simplified in which the viscosity coefficient $$\mu$$ is assumed constant and $$\nabla\cdot V=0$$ in equation (12). Thus, the Navier-Stokes equations for an incompressible three-dimensional flow can be expressed as follows:
$\rho\frac{DV}{Dt}=\rho g-\nabla p + \mu\nabla^2V \tag{14}$
For each dimension when the velocity is $$V(u,v,w)$$:
$\rho\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=\rho g_x-\frac{\partial p}{\partial x}+\mu\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2}\right) \tag{15}$
$\rho\left(\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}\right)=\rho g_y-\frac{\partial p}{\partial y}+\mu\left(\frac{\partial^2v}{\partial x^2}+\frac{\partial^2v}{\partial y^2}+\frac{\partial^2v}{\partial z^2}\right) \tag{16}$
$\rho\left(\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)=\rho g_z-\frac{\partial p}{\partial z}+\mu\left(\frac{\partial^2w}{\partial x^2}+\frac{\partial^2w}{\partial y^2}+\frac{\partial^2w}{\partial z^2}\right) \tag{17}$
$$p$$, $$u$$, $$v$$ and $$w$$ are unknowns where a solution is sought by application of both continuity equation and boundary conditions. Besides, the energy equation has to be considered if any thermal interaction is available in the problem.
### Conservation of Energy¶
The Conservation of Energy is the first law of thermodynamics which states that the sum of the work and heat added to the system will result in the increase of energy of the system:
$dE_t=dQ+dW \tag{18}$
where $$dQ$$ is the heat added to the system, $$dW$$ is the work done on the system, and $$dE_t$$ is the increment in the total energy of the system. One of the common types of energy equation is:
$\rho\left[\underbrace{\frac{\partial h}{\partial t}} _ {I} + \underbrace{\nabla\cdot(hV)} _ {II}\right]=\underbrace{-\frac{\partial p}{\partial t}} _ {III} + \underbrace{\nabla\cdot(k\nabla T)} _ {IV} + \underbrace{\phi} _ {V} \tag{19}$
$$I$$: Local change with time
$$II$$: Convective term
$$III$$: Pressure work
$$IV$$: Heat flux
$$V$$: Heat dissipation term
## Variations of the Navier-Stokes Equations¶
The Navier-Stokes equations are extremely thorough in order to simulate physical incidents. Nonetheless, having a non-linear structure and various complexities, it is hardly possible to conduct an exact solution of those equations. Thus, with regard to the physical domain, both approaches and assumptions are partially applied to grind the equations. Beyond this, though, some assumptions have to be applied as to provide a reliable model in which the equation is carried out, up to a further step in terms of complexity such as turbulence.
The mathematical model merely gives ties among parameters which are part of the whole process. Hence, the solution of the Navier-Stokes equations can be realized with either analytical or numerical methods. The analytical method is the process that only compensates solutions in which non-linear and complex structures in the Navier-Stokes equations are ignored within several assumptions. It is only valid for simple / fundamental cases such as Couette flow, Poisellie flow, etc$$^3$$. On the other hand, almost every case in fluid dynamics comprises non-linear and complex structures in the mathematical model which cannot be ignored to sustain reliability. Hence, the solution of the Navier-Stokes equations are carried out within several numerical methods, the omnipresence of Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs). A computational analysis of fluid flow can be described as shown in Figure 4.
Figure 4: The panoramic structure of a CFD project and its stages
### Time Domain¶
The analysis of fluid flow can be conducted in either steady (time-independent) or unsteady (time-dependent) condition depending on the physical incident. In case the fluid flow is steady, it means the motion of fluid and parameters do not rely on change in time, the term $$\frac{\partial()}{\partial t}=0$$ where the continuity and momentum equations are re-derived as follows:
Continuity equation:
$\frac{\partial(\rho u)}{\partial x}+\frac{\partial(\rho v)}{\partial y}+\frac{\partial(\rho w)}{\partial z}=0 \tag{20}$
The Navier-Stokes equation in $$x$$ direction:
$\rho\left(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right) = \rho g_x-\frac{\partial p}{\partial x}+\mu\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2}\right) \tag{21}$
While the steady flow assumption negates the effect of some non-linear terms and provides a convenient solution, variation of density is a hurdle that keeps the equation in a complex formation.
### Compressibility¶
Due to the malleable structure of fluids, the compressibility of particles is a significant issue. Despite the fact that all types of fluid flow are compressible in a various range regarding molecular structure, most of them can be assumed to be incompressible in which the density changes are negligible. Thus, the term $$\frac{\partial\rho}{\partial t}=0$$ is thrown away regardless of whether the flow is steady or not, as below:
Continuity equation:
$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0 \tag{22}$
The Navier-Stokes equation in $$x$$ direction:
$\rho\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=\rho g_x-\frac{\partial p}{\partial x}+\mu\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2}\right) \tag{23}$
As incompressible flow assumption provides reasonable equations, the application of steady flow assumption concurrently enables us to ignore non-linear terms where $$\frac{\partial()}{\partial t}=0$$. Moreover, the density of fluid in high speed cannot be accepted as incompressible in which the density changes are important. “The Mach Number” is a dimensionless number that is convenient to investigate fluid flow, whether incompressible or compressible$$^3$$:
$Ma=\frac{V}{a}\leq0.3 \tag{24}$
where $$Ma$$ is the Mach number, $$V$$ is the velocity of flow, and $$a$$ is the speed of sound at $$340.29 \frac{m}{s}$$ at sea level. As in equation (24), when the Mach number is lower than 0.3, the assumption of incompressibility is acceptable. On the contrary, the change in density cannot be negligible in which density should be considered as a significant parameter. For instance, if the velocity of a car is higher than 100$$\frac{m}{s}$$, the suitable approach to conduct credible numerical analysis is the compressible flow. Apart from velocity, the effect of thermal properties on the density changes has to be considered in geophysical flows$$^3$$.
### Low and High Reynolds Numbers:¶
The Reynolds number, the ratio of inertial and viscous effects, is also effective on Navier-Stokes equations to truncate the mathematical model. While $$Re\longrightarrow\infty$$, the viscous effects are presumed negligible where viscous terms in Navier-Stokes equations are thrown away. The simplified form of Navier-Stokes equation, described as Euler equation, can be specified as follows$$^8$$:
The Navier-Stokes equation in $$x$$ direction:
$\rho\left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=\rho g_x-\frac{\partial p}{\partial x} \tag{25}$
Even though viscous effects are relatively important for fluids, the inviscid flow model partially provides a reliable mathematical model as to predict real process for some specific cases. For instance, high-speed external flow over bodies is a broadly used approximation where inviscid approach reasonably fits. While $$Re\ll1$$, the inertial effects are assumed negligible where related terms in Navier-Stokes equations drop out. The simplified form of Navier-Stokes equations is called either creeping flow or Stokes flow$$^8$$:
The Navier-Stokes equation in $$x$$ direction:
$\rho g_x-\frac{\partial p}{\partial x}+\mu\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2}+\right)=0 \tag{26}$
Having tangible viscous effects, creeping flow is a suitable approach to investigate the flow of lava, swimming of microorganisms, flow of polymers, lubrication, etc.
### Turbulence¶
The behavior of the fluid under dynamic conditions is a challenging issue that is compartmentalized as laminar and turbulent. The laminar flow is orderly at which motion of fluid can be predicted precisely. Except that, the turbulent flow has various hindrances, therefore it is hard to predict the fluid flow which shows a chaotic behavior. The Reynolds number, the ratio of inertial forces to viscous forces, predicts the behavior of fluid flow whether laminar or turbulent regarding several properties such as velocity, length, viscosity, and also type of flow. Whilst the flow is turbulent, a proper mathematical model is selected to carry out numerical solutions. Various turbulent models are available in literature and each of them has a slightly different structure to examine chaotic fluid flow.
Turbulent flow can be applied to the Navier-Stokes equations in order to conduct solutions to chaotic behavior of fluid flow. Apart from the laminar, transport quantities of the turbulent flow, it is driven by instantaneous values. Direct numerical simulation (DNS) is the approach to solving the Navier-Stokes equation with instantaneous values. Having district fluctuations varies in a broad range, DNS needs enormous effort and expensive computational facilities. To avoid those hurdles, the instantaneous quantities are reinstated by the sum of their mean and fluctuating parts as follows:
$instantaneous\,value = \overline{mean\,value}+fluctuating\,value' \tag{27}$
$u = \overline{u}+u'$
$v = \overline{v}+v'$
$w = \overline{w}+w'$
$T= \overline{T}+T'$
where $$u$$, $$v$$, and $$w$$ are velocity components and $$T$$ is temperature. The differences among values are shown in Figure 5 both for steady and unsteady conditions:
Figure 5: Instant, mean and fluctuating velocities; a) steady process, b) unsteady process$$^8$$
Instead of instantaneous values which cause non-linearity, carrying out a numerical solution with mean values provides an appropriate mathematical model which is named “The Reynolds-averaged Navier-Stokes (RANS) equation”$$^4$$. The fluctuations can be negligible for most engineering cases which cause a complex mathematical model. Thus, RANS turbulence model is a procedure to close the system of mean flow equations. The general form of The Reynolds-averaged Navier-Stokes (RANS) equation can be specified as follows:
Continuity equation:
$\frac{\partial\overline{u}}{\partial x}+\frac{\partial\overline{v}}{\partial y}+\frac{\partial\overline{w}}{\partial z}=0 \tag{28}$
The Navier-Stokes equation in $$x$$ direction:
$\rho\left(\frac{\partial\overline{u}}{\partial t}+\overline{u}\frac{\partial\overline{u}}{\partial x}+\overline{v}\frac{\partial\overline{u}}{\partial y}+\overline{w}\frac{\partial\overline{u}}{\partial z}\right)=\rho g_x-\frac{\partial\overline{p}}{\partial x}+\mu\left(\frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}+\frac{\partial^2u}{\partial z^2}\right) \tag{29}$
The turbulence model of RANS can also vary regarding methods such as k-omega, k-epsilon, k-omega-SST, and Spalart-Allmaras which have been used to seek a solution for different types of turbulent flow.
Likewise, large eddy simulation (LES) is another mathematical method for turbulent flow which is also comprehensively applied for several cases. Tough LES ensures more accurate results than RANS, it requires much more time and computer memory. As in DNS, LES considers to solve the instantaneous Navier-Stokes equations in time and three-dimensional space$$^4$$.
## Application of the Navier-Stokes Equations¶
The simple form of the Navier-Stokes equations only encompasses the change in properties such as velocity, pressure, and density under dynamic conditions for one phase laminar flow. Most engineering applications require further mathematical models to simulate physical incidents with the aim of obtaining affirmative results in the numerical domain. Some of the most common engineering problems and relevant mathematical models as to carry out numerical simulations can be given as below:
• Air flow in a duck: Single phase flow, laminar / turbulent, steady / unsteady
• Water flow in an open channel: Multiphase flow, laminar / turbulent, steady / unsteady
• Combustion in cylinder: Multiphase flow, laminar / turbulent, unsteady, chemical reaction, heat transfer, mass transfer
• Condensation/evaporation of water: Multiphase flow, laminar / turbulent, unsteady, heat transfer, mass transfer
### Microfluidics¶
The Navier-Stokes equations cannot compensate the physical model of the flow at very small scales such as the motion of single bacteria — also called microfluidics. Thereby, it is convenient to either change or reinstate the Navier-Stokes equations with a suitable mathematical model. The Knudsen number (Kn) is a dimensionless number that is the ratio of the mean free path of molecular structure to observation scale. The preferred model in accordance with the Knudsen number is shown in Figure 6:
Figure 6: Preferred mathematical models for motion of fluid in accordance with the Knudsen number$$^7$$
### Real-time simulation:¶
The Navier-Stokes equations have been considered an important issue by animation / video game companies$$^5$$. For the purpose of generating a real-time animation, the application of Navier-Stokes equations provides stunning results when it comes to enhancing reality$$^6$$. They are also part of the reason that modern video games appear to be realistic in many more ways than several years ago. Just think about the movement of flags in the wind: doesn’t this look absolutely realistic in modern games?!
## Resources¶
$$^1$$: White, Frank (1991).Viscous Fluid Flow. 3rd Edition. McGraw-Hill Mechanical Engineering. ISBN-10: 0072402318.
$$^2$$: Stokes, George (1851). “On the Effect of the Internal Friction of Fluids on the Motion of Pendulums”. Transactions of the Cambridge Philosophical Society. 9: 8–106.
$$^3$$: White, Frank (2002). Fluid Mechanics. 4th edition. McGraw-Hill Higher Education. ISBN: 0-07-228192-8.
$$^4$$: Cebeci, T., Shao, J.P., Kafyeke, F., Laurendeau, E (2005). Computational Fluid Dynamics for Engineers. Horizon Publishing Inc. ISBN: 0-9766545-0-4.
$$^8$$: Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2001). Transport Phenomena, 2th edition. John Wiley & Sons. ISBN 0-471-41077-2.
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2019-04-20 23:18:14
|
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|
https://pretextbook.org/doc/guide/html/overview-exceptional-characters.html
|
These first two characters are interpreted by the XML processor very early in the analysis of your source. So they need to be authored specially via the XML entities & and <. In practice, escaping > is rarely necessary. So fundamentally within PreTeXt there are just two characters to type carefully or exceptionally.
If you consistently follow the prescription in the previous paragraph you will avoid a descent into escape-character hell and avoid a lot of head-scratching. In particular, you should have no need of the <![CDATA[ ]]> mechanism of XML, so please just forget we even mentioned it. But see Subsubsection 4.1.4.2 if you are curious, or want a more thorough discussion.
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2022-10-03 02:50:32
|
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|
http://quant.stackexchange.com/questions?page=4&sort=faq
|
# All Questions
651 views
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### Any package to run VAR-GARCH or VECM-GARCH models in R?
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### What are $d_1$ and $d_2$ for Laplace?
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### Extended Hull White Interest Rate Model for Zero Coupon Bond
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### How to normalize stock data
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### Reading recommendation on using statistical analysis in online fraud prevention [closed]
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### Calculating arbitrage- S&P 500 stocks vs S&P 500 Index future?
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### How useful is the genetic algorithm for financial market forecasting?
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16k views
### Switching from C++ to R - limitations/applications
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### Except Zipline, are there any other Pythonic algorithmic trading library I can choose?
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### What are the best sources for equity quantitative research?
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### What C++ math libraries are typically used by quants?
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### Python library for Portfolio Optimization
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### Training set of tick-by-tick data?
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### How to identify technical analysis chart patterns algorithmically?
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### What kind of basic framework or application do you use to run your trading algorithms?
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### Is there any thing out there as a substitute for KDB?
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### Portfolio optimization with monte carlo sampling from predictive distribution
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### Applications of Fourier theory in trading
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### Strategy of Renaissance Technologies Medallion fund: Holy Grail or next Madoff?
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### Why do high frequency traders use rapidly cancelled limit orders?
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### What are the textbooks used to teach Quantitative Trading at universities?
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### Please give a step-by-step explanation on how to build a factor model
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2k views
### How to quickly estimate a lower bound on correlation for a large number of stocks?
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### What are the best Journals & Conferences in Quantitative Finance?
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### What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?
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2k views
### Categories of systematic trading strategies?
What are the main categories of systematic trading strategies (e.g. momentum, mean reversion), as might be considered by an index or fund-of-fund analyst? Are there any common sub-strategies?
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### How to forecast volatility using high-frequency data?
There is a large literature covering volatility forecasts with high-frequency tick data. Much of this has surrounded the concept of "realized volatility", such as: "Realized Volatility and ...
3k views
### Option pricing before Black-Scholes
According to the Wikipedia article, Contracts similar to options are believed to have been used since ancient times. In London, puts and "refusals" (calls) first became well-known trading ...
1k views
### Why is there no “meta-model”?
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2k views
### How can I quantitatively test the validity of momentum indicators?
I am learning about quantitative finance, and I am struck by how different it is from the techniques that make it into magazines and TV, particularly technical analysis. Specifically, if they say an ...
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### Measuring Behavioral Finance Effects in Fund/Portfolio Manager Analysis
I want to know if there are some standardized measures to evaluate how irrationally human a portfolio manager is. Are there any performance measures or scorings for behavioral finance effects? How ...
1k views
### How to estimate the probability of drawdown / ruin?
A fairly naive approach to estimate the probability of drawdown / ruin is to calculate the probabilities of all the permutations of your sample returns, keeping track of those that hit your drawdown / ...
5k views
### portfolio optimisation with VaR (or CVaR) constraints
I would like to optimize a portfolio allocation (maximizing the exposure or the expected return), but with VaR or CVaR contraints. (some parts of my portfolio cannot exceed a certain VaR) How can I ...
3k views
### Main backtesting & trading solutions: QuantFactory, Deltix, etc.
What are the most used/mature/promising commercial solutions today which handle backtesting/ automated trading needs? I'm talking about vertical product suites like QuantFactory or Deltix which ...
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### Diversification, Rebalancing and Different Means
I have found many financial authors making generalizations about GM and AM but they are wrong in certain circumstances. Could someone explain their reasoning? My fact why they are wrong is based ...
3k views
### Can the concept of entropy be applied to financial time series?
I am not familiar with the concept of entropy for time series. I am looking for good reference papers and examples of use.
I tried it in several symbols and timeframes with the same result: $$\frac {mean(HIGH-LOW)}{mean(|CLOSE-OPEN|)}$$ ...
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2016-02-14 10:20:41
|
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https://www.physicsforums.com/threads/eigenvalue-question.315766/
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# Eigenvalue question
1. May 22, 2009
### jeff1evesque
Hello,
I was reading something in my text/wikipedia, and they both said that "...the eigenvalues of a matrix are the zeros of its characteristic polynomial." Do they mean that λ in the characteristic polynomial causes det (A - λI) = 0 (in particular A = λI)?
JL
Last edited: May 22, 2009
2. May 23, 2009
### dx
The characteristic polynomial is p(x) = det(A - xI). The zeroes of the characteristic polynomial are the x values that satisfy det(A-xI) = 0.
3. May 23, 2009
### HallsofIvy
Staff Emeritus
Yes, that's exactly what they mean.
If the determinant of $A- \lambda I$ is not 0, then $A- \lambda I$ has an inverse and so the equation $(A- \lambda I)v= 0$ has a unique solution $(A- \lambda I)^{-1}(A- \lambda I)v= v= (A- \lambda I)^{-1}0= 0$ which contradicts the definition of "eigenvalue" which is that the equation $Av= \lambda v$, equivalent to $(A- \lambda I)v= 0$, has "non-trivial" (non-zero) solutions.
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2017-08-23 02:52:05
|
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http://www.denizyuret.com/2006/05/google-calendar-how-to-delete-multiple.html
|
## May 07, 2006
### Google calendar: how to delete multiple entries
You need to have wget, tidy, grep.
To get authentication:
Note that Auth=XXX field that comes back.
To request the feed (you can play with start-min, start-max, and max-results):
Note the edit URI's of the events you'd like to delete:
wget ... | tidy -xml -wrap 999 | grep edit
Delete the event by using its edit URI; this is a two step process, because wget does not redirect correctly:
Watch the output and note the redirect URI with gsessionid attached, then execute:
Boaz said...
Thank you - very useful!
Unknown said...
Thanks for this, it saved me from manually deleting over 2000 entries. In return, here is a bash script to do everything in one go.
# set up user parameters
minTime=2008-07-18T12:29:00
maxTime=2008-07-18T12:29:59
maxResults=2
# login and get the auth token
authToken=wget -q -O- --post-data 'Email='${guser}'&Passwd='${gpass}'&service=cl&source=Gulp-CalGulp-1.05' https://www.google.com/accounts/ClientLogin | grep Auth | awk '{print substr($0, 6) }' # get all events that match criteria and delete them one by one wget -v -O- --header="Authorization: GoogleLogin auth="${authToken} "http://www.google.com/calendar/feeds/default/private/full?start-min="${minTime}"&start-max="${maxTime}"&max-results="${maxResults} | tidy -q -xml -wrap 999 | grep edit | awk '{ system ("wget -v -nv -O- --header=\"Authorization: GoogleLogin auth='${authToken}'\" --header=\"X-HTTP-Method-Override: DELETE\" --post-data=\"\" " substr($0,52,length($0)-55)) }' 2>&1 | grep gsessionid | awk '{print("Deleting " NR "\11\13"); system("wget -nv -O- --header=\47Authorization: GoogleLogin auth='${authToken}'\47 --header=\47X-HTTP-Method-Override: DELETE\47 --post-data=\47\47 \47" substr($0,index(\$0,"gsessionid")-97,130) "\47")}'
Unknown said...
Hi,
I'm facing the same problem while I need to delete multiple entries at my Google Calendar. Since I'm not a developer, can you give some help on what type of batch I need this code to be run?
Miguel
Unknown said...
Hi,
I'm having the multiple calendar entries problem, and since I'm not a developer I would like to know some details on how to run this batch.
Miguel
Unknown said...
it is a bash script, not a batch script. it is meant to run in a Linux shell.
copy the text in my previous post to a file called delevents.sh.
change the following details to match the entries you want deleted:
minTime=2008-07-18T12:29:00
maxTime=2008-07-18T12:29:59
maxResults=2
set execute permission on the file:
chmod +x delevents.sh
run the file:
/bin/sh delevents.sh
Anonymous said...
Thanks, this is great! The only problem I have is that when trying to get the bash script working I get extra %0D after the dates and maxResults: http://www.google.com/calendar/feeds/default/private/full?start-min=2008-11-03T12:29:00%0D&start-max=2008-11-10T12:29:59%0D&max-results=2%0D
This gives then "Invalid value for start-min parameter:" error.
The script works ok if I hard code the dates in the wget command.
How do I get rid of the extra %0D's?
Thanks, Martti
Unknown said...
0D is hex for a space character, so you either have a space at the end of the lines (where you set minTime, maxTime and maxResults), or there is a space where you are inserting those variables when calling wget.
Sumit said...
use --no-check-certificate if the first command does not return anything. (some version of cygwin might have this problem)
Anonymous said...
I guess you can use the following free web application: http://elementi.ws/gcalendarcleaner/
|
2021-06-25 09:57:26
|
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|
http://www.r-bloggers.com/find-xargs-like-a-boss/
|
# find | xargs … Like a Boss
March 9, 2012
By
(This article was first published on Getting Genetics Done, and kindly contributed to R-bloggers)
*Edit March 12* Be sure to look at the comments, especially the commentary on Hacker News - you can supercharge the find|xargs idea by using find|parallel instead.
---
Do you ever discover a trick to do something better, faster, or easier, and wish you could reclaim all the wasted time and effort before your discovery? I've had this happen many times - learning how to use vim, learning about querying relational databases, switching from EndNote to Mendeley, etc.
Now I wish I could reclaim all the time I spent writing perl code to do something that find|xargs can do much more easily. I'll lead you through an example using a problem I ran into and solved easily with find|xargs.
The problem:
I'm doing an RNA-seq experiment where I have three replicates {1,2,3} for two conditions {C,M}. I've run Tophat to align the raw reads to a reference genome, and saved the output of each run to a separate directory. Within those directories I have an alignment (accepted_hits.bam) and some other stuff.
Now, I want to assemble transcripts separately for each alignment. All the alignments are 1 directory deep in the tophat output directory. Furthermore, I want to submit a separate job for each assembly onto our cluster using qsub. In a former life I would have wrapped a perl script around this to write shell scripts that the scheduler would run, and then write a second perl script that would submit all the jobs to the scheduler.
Here's a command that will do it all in one go:
PROCS=8; find pwd -name "accepted_hits.bam" | xargs -i echo qsub -l ncpus=$PROCS -- which cufflinks -p$PROCS -o {}-cufflinks -g genes.gtf {} | sh
So let's break this down one piece at a time to see what's going on here.
First the find command. If I want to find all the files in the current directory recursively through any subdirectory, I can use the find command with the -name argument. You can see that find is searching "." (the current directory), and is returning the path (relative to ".") for each file it finds.
But if I'm submitting jobs to a scheduler, I want to use the full absolute path. You can modify find's output by telling it to search in "." but give it the full path. Even better, tell find to search in pwd (those are backticks, usually above the tab key. The shell will run the pwd command, and insert that output into the find command. See below.
Now, here's where xargs comes in. xargs lets you build new commands based on the standard input. In other words, you can build a command to run on each line that gets piped to xargs. Use the -i option to create a command for each individual line on the pipe, and use {} as a placeholder. The example below should help.
So here's whats going on. In the first step, I'm piping the output of find into xargs, and xargs is creating a new command that will echo "somecommand {}", where {} is a placeholder for what gets piped into xargs. So you can replace somecommand with anycommand -any -options -you -want, and echo all that back out to the STDOUT.
The second part simply pipes whatever is echo'd to the STDIN to the bash shell ( | sh). So bash will run each command it receives on the pipe. Since somecommand doesn't exist, I'm getting an error.
Below, I'm building the command to run cufflinks on each alignment, and dump that output back out to a new directory based on the pattern of the alignment (bam) file name. But since in the next step I want to parallelize this on the cluster, and the cluster won't know that cufflinks is in my path, I need to tell it where to find cufflinks. I could give it the path, but I would rather use the backtick trick I showed you above to let the shell tell the shell where cufflinks resides by using which cufflinks.
In the final piece, I'm adding a few more components.
First, I'm setting a shell variable called PROCS. I can access this variable later by using $PROCS. This is how many CPUs I want to allocate to each assembly job. The ";" separates two commands. Instead of using xargs to build a cufflinks command to run at the shell directly, I'm using xargs to build a qsub command that will qsub these jobs to the cluster. To qsub something from the command line, the syntax is qsub -- myprog -o -p -t arg1 arg2 Where are the PBS directives to qsub (like the number of processors I want, the amount of RAM I require, etc). myprog is the program you're running. -o, -p, -t are options to myprog, and arg1 and arg2 are the arguments to myprog. The two hyphens are required between the qsub options and the commands you actually want to run. So in the command above, I'm using xargs to build up a qsub command, substituting$PROCS (8 here) for the number of CPUs I require, calling cufflinks from the full path using the backtick trick, telling cufflinks that I want \$PROCS (8) processors, use genes.gtf for reference annotation based transcript (RABT) assembly, and run all that cufflinks stuff on the supplied alignment.
In summary, this one-liner will submit six 8-processor jobs. It sure beats writing perl scripts. There are a zillion other uses for piping together find with xargs. If you have a useful one-liner, please share it in the comments. Happy piping!
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2014-07-31 09:32:58
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https://mathhelpboards.com/threads/self-adjoint-operator-bens-question-at-yahoo-answers.4806/
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### Welcome to our community
#### Fernando Revilla
##### Well-known member
MHB Math Helper
Here is the question:
I have matrix that represent T:V -> V (linear map over $\mathbb{R}$) according to basis $E$.
E is not an orthonormal set.
how can I know if this T is self-adjoin ?
I know that if E was orthonormal basis we would take the transpose matrix.
the matrix is :
1 2
2 1
Here is a link to the question:
I have posted a link there to this topic so the OP can find my response.
Last edited:
#### Fernando Revilla
##### Well-known member
MHB Math Helper
Hello Ben,
We need the expression of the inner product. Suppose $G$ is the Gram matrix of the inner product with respect to $E$ and $A$ is the matrix of $T$ with respect to $E$. Denote $X,Y$ the coordinates of $x,y$ respectively with respect to $E$. Then,
$$T\mbox{ is self-adjoint}\Leftrightarrow\; <T(x),y>=<x,T(y)>\quad \forall x\forall y\in V$$
We can express
$$<T(x),y>=(AX)^TGY=X^TA^TGY\\<x,T(y)>=X^TG(AY)=X^TGAY$$ Then, $$X^TA^TGY=X^TGAY\Leftrightarrow X^T(A^TG-GA)Y=0$$ This happens for all $X,Y$ if and only if $A^TG=GA$. So, $$\boxed{T\mbox{ is self-adjoint}\Leftrightarrow A^TG=GA}$$ Particular case: If $E$ is orthonormal then $G=I$, so $T$ is self-adjoint if and only if $A^T=A$ (i.e. $A$ is symmetric).
#### Ackbach
##### Indicium Physicus
Staff member
$$T\mbox{ is self-adjoint}\Leftrightarrow\; <T(x),y>=<x,T(y)>\quad \forall x\forall y\in V$$
You can use the \langle and \rangle commands in $\LaTeX$ to get better-looking inner products:
$$\langle T(x),y \rangle = \langle x,T(y) \rangle \quad \forall x,y \in V.$$
#### Fernando Revilla
##### Well-known member
MHB Math Helper
You can use the \langle and \rangle commands in $\LaTeX$ to get better-looking inner products:
Thanks, I knew those commads but for me is better-looking < and >. Only a question of particular taste.
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2020-09-24 04:24:41
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https://www.zbmath.org/authors/?q=ai%3Awang.pengyan
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## Wang, Pengyan
Compute Distance To:
Author ID: wang.pengyan Published as: Wang, Pengyan
Documents Indexed: 62 Publications since 1971 Co-Authors: 14 Co-Authors with 14 Joint Publications 273 Co-Co-Authors
all top 5
### Co-Authors
4 single-authored 5 Niu, Pengcheng 3 Daniels, P. G. 2 Cao, Linfen 2 Chen, Wenxiong 2 Dai, Zhaohui 2 Ferraro, Robert D. 2 Shen, Chun 2 Tartakovsky, Alexandre M. 2 Tuo, S. F. 1 Abhyankar, Shrirang 1 Ahmadov, A. I. 1 Barajas-Solano, David A. 1 Berkey, Judith O. 1 Bystritskiy, Yu. M. 1 Chang, Xiaowen 1 Chen, Guo Qian 1 Constantinescu, Emil M. 1 Cwik, Tom 1 DeVore, Ronald A. 1 Foster, Lisa D. 1 Ghosh, Debojyoti 1 Goel, L. R. 1 Hirakata, H. 1 Hu, Yunyun 1 Jarman, K. D. jun. 1 Ji, Chueng-Ryong 1 Ji, Xiaoxue 1 Kadota, Yoshinobu 1 Klingmann, J. 1 Kuraev, E. A. 1 Kyriazis, George C. 1 Ladde, Gangaram S. 1 Le-Ngoc, Tho 1 Li, Yongming 1 Lin, Xiuli 1 Liu, Karen Y. 1 Liu, Zhenxin 1 Melnitchouk, W. 1 Mezić, Igor 1 Niu, Yahui 1 Özgökmen, Tamay M. 1 Qin, C. S. 1 Qu, Annie 1 Ross, Mark 1 Rypina, Irina I. 1 Salamu, Y. 1 Shah, Nirjhar 1 Shao, Ling 1 Smith, Barry F. 1 Song, Peter Xue-Kun 1 Tartakovsky, Daniel M. 1 Thomas, Anthony W. 1 Trevelyan, Jon 1 Walker, S. K. 1 Wang, Jun 1 Wang, Yongzhong 1 Wessman, M. 1 Wu, Leyun 1 Wu, Zi 1 Xing, Weiwei 1 Yang, Xiaohua 1 Yin, Changming 1 Yu, Er Yung 1 Yu, Mei 1 Zeng, Li 1 Zhang, Wei 1 Zhe, Shandian
all top 5
### Serials
4 Acta Mechanica 4 Engineering Analysis with Boundary Elements 2 Computers & Mathematics with Applications 2 International Journal of Engineering Science 2 International Journal of Heat and Mass Transfer 2 Advances in Mathematics 2 Communications on Pure and Applied Analysis 2 Journal of Numerical Mathematics and Stochastics 1 Computers and Electrical Engineering 1 Computer Physics Communications 1 International Journal for Numerical Methods in Fluids 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Nuclear Physics. B 1 Physics Letters. B 1 Applied Mathematics and Computation 1 Biometrika 1 Journal of Approximation Theory 1 Journal of the Operational Research Society 1 Journal of Optimization Theory and Applications 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Operations Research 1 International Journal of Production Research 1 Parallel Computing 1 Real-Time Systems 1 Concurrency: Practice and Experience 1 Applied Mathematical Modelling 1 Communications in Statistics. Theory and Methods 1 Neural, Parallel & Scientific Computations 1 Physics of Fluids 1 Discrete and Continuous Dynamical Systems 1 Journal of Inequalities and Applications 1 Electronic Journal of Qualitative Theory of Differential Equations 1 Chaos 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of High Energy Physics 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Multiscale Modeling & Simulation 1 Advances in Difference Equations 1 Complex Variables and Elliptic Equations 1 IET Communications 1 SIAM/ASA Journal on Uncertainty Quantification 1 Journal of Function Spaces
all top 5
### Fields
22 Fluid mechanics (76-XX) 16 Partial differential equations (35-XX) 13 Numerical analysis (65-XX) 6 Statistics (62-XX) 5 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Computer science (68-XX) 4 Operations research, mathematical programming (90-XX) 3 Probability theory and stochastic processes (60-XX) 2 Integral equations (45-XX) 2 Quantum theory (81-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)
### Citations contained in zbMATH Open
39 Publications have been cited 436 times in 30 Documents Cited by Year
Two-dimensional finite bin-packing algorithms. Zbl 0611.90079
Berkey, J. O.; Wang, P. Y.
1987
A simulation study of ridge and other regression estimators. Zbl 0336.62056
Lawless, J. F.; Wang, P.
1976
Two algorithms for constrained two-dimensional cutting stock problems. Zbl 0517.90093
Wang, P. Y.
1983
A universal solver for hyperbolic equations by cubic-polynomial interpolation. II: Two- and three-dimensional solvers. Zbl 0991.65522
Yabe, T.; Ishikawa, T.; Wang, P. Y.; Aoki, T.; Kadota, Y.; Ikeda, F.
1991
Remnants, fermions’ tunnelling and effects of quantum gravity. Zbl 1342.83143
Chen, D. Y.; Jiang, Q. Q.; Wang, P.; Yang, H.
2013
Large eddy simulation and experimental studies of a confined turbulent swirling flow. Zbl 1187.76548
Wang, P.; Bai, X. S.; Wessman, M.; Klingmann, J.
2004
Solutions of fully nonlinear nonlocal systems. Zbl 1376.45004
Wang, Pengyan; Yu, Mei
2017
A direct method of moving planes for a fully nonlinear nonlocal system. Zbl 1364.35095
Wang, Pengyan; Niu, Pengcheng
2017
CDF solutions of Buckley-Leverett equation with uncertain parameters. Zbl 1267.76088
Wang, P.; Tartakovsky, D. M.; Jarman, K. D. jun.; Tartakovsky, A. M.
2013
Thermoelectric fields and associated thermal stresses for an inclined elliptic hole in thermoelectric materials. Zbl 1423.74250
Wang, P.; Wang, B. L.
2017
Positive solutions for a weighted fractional system. Zbl 1438.35256
Wang, Pengyan; Wang, Yongzhong
2018
Partitioned EDF scheduling for multiprocessors using a $$C=D$$ task splitting scheme. Zbl 1243.68101
Burns, A.; Davis, R. I.; Wang, P.; Zhang, F.
2012
A third-order family of Newton-like iteration methods for solving nonlinear equations. Zbl 1360.65149
Wang, P.
2011
Symmetric properties of positive solutions for fully nonlinear nonlocal system. Zbl 1420.35462
Wang, Pengyan; Niu, Pengcheng
2019
Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy. Zbl 1374.76237
Rypina, I. I.; Pratt, L. J.; Wang, P.; Özgökmen, T. M.; Mezic, I.
2015
Multiscale characterizations of Besov spaces on bounded domains. Zbl 0922.46029
DeVore, R. A.; Kyriazis, G. C.; Wang, P.
1998
Environmental dispersion in a tidal flow through a depth-dominated wetland. Zbl 1417.76020
Wu, Zi; Zeng, L.; Chen, G. Q.; Li, Z.; Shao, Ling; Wang, P.; Jiang, Z.
2012
Radial symmetry and monotonicity for fractional Hénon equation in $$R^n$$. Zbl 1327.35419
Wang, Pengyan; Dai, Zhaohui; Cao, Linfen
2015
Analysis of three-dimensional ellipsoidal inclusions in thermoelectric solids. Zbl 1425.74183
Wang, P.; Wang, B. L.; Wang, K. F.; Hirakata, H.; Zhang, C.
2019
Nonlinear hydroelastic waves traveling in a thin elastic plate floating on a two-layer fluid. Zbl 1410.74042
Wang, P.; Lu, D. Q.
2016
A scheme for engineer-driven mechanical design improvement. Zbl 0995.74526
Trevelyan, J.; Wang, P.; Walker, S. K.
2002
Large eddy simulations of turbulent swirling flows in a dump combustor: a sensitivity study. Zbl 1065.76119
Wang, P.; Bai, X. S.
2005
Impedance-to-scattering matrix method for large silencer analysis using direct collocation. Zbl 1403.65232
Wang, P.; Wu, T. W.
2016
Numerical solutions for the flow near the end of a shallow laterally heated cavity. Zbl 0804.76083
Wang, P.; Daniels, P. G.
1994
An integrated approach to tolerance synthesis, process selection and machining parameter optimization problems. Zbl 1068.90050
Wang, P.; Liang, M.
2005
Liouville’s theorem for a fractional elliptic system. Zbl 1407.35040
Wang, Pengyan; Niu, Pengcheng
2019
Probabilistic density function method for stochastic ODEs of power systems with uncertain power input. Zbl 1339.60090
Wang, P.; Barajas-Solano, D. A.; Constantinescu, E.; Abhyankar, S.; Ghosh, D.; Smith, B. F.; Huang, Z.; Tartakovsky, A. M.
2015
Rogue wave solutions and generalized Darboux transformation for an inhomogeneous fifth-order nonlinear Schrödinger equation. Zbl 1378.35281
Song, N.; Zhang, W.; Wang, P.; Xue, Y. K.
2017
Asymptotic method of moving planes for fractional parabolic equations. Zbl 1455.35281
Chen, Wenxiong; Wang, Pengyan; Niu, Yahui; Hu, Yunyun
2021
Parallel multigrid finite volume computation of three-dimensional thermal convection. Zbl 0952.76048
Wang, P.; Ferraro, R. D.
1999
Boundary element analysis of bar silencers using the scattering matrix with two-dimensional finite element modes. Zbl 1403.76124
Yang, L.; Wang, P.; Wu, T. W.
2017
An adaptive solution of the 3-D Euler equations on an unstructured grid. Zbl 1022.76031
Zhu, Z. Q.; Wang, P.; Tuo, S. F.
2002
Numerical study of thermal convection in tall laterally heated cavities. Zbl 0797.76087
Daniels, P. G.; Wang, P.
1994
Numerical study of thermal convection in shallow cavities with conducting boundaries. Zbl 0795.76074
Wang, P.; Daniels, P. G.
1994
Assessing the validity of weighted generalized estimating equations. Zbl 1437.62587
Qu, A.; Yi, G. Y.; Song, P. X.-K.; Wang, P.
2011
Stabilized Milstein type methods for stiff stochastic systems. Zbl 1218.65013
Wang, P.; Liu, Zhenxin
2009
Adaptive multigrid solution of the 2D Euler equations on an unstructured grid. Zbl 0961.76061
Zhu, Z. Q.; Wang, P.; Lu, X. B.
2000
Construction of global solutions for a symmetric system of Keyfitz-Kranzer type with three piecewise constant states. Zbl 1458.35266
Wang, Pengyan; Shen, Chun; Lin, Xiuli
2019
Symmetric properties for Choquard equations involving fully nonlinear nonlocal operators. Zbl 1479.35930
Wang, Pengyan; Chen, Li; Niu, Pengcheng
2021
Asymptotic method of moving planes for fractional parabolic equations. Zbl 1455.35281
Chen, Wenxiong; Wang, Pengyan; Niu, Yahui; Hu, Yunyun
2021
Symmetric properties for Choquard equations involving fully nonlinear nonlocal operators. Zbl 1479.35930
Wang, Pengyan; Chen, Li; Niu, Pengcheng
2021
Symmetric properties of positive solutions for fully nonlinear nonlocal system. Zbl 1420.35462
Wang, Pengyan; Niu, Pengcheng
2019
Analysis of three-dimensional ellipsoidal inclusions in thermoelectric solids. Zbl 1425.74183
Wang, P.; Wang, B. L.; Wang, K. F.; Hirakata, H.; Zhang, C.
2019
Liouville’s theorem for a fractional elliptic system. Zbl 1407.35040
Wang, Pengyan; Niu, Pengcheng
2019
Construction of global solutions for a symmetric system of Keyfitz-Kranzer type with three piecewise constant states. Zbl 1458.35266
Wang, Pengyan; Shen, Chun; Lin, Xiuli
2019
Positive solutions for a weighted fractional system. Zbl 1438.35256
Wang, Pengyan; Wang, Yongzhong
2018
Solutions of fully nonlinear nonlocal systems. Zbl 1376.45004
Wang, Pengyan; Yu, Mei
2017
A direct method of moving planes for a fully nonlinear nonlocal system. Zbl 1364.35095
Wang, Pengyan; Niu, Pengcheng
2017
Thermoelectric fields and associated thermal stresses for an inclined elliptic hole in thermoelectric materials. Zbl 1423.74250
Wang, P.; Wang, B. L.
2017
Rogue wave solutions and generalized Darboux transformation for an inhomogeneous fifth-order nonlinear Schrödinger equation. Zbl 1378.35281
Song, N.; Zhang, W.; Wang, P.; Xue, Y. K.
2017
Boundary element analysis of bar silencers using the scattering matrix with two-dimensional finite element modes. Zbl 1403.76124
Yang, L.; Wang, P.; Wu, T. W.
2017
Nonlinear hydroelastic waves traveling in a thin elastic plate floating on a two-layer fluid. Zbl 1410.74042
Wang, P.; Lu, D. Q.
2016
Impedance-to-scattering matrix method for large silencer analysis using direct collocation. Zbl 1403.65232
Wang, P.; Wu, T. W.
2016
Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy. Zbl 1374.76237
Rypina, I. I.; Pratt, L. J.; Wang, P.; Özgökmen, T. M.; Mezic, I.
2015
Radial symmetry and monotonicity for fractional Hénon equation in $$R^n$$. Zbl 1327.35419
Wang, Pengyan; Dai, Zhaohui; Cao, Linfen
2015
Probabilistic density function method for stochastic ODEs of power systems with uncertain power input. Zbl 1339.60090
Wang, P.; Barajas-Solano, D. A.; Constantinescu, E.; Abhyankar, S.; Ghosh, D.; Smith, B. F.; Huang, Z.; Tartakovsky, A. M.
2015
Remnants, fermions’ tunnelling and effects of quantum gravity. Zbl 1342.83143
Chen, D. Y.; Jiang, Q. Q.; Wang, P.; Yang, H.
2013
CDF solutions of Buckley-Leverett equation with uncertain parameters. Zbl 1267.76088
Wang, P.; Tartakovsky, D. M.; Jarman, K. D. jun.; Tartakovsky, A. M.
2013
Partitioned EDF scheduling for multiprocessors using a $$C=D$$ task splitting scheme. Zbl 1243.68101
Burns, A.; Davis, R. I.; Wang, P.; Zhang, F.
2012
Environmental dispersion in a tidal flow through a depth-dominated wetland. Zbl 1417.76020
Wu, Zi; Zeng, L.; Chen, G. Q.; Li, Z.; Shao, Ling; Wang, P.; Jiang, Z.
2012
A third-order family of Newton-like iteration methods for solving nonlinear equations. Zbl 1360.65149
Wang, P.
2011
Assessing the validity of weighted generalized estimating equations. Zbl 1437.62587
Qu, A.; Yi, G. Y.; Song, P. X.-K.; Wang, P.
2011
Stabilized Milstein type methods for stiff stochastic systems. Zbl 1218.65013
Wang, P.; Liu, Zhenxin
2009
Large eddy simulations of turbulent swirling flows in a dump combustor: a sensitivity study. Zbl 1065.76119
Wang, P.; Bai, X. S.
2005
An integrated approach to tolerance synthesis, process selection and machining parameter optimization problems. Zbl 1068.90050
Wang, P.; Liang, M.
2005
Large eddy simulation and experimental studies of a confined turbulent swirling flow. Zbl 1187.76548
Wang, P.; Bai, X. S.; Wessman, M.; Klingmann, J.
2004
A scheme for engineer-driven mechanical design improvement. Zbl 0995.74526
Trevelyan, J.; Wang, P.; Walker, S. K.
2002
An adaptive solution of the 3-D Euler equations on an unstructured grid. Zbl 1022.76031
Zhu, Z. Q.; Wang, P.; Tuo, S. F.
2002
Adaptive multigrid solution of the 2D Euler equations on an unstructured grid. Zbl 0961.76061
Zhu, Z. Q.; Wang, P.; Lu, X. B.
2000
Parallel multigrid finite volume computation of three-dimensional thermal convection. Zbl 0952.76048
Wang, P.; Ferraro, R. D.
1999
Multiscale characterizations of Besov spaces on bounded domains. Zbl 0922.46029
DeVore, R. A.; Kyriazis, G. C.; Wang, P.
1998
Numerical solutions for the flow near the end of a shallow laterally heated cavity. Zbl 0804.76083
Wang, P.; Daniels, P. G.
1994
Numerical study of thermal convection in tall laterally heated cavities. Zbl 0797.76087
Daniels, P. G.; Wang, P.
1994
Numerical study of thermal convection in shallow cavities with conducting boundaries. Zbl 0795.76074
Wang, P.; Daniels, P. G.
1994
A universal solver for hyperbolic equations by cubic-polynomial interpolation. II: Two- and three-dimensional solvers. Zbl 0991.65522
Yabe, T.; Ishikawa, T.; Wang, P. Y.; Aoki, T.; Kadota, Y.; Ikeda, F.
1991
Two-dimensional finite bin-packing algorithms. Zbl 0611.90079
Berkey, J. O.; Wang, P. Y.
1987
Two algorithms for constrained two-dimensional cutting stock problems. Zbl 0517.90093
Wang, P. Y.
1983
A simulation study of ridge and other regression estimators. Zbl 0336.62056
Lawless, J. F.; Wang, P.
1976
all top 5
### Cited by 38 Authors
8 Niu, Pengcheng 8 Wang, Pengyan 3 Cao, Linfen 3 Ji, Xiaoxue 3 Wang, Xiaoshan 3 Wu, Leyun 2 Chen, Wenxiong 2 Chen, Xueying 2 Feng, Yiying 2 Geng, Lu-Lu 2 Li, Guanfeng 2 Liu, Jiangen 2 Yang, Xiao-Jun 2 Zeng, Fanqi 1 Alsulami, Hamed Hamdan 1 Bao, Gejun 1 Bao, Sijia 1 Cai, Miaomiao 1 Dai, Zhaohui 1 Fan, Linlin 1 Geng, Qiuping 1 He, Xiaoming 1 Hu, Yunyun 1 Li, Fengquan 1 Lü, Zhongxue 1 Ma, Feiyao 1 Niu, Yahui 1 Ntouyas, Sotiris K. 1 Wang, Jun 1 Wang, Xinjing 1 Wang, Yongzhong 1 Wo, Weifeng 1 Wu, Jiayan 1 Yang, Zuodong 1 Zhang, Biran 1 Zhang, Yajie 1 Zhao, Xin 1 Zou, Wenming
all top 5
### Cited in 20 Serials
5 Communications on Pure and Applied Analysis 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Advances in Mathematics 2 Journal of the Korean Mathematical Society 2 Discrete and Continuous Dynamical Systems 2 Complex Variables and Elliptic Equations 1 Journal of Mathematical Analysis and Applications 1 Pacific Journal of Mathematics 1 Applied Mathematics Letters 1 Fractals 1 Journal of Inequalities and Applications 1 Fractional Calculus & Applied Analysis 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Mediterranean Journal of Mathematics 1 Advances in Difference Equations 1 Boundary Value Problems 1 Advances in Mathematical Physics 1 Analysis and Mathematical Physics
all top 5
### Cited in 8 Fields
27 Partial differential equations (35-XX) 3 Ordinary differential equations (34-XX) 2 Real functions (26-XX) 2 Integral equations (45-XX) 1 Functions of a complex variable (30-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX)
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2022-05-24 06:14:30
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https://answers.ros.org/question/238679/how-to-chain-three-catkin-workspaces/
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ROS Resources: Documentation | Support | Discussion Forum | Service Status | Q&A answers.ros.org
# How to chain three catkin workspaces?
How do you chain three catkin workspaces so that their setup.bash files don't conflict?
I tried following the instructions in the wiki, but they're a bit confusing and don't seem to be correct.
My workspaces are:
1. the base Kinetic workspace installed into the standard /opt/ros/kinetic location
2. a workspace containing third-party packages not available in kinetic (such as robot_upstart), at /usr/local/mybot/overlay
3. a workspace containing my custom application and packages at /usr/local/mybot/ros
Each workspace builds fine when I run catkin_make inside them. However, I can't source their setup.bash scripts to expose all their packages to ROS.
I'm using:
1. rospack list|grep -i actionlib to determine if the base Kinetic workspace is accessible, called check A.
2. rospack list|grep -i upstart to determine if the second workspace is accessible, called check B.
3. rospack list|grep -i mybot to determine if the third workspace is accessible, called check C.
If I run source /opt/ros/kinetic/setup.bash, then A passes, B fails, and C fails, as expected.
If I then run source /usr/local/mybot/overlay/devel/setup.bash, then A passes, B passes, and C fails, as expected.
If I then run source /usr/local/mybot/ros/devel/setup.bash, then A passes, B fails unexpectedly, but C passes.
So it seems that my third workspace is overwriting the environment set by the second workspace. How do I fix this?
edit retag close merge delete
Sort by » oldest newest most voted
Yes, it is possible to source multiple workspaces and use the combined environment of them. You can source a setup file and pass --extend which will extend the current environment (set by another workspace before) instead of "resetting" the environment.
more
Workspaces don't extend the environment; they set it.
The first time you build a workspace, it captures the existing ROS environment and creates a setup file that overlays the new workspace on the existing environment variables. When you source the setup file from this workspace, it sets the environment variables to overlay this workspace on your previous environment.
This means that you only need to source one setup.bash for the workspace at the top of your set of overlays, and that it will always produce the same environment.
To build your overlay, you should:
1. remove the build and devel directories from your workspaces, to reset them to a clean state
2. source /opt/ros/kinetic/setup.bash and build workspace B
3. source workspace B and build workspace C
To use your overlay, you just need to source the setup file in workspace C
If you need to make minor changes in workspace B, you can rebuild it with any environment, but if you need to to a complete rebuild of workspace B, you should source /opt/ros/kinetic/setup.bash before you do, so that you don't overlay it on your other workspaces.
more
It is possible to extend the environment rather then (re)setting it. Please see other answer.
( 2016-07-04 11:05:40 -0600 )edit
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2019-01-19 17:04:07
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https://jro.io/r2c2/
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R2-C2
Reliable RAID Configuration Calculator (R2-C2)
Reliable RAID Configuration Calculator (R2-C2) lets you compare the probability of zpool failure as a function of individual drive failure probability for different ZFS RAID configurations. Enter the number of hard drives per vdev, the parity drives per vdev, and number of vdevs. Click "+" or "-" to add or remove configs. See notes and detailed derivation examples below.
Config. HDDs per vdev Parity per vdev Total vdevs Total HDDs Total data Total parity 1 24 18 6 2 24 18 6 3 24 18 6
x=y line
Number of Iterations:
This graph shows the probability of zpool failure (y-axis) as a function of (assumed independent) individual drive failure probability (x-axis) for the given configurations (smaller numbers indicate a more reliable zpool). Please note the assumptions listed below when considering these results. The failure probability equations are as follows:
GENERAL EQUATION
$$P_n=1-\left(\sum_{i=0}^{r}\left(\binom{d}{i}p^i(1-p)^{d-r}\right)\right)^{v}$$
where
$$P_n = \text{Probability of zpool failure for Configuration n}$$
$$p = \text{Probability of a single drive failure}$$
$$r = \text{Number of parity drives per vdev}$$
$$d = \text{Number of drives per vdev}$$
$$v = \text{Total number of vdevs in zpool}$$
$$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$
Calculator Notes & Assumptions
A couple of notes on RAID, ZFS, and drive failure:
• This calculator assumes that one drive failure is completely independent of another drive's failure, i.e., that drive #3 failing will have no bearing on when (or if) drive #7 fails. This may not always be the case; for example, a set of drives from the same manufacturing lot could share defect characteristics and all fail around the same time. There is also anecdotal evidence that drives, even if not from the same manufacturing run, somehow may tend to fail in groups.
• When one drive has failed in ZFS, the act of rebuilding the zpool is itself a high-risk, high-intensity operation which puts the drive under considerably more stress than its default run condition. Because of this, rebuilding a zpool may actually increase the likelihood that the pool dies. Again, this calculator does not account for that.
• In RAID 5/6 and RAID-Z1/2/3, the RAID controller (be it hardware or software) does not actually dedicate some quantity of the drives to user data and the remainder to parity data. This sort of configuration was employed in RAID 4, but having all the parity information for the whole array reside on a single disk created contention for access to that disk. The solution was to stager the parity data across all the disks in the array, in a sort of barber pole fashion. For the sake of making visualization and discussion easier, I will still refer to "data drives" and "parity drives", but this distinction is purely conceptual. I would encourage readers to familiarize themselves with the standard RAID levels before reading on.
• This calculator is intended for comparative purposes only, and its output should be used as such. It will not tell you the absolute probability of zpool failure in the real world; it only shows an estimate of which configuration might be best. Because of this, and for the sake of better viewing, the axis scales are different by a factor of 50. If you want to overlay an x=y line on the graph for reference, check the "x=y line" box next to the control buttons.
Detailed Derivation Examples
Below is a detailed step-by-step derivation of the failure probability equations for two different configurations. Once this processes is understood, it should be easy to see where the above equations come from.
The two examples we'll review are the first two default configurations supplied when R2-C2 is first loaded. They are as follows:
Example 1: 3 vdevs, each with 8 drives in RAID-Z2 (24 total, 18 data, 6 parity)
Example 2: 2 vdevs, each with 12 drives in RAID-Z3 (24 total, 18 data, 6 parity)
We'll assume that all our drives have a certain probability of failure, and that you would use the same exact drives for either configuration. We can call the probability of failure of a single drive $$p$$:
$$p = \text{Probability(Single drive failure)}$$
A few quick points if you haven't studied basic probability before:
• Multiplication in probability is like an AND operator; if you multiply the probability of event X occurring with the probability of event Y occurring, you get the probability that event X AND event Y will occur.
• Addition in probability is like an OR operator; if you add the probability of event X occurring and the probability of event Y occurring, you get the probability that event X OR event Y will occur.
• We'll make use of the fact that $$\text{1 - Probability(Event X occurring) = Probability(Event X NOT occurring)}$$ several times in these calculations.
• We'll be using binomial distributions to calculate our failure probabilities, which you can read more about here.
Example 1: 3 vdevs, 8 drives per vdev, each in RAIDZ2
We have 3 vdevs and any 3 drives in the same vdev must fail for us to have data loss, and a loss of a single vdev will result in a total loss of the zpool. We'll start by calculating the probability of losing a single vdev of 8 drives using a binomial distribution:
$$f(k;n,p) = \binom{n}{k}p^n(1-p)^{n-k}$$
$$\text{where}$$
$$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$
For example 1, we'll have $$p = \text{Probability(Single drive failure)}, n = 8, k = 3$$:
$$\binom{8}{3}p^3(1-p)^{5}$$
$$=56p^3(1-p)^5$$
This has 3 parts to it:
1. $$\binom{8}{3}$$ is saying "how many ways can I have 3 failures in a vdev of 8 drives?" Using the binomial coefficient, we determine there are 56.
2. $$p^3$$ is the probability of any 3 drives failing.
3. $$(1-p)^5$$ is the probability that the other 5 drives don't fail.
Summed up, these parts are:
The probability that...
...drives 1, 2, and 3 fail, and that 4, 5, 6, 7, and 8 don't fail, OR...
...drives 1, 2, and 4 fail, and that 3, 5, 6, 7, and 8 don't fail, OR...
...drives 1, 2, and 5 fail, and that 3, 4, 6, 7, and 8 don't fail, OR...
...and so on, 56 times, once for each possible combination of failures. Again, all of this is the probability that we'll lose 3 drives on one vdev. However, this alone doesn't fully account for the probability that we'll lose the vdev, since we can lose it by having 4 drives fail, or 5, 6, 7, or even all 8 drives. To account for these, we'd have to add 5 more binomial distributions, with $$n=8$$ and $$k=4 ... 8$$. With all these summed up, we'd have the probability that 3 or more drives in a vdev failed. That's a lot of terms. Another option that's a lot simpler to express makes use of the fact that:
$$\text{Probability(3 or more drives failing) = 1 - Probability(2 or fewer drives failing)}$$
Because of a similar trick you'll see in the next step, we'll actually use $$\text{Probability(2 or fewer drives failing)}$$, i.e., the probability that the vdev is still alive (the same equation as the probability that it's dead, but without the $$(1 - ...)$$ part in front). We'll still use several binomial distributions (3 of them, to be exact, as opposed to 6 with the other way) with $$n=8$$ and $$k=2,1,0$$, and we'll sum them all up. This is what it'll look like (we'll call the whole thing $$A$$):
$$A = \binom{8}{2} p^2(1-p)^{6} + \binom{8}{1} p^1(1-p)^{7} + \binom{8}{0} p^0(1-p)^{8}$$
$$A = 28 p^2(1-p)^{6} + 8 p^1(1-p)^{7} + (1-p)^{8}$$
Notice the 3 terms in this formula. The first term, $$\binom{8}{2} p^2(1-p)^{6} = 28 p^2(1-p)^{6}$$, is the probability that 2 drives in our vdev fail. The second term, $$\binom{8}{1} p^1(1-p)^{7} = 8 p^1(1-p)^{7}$$, is the probability that 1 drive fails. The last term, $$\binom{8}{0} p^0(1-p)^{8} = (1-p)^{8}$$, is the probability that none of the drives fail. Summing all these up is saying "the probability that (2 drives fail -OR- 1 drive fails -OR- 0 drives fail)".
Now we need to account for the fact that we have 3 vdevs, and that if at least one of them fails (2 could fail, or even all 3), we lose the whole zpool. One option is to use a set of 3 binomial distributions, this time using $$p = A$$, $$n = 3$$, and $$k = 1, 2, 3$$. A much easier option is to use the same trick $$1-...$$ as above:
$$\text{Probability(at least one vdev fails) = 1 - Probability(all 3 vdevs are alive)}$$
We calculated the probability of a single vdev being alive in the previous step, and we'll use that here to calculate $$P_1$$, the probability of losing our whole zpool in example 1:
$$P_1 = 1-A^3$$
$$P_1 = 1-\left(\binom{8}{2} p^2(1-p)^{6} + \binom{8}{1} p^1(1-p)^{7} + \binom{8}{0} p^0(1-p)^{8}\right)^3$$
$$P_1 = 1-(28 p^2(1-p)^{6} + 8 p^1(1-p)^{7} + (1-p)^{8})^3$$
To reiterate, $$A$$ is the probability that one of our vdevs is healthy, so $$A^3$$ is the probability that vdev1 AND vdev2 AND vdev3 are healthy, and $$1 - A^3$$, is the opposite of that, i.e., all 3 vdevs are not healthy (at least 1 vdevs has failed) and our whole zpool is lost.
Example 2: 2 vdevs, 12 drives per vdev, each in RAIDZ3
We have 2 vdevs and any 4 (or more) drives in the same vdev must fail for us to have data loss, but a loss of either vdev will result in a total loss of the zpool. We'll proceed in the same way as example 1, using the same trick to compute the probability that one vdev is alive, with $$p = \text{Probability(Single drive failure)}, n = 12, k = 3, 2, 1, 0$$, and we'll call the whole thing $$B$$:
$$B = \binom{12}{3} p^3(1-p)^{9} + \binom{12}{2} p^2(1-p)^{10} + \binom{12}{1} p^1(1-p)^{11} + \binom{12}{0} p^0(1-p)^{12}$$
$$B = 220 p^3(1-p)^{9} + 66 p^2(1-p)^{10} + 12 p^1(1-p)^{11} + (1-p)^{12}$$
Agian, this is the probability that one of our 12-drive vdevs is alive. As above, we'll use a second binomial distribution to determine the probability that at least two vdevs fail by computing $$\text{1 - probability that both vdevs are alive}$$, and we'll call this $$P_2$$:
$$P_2 = 1-B^2$$
$$P_2 = 1-\left(\binom{12}{3} p^3(1-p)^{9} + \binom{12}{2} p^2(1-p)^{10} + \binom{12}{1} p^1(1-p)^{11} + \binom{12}{0} p^0(1-p)^{12}\right)^2$$
$$P_2 = 1-\left(220 p^3(1-p)^{9} + 66 p^2(1-p)^{10} + 12 p^1(1-p)^{11} + (1-p)^{12}\right)^2$$
Source Code
The JavaScript code that generates the probability data that go into the graphing function can be found below. The code for generating the graphs (with flotr2), the LaTeX (with MathJax), and other UI elements can be found towards the bottom of the JS file here. Feel free to contact me with any comments, questions, suggestions, etc.
function Factorial(n) {
// Factorial(n) = n! = n * n-1 * n-2 * ... * 2 * 1
var rval = 1;
for (var i = 2; i <= n; i++) {
rval = rval * i;
}
return rval;
}
function BinomCoeff(n,k) {
// BinomCoeff(n,k) = n choose k = n! / (k! * (n-k)!)
return Factorial(n) / (Factorial(k) * Factorial(n-k));
}
function BinomDistrib(n,k,p) {
// BinomDistrib(n,k,p) = (n choose k) * p^k * (1-p)^(n-k)
return BinomCoeff(n,k) * Math.pow(p,k) * Math.pow(1-p,n-k)
}
function R2C2(numHDD, rLvl, numVdev, pFail) {
// R2C2() returns the probability value of zpool failure given configuration parameters
// numHDD = (number) Number of HDDs per vdev
// rLvl = (number) Redundancy level (1 for RAID-Z1, 2 for RAID-Z2, 3 for RAID-Z3, etc.)
// numVdev = (number) Number of vdevs in zpool
// pFail = (number) Probabililty of an individual drive failing
var P = 0;
// P = probability that rLvl or fewer drives have failed (i.e., vdev is still alive)
for (var i = rLvl; i >= 0; i--) {
P = P + BinomDistrib(numHDD, i, pFail);
}
// 1 - P^numVdev = probability that one or more of the vdevs are not alive
return 1 - Math.pow(P,numVdev);
}
function GenDataset(numHDD, rLvl, numVdev, numIttr) {
// GenDataset() returns an array of zpool failure probability values given a set of configuration parameters
// numHDD = (number) Number of HDDs per vdev
// rLvl = (number) Redundancy level (1 for RAID-Z1, 2 for RAID-Z2, 3 for RAID-Z3, etc.)
// numVdev = (number) Number of vdevs in zpool
// numIttr = (number) Number of iterations to run
var x = [];
for(var i = 0; i <= numIttr; i++) {
x.push([i/(numIttr*10), R2C2(numHDD, rLvl, numVdev, i/(numIttr*10))])
}
return x;
}
❖ back to main
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2022-08-09 18:56:25
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https://stats.stackexchange.com/questions/13847/how-does-dinterval-for-interval-censored-data-work-in-jags
|
# How does dinterval() for interval censored data work in JAGS?
I am trying to understand how dinterval() works in JAGS for censored data. I am modeling coarse data where I only have upper and lower bounds for each data point (not the true value). Here is a simple example of how I think it should work:
Some upper and lower bounds for each point:
> head(lim)
L U
[1,] 14.98266 15.68029
[2,] 21.21827 21.91590
[3,] 18.34953 19.04716
[4,] 19.00186 19.69949
[5,] 15.39891 16.09654
[6,] 17.81705 18.51468
A function to write the model (assuming the data come from a normal with a common mean and variance):
playmodel <- function(){
for (i in 1:50){
is.censored[i] ~ dinterval(t[i], lim[i,])
t[i] ~ dnorm(mu,tau)
}
mu ~ dnorm(0,.001)
tau ~ dgamma(.01,.01)
}
filename <- "toymod.bug"
write.model(toymod,filename)
Some functions and assignments for the jags call:
data <- list("lim"=lim)
inits <- list(mu=rnorm(1),tau=rgamma(1,.01,.01),t=as.vector(apply(lim,1,mean)))
#last part is to ensure the starting value is between the upper and lower limit
#each chain will start at the same place for t but this is just for this case
params <- c("mu","tau")
And run the model:
playmodel.jags <- jags(data,inits, params, model.file="toymod.bug", n.chains=3,
n.iter=50000,n.burnin=30000, n.thin=1, DIC=TRUE,
working.directory=NULL,refresh = 50000/50, progress.bar = "text")
What happens when I run this?
1) my estimate of mu hovers right around 0 when it should be 15
2) it will not run if DIC=TRUE:
error: "Error in jags.samples(model, variable.names, n.iter, thin, type = "trace", : Failed to set trace monitor for node deviance
Note: I can get a similar model running in OpenBUGS by omitting the dinterval() line and appending I(Lower,Upper) to dnorm.
Here is an answer from Martyn Plummer:
As written, your model does not have any observed outcomes. You probably noticed that it runs really really fast. This is because it is forward sampling from the prior. That is why your posterior mean for mu is the same as the prior mean of 0. The variable name "is.censored" is appropriate for left- or right-censored data, as found in survival analysis, but not for your problem. So I'm going to rename it "y". If you have
y[j] ~ dinterval(t[j], lim[j,])
and lim[j] has two columns, then y[j] can take three possible values
y[j] = 0 if t[j] <= lim[j,1]
y[j] = 1 if lim[j,1] < t[j] <= lim[j,2]
y[j] = 2 if lim[j,2] < t[j]
To model interval censored data, you need to supply y[j] as data in your model. In your case, you know that t[j] always falls between lim[j,1] and lim[j,2] so your data should be.
data <- list("lim"=lim, "y"=rep(1,nrow(lim)))
The problem with DIC is fairly deep. Because your model does not have any outcome data, the deviance is not defined. However, even if you supply outcome data you will still not get the deviance statistics you want (including pD). The deviance will be zero and the "jags" function will fall back on the Gelman heuristic for pD (I did not write this so don't ask me to explain it), which will also be zero. The likelihood you really want is
p(lim[j,1] < t[j] <= lim[j,2] | mu, tau)
But JAGS is giving you
p(y[j] | t[j])
which is always 1. The "focus" of DIC is wrong. I don't know what WinBUGS does under these circumstances. Perhaps it has special rules for censored variables.
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2021-04-12 01:51:54
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http://sebastiaanjanssens.nl/
|
## Welcome!
My name is Sebastiaan Janssens and I work in mathematics under supervision of my PhD advisors O. Diekmann, S.A. van Gils and Yu.A. Kuznetsov at Utrecht University and the University of Twente in The Netherlands.
My interests are in dynamical systems: foundations, stability and bifurcation. In particular:
• various classes of delay equations,
• linear algebra and functional analysis,
• discrete dynamics on spaces of measures,
• computational aspects and computer algebra.
I consider myself competent in Maple, MATLAB, modern Fortran and C (but not C++). Also, I enjoy Lisp, but so far mostly just for editing text in Emacs.
Via the menu at the top you find some information on my work, as well as my blog.
### Contact information
You are welcome to contact me via email email or LinkedIn. Optionally, use my PGP key to encrypt your email message.
### Typesetting credits
Formulas in $\LaTeX$ were processed using the QuickLaTeX plugin and, more recently, the MathJax engine. These are both great projects and they each deserve a look.
|
2018-06-25 19:46:04
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https://pos.sissa.it/363/013/
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Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
Interglueball potential in SU(N$_c$) lattice gauge theory
N. Yamanaka,* H. Iida, A. Nakamura, M. Wakayama
*corresponding author
Full text: pdf
Pre-published on: January 03, 2020
Published on:
Abstract
We report on our calculation of the interglueball potentials in $SU(2)$, $SU(3)$, and $SU(4)$ lattice Yang-Mills theories using the indirect (so-called HAL QCD) method. We use the cluster decomposition error reduction technique to improve the statistical accuracy of the glueball correlators. After calculating the glueball scattering cross section in $SU(2)$ Yang-Mills theory and combining with the observational data of the dark matter mass distributions, we derive the lower limit on the scale parameter.
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
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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2020-08-15 05:40:09
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http://slideplayer.com/slide/3193394/
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# Matrices are identified by their size.
## Presentation on theme: "Matrices are identified by their size."— Presentation transcript:
Matrices are identified by their size.
Matrices and Row Operations column A matrix is a rectangular array of numbers. We subscript entries to tell their location in the array rows columns row Matrices are identified by their size.
A matrix that has the same number of rows as columns is called a square matrix.
main diagonal
If you have a system of equations and just pick off the coefficients and put them in a matrix it is called a coefficient matrix. Coefficient matrix
If you take the coefficient matrix and then add a last column with the constants, it is called the augmented matrix. Often the constants are separated with a line. Augmented matrix
Elementary Row Operations
Operations that can be performed without altering the solution set of a linear system 1. Interchange any two rows 2. Multiply every element in a row by a nonzero constant 3. Add elements of one row to corresponding elements of another row We are going to work with our augmented matrix to get it in a form that will tell us the solutions to the system of equations. The three things above are the only things we can do to the matrix but we can do them together (i.e. we can multiply a row by something and add it to another row).
Row Echelon Form "The Goal"
We use elementary row operations to make the matrix look like the one below. The # signs just mean there can be any number here---we don’t care what. "The Goal" After we get the matrix to look like our goal, we put the variables back in and use back substitution to get the solutions.
"The Goal" Use row operations to obtain echelon form:
We already have the 1 where we need it. Work on this column first. Get the 1 and then use it as a “tool” to get zeros below it with row operations. The augmented matrix We’ll take row 1 and multiply it by 3 and add to row 2 to get a 0. The notation for this step is 3r1 + r2 we write it by the row we replace in the matrix (see next screen). "The Goal"
3r1 + r2 2r1 + r3 Now our first column is like our goal. 2r1 2 4 2 2 3r1 3 6 3 3 + r3 + r2 1 0 1 2 0 Now we’ll use 2 times row 1 added to row 3 to get a 0 there.
r2 −2r2 + r3 We need a 1 in the second row second column so we’ll multiply row 2 by −1 We’ll use row 2 with the 1 as a tool to get a 0 below it by multiplying it by −2 and adding to row 3 −2r2 0 −2 −4 0 the second column is like we need it now + r3 −1 −1 Now we’ll move to the second column and do row operations to get it to look like our goal.
Solution is: (−2 , 2 , −1) y column z column x column equal signs
Substitute −1 in for z in second equation to find y Substitute −1 in for z and 2 for y in first equation to find x. Now we’ll move to the third column and we see for our goal we just need a 1 in the third row of the third column. We have it so we’ve achieved the goal and it’s time for back substitution. We put the variables and = signs back in. Solution is: (−2 , 2 , −1)
Solution is: (−2 , 2 , −1) This is the only (x , y , z) that make ALL THREE equations true. Let’s check it. These are all true. Geometrically this means we have three planes that intersect at a point, a unique solution.
Reduced Row Echelon Form
To obtain reduced row echelon form, you continue to do more row operations to obtain the goal below. "The Goal" This method requires no back substitution. When you put the variables back in, you have the solutions.
Let’s try this method on the problem we just did
Let’s try this method on the problem we just did. We take the matrix we ended up with when doing row echelon form: −2r2+r1 3r3+r1 −2r3+r2 Let’s get the 0 we need in the second column by using the second row as a tool. Notice when we put the variables and = signs back in we have the solution Now we’ll use row 3 as a tool to work on the third column to get zeros above the 1. "The Goal"
The process of reducing the augmented matrix to echelon form or reduced echelon form, and the process of manipulating the equations to eliminate variables, is called: Gaussian Elimination
"The Goal" Let’s try another one: The augmented matrix:
We’ll now use row 1 as our tool to get 0’s below it. r1 −r2 We have the first column like our goal. On the next screen we’ll work on the next column. −2r1+r2 −7r1+r3 If we subtract the second row from the first we’ll get the 1 we need for the first column. "The Goal"
"The Goal" We’ll now use row 2 as our tool to get 0’s below it.
Wait! If you put variables and = signs back in the bottom equation is 0 = −19 a false statement! −1/5r2 10r2+r3 INCONSISTENT - NO SOLUTION If we multiply the second row by a −1/5 we’ll get the one we need in the second column. "The Goal"
"The Goal" One more: r1 −r3 1/3r2 −9r2+r3
Oops---last row ended up all zeros. Put variables and = signs back in and get 0 = 0 which is true. This is the dependent case. We’ll figure out solutions on next slide. −2r1+r2 −4r1+r3 "The Goal"
x y z put variables back in solve for x & y
Let’s go one step further and get a 0 above the 1 in the second column No restriction on z x y z 3r2+r1 Infinitely many solutions where z is any real number
works in all 3 What this means is that you can choose any real number for z and put it in to get the x and y that go with it and these will solve the equation. You will get as many solutions as there are values of z to put in (infinitely many). The solution can be written: (z + 2 , z + 1 , z) Let’s try z = 1. Then y = 2 and x = 3 Let’s try z = 0. Then y = 1 and x = 2 Infinitely many solutions where z is any real number
Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar
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2017-08-22 07:42:57
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http://math.stackexchange.com/questions/222450/evaluate-the-triple-integral-int-02-int-0y-int-0-sqrt4-y22xdxdzdy
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# Evaluate the triple integral $\int_0^2\int_0^y\int_0^{\sqrt{4-y^2}}2xdxdzdy\\$.
$$\\ \int_0^2\int_0^y\int_0^{\sqrt{4-y^2}}2xdxdzdy\\ \int_0^2\int_0^y4-y^2dzdy\\ \int_0^2(4-y^2)ydy\\ -\frac{1}{2}\left( \left.4y-\frac{1}{3}y^3\right|_0^2\right )\\ =-\frac{8}{3}$$
I have worked over this problem several times and I cannot find the step where I went wrong.
-
The step where you made mistake is in evaluating the integral $\displaystyle \int_0^2 (4-y^2)ydy$ $$\int_0^2 (4-y^2)ydy = \int_0^2 \left( 4y - y^3\right)dy = \left(2y^2 - y^4/4 \right)_{y=0}^{y=2} = 8 - 2^4/4 = 8 - 4 =4$$
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Thank you very much. It's always the stupid mistakes that get me. This is probably a case of too little sleep and too much studying. Thank you again! – user1405177 Oct 28 '12 at 4:18
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2013-05-23 14:32:30
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http://www.stevebronder.com/news/2014/8/3/8el0szzsaxhfiljvkf8f4uty2yiinh
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Updates and Research from Steve Bronder
The purpose of this site is to give current information on Steve Bronder's (me) research and personal life
# Introduction to R: Graphs and Maps
Introduction to R: Graphs and Maps
### Introduction
The purpose of this tutorial is to be an introductory text for the R programming language’s graphing and mapping features. R is a free software programming language and software environment for statistical computing and graphics. While it performs similar functions to packages such as SAS and STATA, the systems have specific strengths and weaknesses. This paper uses ggplot2 and ggmap to show R’s graphing capabilities. This document is structured as follows. Section two will briefly explain the S language, how R processes input, installing packages, how to find help while exploring R, and importing SAS, Excel, and csv datasets.
Section three is comprised of introductory statistics and data manipulation. Simple summary statistics will first be introduced which will then be used to describe $$R$$‘s second level functions such as the apply family. A simple custom function will also be written. Section four will use the ggplot2 package to create simple graphs and maps. Throughout this document the data set ’iris’ will be used as it comes available with R. This document is made to be worked along with. It is highly encouraged to run the R code while going through this tutorial.
### R and SAS Language
This section will cover the basics of the R computing language, importing and exporting files, and installing packages. There is one main difference which gives R and SAS their respective advantage. When each package was first built, R was made for small geological and natural datasets which were easier to manipulate with an interpreter style language. SAS was made for businesses with larger, dynamic datasets. As such, SAS was made in the style of a compiled language. The lines between what is compiled and intererpreted now are fuzzy, but when it comes to processes such as for loops, R is not as efficient as SAS. To import a datafile, name it shoes, specify a csv, replace existing file, and specify no column names in SAS input.
proc import datafile=“C:.csv” out=shoes dbms=csv replace; getnames=no; run;
proc print data=test; run;
This chunk of code is compiled without any further user instructions. While this is possible in R with its secondary functions, R code to do the same thing looks as such.
Each line of code is interpreted one at a time and is slightly slower than SAS. The read.csv() function specifics the file and tells $$R$$ there are no column headers. The second line tells $$R$$ to take the object shoes and only keep rows 2 through N, N being the total number of rows. A major difference between $$SAS$$ and R is that all R functions not stored as objects are erased immediately. Without the object attached to the code such as
R would simply display the csv as a data frame in the console without creating an object for it. At the bottom of this section is a table which covers some basic info for both languages.
Looking at the code above it seems that with spacing there is not much of a difference between the two languages. However, keep in mind R interprets row by row and SAS interprets chunk by chunk. Spend a moment thinking how a for loop would be interpreted in each. It becomes very clear that a process that chunks code versus going line by line is going to be considerably faster in a compiled processes. While there are ways around this in R, it should be noted SAS language has an advantage in iterative processes.
Unlike SAS, R is not one giant package, but is a connected network of packages written and approved to be uploaded onto the Comprehensive $$R$$ Archive Network, or CRAN. Packages can be downloaded from $$R$$ by typing:
install.packages(“packagename”)
library(package)
Note that installing requires a string and loading requires an object. Rstudio is highly recommended for the purpose of easily keeping track of packages.
### Getting Help
Unlike SAS, R has no live support. Most users learn R from guides such as this. There are several wonderful books and classes available online that are made to teach R. Some of these include Data Mining with R by Luis Torgo, Code schools Online course, and for advanced R programming methods the in progress book Advanced R available at the sites webpage. Documentation is kept of each package on CRAN, but “help” files can tend to appear discouragingly difficult to interpret by newcomers. My best advice would be to work through a package’s documentation. With many examples available online such as ggplot2 or tseries. Many examples are available online from websites such as R-bloggers and . Answers to most questions can be found through either google or posting it to Stackoverflow. Inside of R find help by typing:
?help
For particular functions, such as in the example, it is possible to do the same thing to reach the help section for each function.
Nothing is particularly rocket science and with a little searching, and perhaps writing a new function or two, any task can generally be done in R. On one final note, it should always be recognized that there are times other statistical packages may simply be set up to perform a task in a more efficient or easier manner than R. Between the choice of writing and testing new R code and using another package, I prefer the latter.
Product Developer Written Scripts Processing
SAS SAS Institute PL/I, Fortran, Assembly None Compiler
R R Foundation C, Fortran, S R. Python, Perl Interpreter
### Importing and Exporting Data
In this section the article examines how to import data for analysis. It is easy to import a basic csv into R, but what about Excel spreadsheets, SPSS, STATA, or SAS files? The R packages foreign and RODBC will be used to import data very easily. Like the csv, only one line of code is involved inside of R. For each statistical package the dataset needs to be placed into a transportable format. Here is an example of how this is done in SAS.
libname out xport ‘c:/mydata.xpt’; data out.mydata; set sasuser.mydata; run;
The first line lets SAS know to export the file mydata.xpt. The second line tells SAS to use the data mydata for export. The set function is used to tell SAS to export all of the data, but could have also been used for concatenating data sets or subsetting mydata before export. Once the data is transfereable the code for R is simple.
Each of the other main statistical packages have a similar call within program and a simple line for R to use. It’s usually something like read.stuff(). guessing at the help file (?read.table) can usually get pretty close to the answer.Click here for a link to import methods via Quick-R page on importing and exporting data. Once the data is loaded in R it is possible to view the first few lines with the function head().
This function will display the first 10 rows or so of the data set. The following code takes a data table and exports it to a csv.
write.csv(mydata,“C:/myRdata.csv”)
There will be times when something other than a csv is necessary, but for this introductory lesson it surely serves the purpose of explaining how to take data out of R.
### Manipulating Data
For this section use the dataset iris. The data set contains 3 classes of 50 observations each, where each class refers to a type of iris plant. Many examples use this or the mtcars dataset because they come pre-installed with R. To load the iris dataset use the data() function. The following code finds quick subsets of data which are useful in the rest of this analysis.
data(iris)
Use the head function to see the first few observations.
head(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
By specifying $it is possible to specify just the species column in head head(iris$Species)
## [1] setosa setosa setosa setosa setosa setosa
## Levels: setosa versicolor virginica
To create a new data frame of the top half of iris we use the index of the iris data frame. Here 1:I(nrow(iris)/2) tells R to take the first row and the row that divides the data. the I() allows R to interpret the division of two literally. The blank after the comma tells R we want all columns.
iris.top<- iris[1:I(nrow(iris)/2),]
Knowing the dimensions of your data frame makes manipulation much easier. dim is used to take the dimensions of iris.top. [1] specifies we want the first list in dims output, the number of rows in iris.top. [2] specifies we want the second list in dims output, the number of columns in iris.top.
dim(iris.top)[1]
## [1] 75
dim(iris.top)[2]
## [1] 5
sub.iris<-subset(iris,select=-Species)
iris.num<-iris[,1:4]
The above code starts by using the data function to upload iris to the global enviroment. If you are using Rstudio iris should come up in the global enviroment.
The head() function allows us to examine the first few top rows. There are 5 columns of 150 rows with Species being the class seperator. It is also possible to use the head() function on a single column to examine a single row. Attaching $Species to iris allows us to access the column labeled species. Here iris$Species is a factor with three different levels.
Another way to subset the data is to call specific rows and columns from the object. This takes the form $$object[N_{t}:N_{t+k},M_{v}:M_{v+k}]$$ on the end of the data object where N is rows and M are columns. In iris.top, the function takes the first half of the rows and since no columns are specified R takes all of them. The function I() inside of the call forces R to treat everything inside of it with standard PEMDAS rules. This is complicated. If you ever get something weird from a simple multiply or divide, put an I() around it.. iris.top successfully pulled out the top half of the data set as proven by the dim function. The dim() function accepts a dataset and will either return both the number of columns and rows or it is possible to specify, like in the example, by saying one for rows or two for columns. Why did iris.sub fail? Note that the number of columns selected are more than the possible selection of columns and so R stops. To include more columns on this dataset for later it is necessary to create them and either merge them onto the existing database after creation or create columns of 1s to multiply by later.
### Statistics and Aggregates
This sections code shows how to create some summary statistics that describe the iris dataset. The R function summary() can be used to find quartiles, min, max, average, and median of the dataset. This is similar to SAS’s means function.
summary(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.30 Min. :2.00 Min. :1.00 Min. :0.1
## 1st Qu.:5.10 1st Qu.:2.80 1st Qu.:1.60 1st Qu.:0.3
## Median :5.80 Median :3.00 Median :4.35 Median :1.3
## Mean :5.84 Mean :3.06 Mean :3.76 Mean :1.2
## 3rd Qu.:6.40 3rd Qu.:3.30 3rd Qu.:5.10 3rd Qu.:1.8
## Max. :7.90 Max. :4.40 Max. :6.90 Max. :2.5
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
##
Using the summary() function returns the summary statistics of the iris dataset. This function is useful and informative, but what if the analysis requires the mode, standard deviation, or range of each column? In SAS, PROC MEANS is used to calculate each of these. In R, the function does the same thing. Below is an example.
Take the means of each column.
cmode.iris<-apply(sub.iris,2,mean)
Take standard deviation of the columns
cstd.iris<-apply(sub.iris,2,sd)
Find range of each column, which should be equal.
crange.iris<-apply(sub.iris,2,range)#Find range of columns
cmode.iris
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## 5.843 3.057 3.758 1.199
cstd.iris
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## 0.8281 0.4359 1.7653 0.7622
crange.iris
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## [1,] 4.3 2.0 1.0 0.1
## [2,] 7.9 4.4 6.9 2.5
Start with the dataset created above, sub.iris. To perform an operation on the columns of the data frame specify 2 as the second command. To do a row-by-row operation specify the command as 1.It is possible to perform functions on arrays and receive a matrix by using c(1,2). This means preserve the rows and columns. Finally, input whatever kind of function to perform over the columns or rows. The apply() function is much faster than traditional for loops in R. As such, try to impliment them everytime a for loop is normally used. apply() is also very flexible. The dataset below gives an example of what a base apply() function can do with a bit of know-how. The objective of diff.iris() is to subtract each element of the dataset from one another without subtracting from itself. Notice that it is possible to write custom functions within apply(). To do this, specify a function and the necessary parameters to perform it. In this example the x parameter is sub.iris. The apply() statement is used to fill the dataset with all combinations of sub.iris columnwise. Next, just like in the previous example, the function specifies that the columns are to be manipulated. Finally, the function skips ahead to the next section and creates a function to subtract the first column of sub.iris from the second column of sub.iris. The next line does something similar, but uses a paste() function with a comb() function to get the column names.
Take the mean of each row
rmean.iris<-apply(sub.iris,1,mean)
Use the apply function on all combinations of sub.iris to take the difference of all combinations of sub.iris.
diff.iris <- apply(combn(ncol(sub.iris), 2), 2,
function(x) sub.iris[,x[1]] - sub.iris[,x[2]])
diff.iris currently has no column names. The next function uses a similar apply method as above to take the column names.
colnames(diff.iris) <- apply(combn(ncol(sub.iris), 2), 2,
function(x) paste(names(sub.iris)[x], collapse=' - '))
R’s built in aggregate function allows aggregation by any built in R function or custom function.
agg.species<-aggregate(cbind(Sepal.Length, Sepal.Width,
Petal.Length, Petal.Width)~Species,data=iris,FUN=sum)
The function aggregate() is similar to the by function in SAS. Take the dataset iris and aggregate it by species. This function uses what is known as model syntax where an independent variable is distributed by a dependent variable. First, cbind() is used to concactenate the columns to aggregate. Anything after the tilde sign is used to aggregate the data. FUN is used to specify how we want to aggregate the data. Any base function such as mean() or sum() can be used here as well as custom functions. This function is very useful for taking state data and aggregating it to the national level or can also be used to move from weekly sales to monthly, yearly, etc.
In the apply() functions previously used, custom functions were built in order to perform the operation. One of the largest perks of R is the ability to easily create these custom functions. Because all of R is open source it is possible to type in the name of any function and the underlying code will print out. Try this with apply() or a similar function to get a feel for how R syntax should look. Below is a simple example of a custom function to demean the data and its apply() equivalent.
demean.dat<-function(x){
#take mean of columns
mean.dat<-apply(x,2,mean)
#sweep subtracts mean from x columns
de.dat<-sweep(x,2,mean.dat,FUN="-")
return(de.dat)
}
demean.iris<- demean.dat(sub.iris) #Call custom function
Here is the apply equivalent.
meapply.iris<-apply(sub.iris,2,function(x) x - mean(x))
#Proves they are both the same
sum(demean.iris-meapply.iris)
## [1] 0
The function starts creating an object demeand.dat. The $$x$$ inside of the function call is a placeholder. Anything that needs to be specified for the user can be placed inside of the parenthesis. All functions are placed in between brackets are written like in the R console. Whatever the function should output is placed inside of return().
return(list(data=data,Rsquared=Rvalue, oranges=apples))
In the first example, one object was returned so it was placed in demean.dat. If multiple objects were to be returned it is necessary to create a list such as the second example. Subsets of the list would be accessed by typing something like demean.dat$data. This looks weird, but you have to keep in mind everything in R is kind of a list and this is how to access sub lists. ## Plots and Maps ### Plotting with ggplot2 This section will cover basic graphing and mapping using the R packages ggplot2 and ggmap. I will not be able to cover everything, but with this example you will be able to utilize most of the functions available at the ggplot2 documentation. All ggplot2 functions work for ggmap. ggplot2 is one of R’s most notable packages because of its simplicity and sophistication. One of the more interesting benefits of the gg family packages is that maps and graphs are stored as objects. This allows additions to the graphs to be included like in a model. An example will also be given to show that R does not automatically update objects when underlying objects have been changed. First load ggplot2 into the global enviroment. Using the qplot function we create a scatterplot of Sepal length and Petal width. library(ggplot2) s.colour<-qplot(Sepal.Length, Petal.Length, data = iris, colour = Species,size = Petal.Width,alpha=I(.7)) s.colour Take the s.colour object and add labels for the x and y axis as if we are adding variables in a regression. I.colour<-s.colour+xlab("Sepal Length") + ylab("Petal Length") I.colour To create a more informative graph include the size variable to make each observation a different size depending on petal length. Also note that I.colour will not be updated. s.colour<-qplot(Sepal.Length, Petal.Length, data = iris, colour = Species ,size = Petal.Length,alpha=I(.7)) I.colour If colour is not an option, use facets for the plot to break out each species. s.colour<-qplot(Sepal.Length, Petal.Length, data = iris, ,size = Petal.Length,alpha=I(.7),facets=~Species) s.colour Use the function qplot() to make a scatterplot of Sepal.Length and Petal.Length from iris. To specify which species each point comes from specify the colour to be the type of Species. It is possible to also do this with size, however this function uses Petal.Width. Alpha is used so that as points come closer together they are made less opaque. Displaying this result gives the basic qplot graph. To label the graph attach xlab and ylab to the object and store these new commands as I.colour as seen on page 8. Note that R objects do not automatically update whenever subobjects or functions have been manipulated. ### Mapping with ggmap ggmap, a package by the creator of ggplot2, gives R smooth and easy mapping capabilities. The following code will take a csv file of addresses, turn them into coordinates, plot their real points, and create a heat map of their density. This is all done within the context of ggmap. load the ggmap library and address csv. I do not provide a dataset of addresses, however I do provide the finished coordinates here library(ggmap) add<-"C:/Users/brond_000/Documents/R/WorkingD/Addr.csv" dff<-read.csv(add,header=TRUE,stringsAsFactors=FALSE) The columns may come in a factors so labeling the address variable will ensure the geocode function will work. The geocode function accesses the Google maps API, allowing automatic conversion of the street addresses to coordinates. Any poorly coded addresses will bring back NAs. dff$Address<-as.character(dff$Address) coords<- geocode(dff$Address)
For further mapping, it is important to remove NAs from the dataset
coords2<-na.omit(coords)
Header has already been mentioned and is specified as true because this matrix has column names. $$R$$ automatically converts strings into factors. This was not a problem whenever the strings were factors like in iris, but for addresses it is important to set stringAsFactors to FALSE. Just to make sure the addresses are a character vector set the column Address as a character vector. The addresses are translated to coordinates through a GoogleMaps API call. Once all the coordinates are collected, use the head() function to take a peek at the data. Notice there are some N/As from bad addresses. The mapping function can have some difficulty with this so remove them with the na.omit() function. The following code will make a map of the US, place points at the coordinates in the dataset, and finally make a heat map that shows the clusters of coordinates.
Load up the dataset like normal, specifying stringsAsFactors=FALSE to tell R “If there are strings in the Data do not convert them to factors.”
library(ggmap)
crd<-"C:/Users/brond_000/Documents/R/WorkingD/coords22.csv"
,header=TRUE,stringsAsFactors=FALSE)
We can use the get_map() function to receive a map with the middle of the map equal to the mean of the latitude and longitude of the dataset.
mapgilbert <- get_map(location = c(lon = mean(coords2$lon)-2, lat = mean(coords2$lat))-1, zoom = 4, scale = 1)
## Map from URL : http://maps.googleapis.com/maps/api/staticmap?center=36.021733,-97.064618&zoom=4&size=%20640x640&scale=%201&maptype=terrain&sensor=false
## Google Maps API Terms of Service : http://developers.google.com/maps/terms
Similar to I.colour well add geom_point() in order to place a point on the map for each observation.
DotMap<- ggmap(mapgilbert) + geom_point(data = coords2,aes(x = lon, y = lat,
fill = "red", alpha = 0.7),
size = 1, shape = 22) +guides(fill=FALSE, alpha=FALSE, size=FALSE)
DotMap
## Warning: Removed 12 rows containing missing values (geom_point).
We will create the final map by adding *geom_density2d** to Dotmap. This will use the number of observations in an area as the density to create a heatmap.
FinalMap<-DotMap+geom_density2d(data = coords2, aes(x = lon, y = lat,fill="white"))
FinalMap
## Warning: Removed 12 rows containing non-finite values (stat_density2d).
## Warning: Removed 12 rows containing missing values (geom_point).
After reading in the coordinates the function makes an object arbitrarily titled ‘mapgilbert’. Using the get_{}map() function a map layout ggmap can read is returned with a center at the means of the latitude and longitude. Zoom and scale control for size. The function c() is used to concactenate single numbers together. Mapgilbert is plotted with ggmap and geom_{}point() is used to place dots on the map, with x and y being the longitude and latitude. It is important to note, parameters such as fill, alpha, and size have the same definiton as in ggplot2. Guides() is an additional function to control whether a legend exists or not. Finally. Use geom_density2d() to create the heatmap.
### Conclusion
This document gives examples related to data manipulation, importing, exporting, function creation, and basic graphics. In terms of R usability, this is just the beginning. Packages such as knitR can be used to write documents, such as this one, completely and easily from within R. bayesm and MCMCpack are packages that performs Bayesian Hierarchical models, Gibbs Sampling, Bayesian Logit regressions, and much more. A package named dplyr allows data manipulation in a parallel format. With the only cost to access being time, learning the R language is a wise investment.
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2019-08-18 01:45:51
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https://ftp.aimsciences.org/article/doi/10.3934/dcds.2003.9.1185
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Article Contents
Article Contents
Periodic probability measures are dense in the set of invariant measures
• We show that if a mixing diffeomorphism of a compact manifold preserves an ergodic hyperbolic probability measure, then the measures supported by hyperbolic periodic points are dense in the set of invariant measures. This is a generalization of the result shown by Sigmund.
Mathematics Subject Classification: 37C50, 37D25.
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2023-03-22 09:15:40
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https://www.semanticscholar.org/paper/A-Semicontinuity-Result-for-Monodromy-under-Degene-Katz/6db517f215185390037a8f47de633c110f4effc0
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# A Semicontinuity Result for Monodromy under Degeneration
#### Abstract
We x a a prime number l. We denote by E a nite extension of Ql inside a chosen algebraic closure Ql of Ql, by O the ring of integers in E , by F its residue eld, and by F an algebraic closure of F . We take as coeÆcient eld A one of the elds on the following list: F , F , E , or Ql. We work over a eld k in which l is invertible. We are given a smooth connected k-scheme S=k, separated and of nite type, of dimension r 1. In S, we are given a reduced and irreducible closed subscheme Z, of some dimension d 0. We assume that an open dense set V1 Z is smooth over k (a condition which is automatic if the ground eld k is perfect). On S, we are given a constructible A-sheaf F . Because F is constructible, its restriction to S Z is constructible, so there exists a dense open set U in S Z on which F is lisse. Similarly, the restriction of F to V1 is lisse, so there exists a dense open set V in V1 on which F is lisse. Let us denote by j the inclusion of U into S, and by i the inclusion of V into S. Thus we have a lisse A-sheaf jF on U , and a lisse A-sheaf iF on V . In this generality, there is absolutely nothing one can say relating the monodromy of the lisseA-sheaf iF on V to the monodomy of the lisseA-sheaf jF on U:However, there is a class of constructible A-sheaves F on S for which these monodromies are related, namely those \of perverse origin". We say that a constructible A-sheaf F on S is of perverse origin if there exists a perverse A-sheaf M on S such that
### Cite this paper
@inproceedings{Katz2001ASR, title={A Semicontinuity Result for Monodromy under Degeneration}, author={Nicholas M. Katz}, year={2001} }
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2017-12-14 13:53:31
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https://zbmath.org/?q=ra%3Akoptelov.ya-yu+cc%3A47
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## Diffraction approach in the scattering problem for three charged quantum particles.(English. Russian original)Zbl 1451.81368
Math. Notes 108, No. 3, 457-461 (2020); translation from Mat. Zametki 108, No. 3, 469-473 (2020).
From the introduction: The results obtained in this paper are based on the diffraction approach in the theory of scattering. The approach was proposed by V. S, Buslaev, S. P. Merkur’ev and S. P. Salikov [J. Sov. Math. 21, 260–265 (1983; Zbl 0515.35069)] to describe the asymptotics of the solution at infinity of the problem of scattering of three short-range one-dimensional quantum particles. We also note the paper [M. Gaudin et al., J. Phys. 36, No. 12, 1183–1197 (1975; doi:10.1051/jphys:0197500360120117700)]. Later, it was also shown by the author [J. Math. Sci., New York 226, No. 6, 744–767 (2017; Zbl 1380.81121)] that the proposed method can be generalized to the case of slow (Coulomb) decrease in pair potentials of repulsion in systems of both one-dimensional and multidimensional particles. In particular, a generalization of results of [E. O. Alt and A. M. Mukhamedzhanov, JETP Lett. 56, No. 9, 435 (1992)] was obtained.
We note that the situation becomes most complicated and interesting in the case of the scattering problem of three three-dimensional Coulomb particles in the presence of pair potentials of attraction [S. P. Merkur’ev and L. D. Faddeev, Квантовая теория рассеяния для систем нескольких частиц (Russian). Moskva: “Nauka”, Glavnaya Redaktsiya Fiziko-Matematicheskoĭ Literatury. 400 p. (1985; Zbl 0585.35078)]. A realization of the scheme developed in the framework of diffraction approach, which was described in [the author et al., J. Math. Sci., New York 238, No. 5, 601–620 (2019; Zbl 1419.81038)], allows us to formulate Theorem 1.
We note that such a contribution generated by different pair subsystems (with Coulomb pair potentials of attraction) must be determined independently. Such contributions become substantial in various asymptotic domains of the configuration space when Coulomb scattering is described.
In what follows, we show how an asymptotics of the form (1) can be used to describe quantum scattering with infinitely many asymptotic channels. We consider the scattering problem for three three-dimensional quantum charged particles in the presence of Coulomb pair potentials of attraction. For definiteness, we assume that there is initially a charged particle and a two-particle cluster in the Coulomb bound state. We also assume that the total energy of the system admits the decay of the system, i.e., admits $$2 \rightarrow 3$$ processes.
Our goal is to determine the complete set of scattering amplitudes corresponding to different processes.
### MSC:
81U10 $$n$$-body potential quantum scattering theory 81V10 Electromagnetic interaction; quantum electrodynamics 81U35 Inelastic and multichannel quantum scattering 35P20 Asymptotic distributions of eigenvalues in context of PDEs 47A40 Scattering theory of linear operators
### Keywords:
scattering problem; specrum; quantum particles; eigenfunctions
### Citations:
Zbl 0515.35069; Zbl 1380.81121; Zbl 0585.35078; Zbl 1419.81038
Full Text:
### References:
[1] Buslaev, V. S.; Merkur’ev, S. P.; Salikov, S. P., Problems of Mathematical Physics, Vol. 9: Scattering Theory. Theory of Oscillations, 14-30 (1979), Leningrad: Izd. Leningrad Univ., Leningrad · Zbl 0494.47010 [2] Buslaev, V. S.; Merkur’ev, S. P.; Salikov, S. P., J. Sov. Math., 21, 3, 260 (1983) · Zbl 0515.35069 [3] Gaudin, M.; Derrida, B., J. Phys., 36, 1183 (1975) [4] Buslaev, V. S.; Levin, S. B., St. Petersburg Math. J., 22, 3, 379 (2010) · Zbl 1219.81235 [5] Buslaev, V. S.; Levin, S. B., Functional Anal. Appl., 46, 2, 147 (2012) · Zbl 1272.81185 [6] Levin, S. B., J. Math. Sci. (N.Y.), 226, 6, 744 (2017) · Zbl 1380.81121 [7] Alt, E. O.; Mukhamedzhanov, A. M., JETP Lett., 56, 9, 435 (1992) [8] Merkur’ev, S. P.; Faddeev, L. D., Quantum Scattering Theory for Systems of Several Particles (1985), Moscow: Nauka, Moscow · Zbl 0585.35078 [9] Larsson, M.; Orel, A. E., Dissociative Recombination of Molecular Ions (2008), Cambridge: Cambridge Univ. Press, Cambridge [10] Tennyson, J., Phys. Rep., 491, 29 (2010) [11] Budylin, A. M.; Koptelov, Ya. Yu.; Levin, S. B., J. Math. Sci. (New York), 238, 5, 601 (2019) · Zbl 1419.81038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2022-08-12 00:03:49
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https://webwork.maa.org/moodle/mod/forum/discuss.php?d=333&parent=1282
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## WeBWorK Problems
### Re: Email problem with Questionaire
by Michael Gage -
Number of replies: 0
Hi Curtis,
This is most likely due to the server being unreachable. The code in
question is in webwork2/lib/WeBWorK/Utils/DelayedMailer.pm line 91-92:
my \$smtp = new Net::SMTP($$self{smtp_server}, Timeout=>10) or die "failed to create Net::SMTP object"; Net::SMTP doesn't set any status codes, but we could get a better error on STDERR (goes to the apache error log) from the Debug=>1 flag. Change the above lines to: my smtp = new Net::SMTP($$self{smtp_server}, Timeout=>10, Debug=>1)
or die "failed to create Net::SMTP object";
You might also try increasing the timeout to 20 or more from 10 in case the mail server is slow rather than overloaded. At the very least this should give you a more complete information about the difficulty. You will probably need to discuss the problem with whoever is maintaining the mail server that WeBWorK is using. (If you have more than one mail server available, then switching the mail server might provide a short term fix. The mail server is specified in webwork2/conf/global.conf.)
Hope this helps.
-- Mike
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2021-10-17 23:14:49
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=19&t=47794
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## Homework Question
$\Delta p \Delta x\geq \frac{h}{4\pi }$
JohnWalkiewicz2J
Posts: 103
Joined: Thu Jul 11, 2019 12:17 am
Been upvoted: 1 time
### Homework Question
On problem 1B.27, it gives the indeterminacy of velocity (Δv) as "5.00 ± 5.0 m.s^-1." Why is the indeterminacy of velocity 5 m.s^-1, and not 10 m.s^-1, since it is ± 5.0?
Last edited by JohnWalkiewicz2J on Thu Oct 17, 2019 10:41 am, edited 1 time in total.
005391550
Posts: 103
Joined: Thu Jul 25, 2019 12:15 am
### Re: Homework Question
do you mean the indeterminacy of velocity instead of the change in velocity?
JohnWalkiewicz2J
Posts: 103
Joined: Thu Jul 11, 2019 12:17 am
Been upvoted: 1 time
### Re: Homework Question
005391550
Posts: 103
Joined: Thu Jul 25, 2019 12:15 am
### Re: Homework Question
haha okay well then the indeterminacy would be just the ± 5.00 because that's what the measured amount is varied by? idk. i see what your saying but i think this is just how it is
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2020-08-14 17:13:58
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http://gmatclub.com/forum/a-mixture-of-sand-and-cement-contains-3-parts-of-sand-and-171991.html?fl=similar
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# A mixture of sand and cement contains, 3 parts of sand and 5
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A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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01 Jun 2014, 12:14
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Question Stats:
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A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
E. 1/8
Source: Indian CAT
[Reveal] Spoiler: OA
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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01 Jun 2014, 15:05
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ConnectTheDots wrote:
A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
E. 1/8
Source: Indian CAT
We have total of 8 parts: 3 parts of sand and 5 parts of cement.
In order there to be half sand and half cement (4 parts of sand and 4 parts of cement), we should remove 1 part of cement. With 1 part of cement comes 3/5 parts of sand, so we should remove 1 + 3/5 = 8/5 part of the mixture, which is (8/5)/8 = 1/5 of the mixture.
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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02 Jun 2014, 13:32
1
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ConnectTheDots wrote:
A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
E. 1/8
This is just a weighted average question, so we can apply the formula for that: with $$C$$ as the concentrations and $$V$$ as the volumes...
$$C_1*\frac{V_1}{V_1 + V_2} + C_2*\frac{V_2}{V_1 + V_2} = C_{final}$$
If sand:cement=3:5, then the concentration of sand in the initial mixture is $$\frac{3}{8}$$. Since we are asked for the proportion of the mixture that should be replaced, we can assume a total volume of $$1$$ and let $$x$$ be the "amount" of the mixture to be replaced by pure sand (i.e., concentration of 1). We can then write the following equation:
$$(\frac{3}{8})*(1-x) + (1)*(x)=\frac{1}{2}$$
Thus, $$x=\frac{1}{5}$$
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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02 Jun 2014, 21:15
2
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Expert's post
ConnectTheDots wrote:
A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
E. 1/8
Source: Indian CAT
You can use the scale method here too.
A mix has 3/8 of sand. Another is all sand so fraction of sand is 1. You have to mix them to get 1/2 sand.
w1/w2 = (1 - 1/2)/(1/2 - 3/8) = 4/1
So the mix should be 4 parts and only sand should be 1 part. Hence 1/5 of the mix must have been replaced by sand.
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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04 Jun 2014, 02:08
Initial
Sand ............... Cement ............... Total
$$\frac{3}{8}$$ ..................... $$\frac{5}{8}$$ ...................... 1
Requirement
$$\frac{4}{8} ..................... \frac{4}{8} ..................... 1$$
Just focus on cement:
To have $$\frac{4}{8}$$ cement, we require to remove
$$\frac{5}{8} - \frac{4}{8} = \frac{1}{8}$$cement
In Mixture, the portion of cement is $$\frac{5}{8};$$so to remove $$\frac{1}{8}$$ cement, mixture required to be removed
$$= \frac{\frac{1}{8} * 1}{\frac{5}{8}}$$
$$= \frac{1}{5}$$
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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25 Jun 2014, 16:42
Bunuel wrote:
ConnectTheDots wrote:
A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
E. 1/8
Source: Indian CAT
We have total of 8 parts: 3 parts of sand and 5 parts of cement.
In order there to be half sand and half cement (4 parts of sand and 4 parts of cement), we should remove 1 part of cement. With 1 part of cement comes 3/5 parts of sand, so we should remove 1 + 3/5 = 8/5 part of the mixture, which is (8/5)/8 = 1/5 of the mixture.
Bunuel: I do not quite understand the highlighted section above. 1 part of the mixture will contain 3/8 sand and 5/8 cement. How did you come up with "1 part of cement contains 3/5 parts of sand"?
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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25 Jun 2014, 21:01
1
KUDOS
One more method:
Sand ............. Cement .............. Total
$$\frac{3}{8}$$ .................. $$\frac{5}{8}$$ ........................ 1
Let "x" quantity of mixture be removed;
$$\frac{3}{8} - \frac{3x}{8}$$ ........... $$\frac{5}{8} - \frac{5x}{8}$$ ............... 1 - x
$$\frac{3}{8} - \frac{3x}{8} + x$$ .......... $$\frac{5}{8} - \frac{5x}{8}$$ .............. 1-x+x
Resultant should be half sand & half cement
Two options to set up the equation
Option I
$$\frac{3}{8} - \frac{3x}{8} + x = \frac{1}{2}$$
$$x = \frac{1}{5}$$
Option II
$$\frac{5}{8} - \frac{5x}{8} = \frac{1}{2}$$
$$x = \frac{1}{5}$$
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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25 Jun 2014, 21:09
1
KUDOS
Game wrote:
Bunuel wrote:
ConnectTheDots wrote:
A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
E. 1/8
Source: Indian CAT
We have total of 8 parts: 3 parts of sand and 5 parts of cement.
In order there to be half sand and half cement (4 parts of sand and 4 parts of cement), we should remove 1 part of cement. With 1 part of cement comes 3/5 parts of sand, so we should remove 1 + 3/5 = 8/5 part of the mixture, which is (8/5)/8 = 1/5 of the mixture.
Bunuel: I do not quite understand the highlighted section above. 1 part of the mixture will contain 3/8 sand and 5/8 cement. How did you come up with "1 part of cement contains 3/5 parts of sand"?
Not Bunuel, but seems I can explain it
Mixture .................. Sand ............... Cement
1 ............................ $$\frac{3}{8}$$ ................... $$\frac{5}{8}$$
Multiply by $$\frac{8}{5}$$ to all above
$$\frac{8}{5}$$ ........................ $$\frac{3}{8} * \frac{8}{5}$$ ............. $$\frac{5}{8} * \frac{8}{5}$$
$$\frac{8}{5}$$ ........................ $$\frac{3}{5}$$ ....................... 1
From the above, we can say that 1 part of cement comes with $$\frac{3}{5}$$ parts of sand in $$\frac{8}{5}$$ quantity of mixture.
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A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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25 Jun 2014, 21:19
S1 - 3 parts element 1 , 5 parts element 2
S2 - x parts of mixture removed i.e, -(3/8 * x) parts element 1, -(5/8 * x) parts element 2
S3 - x parts of element 1 added
We thus have 3 - (3*x)/8 +x / 5 - (5*x)/8 = 1/1
x=1.6 . i.e, 1.6/8 = 1/5 of the mixture removed.
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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18 Aug 2015, 23:18
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A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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18 Aug 2015, 23:53
ConnectTheDots wrote:
A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A. 1/3
B. 1/4
C. 1/5
D. 1/7
E. 1/8
Source: Indian CAT
It is easier to answer this type of question using allegation rule.
3/8 parts are sand in the original mixture.
we are adding with only sand to make the new mixture 1:1
therefore, 1/1 part is sand that we add.
3/8 1/1
1/2
1/2 : 1/8
so, the ratio is 1/2 : 1/8 or 4:1
That is, if you remove 4 parts from the original mixture and add 1 part sand, the resultant mixture is 1:1
To elaborate further, if the original mixture is 8 kg (3 kg sand and 5 kg cement), you remove 4 kg of the mixture which contains 1.5 kg sand and 2.5 kg of cement.
Now, add 1 kg of sand. The new mixture becomes 2.5 kg of sand and 2.5 kg of cement.
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A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
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06 Sep 2015, 15:53
let x=fraction of mixture to be substituted
3/8-3x/8+x=1/2
x=1/5
Last edited by gracie on 11 Nov 2015, 20:39, edited 1 time in total.
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Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink]
### Show Tags
07 Sep 2015, 13:36
How can we use the alligation method/shortcut to solve this?
My attempt:
Sand...................Cement
3/8......................5/8
.......\.................../
.........\............../
..............4/8
Re: A mixture of sand and cement contains, 3 parts of sand and 5 [#permalink] 07 Sep 2015, 13:36
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Display posts from previous: Sort by
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2016-05-29 17:31:50
|
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https://math.stackexchange.com/questions/711579/poisson-distribution-and-the-cdf
|
# poisson distribution and the cdf
$Y (t)$ is the number of events occurring in $[0,1]$ where for each $t> 0$, $Y (t)~\sim\operatorname{Poi} (\lambda t)$ and $X$ measures the time taken for the $r$th event to occur.
Am I right in saying that the event $(X \le t) = (Y(t) \ge t)$?
Also, how can I write the cdf of $X$ as the sum of poisson probabilities using the above?
• If $X$ is indeed the waiting time until the $r$-th event, then $X$ is a sum of $r$ independent exponentially distributed random variables with parameter $\lambda$. – André Nicolas Mar 14 '14 at 0:51
• Perhaps you are looking for the details about the distribution of $X$. In that case, search under "gamma distribution." – André Nicolas Mar 14 '14 at 1:05
The $r$th event occurs before time $t$ if and only if the number of events before time $t$ is at least $r$.
So $[X<t] = [Y(t)\ge r]$.
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2019-05-27 11:16:55
|
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https://kristakingmath.squarespace.com/blog/jump-discontinuities
|
# What is a jump discontinuity?
## Jump discontinuities are common in piecewise-defined functions
You’ll usually encounter jump discontinuities with piecewise-defined functions, which is a function for which different parts of the domain are defined by different functions. A common example used to illustrate piecewise-defined functions is the cost of postage at the post office.
Below is an example of how the cost of postage might be defined as a function, as well as the graph of the cost function. They tell us that the cost per ounce of any package lighter than ???1??? pound is ???20??? cents per ounce; that the cost of every ounce from ???1??? pound to anything less than ???2??? pounds is ???40??? cents per ounce; etc.
???f(x)=\begin{cases}0.2 & \quad 0<x<1\\ 0.4 & \quad 1\leq x<2\\ 0.6 & \quad 2\leq x<3\\ 0.8 & \quad 3\leq x<4\\ 1.00 & \quad 4\leq x \end{cases}???
Hi! I'm krista.
Every break in this graph is a point of jump discontinuity. You can remember this by imagining yourself walking along on top of the first segment of the graph. In order to continue, you’d have to jump up to the second segment.
## Take the course
### Want to learn more about Calculus 1? I have a step-by-step course for that. :)
When you’re looking at the behavior of a function at a jump discontinuity, you already know that the general limit doesn’t exist, that the function isn’t continuous, and also that it’s not differentiable. Which means that all you really have left to investigate are the one-sided limits, and the actual value of the function at that point.
The one-sided limits will never be equal if it’s a jump discontinuity, so you want to look at the left-hand limit by tracing the function from the left, or negative side, and identifying the y-value where you run out of graph. You also want to trace the function from the right, or positive side, and identify the y-value where you run out of graph. This will give you the left- and right-hand limits, respectively.
You'll also want to see where the graph has a "filled in" circle. It might be connected to the left piece of the graph, or to the right piece of the graph, or it might be floating somewhere else along the vertical line where the jump discontinuity exists. Regardless of where it is, the filled in circle represents the function's actual value at that point.
When you’re looking at the behavior of a function at a jump discontinuity, you already know that the general limit doesn’t exist
Jump discontinuities are also called "discontinuities of the first kind." These kinds of discontinuities are big breaks in the graph, but not breaks at vertical asymptotes (those are specifically called infinite/essential discontinuities). You’ll often see jump discontinuities in piecewise-defined functions. A function is never continuous at a jump discontinuity, and it’s never differentiable there, either.
Krista King
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2018-09-20 03:06:01
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http://forum.zkoss.org/question/96915/bind-for-macro-component-with-custom-class/
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# @bind for macro component with custom class
viachris
27 5
Hello,
i have the following problem:
I created a new macro component. It combines a textbox with a popup, that is always shown, when the textbox has focus.
myMacro.zul:
<zk>
<textbox id="textbox" value="${arg.value}" width="${empty arg.width ? '98%' : arg.width}"/>
<popup id="popup" width="200px" />
</zk>
<!-- It is registered in language-addon -->
For this Macro i created a HtmlMacroComponent class:
@ComponentAnnotation("value:@ZKBIND(ACCESS=both,SAVE_EVENT=onEdited)")
public class MyMacro extends HtmlMacroComponent {
private static final long serialVersionUID = 1L;
@Wire
private Textbox textbox;
@Wire
private Popup popup;
private Label label;
public MyMacro() {
label = new Label();
setMacroURI("/zul/components/myMacro.zul");
setStyle("display:block");
afterCompose();
popup.appendChild(label);
}
@Listen("onFocus=#textbox")
public void textboxFocus() {
label.setValue("some Text");
popup.open(textbox, "end_before");
}
}
In the .zul pages where i want to use the macro, i want to use @bind for a bean-field:
somePage.zul:
<myMacro value="@bind(vm.bean.field)" /> <!-- vm is the ViewModel Class -->
The Bean is a straightforward JPA-Entity.
My problem: the text i put into the textbox is not given to the bean (everything else works, the popup is shown and so on).
As an alternative to @ComponentAnnotation i found this: http://zkfiddle.org/sample/6sleo1/2-macro-with-manual-reference (link)
But it only works when using a macro component without a custom class. In my case i get a Property not found exception for the pojo.
I can't use @ref because we don't have PE or EE license.
Can someone help me?
ZK version is 6.5.3.
delete retag edit
Sort by » oldest newest most voted
chillworld
5322 4 9
https://github.com/chillw...
Hey viachris,
Your doing it quite good but you only make a few small mistakes.
## First mistake :
In the zul you have :
<textbox id="textbox" value="\${arg.value}"
Don't set the value there.(in the zul)
What you are doing is only a just set the value once and nothing more.
## Second mistake :
In addition of the first mistake, the value has to go to the getter and setter of value. So what you need in the Java class is :
public void setValue(String value) {
textbox.setValue(value);
}
public String getValue() {
return textbox.getValue();
}
@Listen("onChange=#textbox")
public void textboxChange() {
Events.postEvent("onEdited", this, textbox.getValue());
}
And normally this should work.
## Edit for comment getting "bean.string" :
Maybe it's possible through the binder or something.
I have to look that up and try and error that.
Easy solution should be :
<myMacro value="@bind(vm.bean.field)" from="bean.field"/>
And in the class you create a getter and setter like :
private String from;
public void setFrom(String from) {
this.from = from;
}
public String getFrom() {
return from;
}
It's surely not the most cleanest way but it's the only way I can say directly without testing some stuff.
Greetz Chill.
Thanks for the answer, but even with your suggested changes the content of the textbox is not given to the bean. bean.field is still empty.
( 2015-03-26 07:09:20 +0800 )edit
try this now
( 2015-03-26 10:20:58 +0800 )edit
Where do i get the 'value' from in the postEvent method?
( 2015-03-26 15:24:44 +0800 )edit
oh excuse me, textbox.getValue(), that's the problem of not having a fiddle and just write code here :)
( 2015-03-26 16:26:48 +0800 )edit
That's it! Thank you very much! This helpes me immensely :) Sadly i can't upvote because i don't have enough points... that's kind of silly...
( 2015-03-27 13:37:28 +0800 )edit
[hide preview]
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2019-02-21 03:46:39
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https://mathematica.stackexchange.com/questions/208077/using-urlexecute-for-online-data-acquisition
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# Using URLExecute[] for online data acquisition
On the United Parcel Service website(UPS) there is a form where you can enter a zip code and it will return a color coded map that shows shipping times from that zip code. I am trying to use URLExecute[] to automate a search. At this stage I'm just trying to get it to return a particular map. Looking at the HTML code, I can see that the input field for the zip code is labeled "zip" and so I tried:
URLExecute["https:/www.ups.com/maps", {"zip" -> "90210"}]
which returns
"HTTP Status 404 - Not Found
Type Status Report
Description The origin server did not find a current representation
for the target resource or is not willing to disclose that one exists.
Apache Tomcat/9.0.19"
How could we achieve the extraction of a particular map image?
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2020-06-07 06:16:57
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https://socratic.org/questions/what-is-the-most-stable-potassium-ion
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# What is the most stable potassium ion?
Jan 4, 2017
#### Answer:
There is only one stable potassium ion, ${K}^{+}$
#### Explanation:
The cation ${K}^{+}$ is formed when an atom of potassium loses its single valence electron (a $4 s$-electron). This process requires very little energy (the ionization energy of potassium is relatively low), and so the element is readily oxidized (it is a strong reducing agent).
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2019-03-23 12:42:36
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https://economics.stackexchange.com/tags/cobb-douglas/hot
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# Tag Info
25
The proofs I will present are based on techniques relevant to the fact that the CES production function has the form of a generalized weighted mean. This was used in the original paper where the CES function was introduced, Arrow, K. J., Chenery, H. B., Minhas, B. S., & Solow, R. M. (1961). Capital-labor substitution and economic efficiency. The Review ...
14
The regular method of obtaining Cobb-Douglas and Leotief is L'Hôpital's rule. Another methods should be used too. Setting $\gamma=1$ will be return $Q=[a K^{-\rho} +(1-a) L^{-\rho} ]^{-\frac{1}{\rho}}$ and $$Q^{-\rho}=[a K^{-\rho} +(1-a) L^{-\rho} ]$$ By The total derivative via differentials we will have -\rho Q^{-\rho-1}dQ=- a\rho K^{-\rho-1}dK -(... 13 Since a + b=1 the equations are exactly the same. Substituting in for a+b with 1 in the third and fourth equations gives the first and second equations. 11 Utility functions are invariant with respect to positive monotonic transformations (PMT). Take U(x,y)=x^\alpha y^{1-\alpha}, and let V(x,y)=\log(U(x,y)) be a PMT of U. Thus V and U both represent the same preference, and thus demand functions for x and y are the same. 9 It is not true that this function is equivalent to the Cobb-Douglas utility function when c \sim 0 for any values of (a,b); you have to assume a+b=1 for that, i.e. b=1-a. To see why it is true, fix (x,y) and consider the following Taylor expansion of U(x,y) when c gets close to 0. We have \begin{align*} (ax^{-c}+by^{-c})^{-\frac{1}{c}} &... 8 No. Cobb-Douglas utility is monotonic and monotonicity implies L.N.S. The issue here is that you're only considering edge cases. You've correctly reasoned that edge points are not more desirable that the origin. However, LNS simply claims that there exists a more desirable bundle within the open epsilon ball of your allocation under consideration (and this ... 8 Since the exponents add to one the production function has constant returns to scale, which means that, given factor prices, total cost is linear, which means that it's derivative (= marginal cost) is contant. If you change the exponent 1-alpha to beta where alpha+beta < 1, there will be decreasing returns to scale (but still homotheticity) and you will ... 7 This is how you get from your first equation to your second. your utility function is u(x_1, x_2)=x_1^a x_2^b since a+b=1 I'll change it slightly to a and (1-a) In order to optimise these two choices, you need to maximise utility, wrt your choice variables. subject to p_1x_1 + p_2x_2 = w using Walras Law. Basically, in order to optimise utility, all ... 7 To understand the CES utility functions, which I guess is your question, a good starting point is the Wikipedia page on constant elasticity of substitution. In particular, The CES aggregator is also sometimes called the Armington aggregator, which was discussed by Armington (1969). Then, the CES utility function was popularized by Dixit and Stiglitz (1977) ... 6 We know that if u represents \succeq on X, then for any strictly increasing function f: \mathbb{R} \rightarrow \mathbb{R}, then v(x) = f(u(x)) represents \succeq on X (X in this case is \mathbb{R^n}) Consider v(x, \rho) = \ln(u(x, \rho)) - \frac{\ln\left[\sum^n_{i=1}\alpha_i \right]}{\rho}, which is strictly increasing.v(x, \rho) = \...
6
The C.E.S functional has been introduced in Economics in the context of production theory, by Arrow, K. J., Chenery, H. B., Minhas, B. S., & Solow, R. M. (1961). Capital-labor substitution and economic efficiency. The review of Economics and Statistics, 225-250. There you can find a discussion of how it was derived. A more pedagogic and detailed ...
5
Seems to be the second one, so $$Q_t = A_t*(K_t^\alpha N^\beta_t T_t^\rho).$$ Two clues: This is the usual specification. On the top of page 14 it is written that $$w_t = \beta Q_t/N_t.$$ Given a competitive labor market you have $$w_t = \frac{\partial Q_t}{\partial N_t}.$$ If you assume the production function above then you indeed have $$\frac{\... 5 This is the CES production function, where CES stands for constant elasticity of substitution. The parameter \sigma captures the (constant) elasticity of substitution and \alpha is the share parameter. The Cobb-Douglas production function can be obtained as a special case of the CES class by taking \sigma\to1. For proof, I'd refer you to this post. 5 Let a+b<1,\;\; a,b>0. Pay the factors of production their marginal product:$$rK = \frac {aQ}{K} K= aQ,\;\;\ wL=\frac {bQ}{L} L=bQ$$So total payments to factors of production will be$$rK +wL = aQ + bQ = (a+b)Q < Q$$And the question is: who gets the rest of the output that has been produced? 5 What is the proof of this formula? There is actually no proof for what the production function should be. There are infinite many possible production functions and to discover which one is the most appropriate we need to make some empirical observations. In different cases different production functions are appropriate. Cobb-Douglas is popular production ... 5 A "fixed fraction" doesn't mean an "equal fraction", or at least that's not the intended meaning. It can be easily verified that the solution to $$\max_{x_1,x_2}\;x_1^{a_1}x_2^{a_2}\qquad\text{s.t.}\; \pi_1x_1+\pi_2x_2\le w$$ is x_1^*=\frac{a_1}{a_1+a_2}\frac{w}{\pi_1}\quad\text{and}\quad x_2^*=... 4 If \alpha rises, the utility puts more weights to the x. Then you must give up more x for one y (for the same utility). Your MRS, for a given y, increases in absolute value. Graphically: If you set y and x, the slope is lower for higher \alpha (be careful to only change one thing at a time). Concerning your "loop" problem, look at the ... 4 These are standard mathematical results for generalized means. For example,for the \rho \rightarrow 0 result, write (setting without loss of generality \sum_{i=1}^na_i =1),$$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho} = \exp\left\{\frac 1\rho\ln \left(\sum^n_{i=1} \alpha_i x^\rho_i\right)\right\}$$Apply L'Hopital's rule on$$\...
4
Try to think what you mean when you ask whether they're complements or substitutes. You could mean: "Does my marginal utility in $x$ increase when I get more $y$? That would correspond to the cross derivative $\frac{\partial U^2}{\partial x \partial y}$. You could (and this is the convention) mean the response to a change in prices. Denote with stars the ...
4
Note that the wikipedia article is very specific: [...] defined a preference to be homothetic, if they CAN be represented by A utility function [...] You chose a specific utility function to represent your Cobb-Douglas preferences. However there are infinitely many others. All monotonic transformations of your utility function represent the same ...
4
Yes. Write $$U(x,y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} = \exp\left\{\frac {-1}{c}\ln \left(ax^{-c} + by^{-c}\right)\right\} \tag{1}$$ Now if $a+b=1$ then as $c\rightarrow 0$, expression $$\frac {\ln \left(ax^{-c} + by^{-c}\right)}{-c} \tag{2}$$ will be an indeterminate form $0/0$ and so we can apply L'Hopital's rule on it to get $$\frac {1}{-c}\... 4 No, preferences are stable. That is not to say that the quantity demanded or marginal utility obtained at the new price level is the same though. If we'd allow the exponent of the utility function to vary for different price levels we'd let utility depend on prices, which it does not. Of course the actual utility that can be obtained depends on prices, but ... 4 Any constant returns to scale function is compatible witha competitive economy. Cobb-Douglas is not the only one. Google CES production function. Also, product can be wasted or be an externality, so even in non CRS competitive economy can exist. 4 If one reads the original article by Cobb and Douglas (1928), https://www.aeaweb.org/aer/top20/18.1.139-165.pdf , one will find at the end of page 152 that the authors stress that they took into account two properties that had been theoretically discussed in the past: That production exhibits constant returns to scale, meaning that doubling all inputs will ... 4 Simply multiply and divide one \left(a_{F} \boldsymbol{F}\right)^{\frac{(\sigma-1)}{\sigma}} in the bracket and then take one outside the bracket. And by the way your FOC is incorrect in that \frac{\sigma}{(\sigma-1)} should be cancelled out. 4 Demand is positive, so A>0. If p_1 goes to \infty, x_1 has to go to 0, since p_1x_1 is bounded by M. Thus \alpha < 0. If p_2 goes to 0, x_1 cannot go to \infty, since p_1x_1 is bounded by M. Thus \beta\ge 0. If M goes to 0, x_1 has to go to 0, since p_1x_1 is bounded by M. Thus \gamma > 0. If both prices and ... 4 Yes. I have to include at least 30 characters in an answer, so let me repeat: Yes. 4 If your aim is to maximize the production then your approach is correct. But if the aim is to find the optimal number of units of labor, then you should solve it as a profit maximization problem with a budget constraint. Then the problem should be as following Maximize the profit such that the total cost spent on production does not exceed the budget$$ Max_{...
3
Interesting question. In effect, while factor shares were thought to have remained fairly stable over a long time (the first of the Kaldor's facts), more recently they have varied, particularly in the direction of a fall in the labour share. This short paper from (2012) shows that under such scenario, a growth accounting exercise which assumes constant ...
3
You correctly derived the Marshallian demand function for Cobb-Douglas utility, you notice that the optimal level of consumption of $x$ or $y$ is a function only of the individual's income and the price of said good. This is an interesting feature of CD-utility, that when the price of good $y$ changes the demand for $x$ doesn't change. This means that $x$ ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2021-12-09 11:45:32
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https://www.the-cryosphere.net/12/1211/2018/
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Journal topic
The Cryosphere, 12, 1211–1232, 2018
https://doi.org/10.5194/tc-12-1211-2018
The Cryosphere, 12, 1211–1232, 2018
https://doi.org/10.5194/tc-12-1211-2018
Research article 10 Apr 2018
Research article | 10 Apr 2018
# Multi-year analysis of distributed glacier mass balance modelling and equilibrium line altitude on King George Island, Antarctic Peninsula
Multi-year analysis of distributed glacier mass balance modelling and equilibrium line altitude on King George Island, Antarctic Peninsula
Ulrike Falk1,2, Damián A. López2,3, and Adrián Silva-Busso4,5 Ulrike Falk et al.
• 1Climate Lab, Institute for Geography, Bremen University, Bremen, Germany
• 2Center for Remote Sensing of Land Surfaces (ZFL), Bonn University, Bonn, Germany
• 3Institute of Geology and Mineralogy, University Cologne, Cologne, Germany
• 4Faculty of Exact and Natural Sciences, University Buenos Aires, Buenos Aires, Argentina
• 5Instituto Nacional de Agua (INA), Ezeiza, Buenos Aires, Argentina
Correspondence: Ulrike Falk (ulrike.falk@gmail.com)
Abstract
The South Shetland Islands are located at the northern tip of the Antarctic Peninsula (AP). This region was subject to strong warming trends in the atmospheric surface layer. Surface air temperature increased about 3 K in 50 years, concurrent with retreating glacier fronts, an increase in melt areas, ice surface lowering and rapid break-up and disintegration of ice shelves. The positive trend in surface air temperature has currently come to a halt. Observed surface air temperature lapse rates show a high variability during winter months (standard deviations up to $±\mathrm{1.0}\phantom{\rule{0.125em}{0ex}}\mathrm{K}\phantom{\rule{0.125em}{0ex}}\left(\mathrm{100}\phantom{\rule{0.125em}{0ex}}\mathrm{m}{\right)}^{-\mathrm{1}}$) and a distinct spatial heterogeneity reflecting the impact of synoptic weather patterns. The increased mesocyclonic activity during the wintertime over the past decades in the study area results in intensified advection of warm, moist air with high temperatures and rain and leads to melt conditions on the ice cap, fixating surface air temperatures to the melting point. Its impact on winter accumulation results in the observed negative mass balance estimates. Six years of continuous glaciological measurements on mass balance stake transects as well as 5 years of climatological data time series are presented and a spatially distributed glacier energy balance melt model adapted and run based on these multi-year data sets. The glaciological surface mass balance model is generally in good agreement with observations, except for atmospheric conditions promoting snow drift by high wind speeds, turbulence-driven snow deposition and snow layer erosion by rain. No drift in the difference between simulated mass balance and mass balance measurements can be seen over the course of the 5-year model run period. The winter accumulation does not suffice to compensate for the high variability in summer ablation. The results are analysed to assess changes in meltwater input to the coastal waters, specific glacier mass balance and the equilibrium line altitude (ELA). The Fourcade Glacier catchment drains into Potter cove, has an area of 23.6 km2 and is glacierized to 93.8 %. Annual discharge from Fourcade Glacier into Potter Cove is estimated to $\overline{q}=\mathrm{25}±\mathrm{6}\phantom{\rule{0.125em}{0ex}}{\mathrm{hm}}^{\mathrm{3}}\phantom{\rule{0.125em}{0ex}}{\mathrm{yr}}^{-\mathrm{1}}$ with the standard deviation of 8 % annotating the high interannual variability. The average ELA calculated from our own glaciological observations on Fourcade Glacier over the time period 2010 to 2015 amounts to 260±20m. Published studies suggest rather stable conditions of slightly negative glacier mass balance until the mid-1980s with an ELA of approx. 150 m. The calculated accumulation area ratio suggests dramatic changes in the future extent of the inland ice cap for the South Shetland Islands.
1 Introduction
Antarctic peripheral glaciers and ice caps cover an area of 132 867±6643 km2 and therefore represent about 18 % of all of earth's mountain glaciers and ice caps . Changes in polar ice mass balance are observed as a direct consequence of changing atmospheric and oceanic conditions acting at different spatial and temporal scales, but also changes in internal dynamics . The Antarctic Peninsula (AP) has been warming with a rate exceeding 0.5 K decade−1 at least during the last five decades . This is likely caused by atmospheric and oceanic changes associated with the stratospheric ozone depletion , strengthening of the westerlies and the increased presence of modified warm circumpolar deep water on the continental shelf . This leads to changes in sea-ice season length, extent and concentration in the neighbouring seas . More specifically, the increase in near-surface air temperature shows significantly higher warming trends during winter months for the South Shetlands . The east coast of the AP is mostly influenced by cold and dry air masses stemming from the adjacent Weddell Sea. In contrast, the west coast and the South Shetland Islands are directly exposed to the humid and relatively warm air masses from the South Pacific Ocean carried by the strong and persistent westerly winds. The interaction of the westerlies with the topography of the AP can lead to extreme foehn events on the eastern side .
Trends in surface air temperature in the AP have been analysed and discussed in several studies obtained from meteorological observations of either manned or automatic weather stations (AWSs) , sometimes complemented by satellite remote sensing data . These studies congruently show the statistical significance of the observed positive trends in near-surface air temperatures of approx. 2.5 K over the last five decades along the AP and the strong climatic change in the AP on a regional scale. Different drivers of the observed changes have been identified for winter and summer seasons: winter sea ice concentration and mean sea level pressure anomalies are strongly connected with tropical variability, i.e. the El Niño–Southern Oscillation , whereas changes of summer month's atmospheric circulation are driven by stratospheric ozone depletion and greenhouse gas concentrations . The seasonal variability is represented by the Southern Annular Mode (SAM) index. The SAM is a low-frequency mode of atmospheric variability that describes the north–south movement of the westerly wind belt around Antarctica. It shows high a positive numbers during fall–winter, associated with a contraction of the Antarctic high-pressure cell, and a variability that is of the same order of magnitude as the linear trend observed over the past four decades .
As a consequence of the observed warming, striking glaciological changes have happened along the whole length of AP's western and eastern coasts. Studies along the AP show basal and surficial enhanced melting on ice shelves accompanied by subsequent collapse , widespread glacier acceleration and thinning , grounding line and calving front retreat and others. Ice shelves and glaciers of the AP region have been under a generalized retreat and disintegration trend at least during the last five decades . Ongoing atmospheric and cryospheric change are directly linked to profound changes of the adjacent ocean . Marine species in the AP region show extreme sensitivities to environmental conditions and their changes . Glacial meltwater input to the coastal systems significantly changes physical and chemical properties, e.g. salinity, turbidity, light transmission and trace metals . These studies rely on an accurate estimation of glacier melt.
Systematic glaciological field studies are very scarce on both sides of the AP and in especially there are none that try to sufficiently capture inter- and intra-annual variability. In this paper, we present a 6-year record of continuous glaciological observations obtained on very high temporal resolution to resolve winter melt periods and properly define the start of glacial accumulation and ablation periods. The time series is analysed with regard to climatic drivers and glacial melt is estimated to provide the necessary boundary conditions for interdisciplinary studies on the ongoing changes in the biota and species composition of the coastal waters in the South Shetland region. The following sections will describe the meteorological and glaciological data time series, evaluate calibration and validation of the glaciological model, and discuss surface mass balance and simulated glacial discharge with regard to seasonal and interannual variability. Finally, results of equilibrium line altitude (ELA) and accumulation area ratio (AAR) are used to assess future glacier extent.
The main scientific objective of this paper is to investigate the impact of the concurrent climatic conditions on meltwater discharge to the coastal environments and the glacier ELA, which sets the boundary conditions for the observed environmental change.
Figure 1Map of research area on King George Island (South Shetland Islands, northern Antarctic Peninsula) including the locations of our own installations and external data time series. Potter creek basins of Potter North and Potter South with drainage channels and mass balance stake locations along two transects, PG0x and PG1x (where x is a placeholder for stake number), in the catchment area. Background: SPOT-4, 18 November 2010, © ESA TPM, 2010.
2 Study area
King George Island (KGI) is the largest of the South Shetland Islands, located 130 km from the northwestern tip of the AP (see Fig. 1). The coast and the slopes facing north are relatively uniform and smooth, whereas the south-facing coast and slopes are rugged and steep. Around 90 % of its 1250 km2 area is covered by a polythermal ice cap and is influenced by its maritime climate. have surveyed a significant part of it, finding that the mean ice thickness is approx. 240 m, with a maximum value of 422 m. The maximum elevation is 720 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$ in the central ice dome, with frequent secondary maxima of about 500–600 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$ across the island . The ice cap is divided into drainage basins according to the underlying geological structure . The different draining glaciers end either on land or as tidewater glaciers. Most of the glacier systems on the South Shetland Islands have shown significant retreats in recent past . The Warszawa Icefield covers the southwestern part of KGI including the Potter Peninsula. It includes two tidewater glaciers: Polar Club Glacier and Fourcade Glacier. The latter drains into Potter Cove. Our data were mainly obtained on these two glaciers or in the neighbouring areas (see map in Fig. 1). and report an annual average surface air temperature of −2.4 and $-\mathrm{2.8}\phantom{\rule{0.125em}{0ex}}{}^{\circ }\mathrm{C}$, respectively. show a strong positive trend in surface air temperature especially in the winter, whereas for the summer month December the trend is slightly negative over the past four decades. In general, days with temperatures above freezing are rarely absent in winter and are frequent in summer. The occurrence of temperatures above the melting point all year round is well recorded by thick and multiple ice lenses even in high elevations of the ice cap. Air temperatures above the melting point are generally associated with presence of low-pressure systems and advection of warm and moist air from the mid-latitudes over the surrounding oceans often resulting in precipitation in form of rain .
3 Data and methods
In this study, a physical-process-based, fully distributed energy balance model is applied to estimate glacier melt and glacier runoff into the Potter cove. The temporal resolution is defined by the resolution of the meteorological input data, which were sampled to hourly values. The spatial resolution is defined by the spatial input grids of the digital terrain model (DTM), the surface facies, aspect and slope, etc. First, the meteorological data sets, quality control and gap filling are discussed. Second, the glaciological measurements and post-processing are reviewed. Third, the glaciological model is described, and the necessary input grids are defined.
Figure 2AWS installed on the Fourcade Glacier with view to the Potter Cove and Three Brothers Hill. The photo was taken during winter on 30 May 2012.
## 3.1 Meteorological data sets
### 3.1.1 Meteorological measurements on Fourcade and Polar Club glaciers, Potter Peninsula, KGI
An AWS was installed in November 2010 at 621409.8${}^{\prime \prime }$ S and 583648.7${}^{\prime \prime }$ W at 196 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$, close to the approximate divide of Fourcade and Polar Club glaciers, which are both part of Warszawa Icefield. The AWS is equipped with wind anemometers and vanes (Alpine Wind Monitor); air temperature and relative humidity sensors (HMP155A) at 1.4 and 2.5 m above ground; and snow and ice temperature measurements (107 thermistor probes) installed at 10, 5 and 1 m depth in the glacier and 0.1 and 0.3 m above ground to measure snow temperature during winter. The AWS included a four-component radiation sensor (NR01) for up- and downwelling long- and shortwave radiation fluxes, two narrow-field infrared temperature sensors (IR120) facing northwest and southeast at a zenith angle of 40 to measure surface temperatures, and a sonic ranging sensor (SR50A) installed at an initial height of 1.9 m to measure surface elevation changes. For data acquisition and storage, a CR3000 Micrologger with extended temperature testing was used. The meteorological sensors were installed on a 3 m tripod that was fixed to 3 m aluminum poles drilled into the ice. The AWS is shown in Figs. 2 and 3. To ensure good quality of radiation measurements, all radiation sensors were mounted at a 3 m boom extended from the tripod and fixed to additional poles drilled into the ice. Levelling and adjustment of sensors were carried out according to ablation and accumulation. In case it was necessary outside of periods of summer field campaigns, this work was carried out by the overwintering scientist at Carlini Station. In particular at the end of the ablation season, the whole system needed to be lowered with a maximum of 2 to 3 m each year due to ablation at the AWS station. Power supply was realized with solar panels and a battery stack. Measurement rate was set to every 5 s with an averaging interval of 10 min. During the summer field campaign January–March 2012, an additional AWS (denoted as ZAWS) was installed in the accumulation area of the Warszawa Icefield at 62125.7${}^{\prime \prime }$ S and 583458.4${}^{\prime \prime }$ W at 424 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$ to measure wind speed and direction, air temperature and relative humidity, as well as downward shortwave radiation (Li190SB) for the time period of 2 weeks. All sensors and station equipment were purchased from Campbell Scientific, Logan, Utah. Four additional air temperature and data logger sensors (UTL, Geotest Schweiz) were distributed on the investigated glaciers (621432${}^{\prime \prime }$ S, 583554${}^{\prime \prime }$ W, 144 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$; 621351${}^{\prime \prime }$ S, 583805${}^{\prime \prime }$ W, 65 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$; 6213 58${}^{\prime \prime }$ S, 583828${}^{\prime \prime }$ W, 36 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$) to assess the spatial variability and lapse rates of surface air temperature. One UTL sensor was kept at 2 m height at the AWS site to ensure the continuity of air temperature records during power failure of the AWS. The meteorological data time series and climatology of the Potter Peninsula are discussed in detail by .
Figure 3AWS installed on the Fourcade Glacier with view to the Potter Cove and Three Brothers Hill. The photo was taken on 4 March 2012 and shows the AWS during the ablation period when pyroclastic material resurface due to melting of the winter snow layer.
### 3.1.2 Meteorological observations at Carlini Station
The Argentinean Carlini Station (formerly Jubany Station) is located at 6214 S, 5840 W at 15 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$ at a distance of 2.7 km to the AWS. Meteorological observations are carried out by the National Meteorological Service of Argentina (SMN). The data used here represent the time period from 1 January 2001 until 1 January 2016 and contain 3-hourly observations of surface air temperature, wind direction and velocity, barometric pressure and cloudiness (SMN2016). This time series was resampled to hourly data by linear interpolation and smoothed by applying a moving average with a 24 h window to yield a more realistic daily course. The data set was used to investigate lapse rates between the AWS and Carlini Station in order to gap fill the time series at the AWS during power outages. Details will be discussed in the following sections on meteorological post-processing and gap filling.
### 3.1.3 Long-term climate data set of meteorological observations at Bellingshausen Station
The Russian Bellingshausen Station is located on Fildes Peninsula of KGI at $\mathrm{62}{}^{\circ }{\mathrm{11}}^{\prime }{\mathrm{55}}^{\prime \prime }$ S, $\mathrm{58}{}^{\circ }{\mathrm{57}}^{\prime }{\mathrm{38}}^{\prime \prime }$ W at about 14 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$ at a distance of 18.5 km to the AWS. The Bellingshausen climate observations are on 6-hourly measurements of barometric pressure, surface air temperature, dew point temperature, relative humidity, total cloud and low cloud cover, surface wind direction, surface wind speed and precipitation. This time series starts in October 1968 and it is available in 6-hourly resolution . The time period for the analysis of this paper is from November 2010 to December 2015. The data used here were taken from AARI (2016) and were downloaded from the Russian weather data centre (http://wdc.aari.ru/datasets/). This data set was used to reconstruct the precipitation time series at the AWS because the ultrasonic sensor to measure distance to the surface was malfunctioning after less than a year.
### 3.1.4 Meteorological data processing and gap filling
The 5-year meteorological data time series for the AWS location on the glacier of the Potter Peninsula was screened for flawed and unrealistic values caused either by instrument malfunctioning or by environmental impacts such as hoar frost. During wintertime, power outages are more likely to occur and maintenance is often prevented by unfavourable weather conditions. Gap-filling routines were implemented and are discussed in the following.
Methods using the monthly mean diurnal cycle to fill data gaps were rejected, because (a) data gaps in wintertime are by far more frequent and also the time period of missing data longer, and (b) the diurnal variability is dominated by the seasonal course. For each sensor, the data were checked for malfunctioning or other environmental impact, but also for statistical properties according to . The meteorological data set was aggregated to hourly time steps to reduce computation time during the modelling work (see Sect. 3.3).
The AWS air temperature measurements were screened for spikes (every value outside the 6-fold standard deviation of the long-term average) and air temperature readings below $-\mathrm{40}\phantom{\rule{0.125em}{0ex}}{}^{\circ }\mathrm{C}$ were discarded. The resulting gaps (11.6 % of the data set) were filled with records of the UTL air temperature and, where not available, were extrapolated from Carlini (CAR) Station air temperature observations based on the monthly mean adiabatic lapse rate analysis carried out by .
Apart from a crossing of a synoptic frontal system, sudden spikes to low values in the barometric pressure are usually associated with problems and sudden drops in the power supply. All values below 930 hPa were thus disregarded. The 5-year average of the barometric pressure sensor computes to 967 hPa with a maximum value of 1009 hPa. Data gaps (25 % of the data set) were then filled by extrapolating the meteorological observations at Carlini Station applying the hydrostatic equation:
$\begin{array}{}\text{(1)}& {p}_{\text{AWS}}={p}_{\text{CAR}}\cdot {e}^{\frac{-\mathrm{9.83}\mathrm{\Delta }z}{{R}_{L}{T}_{\text{AWS}}}},\end{array}$
where the barometric pressure pCAR is the resampled time series at Carlini Station, Δz the elevation difference, RL the specific gas constant and TAWS the AWS absolute air temperature in Kelvin.
The 2 m wind velocity was screened for sensor malfunctioning. The cleaned 5-year statistics show a linear relationship between the horizontal wind speeds measured at Carlini Station and the AWS on the glacier of
$\begin{array}{}\text{(2)}& {v}_{\text{AWS}}=\mathrm{1.15}\cdot {v}_{\text{CAR}}-\mathrm{2}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{-\mathrm{1}},\phantom{\rule{0.125em}{0ex}}{R}^{\mathrm{2}}=\mathrm{0.6}.\end{array}$
This relation was used to fill the gaps in the time series of the AWS wind speed observations (25 % of the data set).
The search of a similar relationship for the relative humidity yielded a linear regression between the time series at Carlini Station and at the AWS with a very poor correlation coefficient of R2=0.3. The comparison of first-order statistics shows that
$\begin{array}{}\text{(3)}& {\mathrm{RH}}_{\text{AWS}}=\mathrm{1.08}\cdot {\mathrm{RH}}_{\text{CAR}}±\mathrm{0.5}\phantom{\rule{0.125em}{0ex}}.\end{array}$
Generally, the value range of relative humidity is between 60 and 100 %. The diurnal variability is usually of the same magnitude (σRHAWS≈0.4). For this value range the error is thus acceptable. Values for the relative humidity are generally very high at the AWS site; 25 % of the complete data set of relative humidity were gap filled.
Ice temperature measurements were taken from the lowest sensor level, originally installed at 10 m depth in November 2010. The extensive ablation over the years led to a siginficant change in sensor depth over time. The 5-year statistics reveal that ice temperatures do not drop below $-\mathrm{5}\phantom{\rule{0.125em}{0ex}}{}^{\circ }\mathrm{C}$. The near-surface levels of ice temperature measurements include values lower than this minimum value and higher than 0 C concurrent with a high diurnal variability due to direct contact of the sensor with either meltwater or air. Hence, these periods are excluded from the measurements. This affected 8 % of the data set. Figure 4 shows the course of ice temperature over 5 years in the lowest level.
Figure 4Meteorological time series (gap-filled) aggregated to hourly resolution at the AWS site on the Fourcade Glacier, King George Island, during the time period November 2010–November 2015.
The cloud coverage data were taken from the observations (cloud coverage c8 in one-eighth of total sky area) at Carlini Station, smoothed with a 48 h window. This window size is well adjusted not to eliminate the synoptic changes between low-pressure systems, usually associated with overcast sky, and high-pressure systems over continental Antarctica that are often accompanied with clear sky. The timescale of these changes are considered to be at least 3 days to 1 or 2 weeks. The cloudiness c is given in decimal format of c8 with a value range between 0 and 1.
The four-component radiation sensor is prone to icing or riming due to advection of warm, moist air masses into the region. This affects especially the upward looking sensors for long- and shortwave radiation. As criteria for detection of sensor riming, suggest that the downward longwave radiation flux density equals the upward flux. Here, the criterion was chosen as
$\begin{array}{}\text{(4)}& \text{LW}↓=\mathrm{|}\text{LW}↑\mathrm{|}±\mathrm{0.5}\phantom{\rule{0.125em}{0ex}}\mathrm{W}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{2}},\end{array}$
where LW↓ and LW↑ are the upward and downward longwave radiation flux densities, respectively. Additionally, values of ${R}_{\mathrm{n}}<-\mathrm{500}\phantom{\rule{0.125em}{0ex}}\mathrm{W}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{2}}$ were discarded. The above criterion was met on less than 1 % of the observations. Since air and surface temperatures are often around melting conditions together with overcast skies or high cloud coverage, the applied criterion was deliberately chosen as very sharp to avoid filtering real values for longwave radiation flux densities. To fill the gaps in the radiation data time series, the different up- and downward flux densities of the long- and shortwave components were simulated by applying basic geographic and astronomic equations using the Julian day (J), local time (t), location information (longitude θ and latitude ϕ) in decimal-degree, absolute surface air temperature (Ta) in K, barometric pressure (Pa) in kPa, absolute surface temperature (Ts) derived from ice temperatures and upward longwave radiation measurements, cloudiness in decimal numbers (c) and the gap-filled (33 %) albedo measurements (α).
The optical air mass number is given for $\mathit{\psi }<\mathrm{80}{}^{\circ }$ by $m={P}_{\mathrm{a}}/\left(\mathrm{99}\cdot \mathrm{cos}\mathit{\psi }\right)$, where ψ is the solar zenith angle. The atmospheric transmittance τ is calculated by adapting to
$\begin{array}{}\text{(5)}& \mathit{\tau }=\mathrm{0.5}+\mathrm{0.45}\left(\mathrm{1}-c\right)\phantom{\rule{0.125em}{0ex}}.\end{array}$
The top-of-atmosphere (TOA) solar incidental radiation flux (SWTOA) is then computed by ${\mathrm{SW}}_{\text{TOA}}=\mathrm{1367}\cdot \mathrm{cos}\mathit{\psi }$ and the total solar incidental radiation flux to the surface as the sum of direct (${\mathrm{SW}}_{\text{direct}}={\mathrm{SW}}_{\text{TOA}}\cdot \mathit{\tau }$) and diffuse (${\mathrm{SW}}_{\text{diffuse}}=\mathrm{0.4}\cdot \left(\mathrm{1}-\mathit{\tau }\right)\cdot {\mathrm{SW}}_{\text{TOA}}$) components by
$\begin{array}{}\text{(6)}& {K}_{\text{down, sim}}={\mathrm{SW}}_{\text{TOA}}\cdot \mathit{\tau }+\mathrm{0.4}\cdot \left(\mathrm{1}-\mathit{\tau }\right)\cdot {\mathrm{SW}}_{\text{TOA}}\phantom{\rule{0.125em}{0ex}}.\end{array}$
The solar radiation reflected (Kup, sim) at the surface is then calculated by multiplying the albedo to the simulated downward shortwave flux, i.e. the sum of diffuse and direct radiation flux.
The downward component of the longwave radiation budget at the surface is calculated using the emissivity of the atmosphere ($\mathit{\epsilon }=\mathrm{9.2}\cdot {T}_{\mathrm{a}}^{\mathrm{2}}×{\mathrm{10}}^{-\mathrm{6}}$) to estimate the emissivity under cloud coverage (εac):
$\begin{array}{}\text{(7)}& {\mathit{\epsilon }}_{\text{ac}}=\left(\mathrm{1}-\mathrm{0.84}\cdot c\right)\cdot \mathit{\epsilon }+\mathrm{0.84}\cdot c.\end{array}$
Applying the Boltzmann law this gives for the longwave downward component (LW↓)
$\begin{array}{}\text{(8)}& \text{LW}↓={\mathit{\epsilon }}_{\text{ac}}\cdot \mathrm{5.67}×{\mathrm{10}}^{-\mathrm{8}}\cdot {T}_{\mathrm{a}}^{\mathrm{4}}\phantom{\rule{0.125em}{0ex}}\mathrm{W}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{K}}^{-\mathrm{4}}\end{array}$
and for the longwave upward component (LW↑) with a surface emissivity of ε=0.9
$\begin{array}{}\text{(9)}& \text{LW}↑=\mathrm{0.9}\cdot \mathrm{5.67}×{\mathrm{10}}^{-\mathrm{8}}\cdot {T}_{\mathrm{a}}^{\mathrm{4}}\phantom{\rule{0.125em}{0ex}}\mathrm{W}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{K}}^{-\mathrm{4}}.\end{array}$
The statistics of the simulated radiation fluxes are then compared to the statistics of the measured time series, resulting in correlation coefficients generally above R2>0.7. The simulated longwave fluxes were adjusted to the observations by fixating the mean values of the simulated to the observed values. A difference in long-term average of 29 and 35.5 W m−2 was added to the simulated atmospheric longwave emittance and simulated earth's longwave emittance, respectively. The comparison of simulated shortwave fluxes to the long-term observations suggested a further refinement of the impact of cloud coverage on the shortwave radiation fluxes according to
$\begin{array}{}\text{(10)}& {K}_{\text{up/down, obs}}={K}_{\text{up/down, sim}}\cdot \left(\mathrm{1}-\mathrm{0.4}\cdot c\right)\cdot \mathrm{1.171},\end{array}$
with an R2=0.7. The overall comparison of the simulated (sim) and observed (obs) net radiation flux resulted in a linear regression with very good correlation:
$\begin{array}{}\text{(11)}& {R}_{\text{n, sim}}=\mathrm{15.9}+\mathrm{0.987}\cdot {R}_{\text{n, obs}},\phantom{\rule{0.125em}{0ex}}{R}^{\mathrm{2}}=\mathrm{0.7}\phantom{\rule{0.125em}{0ex}}.\end{array}$
The root-mean-squared error amounts to 39 W m−2 and the mean bias deviation to 10 W m−2. The remaining data gaps were closed using the simulated and fitted shortwave radiation fluxes. In summary, about 50 % of the shortwave and upward-facing radiation data needed to be gap filled with the simulated data, whereas only 25 % of the earth's longwave radiation data were identified as missing or flawed data.
Accumulation measurements based on sonic ranging are available during November 2010 to May 2011 and March 2012 to November 2012. Outside these periods, accumulation was reconstructed using the readings of the Bellingshausen 6-hourly precipitation data. These were resampled to hourly data time series by linear interpolation, smoothed and normalized with the total daily sum. The mass balance stake (MBS) data at the AWS location were then used as an envelop for the daily sums of the resulting accumulation time series. Figure 4 shows the resulting quality-controlled and gap-filled data time series of the meteorological variables.
## 3.2 Glaciological measurements on Fourcade Glacier, Potter Peninsula, KGI
Two transects of MBSs were installed from the top of the Warszawa Ice Dome down to the border of the glaciers Fourcade and Polar Club to serve for calibration and validation of modelling efforts (see Fig. 1 and Table 1). Additional transects were installed along glacier ridge on Barton Peninsula on the Fourcade Glacier on the opposite side of the Potter Inlet. The stakes were measured at the beginning and end of each summer field campaign in November 2010, February–March 2011 and January–March 2012 and every 10 to 14 days, depending on weather conditions, during the austral winter 2012 up to March 2013. During the austral winter 2013 and until May 2016 the measurements were conducted every 20 to 30 days. MBS readings during winter months were mostly conducted in the ablation area of the glacier except for four stakes (PG04, PG14, PG05 and PG15). Additional measurements in the accumulation area were carried out during summer and fall seasons. The high wind speeds, high precipitation rates during austral winter and potentially the material of the stakes (aluminum) resulted in regular loss of the stakes in the accumulation zone of the Warszawa Icefield and thereby the loss of the time series. For the measurements of stakes that were not protruding vertically from the ice but at an inclination caused by the high wind speeds, a geometric correction was applied to yield the correct exposition length. During the summer field campaigns November 2010 to March 2013, repeat measurements with differential GPS (DGPS) at static points of the MBSs yielded an average velocity for the lower transect up to elevations of approx. 250 m of below 1 m a−1 and up to 6.3 m a−1 for the MBSs on the upper glacier. Figure 5a shows a sampling at the MBS transect.
Table 1Locations of the mass balance stake (MBS) at the AWS and the transects (PG0x and PG1x) on Potter Peninsula and the mass balance stake transect (PDx) on Barton Peninsula, Fourcade Glacier, on King George Island (see map in Fig. 1), during the time period November 2010 to December 2016.
Figure 5MBS transects installed on the Fourcade Glacier during the ablation period on 28 March 2012 (a) and during the accumulation period on 10 November 2012 (b).
Figure 6Displayed is the time series of snow density observations on the Fourcade Glacier, Potter Peninsula, during the time period June 2012 to February 2016 (a). Red lines are linear regression lines from onset of winter accumulation until the end of the glaciological year. The snow density profile measurements along the mass balance stake transects (see Fig. 1) on the dates 21 January 2014 (summer) and 10 March 2014 (late fall) on the Fourcade Glacier, Potter Peninsula, are shown (b). Measurements were taken at a depth of 30 cm.
Figure 7(a) Time series of snow depth measured at the two mass balance stake transects (PG0x and PG1x) on the Fourcade Glacier, Potter Peninsula, during the time period November 2011 to May 2016. (b) Snow depth profile with elevation measured during summer and late fall 21 January and 10 March 2014. The location of the individual mass balance stakes (MBS) is shown in Fig. 1.
Snow density samples were taken with an aluminum snow density cutter (SnowHydro, Fairbanks, Alaska) with a defined volume of 0.001 m3 and a balance scale with an accuracy of 0.1 g (Carl Roth GmbH, Germany) calibrated at least once each summer campaign. For the snow density sampling, a snow pit of about 0.5 m depth was dug out and at least three sample volumes, extracted at a depth of about 0.3 m by putting the snow cutter horizontally into the pit wall, were then averaged. The snow depth was measured with a regular snow sonde used as mountaineering equipment. Around each stake about 10 measurements were taken and then averaged. Snow densities were measured 15 November 2010 in the glacier ablation zone and on 7 March 2011 in the glacier accumulation zone, yielding a snow density of ρs=503±16 kg m−3 and ρs=488±20 kg m−3, respectively. On 23 January 2012, a snow pit was dug out in the accumulation zone of the Warszawa ice cap at the additional AWS . Snow density measurements were taken every 0.2 m up to a depth of 2 m and resulted in an average value of ${\mathit{\rho }}_{\mathrm{s}}=\mathrm{416}±\mathrm{47}\phantom{\rule{0.125em}{0ex}}\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{3}}$. The correlation with depth was found to be not significant.
Starting in June 2012 until February 2016, regular snow density values were taken together with the MBS transect measurements. A seasonality in the snow density time series is evident and presented in Fig. 6a. With rising temperatures during the austral summer and fall, the snow density also shows rather high values up to approx. 500kg m−3. With the onset of the winter, the precipitation changes to low-density snow, which then compacts over the course of the winter. During austral winter, the overwintering scientist was responsible for the glaciological measurements of the whole campaign. The snow density time series of winter 2015 shows a high variability and particularly low values, well below any observation before. Although the values by themselves are reasonable for very cold and dry conditions (Patterson, 1980), the contemporary surface air temperature measurements do not show any behaviour that would satisfy the requirements for the very low snow density observation. We therefore suspect the measurement to be affected by errors, leading to an underestimation of the snow density. This seems to have been the case during winter 2015. Thus, for the time period before June 2012 and after March 2015, mass balance and related variables were computed using the monthly averages of the period in between for snow density values. Figure 6b shows measured elevation profiles of snow density for two dates, i.e. the beginning of summer and late fall. The upper profiles show less variability and no significant change for the accumulation area above 250 m, whereas for the lower transect the absolute value of snow density and the variability of the observations is considerably higher.
These findings are supported by the snow depth measurements (DS) displayed in Fig. 7, which show the transects PG0x and PG1x where x is the index of the actual stake number. The snow depth measurements were carried out as far as possible at the beginning and the end of the summer campaigns and, since 2012, on a more regular basis together with the accumulation and ablation measurements of the MBSs. In a circle around the MBS at a distance of 1 to 2 m, about 5 to 10 snow depth measurements were taken with a snow sonde, with the average value taken as snow depth. Due to frequent rain events, ice lenses in the snow layer were common. These values were excluded. The lowest MBSs of both transects show a higher snow accumulation than the stakes at higher elevation. A reasonable conclusion is a different atmospheric turbulence regime that leads to a higher snow deposition at the glacier border due to the vicinity of the glacier end moraine and moraine. Also in the snow depth measurement, the more distinct stratification of transect PG0x with elevation is evident.
The snow density and snow depth time series were used to compute the cumulative mass balance (CMB) in metres of water equivalent (m w.e.) from MBS observations along the mass balance transects shown in Figs. 8 and 9. To convert to m w.e., values needed to be divided by the density of water at standard conditions, ${\mathit{\rho }}_{\mathrm{w}}=\mathrm{999.972}\phantom{\rule{0.125em}{0ex}}\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{3}}$. The mass balance stake readings were referred to the initial value measured when the stake was installed, which was later considered as the zero for each stake. The observed height change of the mass balance stake (ΔH) translated into surface mass balance change in m w.e. by
$\begin{array}{}\text{(12)}& \mathrm{\Delta }b=-\mathrm{\Delta }H\cdot {\mathit{\rho }}_{\text{s/i}}/{\mathit{\rho }}_{\mathrm{w}}\phantom{\rule{0.125em}{0ex}}.\end{array}$
When there was a snow pack, the measured snow density ρs was used. During glacier facies conditions of bare ice, the ice density of ${\mathit{\rho }}_{\mathrm{i}}=\mathrm{900}\phantom{\rule{0.125em}{0ex}}\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{3}}$ was assumed. To convert the unit of Δb from kg m−2 to m w.e., values are divided by the density of water, ${\mathit{\rho }}_{\mathrm{w}}=\mathrm{1000}\phantom{\rule{0.125em}{0ex}}\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{3}}$.
Figure 8Shown is the cumulative mass balance in m w.e. (water equivalent) measured at the calibration mass balance stake transect PG0x on the Fourcade Glacier, Potter Peninsula, during the time period November 2011 to May 2016. The location of the individual stakes is shown in Fig. 1. The lines are interpolation lines between observation points. The grey shade indicates the spread of the GMM-simulated cumulative mass balance at the stake locations PG05 to PG08.
Figure 9Shown is the cumulative mass balance in m w.e. (water equivalent) measured at the validation mass balance stake transect PG1x on the Fourcade Glacier, Potter Peninsula, during the time period November 2011 to May 2016. The location of the individual stakes is shown in Fig. 1. The lines are interpolation lines between observation points. The grey shade indicates the spread of the GMM-simulated cumulative mass balance at the stake locations PG15 to PG18.
The resulting MBS time series graphs is differentiated by the transect ID PG0 and PG1. The gradual shift from ablation at the lowest MBS PG09 to accumulation at the highest MBS PG04 is clearly visible. The PG1 transect, however, does not follow this behaviour: there is considerably more accumulation at MBS PG19 than at the higher elevation PG17. Also within the accumulation zone, the expected increase of accumulation with elevation does not apply: the cumulative accumulation at MBS PG14 is considerably lower than at MBS PG15. This can be explained by the different degree of exposure to weather. KGI is prone to transient low-pressure systems connected to storm events with high wind speeds from the northwest and precipitation mostly in the form of rain, but also to katabatic winds due to influence of the Antarctic high-pressure systems with high wind speeds from the southeast . The southern MBS transect PG1 is more exposed to these synoptic changes and prone to snow drift by the high wind speeds. MBS PG19 and partly PG18 show this extra accumulation of the snow, but PG14 also shows a lower accumulation than PG15 although elevations are reversed (see Fig. 9). For the MBS transect PG1 it can be assumed that these include effects of aeolic snow drift.
The very high temporal resolution of mass balance observation is unique for the AP region and was chosen not only to resolve the high seasonal and interannual variability of the onset of accumulation and ablation period but also to capture winter melt periods to estimate glacier meltwater runoff also during wintertime. The time series analysed here encompass 6 years, but are still ongoing. Figures 6 to 9 show the respective time series of snow density, snow depth and surface mass balance observations.
## 3.3 Glacier surface mass balance model
### 3.3.1 Model description
The glacier surface mass balance model (GMM) by and computes accumulation and ablation, including glacier melt and discharge, at the temporal resolution of the meteorological input data, here chosen as hourly. The GMM was run in energy balance mode and the requested climatological input consists of air temperature (θair), relative humidity (RH), wind velocity (v), shortwave downwelling radiation (Kd), precipitation (P), shortwave upwelling radiation (Ku), net radiation (Rn), longwave radiation emitted by the earth's surface (E), atmospheric longwave radiation (A), barometric surface air pressure (pair), albedo (α), ice temperature at 5 m depth (θice) and cloud cover in eighths (c8). The GMM is fully distributed, meaning that calculations of glacier surface mass and energy balance terms are performed for each grid cell of a defined model area on a digital elevation model as discussed in the last paragraph. Discharge is calculated from the water provided by melt plus liquid precipitation by three linear reservoirs corresponding to the different storage properties of firn, snow and glacier ice volumes. The energy available for melt (QM) is computed by
$\begin{array}{}\text{(13)}& {Q}_{\mathrm{M}}=G\left(\mathrm{1}-\mathit{\alpha }\right)+{L}_{\text{net}}+H+\mathit{\lambda }E+{Q}_{\text{ground}}+{Q}_{\mathrm{R}}\phantom{\rule{0.125em}{0ex}},\end{array}$
where G is the global (solar incidental radiation) radiation, H the sensible heat flux, λE the latent heat flux, Qground the ground or ice heat flux and QR the sensible heat supplied by rain. Global radiation, albedo and up- and downwelling longwave radiation were taken from the AWS time series. The model configuration in energy balance mode allows for the specification of average monthly air temperature lapse rates. These were taken from . The roughness lengths for wind were set in the GMM configuration and used to tune the model to the mass balance stake observations at the transect PG0x. In the configuration of for a summer period on the little Bellingshausen ice dome during a weeks during austral summer, a value for z0=0.0026 was chosen. This choice proved inadequate for the wider region of the Warszawa Icefield. and found an aerodynamic roughness length of ${z}_{\mathrm{0}}\approx {\mathrm{10}}^{-\mathrm{4}}$ to 10−5 near the equilibrium line on the Greenland ice sheet. A study on roughness lengths and parametrizations of sensible and latent heat fluxes in the atmospheric surface layers for alpine glaciers suggests a significant lower value for ${z}_{\mathrm{0}}\approx {\mathrm{10}}^{-\mathrm{5}}$ m, depending on the very high wind speeds and a surface that is during most summer periods characterized by slush and bare ice with water-filled gaps (see photo in Fig. 2). Here, z0=0.00005 was chosen. The roughness lengths for temperature and vapour pressure were computed according to . Lapse rates for air temperature, precipitation and wind are configured in the GMM input parameters according to . Air temperature, wind velocity and relative humidity were then calculated on spatial distribution over the whole area. The turbulent fluxes of latent and sensible heat were computed according to the Monin–Obukhov similarity theory considering atmospheric stability. The surface temperature is derived by the GMM by iteration from the energy balance equation, where the surface temperature is lowered in case of a negative QM until the term becomes zero. The ground or ice heat flux, otherwise neglected, is thereby considered indirectly: if the energy balance equation is negative, the surface temperature is being increased using negative surplus. No melt is allowed until the negative energy balance has been compensated for. The energy amount supplied by rain is computed by
$\begin{array}{}\text{(14)}& {Q}_{\mathrm{R}}={c}_{\mathrm{w}}{R}^{\star }\left({T}_{\mathrm{r}}-{T}_{\mathrm{s}}\right)\phantom{\rule{0.125em}{0ex}},\end{array}$
where Tr is the temperature of rain assumed to be identical to surface air temperature.
### 3.3.2 Hydrological catchment definition of Potter Cove and input grids
To estimate the complete input of glacial and snow meltwater into the Potter Cove, the GMM was run in catchment configuration. The model area encompasses glacial and periglacial areas that are part of the Fourcade Glacier catchment area draining into Potter Cove. The boundary of the Fourcade Glacier is taken from and refined with the analysis of glacial divides by our own kinematic differential GPS mapping of surface elevation. The surface topography is based on an analysis of TerraSAR TanDEM-X remote sensing data performed by with a resolution of this DTM is 10 m by 10 m. Both a resolution of 50 m by 50 m using the DTM for KGI by and a resolution of 10 m by 10 m using the DTM by were applied. The output of these, as well as runs using 100 and 250 m resolution for the whole of King George Island, showed no significant differences.
The GMM was applied to two different catchment areas: (1) the hydrological catchment area draining into the Potter meltwater and discharge creeks and (2) the Potter Cove catchment, i.e. the Fourcade Glacier, defined as the part of the Warszawa Icefield that drains into Potter Cove. The Potter Cove catchment has an area of 25.1 km2 and is glacierized to 94 % where the greatest non-glacierized part is located on Potter Peninsula. The map in Fig. 1 displays the catchment definitions, the location of MBS transects in the catchment area. The input data grids to the GMM are based on this DTM. The DTM published by has a spatial resolution of only 50 m by 50 m but its accuracy is rather low especially for the Warszawa Icefield due to missing in situ ground truth data. Apart from the DTM and the catchment area definition, further input grids comprising information on slope, aspect and sky view factor were calculated from the DTM. The grids containing the information of glacier facies, i.e. firn, ice and rock area, were derived from the glacier zonal mapping published by . The grid containing initial snow water equivalent values in cm were taken from our own in situ measurements along the MBS transects and spatially extrapolated by using the elevation from the DTM. The inaccuracies of the different grids on information of glacier facies and initial snow height, are taken into account by introducing a relaxation period by duplicating the first 44 days and cutting off the first 1056 hourly data time steps of the model run. During this initialization period, the GMM adjusts the inaccurate spatial input data. After these initial 1056 hourly time steps the model's internal physics are assumed to be according to the actual state of physics of the glacier under investigation and a realistic discharge pattern established.
For the catchment boundary refinements, flow directions were calculated on the basis of the data from our own differential GPS measurements on the MBS transects taken at the glacial surface and then were interpolated to form a topography of the surface. For the austral summer 2010–2011, the drainage basins were estimated to encompass glacier elevations between 80 and 450 m with slope to the SW. The supra-interglacial drainage pattern analysis using water drainage channels on the glacier surface were identified using sensors in optical remote sensing satellite data (SPOT-4, 18 November 2010, © ESA TPM, 2010). The drainage of the mass of a glacier can be interpreted similar to a karst rock . The Fourcade Glacier surface drainage shows a straight, poorly integrated and strong direction towards the southwest. The glacier divides then served for further refinement of the catchment area definition in especially of the southern part of the Potter Cove catchment (see Fig. 1).
4 Results
## 4.1 GMM calibration and validation
The GMM run period was chosen for the 5-year period 22 November 2010 to 21 November 2015. The glaciological observations encompass the time period November 2010–May 2016, but the high-frequency data acquisition does not start before February 2012. For calibration of the GMM, the mass balance observations at the transect with transect ID (TID) PG0 were used (see Fig. 10); for validation, the MBS transect with TID PG1 (see Fig. 11) was used. In both figures, each start of the ablation period was chosen as null reference for the CMB to highlight two main drivers of the GMM deviation from observations, defined as the summer year (SY). The errors are cumulative over the course of each year starting with the ablation period (e.g. SY 2012 starts 2 December 2011; Table 2). found layers of pyroclastic material in ice cores from the King George Island ice cap, dating them to volcanic eruptions on Deception Island in December 1967, February 1969 and August 1970. These layers are surfacing in the ablation zone of the westward-facing side of the Fourcade Glacier on Potter Peninsula during melt periods (see Fig. 3). The dark material significantly changes the surface albedo and surface ablation. Since albedo is included in the meteorological input variables, this process is taken into account by the GMM run. The glaciological observations reflect the heterogeneous pattern of accumulation and ablation areas reported by . Hence, spatial extrapolation of surface properties, as the albedo, is expected to add to the uncertainty of the modelling results.
Figure 10Cumulative mass balance (CMB) from simulations with the glacier melt model (modelled CMB) and observation (observed CMB) on the Warszawa Icefield (transect ID PG0x) for calibration purposes. Year numbers give the year of start of the glaciological mass balance year. It encompasses the glaciological years 2012/13 to 2014/15.
Figure 11Cumulative mass balance (CMB) from simulations with the glacier melt model (modelled CMB) and observation (observed CMB) on the Warszawa Icefield (transect ID PG1x) for validation purposes. Year numbers give the year of start of the glaciological mass balance year. It encompasses the glaciological years 2012/13 to 2014/15.
Figures 8 and 9 include the spread of the GMM output of accumulation and ablation for the DEM pixels at MBS locations PG05 and PG08 (Fig. 8) and PG15 and PG18 (Fig. 9). The GMM outputs the cumulative accumulation and ablation for 10 m by 10 m grid cells at the stake locations. Model calculations are shaded in grey. Figures 8 and 9 show that model and observations are generally in agreement. The GMM does not fully account for the spread in the observations, which is attributed to the significant snow drift due to high wind speeds and snow deposit due to turbulence at the glacier end moraine and to the high contribution of snow erosion by rain.
Figures 10 and 11 show the high interannual variability. The high frequency of observations allows one to differentiate between periods with different climatic settings. The high deviation of CMB, especially towards the end of the ablation period, shows that the GMM clearly underestimates the accumulation due to snow drift and turbulence-driven snow deposition at the glacier border (see Figs. 10 and 11). The closer the MBSs are to the glacier border, the more the effect of turbulence-driven snow deposition comes into effect.
SY 2014 contained the coldest summer in the GMM run period, with the highest amount of precipitation as well. In the beginning of the ablation period, air temperatures were below freezing and snow fall occurred together with high wind speeds. This leads to an underestimation in the simulated CMB since the GMM does not account for snow drift. Then there is a period when model and observations are in very good agreement. During the fall of SY 2014, there were frequent rain events. Since the GMM was run in catchment configuration, meaning that the model area contained also the periglacial parts of the hydrological catchment, the snow module could not be applied. Refreezing processes could, thus, not be considered, and the simulated CMB is also underestimated. The accumulation period at the end of SY 2014 is again marked with the underestimation in CMB due to the disregard of snow drift in the GMM.
Apart from these two climatic boundary conditions, the model results and the glaciological observations are in good agreement, and a drift or disagreement over the 5-year GMM run period cannot be seen in the data.
## 4.2 Glacier surface mass balance
give the annual (surface) mass balance (bn) at the end of a balance year as the sum of winter mass balance (bw), i.e. the sum of winter accumulation (cw) and ablation (aw), and summer mass balance (bs), i.e. the sum of summer accumulation (cs) and ablation (as):
$\begin{array}{}\text{(15)}& {b}_{\mathrm{n}}={c}_{\mathrm{w}}+{a}_{\mathrm{w}}+{c}_{\mathrm{s}}+{a}_{\mathrm{s}}={b}_{\mathrm{w}}+{b}_{\mathrm{s}}\phantom{\rule{0.125em}{0ex}}.\end{array}$
All mass balances calculated here refer to the points of the MBS transects and are referred to by lowercase letters (b). Ice density is assumed to be ${\mathit{\rho }}_{\text{ice}}=\mathrm{900}\phantom{\rule{0.125em}{0ex}}\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{3}}$ equivalent to 0.9 kg L−1. All units are in kg m−2. Assuming an uncertainty in snow height measurements of ΔH=0.2m to account for natural surface heterogeneity around each stake and of $\mathrm{\Delta }\mathit{\rho }=\mathrm{10}\phantom{\rule{0.125em}{0ex}}\mathrm{kg}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{3}}$ for the variability in snow density measurements leads to an uncertainty of Δb=0.35m w.e. in specific glacier mass balance estimates.
Table 2Definition of beginning and end of the glaciological summer deducted from observations of local minima and maxima of the accumulation/ablation time series at the mass balance transects (PG0x and PG1x) on Potter Peninsula, King George Island, during the time period November 2010 to December 2016.
The GMM outputs for the first glaciological year 2010 (meaning 2010/11) were not considered in the further analysis due to the model spin-up for the first few months. Results for the stake locations close to the glacier border, i.e. PG09 and PG19, were excluded in the graphs, as already discussed (Sect. 3.2). The beginning and end of the accumulation and ablation period of each year are listed in Table 2 and show the seasonal shift towards late start of the ablation period until November or December and the late end of the ablation period until end of May, except for the glaciological year 2013/14. The start of the accumulation period was used for the definition of the glaciological year. Interannual variability is very high and can differ by more than 2 months in between years. It reflects the variability in the meteorological drivers that is discussed in detail by . Therefore, the annual mass balances were calculated in sub-stratigraphic system (see Figs. 12 and 13). In the following, we only differentiate between winter (i.e. June to November) and summer period (i.e. December to May).
Figure 12Specific summer, winter and net mass balance (bs, bn and bn, respectively) in m w.e. derived from mass balance stakes observation at transects PG0x during 2010 to 2016.
Figure 13Specific summer, winter and net mass balance (bs, bw and bn, respectively) in m w.e. derived from mass balance stakes observation at transect PG1x during 2010 to 2016.
The glaciological year 2011/12 contained a very cold and dry winter in 2011. The summer 2012 showed an exceptionally high net radiation balance amounting to 156 % of the seasonal 5-year average. The resulting high ablation entails a strongly negative specific net balance. In July of winter 2012 brought a 2-week period of rain together with above freezing air temperatures, leading to the erosion of the fresh snow pack and to low accumulation in the net balance. Although the summer 2013 showed low ablation due to high cloud coverage and less precipitation, the glaciological year 2012/13 remains in its net balance negative. It was also a year with very low winds during summer and very high winds during winter. The glaciological year 2013/14 reveals a wet winter with high accumulation rates but also a very cold and very wet summer resulting in low ablation. Regardless of this, the net balance was negative. The glaciological year 2014/15 started with a warm and wet winter, followed by a warm and dry summer leading to higher ablation rates. The period of 2015/16 was a very strong El Niño year with a very cold winter in 2015, followed by a warm and very long summer in 2016. The MSB PG19 (at the elevation of ca. 100 m) clearly reflects the effect of turbulence-driven snow accumulation at the glacier end moraine. Estimates of bn are significantly higher than the GMM output for this stake location. The variability and impact of snow drift and turbulence-driven snow deposition is evident in the locally calculated estimates of bn of the MBS observations. From the graphs (Figs. 12 and 13), it becomes clear that winter accumulation is in most of the years not sufficient to cover for the summer ablation. Summer ablation or the specific summer mass balance, in contrast, is revealed to be highly variable between years, depending on climatic conditions and the length of the ablation period of the respective glaciological year.
Figure 14Time series of meltwater discharge from GMM run November 2010 to November 2015 for the Fourcade Glacier, catchment of the Potter Cove, separated into the different source areas (AID) of snow, firn, ice and rock terrain (${q}_{\text{snow}},\phantom{\rule{0.125em}{0ex}}{q}_{\text{firn}},\phantom{\rule{0.125em}{0ex}}{q}_{\text{ice}}$ and qrock). The complete simulated meltwater discharge (qcalc) is shown in black solid circle with the standard deviation of the time series in grey envelope.
## 4.3 Meltwater discharge into Potter Cove
The GMM calculates the discharge on an hourly basis according to the temporal resolution of the meteorological input time series. The GMM configuration allows for computation of partly glaciated catchment areas as is the case for the Potter Cove catchment. The GMM differentiates between the source areas of the meltwater discharge:
$\begin{array}{}\text{(16)}& {q}_{\text{sim}}={q}_{\text{firn}}+{q}_{\text{snow}}+{q}_{\text{ice}}+{q}_{\text{rock}}+{q}_{\text{ground}}.\end{array}$
Figure 14 shows the temporal evolution of the total meltwater discharge from the complete Potter Cove catchment (qsim) and the respective source areas (firn, ice, snow and rock). The penetration and discharge through ground is negligible, qground≈0. Area sizes change over the course of a year. Figure 14 shows the transitional importance of the dominating source area to glacial discharge throughout the seasons. The contribution of firn areas to glacial discharge is mainly controlled by the seasonal course of surface air temperature and net radiation balance. Since the albedo for firn areas remain high during the summer (α>0.75), firn surface melt starts in spring and consistently pertains throughout the summer with monthly discharge quantities of $<\mathrm{0.5}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{3}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{-\mathrm{1}}$. The glaciological year 2014/15 contained a very cold and moderately wet winter followed by a very warm but dry summer. This resulted in a pronounced time lag between snow and ice area contribution to glacial discharge but also high meltwater quantities due to the amount of winter precipitation. Glacial discharge from snow areas predominate the first part of a summer season and from ice areas in the second part. Differences in monthly discharge from snow areas can amount to nearly 1 m3 s−1 between years. The high variability of ablation and accumulation reflects the very high inter- and intra-annual variability of the meteorological boundary conditions . The frequent occurrence of melt periods during winter is attributed to advection of moist and warm air masses from mid-latitudes by synoptic low-pressure systems. This results in non-zero discharge for winter season (JJA: June to August). Figure 15 shows the seasonal sums of glacial discharge from Fourcade Glacier into Potter Cove as sums.
Figure 15Seasonal meltwater discharge from GMM run for the Fourcade Glacier, a hydrological catchment of the Potter Cove (DJF: austral summer December–February; MAM: austral fall March–May; JJA: austral winter June–August; SON: austral spring September–November).
Linearly relating the time series of simulated discharge to the positive degree day (PDD) time series derived from the Carlini air temperature series shows a high correlation coefficient:
$\begin{array}{}\text{(17)}& {q}_{\text{sim}}=\mathrm{0.2}+\mathrm{0.05}\cdot \text{PDD},\phantom{\rule{0.125em}{0ex}}{R}^{\mathrm{2}}=\mathrm{0.84}.\end{array}$
This means that 84 % of the changes in discharge can be explained by changes in air temperature. Observed temperature trends are highest in winter months, i.e. a trend in minimum air temperature of nearly 5 C over four decades for August . This might result in lesser accumulation during winter and, thus, in a more negative mass balance. The linear regression between the simulated discharge to the PDD time series calculated from the AWS data shows a lesser correlation:
$\begin{array}{}\text{(18)}& {q}_{\text{sim}}=\mathrm{0.4}+\mathrm{0.14}\cdot \text{PDD},\phantom{\rule{0.125em}{0ex}}{R}^{\mathrm{2}}=\mathrm{0.74}.\end{array}$
Above glaciated areas, surface air temperature is being reduced by the melt processes. Thus, PDD and degree day factor analysis are best derived from air temperature observations that are within the catchment area but on non-glaciated areas.
Figure 16Equilibrium line altitude calculated from observations at transects PG0x (black, solid circle) and PG1x (black, solid triangle) and from GMM simulation (M) output at transects pixels PG0x (red, solid circle) and PG1x (red, solid triangle) for the time period 2010 to 2016. The 5-year average ELA from MBS observations (MBS obs) and from GMM model results (GMM) are displayed with the grey shading indicating the uncertainty around the average observed ELA.
The observed trend in SAM and surface air temperature especially during wintertime can lead to significant glacial discharge within the winter season. Glacier facies with bare-ice conditions promote enhanced glacial discharge (see Fig. 14). The dark material, periodically resurfacing in the ablation area, significantly changes albedo to values α<0.1 and, thus, reinforces the effect on surface melt. Hence, winters with missing or lesser accumulation can be expected to be followed by summers with higher rates of glacier discharge.
Figure 17Equilibrium line altitude estimates from this study (PG) and former glaciological studies during the last decades. ELA estimates taken from literature encompass: BD is Bellingshausen Dome, KGI (); EG is Ecology Glacier, KGI (Bintanja1995); LI is Livingston Island (); NI is Nelson Island ; SG is Stenhouse Glacier, KGI (Curl1980); SSI is South Shetland Islands .
Figure 18Glacier extent for equilibrium with actual climatic boundary conditions and an ELA of 260 m (pink line) for the Potter Cove catchment on KGI, according to an AAR between 0.5 (yellow line) and 0.8 (orange line). The actual glacier extent is marked as green and light blue line and represents our own differential GPS measurements in austral summer 2012/13 and 2016/17.
5 Discussion
Time series of accumulation and ablation show a very high intra- and interannual variability that concurs with the climatological variability that is reported by . The observations at two mass balance stake transects demonstrate the high spatial variability, regular occurrence of winter melt periods and the impact of snow drift, turbulence-driven snow deposition, snow layer erosion by rain and high exposition to synoptic impact. These processes are not yet included in the model physics and can lead to discrepancies between GMM simulation and observations under specific climatic conditions. Overall, observations and model are in good agreement though. The high interannual variability in climate conditions, accumulation and ablation patterns is propagated to variability in glacial discharge time series. The difference between years can be as high as 40 %. The simulated glacier discharge is highly correlated to PDD time series with a coefficient of determination of R2=0.84.
The ELA is defined as a set of points on a glacier surface where the climatic mass balance is zero , thus separating accumulation from ablation area. The ELA conveys an instantaneous response to the climatic boundary conditions. The AAR is the ratio of accumulation area to total glacier surface area and defines the boundaries of the glacier in equilibrium state with its climatic boundary conditions. The expected future extent of the ice cap of the Fourcade will be assessed by the AAR in the conclusions.
Figure 16 shows the ELA estimates from observations (black) at the transects PG1x and PG0x and from the GMM output (red). Error bars are derived from the regressions. The calculated ELAs are generally around 260 m altitude. Curl (1980) states that all glaciers on KGI appear in near-equilibrium and slightly negative conditions and that geological evidence shows no major detectable advance within the past two centuries. have compiled values of the ELA obtained by different authors in the South Shetland Islands region along the last decades. do not give uncertainties of their glaciological observations and ELA estimates but state that a high variability between different consecutive years was observed. and concluded from mass balance studies on Collins or Bellingshausen Dome that this small ice cap was in steady state between 1971 and 1991 in agreement with Curl (1980). presented a concurrent ELA for the South Shetland Islands located around 165 to 250 $\mathrm{m}\phantom{\rule{0.125em}{0ex}}\mathrm{a}.\mathrm{s}.\mathrm{l}.$ asserted that the ELA was around 100 m in the Ecology Glacier, KGI. Despite the strong variability, the ELA has increased by more than 100 m from the late 1960s up to the 1990s. More recently , and have placed the ELA at ∼230m and ∼187m for Hurd and Johnsons glaciers, respectively, both located at Livingston Island ice cap.
Until recently, the remote sensing data from synthetic aperture radar (SAR) measurements only allowed for analysis during the summer months due to seasonal manning of the Chilean base O'Higgins responsible for the download of data from the overpassing satellite, thus only resulting in the estimation of the transient snow line, in this case the firn line. Hence, the ELA would be systematically underestimated during a negative surface mass balance year. Additionally, SAR data were not corrected for incidental angles, thus not allowing for differentiation of ablation patterns from superimposed ice. The ELA analysis here is based on ground-based glaciological studies only, and remote sensing studies have been disregarded to avoid methodological bias in the ELA analysis. Multi-temporal SAR data analysis carried out by resulted in an ELA of ca. 250 m for the glaciological year 2010/11 during a cold and snowy summer. Field observations support the importance of snow drift on the accumulation patterns due to the high wind speeds and the related snow drift and accumulation according to domes and troughs. The average ELA was derived from our own glaciological studies on KGI over the time period 2010–2015 to 260±20m and is displayed in Fig. 16 as a dot-dashed line with the uncertainty in grey shading.
Figure 17 places the results from our own glaciological observations into the long-term context. Where available, error or uncertainty bars were included. The temporal evolution of the ELA estimates from the different glaciological studies show clearly that until the 1980s the glaciers on KGI were in near-equilibrium (Curl, 1980), but after this time period there is a clear increase in the ELA. Our analysis in the preceding paragraphs shows not only that the accumulation of Fourcade Glacier generally does not suffice to account for the ablation but also that the interannual variability is high especially during the ablation period. The Fourcade Glacier is clearly in retreating mode, also due to the fact that ice flow velocities in lower glacier on Potter Peninsula are below 1 m yr−1 . The ice mass flux cannot compensate the melt losses in the ablation zone.
The expected ratio of accumulation area to the total glacierized area for a glacier in equilibrium with its climate (AAReq) is within the range of 0.5 to 0.8, e.g. and . Corresponding to the observed average ELA of 260m with concurrent glacier extent is a ratio of approx. 0.26 for the Potter Cove catchment, meaning the glacier is clearly retreating until it reaches its equilibrium state shown in Fig. 18. Here, the yellow line marks the glacier extent for elevations above 110 m referring to an AAR=0.8 and the orange line marks the glacier extent for elevations above 230 m referring to an AAR of 0.5. Underlying is the assumption that lower elevations will melt homogeneously and ice velocities are negligible as soon as the glacier terminates on land in the Potter Cove catchment.
6 Conclusions
One of the most intuitive parameters to describe the equilibrium state of a glacier is the AAR, meaning the state and health of a glacier. Particularly, it is an indicator for expected future retreat or growth of a glacier until it gets into equilibrium with concurrent climatic conditions. It thus relates via the ELA with the specific mass balance and changes of total glacier area. The more negative the mass balance, the higher the elevation line of ELA and the smaller the AAR. Once the long-term ELA reaches values higher than the maximum altitude of the glacier dome, there is no more accumulation area and the glacier will disappear sooner or later. define this as the turning or tipping point of the glacier evolution.
This behaviour also depends on the bedrock topography, which remains largely unknown for the Warszawa Icefield. If underneath the glacier is mountainous terrain, then the stratigraphy of glacier ice mass would persist longer due to higher elevation than if it would all be ice mass underneath. Glaciers respond to climatic boundary conditions with a time lag of a few decades to centuries until they are in equilibrium with the climatic conditions (Paterson1994). The already committed mass change will lead to further retreat of the glacier border within the near future.
A tipping point will be reached for the glacier when the ELA rises above the highest point of the glacier which implies that the accumulation area goes to zero, i.e. an ELA>490m. Even if the observed trends in climatic boundary conditions do not continue, the Fourcade Glacier would still retreat until it reaches equilibrium with climatic conditions. Its extent will be defined by these conditions and the glacier border located between the yellow and the orange line in Fig. 18. The equilibrium state corresponds to a glacier extent that would approximately end between the elevation lines of helev=110m (Fig. 18 yellow line) and helev=230m (Fig. 18 orange line), referring to an AAReq of 0.8 and of 0.5, respectively. Thus, further retreat of the glacier border is to be expected. The southern part of the Fourcade Glacier on Potter and on Barton Peninsula contains a major area of very low ice flow velocities <1m2 and below the ELA in the ablation zone. These areas can be assumed to decrease the most and the glacial meltwater streams are likely to significantly increase their sediment freight due to larger distances through moraine landscape.
The high variability in melt conditions and in especially missing winter accumulation is found to enhance glacial discharge. Positive air temperatures and thus non-frozen moraine landscape surface also promote the intake of sediment load into the meltwater streams that is then introduced into the coastal waters. Assuming the most extreme scenario of glacial retreat according to the ELA–AAR analysis (Fig. 18), the length of meltwater streams through moraine landscape could increase by as much as three times the current stream length, expecting to pick up more sediment load in the near future. This would increase changes in physical and chemical properties of coastal environments, hence leading to a higher impact on the biological communities. Considering the high adaptation required for Antarctica's extreme environments, the high seasonal and interannual variability in climatic and glacial melting conditions can be assumed to have a direct impact on coastal ecosystems.
Code availability
Code availability.
All R codes are available on request from Ulrike Falk.
Data availability
Data availability.
Author contributions
Author contributions.
UF was the PI of the glaciological and climatological work package within the IMCOAST project and also led the glaciological modelling work on KGI within the IMCONet project. DL was responsible for the quality assessment and control of mass balance data time series, the establishment of final glaciological protocols and all communication with the overwinterers. All final analysis and post-processing of climatological and glaciological data time series was performed by UF. ASB investigated the hydrology of Potter Cove and refined the catchment definition grids for the glaciological surface mass balance model. Glaciological modelling work was carried out by UF, with ASB contributing to the calibration and validation procedures. The manuscript was mainly written by UF. DL contributed to the sections concerning mass balance stake observations and analysis, as well as glacier mass balance. ASB wrote parts for the hydrological catchment definition and contributed to the sections on glacier discharge and meltwater analysis.
Competing interests
Competing interests.
There are no potential conflicts of interest regarding financial, political or other matters.
Acknowledgements
Acknowledgements.
We would like to thank the Alfred Wegener Institute (AWI) from Germany and the Instituto Antártico Argentino – Dirección Nacional del Antártico (IAA-DNA) from Argentina for their support in Antarctica. A special acknowledgement goes to Hernán Sala for assistance in the field and help with logistics and to the overwintering scientists at Carlini Station and Dallmann Laboratory: Daniel Viqueira, Juan Piscicelli, Facundo Alvarez, Francisco Ferrer, Pablo Saibene, Martín Gingins and Julia Luna without whom this work would not have been possible. During the period 2010–2015, the overwintering crews from the Ejército Argentino at Carlini Station continuously supported our scientific tasks and we would like to specifically mention SP Norberto Leonardo Galván. We also than Regine Hoch and the University of Fairbanks in Alaska for the introduction to the glacier melt model. All graphs in this paper were produced using the R programming language and QGIS software . We also thank the funding support provided by the ESF ERANET Europolar IMCOAST project (BMBF award AZ 03F0617B) and the Marie Curie Action IRSES (FP7 IRSES, action no. 318718), the logistic support by the Universities of Bonn, Bremen and Erlangen-Nuremberg and the Argentinean Antarctic Institute (IAA-DNA). We thank Ben Marzeion for the careful reading of and his very helpful comments on the manuscript.
The article processing charges for this open-access
publication were covered by the University of Bremen.
Edited by: Thomas Mölg
Reviewed by: two anonymous referees
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2019-11-21 06:35:34
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https://www.scienceforums.net/topic/47314-supersymmetry/?tab=comments
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# Supersymmetry
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"The correspondence between fermions and bosons of identical mass that is postulated to have existed during the opening moments of the big bang and that relates gravity to the other forces of nature"
How and why does this correspondence relate gravity to the other forces of nature?
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Only with supersymmetry do the 3 forces found in the standard model of particle physics unify. A little more specifically, the running gauge coupling in the minimal supersymmetric standard model all converge at about 10^16 GeV or so. Thus it seems important if not essential in any unification scheme.
This does not include gravity. Now, if one localises supersymmetry one automatically gets a theory of gravity. This is because supersymmetry "contains" Poincare symmetry, the symmetries of flat space-time. It may be possible that a supergrvity theory is "large enough" to contain the symmetries of the standard model, for sure 11d supergravity is important from an M-theory/stringy angle.
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Yes, but it's the "correspondence between fermions and bosons of identical mass" that I don't understand.
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There is a morphism between bosonic and fermionic states of the theory. The SUSY algebra forces the paired states to have the same mass.
You can also discuss supersymmetry pseudoclassically.
I'd suggest you have a look in to supersymmetric quantum mechanics. You can get the main features of SUSY without getting in trouble with relativity or infinite dimensions.
If you give me a day or two, I'll post something more useful.
Merged post follows:
Consecutive posts merged
So, lets have a think about N=1 SUSY in 1-dimension. This is sufficient to get the important features.
Definition
A supersymmetric quantum mechanical system with N=1 SUSY is the triple $\{\mathcal{H}, Q, H \}$ where the Hilbert space decomposes as $\mathcal{H}= \mathcal{H}^{0}\oplus \mathcal{H}^{1}$ which we will call the bosonic (even) and fermionic (odd) sector respectively. The operator $Q$ is selfadjoint and odd: $Q = Q^{\dagger}$ and $Q : \mathcal{H}^{\pm} \rightarrow \mathcal{H}^{\mp}$. The Hamiltonian $H$ is an even operator.
The SUSY algebra is
$[Q,Q] = \frac{1}{2}Q^{2} = H$.
Here the brackets are the graded commutator, or in older language the anticommuator.
The first constraint from the above algebra is the the spectrum of the Hamiltonian is always non-negative. This is very important.
The second constraint imposed by the above algebra is
$[H,Q] = 0$.
That is the supercharge $Q$ is a constant of motion.
Now to your question about the pairing of states. Let us assume we have a bosonic eigenstate of the Hamiltonian (there is no loss in generality here picking this to be bosonic rather than fermionic). That is
$H |\psi^{+}\rangle = E|\psi^{+}\rangle$.
So as the supercharge is odd we can always write its action on the above eigenstate as
$Q |\psi^{+}\rangle = 2E |\psi^{-}\rangle$.
I have explicitly assumed that $E \neq 0$, more about this in a moment.
From the eigenequation for the Hamiltonian this all makes sense if
$Q |\psi^{-}\rangle = |\psi^{+}\rangle$. (apply $Q$ again in the above.)
So what about the energy? Remember than in a relativistic theory mass and energy and interchangeable. So in our non-relativistic toy model it is the energy we are worried about. So,
$H |\psi^{-}\rangle = \frac{1}{2} Q \left ( Q |\psi^{-}\rangle \right) = \frac{1}{2}Q |\psi^{+}\rangle = E |\psi^{-}\rangle$.
We see that the energy of the bosonic and fermionic states are identical. Again with the proviso of non-zero energy.
We no need to think about supersymmetry spontaneously breaking. That is the Lagrangian of the theory (which I have said nothing about) is invariant under the SUSY transformations but the vacuum/ground state is not annihilated by the action of the supercharges.
Definition
The above theory is said to posses a "good supersymmetry" if
$Q|\psi_{0}\rangle = 0$
$Q|\psi_{0}\rangle > 0$.
As we are thinking about quantum mechanics in 1-d we can assume that the ground state is either bosonic or fermionic and is nondegenerate without any loss of generality.
Now it is quite easy to see that good supersymmetry requires that the ground state energy be identically zero. That is
$H|\psi_{0}\rangle = 0$.
$H|\psi_{0}\rangle > 0$.
Thus we can think of the vacuum energy as the "order parameter".
So, our toy theory has a nice structure. If supersymmetry is good then there is a single (bosonic or fermionic) zero energy ground state and all the positive energy states are paired. If supersymmetry is bad then all the states have positive energy and are paired.
The situation is similar in supersymmetric field theories. But I hope the above is enough to give you a flavour of what is involved.
Edited by ajb
Consecutive posts merged.
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Tighter restrictions on supersymmetry (string theory) at the detector
It looks like it smells like a grave for string theory (and higher dimensional models).
I miss AJB...
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12 hours ago, Kuyukov Vitaly said:
It looks like it smells like a grave for string theory (and higher dimensional models).
I don’t agree. The largest colliders we currently have operate at around ~14TeV, this is nowhere near what is needed to definitively rule out String Theory and most other models with compactified dimensions - it’s in fact off by many orders of magnitude.
But I do agree that the failure to detect any of the other Higgs particles within this energy range puts serious constraints on possible supersymmetry extensions to the Standard Model. In fact I don’t know of any SUSY models that contain Higgs bosons with more than around 10TeV, so if SUSY is really a thing, then we should have seen those signatures by now - but someone please correct me if I’m wrong on this.
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2020-09-28 14:44:10
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https://solvedlib.com/problem-17-answer-166a-16-to-a-20-10-t-t,324718
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# Problem 17 Answer 1.66A 16: to. A 20 10 t, msec t, msec K2)-3A K3)-1.75 A...
###### Question:
Problem 17
16: to. A 20 10 t, msec t, msec K2)-3A K3)-1.75 A 30 What is the vabue of L, the inductance of the inductor, in mli? 17: (t), V i(t) 30 20 10 1 2 3 4 5 6 7 8 v(t) 30 mH t,msec --10 -20 30 -40 50 i(0)-3A What is the value of i(0.004), the current at time 4 msec, in A? 18: 12 ar
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##### Considerone-dim random ficld {Z(s)2 0}; which satisfies E[Z(s)] Cov[Z(s) ; Z(t)] = o?min(s,t) . Note that min(s,t) = 8 if s < t(= otherwise ) .anda) Show that Z(s) is intrinsic stationary and that intrinsic stationarity docs not imply the second-order stationarity:b) Define Y(s) Z(s + 1) - Z(s) s € R. Show that {Y(s) stationary:R} is second-orderDerive the covariance function Cy(h) of {Y(s) € R} Find also its semivariogram and identify its nugget cffect, sill and range:
Consider one-dim random ficld {Z(s) 2 0}; which satisfies E[Z(s)] Cov[Z(s) ; Z(t)] = o?min(s,t) . Note that min(s,t) = 8 if s < t(= otherwise ) . and a) Show that Z(s) is intrinsic stationary and that intrinsic stationarity docs not imply the second-order stationarity: b) Define Y(s) Z(s + 1) -...
##### 14. What is Polymorphism? What are the different types of crystalline forms? And what factors influence...
14. What is Polymorphism? What are the different types of crystalline forms? And what factors influence the types that are formed. Which form is preferred in margarine and why? (20 points)...
##### Chapter 34 Assisting in Minor Surgery VOCABULARY REVIEW Using the word pool on the right, find...
Chapter 34 Assisting in Minor Surgery VOCABULARY REVIEW Using the word pool on the right, find the correct word to match the definition. Write the word on the line after definition Group A 1. Localized collections of pus, which may be under the skin or deep in the body, that cause tissue destruction...
##### Que TU Question 4 10 points Save Answer Let's suppose that you are planning a night...
que TU Question 4 10 points Save Answer Let's suppose that you are planning a night out with friends. You do not want to drive, so instead, you will use one of the popular ride-share apps de Uber and Lyft). Further, a ride with Uber (1) provides you with the same level of satisfaction as a ride ...
##### (20 points) For the complex ion [Niten)(SO4) (COJSCN]" note: CO is carbon monoxide. its ligand namC carbonyl: (This complex ion possesses four diflerent ligands )(WRITE short ANSWERS on BLANKS for FULL CREDIT)(a) (4 pts) Charge Of' the central metal atom in above iOn and number of valence electrons equal:ChargeNumber of" *d" electronspoints) Name the complex ion; (no abbreviations) WRITE ON LINE BELOW for CREDITNAME:(6 pts) Assuming that all ligands follow the same trend as i
(20 points) For the complex ion [Niten)(SO4) (COJSCN]" note: CO is carbon monoxide. its ligand namC carbonyl: (This complex ion possesses four diflerent ligands ) (WRITE short ANSWERS on BLANKS for FULL CREDIT) (a) (4 pts) Charge Of' the central metal atom in above iOn and number of valenc...
##### RON C11H21NO, 2 R3NH Br NH2 Br A Treatment of 3-methylpentan-3-amine with methyl 2,4- dibromobutanoate in...
RON C11H21NO, 2 R3NH Br NH2 Br A Treatment of 3-methylpentan-3-amine with methyl 2,4- dibromobutanoate in the presence of a nonnucleophilic base, R3N, involves two successive Sn2 reactions and gives compound A. Propose a structural formula for compound A. • You do not have to consider stereoche...
##### Show Intro/Instructions Suppose that the distance of fly balls hit to the outfield (in baseball) is...
Show Intro/Instructions Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 244 feet and a standard deviation of 47 feet. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers...
##### How does the position of an element on the Periodic Table reflect the oxidizing ability of that element?
How does the position of an element on the Periodic Table reflect the oxidizing ability of that element?...
##### Shown in the figure is the graph of $x=y^{2}$ and a line of slope $m$ that passes through the point $(4,2) .$ Find the value of $m$ such that the line intersects the graph only at $(4,2)$ and interpret graphically.
Shown in the figure is the graph of $x=y^{2}$ and a line of slope $m$ that passes through the point $(4,2) .$ Find the value of $m$ such that the line intersects the graph only at $(4,2)$ and interpret graphically....
##### The figure below shows three capacitors with capacitances CA 1,00 HF;2.40 pF; and Cc 4,50 HF connected to 3.00- battery.What is the equivalent capacitance of the three capacitors?What charge storedeach of the capacitors?(c) What the potential difference across each of the capacitors? AVAAVeAVc
The figure below shows three capacitors with capacitances CA 1,00 HF; 2.40 pF; and Cc 4,50 HF connected to 3.00- battery. What is the equivalent capacitance of the three capacitors? What charge stored each of the capacitors? (c) What the potential difference across each of the capacitors? AVA AVe AV...
##### Chapter 31, Problem 029 A 61.3 mH inductor is connected as in the figure to an...
Chapter 31, Problem 029 A 61.3 mH inductor is connected as in the figure to an ac generator with ε kHz? 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is (a) 1.42 kHz and (b) 11.4 (a) Number Units (b) Number Units...
##### Omega-6 fatty acids are: O A form of saturated fatty acids O Contain a double bond...
Omega-6 fatty acids are: O A form of saturated fatty acids O Contain a double bond at the third omega carbon O Synthesized in the liver Help to regulate the constriction of blood vessels Omega-6 and omega-3 fatty acids are both polyunsaturated fatty acids that are essential to the human body. Howeve...
##### 10A. The profitability index for a project costing $100,000 and returning$32,000 annually for four years...
10A. The profitability index for a project costing $100,000 and returning$32,000 annually for four years at an opportunity cost of capital of 10% is .... 10B. The profitability index for a project costing $100,000 and returning$40,000 annually for five years at an opportunity cost of capital of 10...
##### OrganismHintHaploid of chromosomesDiploid of chromosomesHumans46 chromosomes in cell In G1Whale21 chromosomes in a sperm cellKangaroo20 chromosomes in liver cellMaple trec26 chromosomes in pollen (gametesPea plant14 chromosomes in a leaf cellRose plantn = 38Garlicchromosomes in a somatic cell0og
Organism Hint Haploid of chromosomes Diploid of chromosomes Humans 46 chromosomes in cell In G1 Whale 21 chromosomes in a sperm cell Kangaroo 20 chromosomes in liver cell Maple trec 26 chromosomes in pollen (gametes Pea plant 14 chromosomes in a leaf cell Rose plant n = 38 Garlic chromosomes in ...
##### Imuk,and € 47.0enLdnneeEad_cremnietHal [eenantLacanEteimdu dtau alees7aEFLAEm(d Uer suuachE {ocualal pademtsecndEumtinneHertaattUtubNrou AannOmae1333.38eHdbreuma Iniendcaltoconioenuakualaledo Jeltaloilata anetanmroundollcnlhamcalEaaeinItetutleooary Haln
imuk,and € 47.0en Ld nneeEad_cremniet Hal [eenant Lacan Et eimdu dtau alees7a EFLAEm (d Uer suuachE {ocualal pademtsecnd Eumtinne Hertaatt UtubNrou Aann Omae 1333.38e Hdbreuma Iniend caltoconio enuakualaledo Jeltalo ilata anetanm roundoll cnlha mcal Eaaein Itetutle ooary Haln...
##### Draw the products formed when the following alkene is treated with O3 followed by Zn, H2O....
Draw the products formed when the following alkene is treated with O3 followed by Zn, H2O. Be sure to answer all parts....
##### [The following information applies to the questions displayed below.] Glasgow Enterprises started the period with 80...
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##### Solve the given differential equations.$rac{d^{2} y}{d x^{2}}-2 rac{d y}{d x}+y=0$
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##### Fill in the blank to complete the trigonometric formula. (Select all that apply.)sin u2 = ______
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##### Make a code for the additions of fractions. use the attached code to find LCM. define...
make a code for the additions of fractions. use the attached code to find LCM. define _CRT_SECURE_NO_WARNINGS #include <stdio.h> int Icm(int, int); int main() int n1, n2, min Multiple; printf("Enter two positive integers: "); scanf("%d %d", &n1, &n2); // maximum nu...
##### Points) Select the FIRST correct reason why the given series diverges.A Diverges because the terms don"t have limit zero B. Divergent geometric series Divergent series Integral test E. Comparison with divergent senes F Diverges by Iimit comparison test Diverges by alternating seres test3n + 7 (-1)" In(n) 1 J 1)4? + (-l)" (Zn)l "el 2 n In(n)
points) Select the FIRST correct reason why the given series diverges. A Diverges because the terms don"t have limit zero B. Divergent geometric series Divergent series Integral test E. Comparison with divergent senes F Diverges by Iimit comparison test Diverges by alternating seres test 3n + 7...
##### Please answer the following question in 250 word count in your own words Considering legislation and...
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##### (I5 poits) Given the infonation thc box on the right detcrmine you know find the pruductIH and explain the ExsiestL; HHT [email protected] and H+IHT-B 9 or cxplain why it is impossible to do Find , matrix [C such that [ H1C (15 points) so . Show all work and . explain your answer:
(I5 poits) Given the infonation thc box on the right detcrmine you know find the pruduct IH and explain the Exsiest L; HHT [email protected] and H+IH T-B 9 or cxplain why it is impossible to do Find , matrix [C such that [ H1C (15 points) so . Show all work and . explain your answer:...
##### Find r'(t) , r"(t), r'(t) r"(t), and r'(t) x r"(t). r(t) = 3t2; _ 3tj + 2 ick (a) r(t)(b) r"(t)(c) r(t) r"(t)(d) r'(t) r"(t)
Find r'(t) , r"(t), r'(t) r"(t), and r'(t) x r"(t). r(t) = 3t2; _ 3tj + 2 ick (a) r(t) (b) r"(t) (c) r(t) r"(t) (d) r'(t) r"(t)...
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2022-07-05 10:05:32
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http://www.intmath.com/blog/computers/sorry-about-the-page-errors-149
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# Sorry about the page errors…
By Murray Bourne, 25 Oct 2005
You've arrived here because the article you were looking for has expired.
Maybe the topic became too old, or I was discussing some link and it's disappeared, or maybe the featured video no longer exists.
Nothing is forever on the Web...
You may find something interesting in these sections of the blog:
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## Blog sitemap
All of the articles are listed here: Blog sitemap.
Be the first to comment below.
### Comment Preview
HTML: You can use simple tags like <b>, <a href="...">, etc.
To enter math, you can can either:
1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
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(See more on ASCIIMath syntax); or
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$$\int g dx = \sqrt{\frac{a}{b}}$$
(This is standard simple LaTeX.)
NOTE: You can't mix both types of math entry in your comment.
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2016-12-05 12:33:37
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https://villavu.com/forum/showthread.php?t=108953&page=2&s=6785f65903a34153fd3bd3fee367259d
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# Thread: AeroLib Include
1. Great work Flight! I think what needs to happen is this should replace srl-osr and be written like srl6. Reflection also needs to be converted so all the includes are the same. This will make all the tutorials much easier to understand and people can script for both versions of the game without learning what seems like a multiple language.
2. Originally Posted by The Mayor
Great work Flight! I think what needs to happen is this should replace srl-osr and be written like srl6. Reflection also needs to be converted so all the includes are the same. This will make all the tutorials much easier to understand and people can script for both versions of the game without learning what seems like a multiple language.
That's a really good point. Thanks to Olly I've plans to really make AeroLib a more object-oriented library, which I assume is would SRL-6 scripters are already comfortable with. But there's already custom content in here that I assume wouldn't be appropriate for an official include, not to mention much more to come...
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Hey man, im having trouble getting this include working.
I have followed the instructions multiple times, each time being precise and making sure to follow each step to completion. The problem is, that every time i try to run the test script, i gives me this error :
[Error] (3:1): Unable to register function function CreatePerspective(const sx0, sy0, sx1, sy1, sx2, sy2, sx3, sy3, dx0, dy0, dx1, dy1, dx2, dy2, dx3, dy3: Double): TPerspective; at line 3
Compiling failed.
I assume it has something to do with my SPS but even updating and re installing it, it still wont work.
any help would be greatly appreciated.
4. Originally Posted by imgonnaeatu
Hey man, im having trouble getting this include working.
I have followed the instructions multiple times, each time being precise and making sure to follow each step to completion. The problem is, that every time i try to run the test script, i gives me this error :
[Error] (3:1): Unable to register function function CreatePerspective(const sx0, sy0, sx1, sy1, sx2, sy2, sx3, sy3, dx0, dy0, dx1, dy1, dx2, dy2, dx3, dy3: Double): TPerspective; at line 3
Compiling failed.
I assume it has something to do with my SPS but even updating and re installing it, it still wont work.
any help would be greatly appreciated.
Yes I had another users who had this problem as well, you just need to switch your Interpreter to Lape rather than PascalScript. The instructions on how to do that are on the OP under How to install.
5. I've updated the include with revision 0.1 which is mostly an update to make AeroLib more F2P friendly, but it also includes some modifications to SPS as well as other random files. You'll find the TPlayer now has a 'Member' variable which you should be setting in your DeclarePlayers procedure. This will allow the include to choose which worlds to log you into, should you choose to hop to a random world. It will also determine help if you've gotten a XP reward from a random event and you've not set your player's LampSkill to a F2P skill; the default for this will be Mining so if you don't want that be sure to set this manually before running your scripts. Of course the world list has also been updated.
SPS's accuracy has been increased a bit and at the moment Olly is working on a new color-based positioning system based off the work of Slacky. Should that project be a success then it will certainly be included in AeroLib in the near future.
Happy scripting!
P.S. AeroLib has been moved to GitHub so the absolute newest revisions will be uploaded there. This also might mean AL will get an updater in Simba; here's hoping. You can check out AeroLib's GitHub page if you'd like to see the most recent changes.
6. Awesome release Flights, looks like you have gone to lots of effort.
You effort is appreciate
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Hey, amazing work man. Are you going to continue updating it? It hasn't been updated in a month :/ i really want fully random supported color include
can't wait
8. Originally Posted by Unfold
Hey, amazing work man. Are you going to continue updating it? It hasn't been updated in a month :/ i really want fully random supported color include
can't wait
This very day I'll be adjusting quite a bit. The next revision will include a new color-based walking method designed by Olly which utilizes Slacky's SimbaExt library. I'm also getting to know this include as well, I believe, if used correctly, it will be a powerful tool in building more complex color random-solvers. Also the next revision will include some reflection for walking only. I actually only added this for my most recent work (Abyssal runecrafter) and when the new color walking system (SEWalker) is able to load multiple custom maps then I'll remove reflection from AeroLib to retain the state of color only. Aside from that there will be a few logical changes here and there, and if there's time I'll work on some user-friendly tutorials on how to script with AeroLib.
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Originally Posted by Flight
This very day I'll be adjusting quite a bit. The next revision will include a new color-based walking method designed by Olly which utilizes Slacky's SimbaExt library. I'm also getting to know this include as well, I believe, if used correctly, it will be a powerful tool in building more complex color random-solvers. Also the next revision will include some reflection for walking only. I actually only added this for my most recent work (Abyssal runecrafter) and when the new color walking system (SEWalker) is able to load multiple custom maps then I'll remove reflection from AeroLib to retain the state of color only. Aside from that there will be a few logical changes here and there, and if there's time I'll work on some user-friendly tutorials on how to script with AeroLib.
Awesome, Can't wait :P
10. Originally Posted by Flight
...
No-no no it's all slackys work, I only tested it quite alot and just passed it though to you :P
And can't you already do multiple maps?
Simba Code:
var map1: TSEWalker; map2: TSEWalker;begin map1.create(); map2.create(); //etc..end;
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Am i suppose to include {\$i AeroLib/AeroLib.Simba} infront of scripts because they mainly run on pascal.
Also my comp says the allinone zip is a virus but idk if I believe it.
Last edited by klew1102; 07-26-2014 at 02:08 PM.
12. Finally pushed out revision 0.3 which is multiple fixes and adjustments as well as the addition of SEWalker, an alternative color-based positioning system which utilizes Slacky's SimbaExt include. Be sure to thank him for this, it's a masterpiece and really a shame it's not receiving more attention... In the future I'll experiment with it as I believe it'll be a powerful tool and I'd love to apply it to random-solvers. Anyways, be sure to update everyone.
Oh yeah... I believe this update may give compile errors for my already released AL-based scripts. I'll update these tomorrow night, I apologize for any issues users might be having because of this.
Last edited by Flight; 07-30-2014 at 04:10 PM.
13. It's awesome that you are using SimbaExt man
If I knew you where going to use that SEWalker, I would have made it more reliable, and less hacky.. like as it's now it's just some prototype code I wrote to "help"/show Olly.
Tho, I am skeptical about the changes you made to SEWalker:
I see some are for the better, but it's very hacky. Hopefully you did some proper tests with your changes.
- Like, making a var "sdist", which is staticly defined as 20px, instead of using the "SkipDist" variable in the record which was added for that purpose (and originally used), was just stupid, and gives the user less control, you could have just defaulted skipdist to default at 20px (however 20px skipdist is too much).
- You also removed the "blindwalk" thingy I added, which was utilized whenever the walker failed at finding the correct current position, that "blindwalk"-thingy made me able to walk from [Al-kharid > Lumby > Fally] and back through [Varrok > Al-kharid (bank)], all in one path. I do not think that will work now, as the "blindwalk" was utilized multiple times over that path.
- You also seem to have dropped using ValidatePath which is not so "scripter-friendly": It ensured that the distance between points in the "Path" was no more then "SEW_Outer", and told the scripter about this before it started walking, so that they KNOW why it would fail, rather then having to walk the path, and see it fail, and then having to guess why it failed...
And for no reason (what so ever), you randomly prefixed all the functions you added to IE: SEW_WalkPath(..) rather then following the object-oriented style the rest of the module was written with (SEWalker.WalkPath()).. That was just a dumb thing to do, and just makes it harder for users to use, it's much less CC-friendly versus having all record-methods related to SEWalker, under the SEWalker-type.
That's about all I have to bitch about right now.
Last edited by slacky; 07-31-2014 at 12:45 PM.
14. Yes my testing with the SEWalker is near none infact, below I'll answer your questions individually.
Originally Posted by slacky
- Like, making a var "sdist", which is staticly defined as 20px, instead of using the "SkipDist" variable in the record which was added for that purpose (and originally used), was just stupid, and gives the user less control, you could have just defaulted skipdist to default at 20px (however 20px skipdist is too much).
Yes I added this parameter to work with the SEW_WalkPath function which would have acted the same as my previous forms of walking for SPS; tiles < the target tile, in a path, will have a greater flag distance before the next tile in the path is found and the last tile having a shorter flag distance. Cannot accomplish this with a static "SkipDist". It is, in fact, just the opposite of what you say of restricting user control.
Originally Posted by slacky
- You also removed the "blindwalk" thingy I added, which was utilized whenever the walker failed at finding the correct current position, that "blindwalk"-thingy made me able to walk from [Al-kharid > Lumby > Fally] and back through [Varrok > Al-kharid (bank)], all in one path. I do not think that will work now, as the "blindwalk" was utilized multiple times over that path.
I'll look again at the original that was sent to me, I don't remember removing anything similar to that.
Originally Posted by slacky
- You also seem to have dropped using ValidatePath which is not so "scripter-friendly": It ensured that the distance between points in the "Path" was no more then "SEW_Outer", and told the scripter about this before it started walking, so that they KNOW why it would fail, rather then having to walk the path, and see it fail, and then having to guess why it failed...
I believe I did this because of the new SEW_WalkPath function which needed SEW.WalkToPos to return if it was successful or not, and within that function already exist distance checkers, if I understood it correctly. Should SEW_WalkPath fail to walk to the next tile in a path for 10-12 seconds the function will also result false. It's my preference to use functions over procedures for the reason of appropriate fail-safes.
Originally Posted by slacky
And for no reason (what so ever), you randomly prefixed all the functions you added to IE: SEW_WalkPath(..) rather then following the object-oriented style the rest of the module was written with (SEWalker.WalkPath()).. That was just a dumb thing to do, and just makes it harder for users to use, it's much less CC-friendly versus having all record-methods related to SEWalker, under the SEWalker-type.[/FONT]
Two functions, yes. This is because your SEWalker type already has your own version of "FFlag()" which does not function as the real, normal "FFlag". It would be more appropriate to rename yours to "flagPresent()". For this reason I was not able to use the standard "FFlag()" function with a distance parameter and had to make a separate function from the object-oriented SEWalker type, which excludes your "FFlag()".
Now, as I said at the top, I've tested this next to nothing. The changes I've made are mostly based off positioning & walking in a custom map so, granted, it's not fair to shape your include around a single style of usage. If you'd like I'll be happy to revert everything back to your original version, I don't mind it at all, and if you've adjustments and/or improvements to make then, again, I'll be more than happy to add them in. My work to the SEWalker.simba file clearly was not yet finished, and should it return to its original form then I imagine nearly all my scripts in the future which utilize it will have many overrides to your procedures, simply because I like A: Failsafes and B: more scripter-control. I'm not a fan of static code, as my include and scripts clearly reflect.
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hello.
I would like to report to you that whenever i use aerolib with this script [AL]DroiFletch in the fleching section( here's the link to it https://villavu.com/forum/showthread.php?t=109071), with all my details filled in username and password etc. It mixes the characters of my username and password in the runescape 2007 login screen. for example say in the script i have filled my username to be "tom" and my password is 123. When i run the script , it fills my username to 1t3 and password to o2m. all characters are there but it just mixes them up... again thanks in advance in looking for this problem. I have also posted this in script thread , your aerolib include thread so it could grab your attention quicker. Thanks
16. Originally Posted by tomjerry
hello.
I would like to report to you that whenever i use aerolib with this script [AL]DroiFletch in the fleching section( here's the link to it https://villavu.com/forum/showthread.php?t=109071), with all my details filled in username and password etc. It mixes the characters of my username and password in the runescape 2007 login screen. for example say in the script i have filled my username to be "tom" and my password is 123. When i run the script , it fills my username to 1t3 and password to o2m. all characters are there but it just mixes them up... again thanks in advance in looking for this problem. I have also posted this in script thread , your aerolib include thread so it could grab your attention quicker. Thanks
Thanks mate I got your PM as well. I won't be at home until late tonight but when I arrive I'll try recreating your problem so I can see what's going wrong. From what you told me before it's an issue when logging in via the browser; that's a start. Thank you for bringing it to my attention.
17. SRL Junior Member
Join Date
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I can't load slackworlds's extension to get simbaext.rar, can anyone upload it for me somewhere?
18. Originally Posted by hakishakataki
I can't load slackworlds's extension to get simbaext.rar, can anyone upload it for me somewhere?
I just tested the download link, it works fine for me. Try it again and if you have trouble let me know; I'll re-upload it for you.
19. SRL Junior Member
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Originally Posted by Flight
I just tested the download link, it works fine for me. Try it again and if you have trouble let me know; I'll re-upload it for you.
Sorry Flight, for some reason I still cant access the website. I have no idea what's up.
20. Is there a reflection include that works with lape? and more importantly with this include?
21. Originally Posted by Fitta
Is there a reflection include that works with lape? and more importantly with this include?
This is a colour only include.
22. Originally Posted by Harrier
This is a colour only include.
Captain Obvious heh..
Maybe I was unclear. Is there a reflection include you could COMBINE with this(that also runs with lape)?
23. Originally Posted by Fitta
Captain Obvious heh..
Maybe I was unclear. Is there a reflection include you could COMBINE with this(that also runs with lape)?
We only have one reflection include in development and as far as I'm aware it's only PascalScript compatible unfortunately.
24. Originally Posted by Fitta
Captain Obvious heh..
Maybe I was unclear. Is there a reflection include you could COMBINE with this(that also runs with lape)?
No, I meant there was no addons to make it reflection currently. Making it a 100% color only include.
25. @Flight, If I was to make a some suggestions on the include, would that be here in this thread or via PM?
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2020-07-03 09:33:05
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https://www.physicsforums.com/threads/faster-than-c-communication.976053/
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# I Faster than c communication?
#### f todd baker
On my web site (unnamed since I have been previously reprimanded for "promoting" the site!) I got a question, pretty straightforward, the essence of which is: Two long wires are not parallel and make an angle θ with each other; they cross at one point and one wire is moving with velocity v perpendicular to the first; the point where they cross moves with a velocity u.
It is easy to show that u=v/tanθ and u may be larger than c. But this point has no mass and carries no information so, no problem with special relativity (just like a sweeping laser spot moving across the moon with v>c). But then I got a followup question suggesting having an array of moving wires the spacing of which is coded information. What am I missing?
#### Attachments
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#### FactChecker
Gold Member
2018 Award
If the distance between the wires changes, that change can not travel along the wire at infinite speed. In fact it is limited to c or less.
#### f todd baker
All wires but one are moving with the same velocity and are parallel. The distance between any two of them does not change.
#### FactChecker
Gold Member
2018 Award
Oh. I missed that. There is nothing that says that information set up earlier can not be read fast. The wires that you describe can not be set up over a distance faster than c. It would take a long time to set up the parallel wires of that length. Your example is just a more complicated case of sending information and storing it in a safe in a distant location. Then the safe can be opened and read instantly. That does not mean that the information was transmitted instantly.
#### Dale
Mentor
I second @FactChecker here. The information is transmitted at the time of setting up the spacing between the wires. The diagonal wire is actually completely irrelevant.
#### Ibix
No information is being transmitted in the u direction - it's being transmitted in the v direction. It's just that observers spaced perpendicular to that get the information with different delays. The only way to communicate in the u direction is to poke one of the wires as it passes, and then this is just a complicated variant on "can I communicate faster than light by pushing a rigid rod".
#### Mister T
Gold Member
But then I got a followup question suggesting having an array of moving wires the spacing of which is coded information. What am I missing?
The coding can't travel faster than $c$.
#### DaveC426913
Gold Member
Though this is an idealized thought experiment: here's some practical cold water tossed on it:
The speed of transmission will be far slower than c; it is limited to the speed of sound in the material that the wires are made of.
Even if they were made of the hardest substance currently known - diamond - their best transmission speed will be only 12km/s - the speed of sound in diamond.
"Faster than c communication?"
### Physics Forums Values
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2019-08-19 23:27:15
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http://www.scientificlib.com/en/Physics/LX/Kelvin.html
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- Art Gallery -
# .
The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven base units in the International System of Units (SI) and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F).[1] In other words, it is defined such that the triple point of water is exactly 273.16 K.
The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin (1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the primary unit of measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. Subtracting 273.16 K from the temperature of the triple point of water (0.01 °C) makes absolute zero (0 K) equivalent to −273.15 °C (−459.67 °F).
Kelvin temperature conversion formulae
from Kelvin to Kelvin
Celsius [°C] = [K] − 273.15 [K] = [°C] + 273.15
Fahrenheit [°F] = [K] × 95 − 459.67 [K] = ([°F] + 459.67) × 59
Rankine [°R] = [K] × 95 [K] = [°R] × 59
For temperature intervals rather than specific temperatures,
1 K = 1°C = 95°F = 95°R
Comparisons among various temperature scales
History
See also: Thermodynamic temperature – History and Properties of water – Physics and chemistry
Lord Kelvin, the namesake of the unit
In 1848, Lord Kelvin wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" (absolute zero) was the scale's null point, and which used the degree Celsius for its unit increment. Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time.[2] This absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin's value of "−273" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.
In 1954, the Resolution 3 of the 10th CGPM gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to exactly 273.16 kelvins.[3]
In 1967/1968 Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K.[4] Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water."[1]
In 2005 The Comité International des Poids et Mesures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the Kelvin thermodynamic temperature scale would refer to water having an isotopic composition specified as VSMOW.[5]
Usage conventions
When spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm (e.g. "the triple point of water is exactly 273.16 kelvins"[6]). When reference is made to the "Kelvin scale", the word "kelvin"—which is normally a noun—functions adjectivally to modify the noun "scale" and is capitalized. As with most other SI unit symbols (angle symbols, e.g. 45°3′4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g. "99.987 K").[7][8]
Before the 13th General Conference on Weights and Measures (CGPM) in 1967–1968, the unit kelvin was called a "degree", the same as with the other temperature scales at the time. It was distinguished from the other scales with either the adjective suffix "Kelvin" ("degree Kelvin") or with "absolute" ("degree absolute") and its symbol was °K. The latter (degree absolute), which was the unit's official name from 1948 until 1954, was rather ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural form was "degrees absolute". The 13th CGPM changed the unit name to simply "kelvin" (symbol K).[9] The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales (although the Rankine scale continued to use "degree Rankine"), but rather an absolute unit of measure which can be manipulated algebraically (e.g. multiplied by two to indicate twice the amount of "mean energy" available among elementary degrees of freedom of the system).
Use in conjunction with Celsius
A thermometer calibrated in degrees Celsius (left) and kelvins (right).
In science and engineering, degrees Celsius and kelvins are often used simultaneously in the same article (e.g. "...its measured value was 0.01028 °C with an uncertainty of 60 µK..."). This practice is permissible because the degree Celsius is a special name for the kelvin for use in expressing Celsius temperatures and the magnitude of the degree Celsius is exactly equal to that of the kelvin.[10] Notwithstanding that the official endorsement provided by Resolution 3 of the 13th CGPM states, "a temperature interval may also be expressed in degrees Celsius", the practice of simultaneously using both "°C" and "K" remains widespread throughout the scientific world as the use of SI prefixed forms of the degree Celsius (such as "µ°C" or "microdegrees Celsius") to express a temperature interval has not been widely adopted.[4]
Proposed redefinition
Main article: Proposed redefinition of SI base units
In 2005 the CIPM embarked on a program to redefine, amongst others, the kelvin using a more rigorous basis than was in use. The current (2010) definition is unsatisfactory for temperatures below 20 K and above 1300 K.[11] The committee proposes defining the kelvin as the temperature scale for which Boltzmann's constant is 1.3806505×10−23 J/K exactly.[12] The committee hoped that the program would be completed in time for its adoption by the CGPM at its 2011 meeting, but at the 2011 meeting the decision was postponed to the 2014 meeting when it would be considered as part of a larger program.[13]
From a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed; water will still freeze at 0 °C (273.15 K or 32 °F).[14]
Practical uses
Colour temperature
Main article: Colour temperature
The kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light of which the colour depends on the temperature of the radiator. Black bodies with temperatures below about 4000 K appear reddish whereas those above about 7500 K appear bluish. Colour temperature is important in the fields of image projection and photography where a colour temperature of approximately 5600 K is required to match "daylight" film emulsions. In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature. The photosphere of the Sun, for instance, has an effective temperature of 5778 K.
Kelvin as a measure of noise
Main article: Noise figure
In electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. the noise temperature. The so-called Johnson–Nyquist noise of discrete resistors and capacitors is a type of thermal noise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using the Friis formulas for noise.
Unicode character
The symbol is encoded in Unicode, in the Letterlike Symbols range, at codepoint U+212A K kelvin sign.
Comparison of temperature scales
International Temperature Scale of 1990
Negative temperature
Rankine scale
Thermodynamic temperature
Triple point
Notes and references
"Resolution 4: Definition of the SI unit of thermodynamic temperature (kelvin)". Resolutions of the 13th CGPM. Bureau International des Poids et Mesures. 1967. Retrieved 2008-02-06.
Lord Kelvin, William (October 1848). "On an Absolute Thermometric Scale". Philosophical Magazine. Retrieved 2008-02-06.
"Resolution 3: Definition of the thermodynamic temperature scale". Resolutions of the 10th CGPM. Bureau International des Poids et Mesures. 1954. Retrieved 2008-02-06.
"Resolution 3: SI unit of thermodynamic temperature (kelvin)". Resolutions of the 13th CGPM. Bureau International des Poids et Mesures. 1967. Retrieved 2008-02-06.
"Unit of thermodynamic temperature (kelvin)". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 2.1.1.5. Retrieved 2008-02-06.
"Rules and style conventions for expressing values of quantities". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 2.1.1.5. Retrieved 2012-08-27.
"SI Unit rules and style conventions". National Institute of Standards and Technology. September 2004. Retrieved 2008-02-06.
"Rules and style conventions for expressing values of quantities". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 1967. pp. Section 5.3.3. Retrieved 2008-02-06.
Barry N. Taylor (2008). "Guide for the Use of the International System of Units (SI)" (.PDF). Special Publication 811. National Institute of Standards and Technology. Retrieved 2011-03-05.
"Units with special names and symbols; units that incorporate special names and symbols". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 2006. pp. Section 2.2.2, Table 3. Retrieved 2008-02-06.
J. Fischer1 et al. (2007-05-02). "Report to the CIPM on the implications of changing the definition of the base unit kelvin" (PDF). International Committee for Weights and Measures (CIPM). Retrieved 2010-02-23.
Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (PDF). CCU. Retrieved 2011-01-01.
"General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram." (PDF) (Press release). Sèvres, France: General Conference on Weights and Measures. 23 October 2011. Retrieved 25 October 2011.
"Updating the definition of the kelvin" (PDF). International Bureau for Weights and Measures (BIPM). Retrieved 2010-02-23.
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2021-10-18 16:59:37
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https://cs.stackexchange.com/questions/47024/what-are-some-results-for-non-trivial-lower-bounds-for-the-time-complexity-of-de
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# What are some results for non-trivial lower bounds for the time complexity of decision problems?
Typically decision problems are studied in complexity theory and function problems are studied in the Analysis of Algorithms. Unfortunately, Complexity Theory tends to abstract over the exact time complexity of a problem.
I know that Decision-Tree Complexity and more generally Query Complexity (Boolean Complexity) aim to lower bound the time complexity of decision problems. However, I'm not yet steeped in the literature and would just like to see some of the results before I spend years trying to understand them.
Even NP-Complete problems only have the trivial $\Omega(n)$ lower bounds trivial for any decision problem. I would like to find a problem with something better than this. I will also accept problems where the best algorithm we know is strongly conjectured to be optimal.
So far, I've only found the problem of recognizing palindromes.
Ultimately, I would like to attempt to prove lower bounds for some problems myself and would like to "check my answers."
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2019-06-18 17:09:47
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http://mathhelpforum.com/calculus/117181-solved-latitude.html
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# Math Help - [SOLVED] latitude
1. ## [SOLVED] latitude
How would i show the following:
Show that about 4% of the Earth's surface lies north of the Arctic circle (at latitude +66.5 degrees).
2. How would i show the following:
Show that about 4% of the Earth's surface lies north of the Arctic circle (at latitude +66.5 degrees).
3. Originally Posted by nerdo
How would i show the following:
Show that about 4% of the Earth's surface lies north of the Arctic circle (at latitude +66.5 degrees).
Do an internet search for "SPHERICAL CAP"
or look here:Spherical Cap -- from Wolfram MathWorld
Since you are looking only for a per cent value, you do not require the radius of the earth in miles or kilometers, just use "R" for the radius.
Calculate the total surface area of a sphere,
then the area of the spherical cap.
$\dfrac{\text{AreaSphericalCap}}{\text{SurfaceAreaS phere} }100 = \text{percentage}$
.
4. Originally Posted by aidan
Do an internet search for "SPHERICAL CAP"
or look here:Spherical Cap -- from Wolfram MathWorld
Since you are looking only for a per cent value, you do not require the radius of the earth in miles or kilometers, just use "R" for the radius.
Calculate the total surface area of a sphere,
then the area of the spherical cap.
$\dfrac{\text{AreaSphericalCap}}{\text{SurfaceAreaS phere} }100 = \text{percentage}$
.
Thanks for the help, but i would like to ask how would you calculate the radius.
5. Originally Posted by nerdo
Thanks for the help, but i would like to ask how would you calculate the radius.
Surface Area of a sphere:
$S_{\text{sphere}} = 4 \, \pi \, r^2$
Surface Area of a spherical cap
$S_{\text{cap}} = 2 \, \pi \, r \, h$
If you sliced the earth along the latitude 66.5 degress,
the distance from the plane ( the flat part )
to the north point is the distance h.
$h = R - R \sin (latitude)$
$h = R(1 - \sin (latitude))$
replacing h (in the spherical cap equation above)
$S_{\text{cap}} = 2 \, \pi \, r^2 (1-sin(latitude))$
the ratio:
$\dfrac{ \text{SphericalCapArea}}{\text{SurfaceAreaOfSphere }}$
$\dfrac{2\,\pi\,r^2(1-\sin(latitude))}{4\,\pi\,r^2}$
Pi cancels.
.
6. Originally Posted by aidan
Surface Area of a sphere:
$S_{\text{sphere}} = 4 \, \pi \, r^2$
Surface Area of a spherical cap
$S_{\text{cap}} = 2 \, \pi \, r \, h$
If you sliced the earth along the latitude 66.5 degress,
the distance from the plane ( the flat part )
to the north point is the distance h.
$h = R - R \sin (latitude)$
$h = R(1 - \sin (latitude))$
replacing h (in the spherical cap equation above)
$S_{\text{cap}} = 2 \, \pi \, r^2 (1-sin(latitude))$
the ratio:
$\dfrac{ \text{SphericalCapArea}}{\text{SurfaceAreaOfSphere }}$
$\dfrac{2\,\pi\,r^2(1-\sin(latitude))}{4\,\pi\,r^2}$
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2015-03-02 00:38:50
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https://www.physicsforums.com/threads/a-simple-presentation-of-an-exceptionally-simple-toe.265128/
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# A simple presentation of an exceptionally simple TOE
1. Oct 17, 2008
### humanino
If you always wanted to understand how we discover new particle, Garrett Lisi gave a delightful presentation at TED of his works :
A beautiful new theory of everything
2. Oct 17, 2008
### MTd2
Did you know, or are you aware, that the Standard Model is not a subgroup his theory, but merely a subset? That means new particles should violate the standard model at tree level, that means, at the lowest apoximation, that is with no loops.It should violate all particle interactions, in all three generations. Jacques Distler pans out his most heavily criticisms on this fact.
But, I sure that no one verified if experiments can already rule out his theory, not even calculated the order of magnetude of the cross sections of any these new interactions.... not even Garrett himself tried.
3. Oct 17, 2008
### humanino
That's a known fact indeed, and deserves worries. But nobody really has an explanation for the CKM or CMN matrices anyways, so I would interpret the situation as most interesting.
4. Oct 17, 2008
### marcus
Humanino, would you say that 80 percent of the talk is about a visual way to think about the Standard Model, and some small extensions that other people have already proposed?
That is my rough estimate.
It is about a way to understand non-verbally how Standard Particle zoo might be built up, and incrementally predicted/discovered----and to understand different ways a physicist might intuitively want to extend. One gets an idea of the way a good theorist might look at it and want to complete the symmetry.
I didn't time it with a stopwatch so I couldn't say for sure, but I guess that less than less than 5 percent of the talk is specific to Garrett's own proposals.
What he is doing is a favor to that bunch of Silicon Valley and smart media people, who get invited to TED (attendance is by invitation and it tends to bring intelligent edgy generalists).
I would say he is doing them a favor by opening a window for them to look into the head of a generic topclass theorist without being obstructed by a blackboard full of equations.
He is good at communicating. And also he is at a certain level, well, competitive. surfers can be that. My take is, that he wanted to have one of the best and toprated TED talks of this year. TED rates talks by collective audience response. You can hit high on their charts.
Not every physicist could make a hit on TED charts. You need special skill and creativity of approach. It is not like the National Geographic. So it is challenging. When you turn it on you can see that Garrett is challenged by the challenge of it. For a moment he thinks to himself "I have never done this. Will I be able to reach these people?" There is a scary moment at the start where he speaks with a different voice----no one there has ever heard his real voice and they could be fooled and think it was him. Then suddenly, he goes himself, and he is on. It is a very good talk. Not like any other physics talk I can remember, but good in its own way.
I think someone who doesn't think they need to know what they are talking about could come into this thread and start talking about what they think on this or that topic without having watched this particular video lecture. So what I am trying to point out is--- this talk is what the thread you started is about---Garrett's talk of September or October 2008. This is the focus that we can discuss, those who have watched the talk. I would say without question it is one of the great physics lectures (given the size of the problem of explaining Standard Model to intelligent people who wouldn't otherwise be interested in it, and not talking down to them.)
Last edited: Oct 17, 2008
5. Oct 18, 2008
### Fra
I watched the video and his slides and the visualization of the higher dimensional transformation are very appealing.
What striked me personally the most, is the impression of his methodology you get from watching this video. The impression is a guidane by mathematical beautiful patterns, and extrapolations of models guided by trying to maintain or extend symmetries, and the conviction that nature are likely to be constructed by the same mathematical beauty.
This is a way of thinking that is very different from my personal way of thinking, but it is very interesting to understand not only other peoples conclusions, but also their way of reasoning!
In all, I liked the talk and his very nice slides. Excellent intuitive visual presentation, almost artistic, like the saying that an image says more than thousand equations ;)
/Fredrik
6. Oct 18, 2008
### Orion1
Based upon what I watched in this lecture, according to the Garrett Lisi model, there are 2 gravitational force spin charges: spin up, spin down.
The Garrett Lisi model for 7 charge dimensions E(7), corresponds to the Pati-Salam model with 2 new particles as 'super weak' force particles.
Pati-Salam model:
$$SU(4) \times SU(2) \times SU(2)$$
According to Wikipedia, these 2 new particles corresponds to neutral 'sterile neutrinos', a sterile neutrino and a sterile anti-neutrino.
And at 8 charge dimensions E(8), there are 18 new coloured strong force particles, for a total of 20 new particles.
What does the symmetry pattern appear like for E(9)?
Reference:
Pati-Salam model - Wikipedia
Last edited: Oct 18, 2008
7. Oct 19, 2008
### humanino
Thank you Marcus for the comments. I fully agree with them. I think it is also interesting to contemplate the viewpoint of a relative "outsider" to mainstream physics. This presentation tells a lot about Garrett's personality as well.
What is E(9) ?
8. Oct 19, 2008
### Autochthon
Perhaps someone can clarify let me start simple is he describing a single common class of entity that is uniquely defined by it's movement through various degree's of freedom as defined by an E(8) shaped space? or multiple classes each of whose properties and interactions are described by that shape? From his coral analogy at the start I took it he meant the former.
9. Oct 23, 2008
### Orion1
Last edited: Oct 23, 2008
10. Oct 23, 2008
### MTd2
A found this on wikipedia
"In geometry, a semiregular k21 polytope is a polytope in (k+4) dimensions constructed from the En Coxeter group, and having only regular polytope facets. The family was named by Coxeter as k21 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the k-node sequence.
Thorold Gosset discovered this family as a part of his 1900 enumeration of the regular and semiregular polyopes, and so they are sometimes called Gosset's semiregular figures. Gosset named them by their dimension from 5 to 9, for example the 5-ic semiregular figure.
The sequence as identified by Gosset ends as an infinite tessellation (space-filling honeycomb) in 8-space, called the E8 lattice. (A final form was not discovered by Gosset and is called the E9 lattice: 621. It is a tessellation of hyperbolic 9-space constructed of (∞ 9-simplex and ∞ 9-orthoplex facets with all vertices at infinity.)"
http://en.wikipedia.org/wiki/Semiregular_E-polytope
11. Oct 23, 2008
### MTd2
The use of this E(n), n>8 is due to the resemblance that the Coxeter representation of some groups have with the ones of E(8), E(7), E(6).
Some people that study M-Theory like these groups. There is a fairly famous one, from last year, that argues supergravities, superstrings and stuff, can be derived from E(11):
http://arxiv.org/abs/0705.0752v1
12. Oct 24, 2008
### humanino
So with infinite dimensional Lie algebras, you would have an infinite number of interactions ?
13. Oct 24, 2008
### MTd2
Why are you saying that?
14. Oct 24, 2008
### Orion1
E(n) Lie algebras have an infinite number of families.
The E(8) Vertices total number 240, is equivalent to the total number of individual charges and fundamental particles in the Garrett Lisi model, including the 20 new fundamental particles.
E(9) is a 'E8 lattice' Euclidean 8-space lattice (E8), (∞ 8-simplex and ∞ 8-orthoplex facets), with the largest exceptional Lie algebra Gosset semiregular polytopes, with and an infinite number of Vertices, therefore, according to the Garrett Lisi metaphysical pattern, it is predicting an infinite number of charges and fundamental particles and interactions and apparently cannot be visually depicted.
Is a Gosset E(9) Euclidean 8-space lattice (E8) really capable of breaking symmetry into a subset Gosset polytope Garrett Lisi E(8) TOE model?
Attachment: left Gosset E(8) with Vertices, right Garrett Lisi E(8) with new particles.
Reference:
Semiregular_E-polytope - Wikipedia
Lie group - Wikipedia
#### Attached Files:
• ###### TOE01.JPG
File size:
91.2 KB
Views:
100
Last edited: Oct 24, 2008
15. Oct 24, 2008
### MTd2
Oh, what Garrett uses is the algebra of the group e(8), that is, it gives the possible combinations that one particle can have with each other. In that page of wikipedia, what is discussed are polytopes, that is, kinds of polyhedra in higher dimensions, except that in that case, it follows a certain formula, a certain pattern of coxeter-dynkin diagram, to generalize in higher dimensions.
Now, we have to distinguish a few things,
1. All polyhedra in that sequence are finite, except for the last 2, which are infinite
2. The 3rd last polytope, 4_21, is what Garrett lie uses.
3. The 2nd last polytope, 5_21 polytope, turns out to be also the E(8) lattice. The smaller, polytopes, in that sequence, are just finite things.
4. The last polytope, E(9) is also infinite, except that the space in which it is embended, it is infinite. In that case, it is a lattice in a hyperbolic space.
5. E(10) and beyond are not even polytopes, just algebras.
6. Calling anything E(n), n>8, is an abuse of language, because an exceptional group or algebra, is at first place a simple algebra. A simple algebra is a kind of "prime number" of non abelian algebras. The only normal subgroups, or sub algebras, are the idendity and itself.
7. But calling E(n), n>8, is useful to some people because they can remember how they behave easily.
8. E(11)
*So, what garrett algebra could do with E(8) lattice is to map n-dimensional planes, to other n-dimensional planes, by telling what goes to where and such.*-> wrong
Last edited: Oct 25, 2008
16. Oct 25, 2008
### humanino
Because you will have an infinite number of generators of your algebra, hence an infinite number of gauge fields. I am just questioning whether it can be a physical proposal, because I can not imagine how one can convince oneself of the existence of an infinite number of possible interactions, considering how long and difficult it is to study just one.
17. Oct 25, 2008
### Orion1
For purposes of this thread, simply calling E(n) as an 'Element' with n dimensions, instead of an 'exceptional' Lie algebra, should be appropriate, since the original exceptional labeling does not use any brackets.
18. Oct 25, 2008
### MTd2
So, following the pattern of coxeter dynkin diagrams k_21 semiregular polytopes, and calling them E(k+2), we have the following structures:
0<n<9 -> polytopes/ finite algebras
n =9 -> E(8) lattices/ infinite dimensional algebra
n = 10 -> E(9) hyperbolic lattice/ infinite dimensional algebra
n=11 -> infinite dimensional algebra, conjetured to be the symmetry group of M-Theory
n>11 -> infinite algebras, without any known use.
I found this here:
http://en.wikipedia.org/wiki/En_(Lie_algebra)
PS.: Interesting thoughts guys.
Last edited: Oct 25, 2008
19. Oct 25, 2008
### MTd2
Yes, and also the other 2 exception Lie algebras do not have an E, that is G_2 and F_4
20. Oct 25, 2008
### Orion1
Last edited: Oct 25, 2008
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2017-02-23 02:45:41
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https://socratic.org/questions/how-do-you-find-the-vertical-horizontal-and-oblique-asymptote-given-x-4x-2-7x-2
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# How do you find the Vertical, Horizontal, and Oblique Asymptote given x /( 4x^2+7x-2)?
Sep 15, 2016
vertical asymptotes at x = -2 , x $= \frac{1}{4}$
horizontal asymptote at y = 0
#### Explanation:
The denominator of the function cannot be zero as this would make the function undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for these values then they are vertical asymptotes.
solve: $4 {x}^{2} + 7 x - 2 = 0 \Rightarrow \left(4 x - 1\right) \left(x + 2\right) = 0$
$\Rightarrow x = - 2 \text{ and " x=1/4" are the asymptotes}$
Horizontal asymptotes occur as
${\lim}_{x \to \pm \infty} , f \left(x\right) \to c \text{ (a constant)}$
divide terms on numerator/denominator by the highest power of x that is ${x}^{2}$
$f \left(x\right) = \frac{\frac{x}{x} ^ 2}{\frac{4 {x}^{2}}{x} ^ 2 + \frac{7 x}{x} ^ 2 - \frac{2}{x} ^ 2} = \frac{\frac{1}{x}}{4 + \frac{7}{x} - \frac{2}{x} ^ 2}$
as $x \to \pm \infty , f \left(x\right) \to \frac{0}{4 + 0 - 0}$
$\Rightarrow y = 0 \text{ is the asymptote}$
Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 1 ,denominator-degree 2 ) Hence there are no oblique asymptotes.
graph{x/(4x^2+7x-2) [-10, 10, -5, 5]}
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2019-08-21 02:40:47
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http://gmatclub.com/forum/in-the-xy-plane-point-p-m-n-and-point-q-n-m-what-is-the-101518.html
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# In the xy plane point P (m,n) and point Q (n,m) what is the
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In the xy plane point P (m,n) and point Q (n,m) what is the [#permalink] 22 Sep 2010, 12:07
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In the xy plane point P (m,n) and point Q (n,m) what is the distance between P and Q
(1) m - n = 2
(2) m + n = 5
[Reveal] Spoiler: OA
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 12:13
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rxs0005 wrote:
In the xy plane point P ( m,n) and point Q ( n,m) what is the distance between P and Q
m - n = 2
m + n = 5
The formula to calculate the distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$.
So we are asked to calculate: $$d=\sqrt{(m-n)^2+(m-n)^2}=\sqrt{2(m-n)^2}=\sqrt{2}*|m-n|$$.
(1) $$m-n=2$$. Sufficient.
(2) $$m+n=5$$. Not sufficient.
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 12:14
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Distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$
put the values you will get $$\sqrt{(m - n)^2 + (n - m)^2}$$
= $$\sqrt{2(m - n)^2}$$
Hence A is sufficient.
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 12:17
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 12:45
Thanks Gentlemen for the algebraic approach i was using the graphical approach and was confused
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 13:02
A.
You can not rely on the graphical solution. I mean you can plot it, but then eventually you will have to play with the equation for distance between two points.
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 13:25
rxs0005 wrote:
Thanks Gentlemen for the algebraic approach i was using the graphical approach and was confused
A.
You can not rely on the graphical solution. I mean you can plot it, but then eventually you will have to play with the equation for distance between two points.
Actually you can solve this graphically. What you need to note is that points (m,n) and (n,m) are mirror reflections across the x=y (45 degree) line on the coordinate plane.
And the final piece in the puzzle is, if you draw a horizontal and a vertical line from (m,n) & the point (n,m) to intersect x=y, both lines will intersect at the points (m,m) and (n,n). This square you form has side (m-n) & its diagnol is the straight line joining (m,n) and (n,m)
So distance = Sqrt(2) * (m-n)
Hence all you need is m-n
The solution seems a bit involved, but if you draw it out it'll be pretty straight forward.
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 13:29
shrouded1 wrote:
rxs0005 wrote:
Thanks Gentlemen for the algebraic approach i was using the graphical approach and was confused
A.
You can not rely on the graphical solution. I mean you can plot it, but then eventually you will have to play with the equation for distance between two points.
Actually you can solve this graphically. What you need to note is that points (m,n) and (n,m) are mirror reflections across the x=y (45 degree) line on the coordinate plane.
And the final piece in the puzzle is, if you draw a horizontal and a vertical line from (m,n) & the point (n,m) to intersect x=y, both lines will intersect at the points (m,m) and (n,n). This square you form has side (m-n) & its diagnol is the straight line joining (m,n) and (n,m)
So distance = Sqrt(2) * (m-n)
Hence all you need is m-n
The solution seems a bit involved, but if you draw it out it'll be pretty straight forward.
Actually, it is the same thing as plotting two points and then writing the equation of distance between two points. As far as being a faster way, the fact that the pyth theorem uses a difference is enough to get the soultion.
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 13:31
Ultimately it has to be the same thing, same problem same solution ... just saying that you can solve the question by plotting a graph and without knowing the distance formula
Alternate solution if you may
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Re: Co-ordinate geometry DS [#permalink] 22 Sep 2010, 13:33
shrouded1 wrote:
Ultimately it has to be the same thing, same problem same solution ... just saying that you can solve the question by plotting a graph and without knowing the distance formula
Alternate solution if you may
Agree
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Re: Co-ordinate geometry DS [#permalink] 29 Oct 2010, 17:47
+1 A
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Re: Co-ordinate geometry DS [#permalink] 09 May 2013, 18:20
I'm not understanding how A is sufficient to answer the question. All A says is that m-n=2. What about n-m? How are m-n and n-m the same?
gurpreetsingh wrote:
Distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$
put the values you will get $$\sqrt{(m - n)^2 + (n - m)^2}$$
= $$\sqrt{2(m - n)^2}$$
Hence A is sufficient.
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Re: Co-ordinate geometry DS [#permalink] 09 May 2013, 20:46
Expert's post
josemnz83 wrote:
I'm not understanding how A is sufficient to answer the question. All A says is that m-n=2. What about n-m? How are m-n and n-m the same?
gurpreetsingh wrote:
Distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$$
put the values you will get $$\sqrt{(m - n)^2 + (n - m)^2}$$
= $$\sqrt{2(m - n)^2}$$
Hence A is sufficient.
(m-n) and (n-m) are not the same thing, however, (m-n)^2 and (n-m)^2 are the same thing. Take (m-n) = 2, thus (n-m) = -2. However, (m-n)^2 = (n-m)^2 = 4.
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Re: In the xy plane point P (m,n) and point Q (n,m) what is the [#permalink] 14 Nov 2013, 03:09
I solved this question by drawing a rough diagram.
Option A > m-n = 2 which means OP = 2, OQ =2
Since OPQ is a right triangle, we can easily calculate the distance PQ. Sufficient
Option B > m+n = 2, clearly insufficient to come to any solution
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Re: In the xy plane point P (m,n) and point Q (n,m) what is the [#permalink] 14 Nov 2013, 03:09
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2015-09-02 10:51:22
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https://www.springerprofessional.de/recent-developments-of-mathematical-fluid-mechanics/7824002
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main-content
## Über dieses Buch
The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as:
1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.
## Inhaltsverzeichnis
### The Work of Yoshihiro Shibata
Abstract
Introducing his research carrier, we address Prof. Yoshihiro Shibata’s great contributions to the mathematical analysis. His out-standing influence to the mathematical society is also clarified.
Herbert Amann, Yoshikazu Giga, Hisashi Okamoto, Hideo Kozono, Masaso Yamazaki
### Existence of Weak Solutions for a Diffuse Interface Model of Power-Law Type Two-Phase Flows
Abstract
We first review results about existence of generalized or weak solutions for Newtonian and power-law type two-phase flows. Then we state a recent result by the authors about existence of weak solutions for diffuse interface model of power-law type two-phase flows and give a sketch of its proof. The latter part is a summary of Abels et al. (Nonlinear Anal Real World Appl 15:149–157, 2014).
Helmut Abels, Lars Diening, Yutaka Terasawa
### Stationary Solutions for a Navier-Stokes/Cahn-Hilliard System with Singular Free Energies
Abstract
We consider a stationary Navier-Stokes/Cahn-Hilliard type system. The system describes a so-called diffuse interface model for the two-phase flow of two macroscopically immiscible incompressible viscous fluids in the case of matched densities, also known as Model H. We prove existence of weak solutions for the stationary system for general exterior forces and singular free energies, which ensure that the order parameter stays in the physical reasonable interval. To this end we reduce the system to an abstract differential inclusion and apply the theory of multi-valued pseudo-monotone operators.
Helmut Abels, Josef Weber
### Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems
Abstract
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying approach to problems with strong degeneracies in the interior or at the boundary.
Herbert Amann
### A Generalization of Some Regularity Criteria to the Navier–Stokes Equations Involving One Velocity Component
Abstract
We present generalizations of results concerning conditional global regularity of weak Leray–Hopf solutions to incompressible Navier–Stokes equations presented by Zhou and Pokorný in articles (Pokorný, Electron J Differ Equ (11):1–8, 2003; Zhou, Methods Appl Anal 9(4):563–578, 2002; Zhou, J Math Pure Appl 84(11):1496–1514, 2005); see also Neustupa et al. (Quaderni di Matematica, vol. 10. Topics in Mathematical Fluid Mechanics, 2002, pp. 163–183) We are able to replace the condition on one velocity component (or its gradient) by a corresponding condition imposed on a projection of the velocity (or its gradient) onto a more general vector field. Comparing to our other recent results from Axmann and Pokorný (A note on regularity criteria for the solutions to Navier-Stokes equations involving one velocity component, in preparation), the conditions imposed on the projection are more restrictive here, however due to the technique used in Axmann and Pokorný (A note on regularity criteria for the solutions to Navier-Stokes equations involving one velocity component, in preparation), there appeared a specific additional restriction on geometrical properties of the reference field, which could be omitted here.
Šimon Axmann, Milan Pokorný
### On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case
Abstract
We consider the p-Laplacian system of N equations in n space variables, 1 < p ≤ 2 , under the homogeneous Navier slip boundary condition without friction. Here, the gradient of the velocity is replaced by the (more physical) symmetric gradient, and the classical non-slip boundary condition is replaced by the Navier slip boundary condition without friction. These combination of circumstances leads to some additional obstacles. We prove W 2, q regularity, up to the boundary, under suitable assumptions on the couple p, q . The singular case μ = 0 is covered.
H. Beirão da Veiga
### Thermodynamically Consistent Modeling for Dissolution/Growth of Bubbles in an Incompressible Solvent
Abstract
We derive mathematical models of the elementary process of dissolution/growth of bubbles in a liquid under pressure control. The modeling starts with a fully compressible version, both for the liquid and the gas phase so that the entropy principle can be easily evaluated. This yields a full PDE system for a compressible two-phase fluid with mass transfer of the gaseous species. Then the passage to an incompressible solvent in the liquid phase is discussed, where a carefully chosen equation of state for the liquid mixture pressure allows for a limit in which the solvent density is constant. We finally provide a simplification of the PDE system in case of a dilute solution.
Dieter Bothe, Kohei Soga
### On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary
Abstract
In the analysis of weak solutions relevant to evolutionary flows of incompressible fluids with non-constant viscosity or with non-linear constitutive equation, it is in general an open question whether a globally integrable pressure exists if the flows are subject to no-slip boundary conditions. Here we overcome this deficiency by considering threshold boundary conditions stating that the fluid adheres to the boundary until certain critical value for the wall shear stress is reached. Once the wall shear stress exceeds this critical value, the fluid slips. The main ingredient in our approach is to look at this type of activated, stick-slip, boundary condition as an implicit constitutive equation on the boundary.
We prove the long-time and large-data existence of weak solutions, with integrable pressure, to unsteady internal flows of Bingham and Navier-Stokes fluids subject to such threshold slip boundary conditions.
Miroslav Bulíček, Josef Málek
### Inhomogeneous Boundary Value Problems in Spaces of Higher Regularity
Abstract
Uniform a priori estimates for parameter-elliptic boundary value problems are well-known if the underlying basic space equals $$L^{p}(\Omega )$$. However, much less is known for the $$W_{p}^{s}(\Omega )$$-realization, s > 0, of a parameter-elliptic boundary value problem. We discuss a priori estimates and the generation of analytic semigroups for these realizations in various cases. The Banach scale method can be applied for homogeneous boundary conditions if the right-hand side satisfies certain compatibility conditions, while for the general case parameter-dependent norms are used. In particular, we obtain a resolvent estimate for the general situation where no analytic semigroup is generated.
Robert Denk, Tim Seger
### Blow-Up Criterion for 3D Navier-Stokes Equations and Landau-Lifshitz System in a Bounded Domain
Abstract
In this paper we prove a blow-up criterion for the 3D Navier-Stokes equations in a bounded domain in terms of a BMO norm of vorticity. We will also prove a regularity criterion for the Landau-Lifshitz system in a bounded domain.
Jishan Fan, Tohru Ozawa
### Local Regularity Results for the Instationary Navier-Stokes Equations Based on Besov Space Type Criteria
Abstract
Consider a weak instationary solution u of the Navier-Stokes equations in a domain $$\Omega \subset \mathbb{R}^{3}$$, i.e.,
$$u \in L^{\infty }\big(0,T;L^{2}(\Omega )\big) \cap L^{2}\big(0,T;W_{0}^{1,2}(\Omega )\big)$$
and u solves the Navier-Stokes system in the sense of distributions. It is a famous open problem whether weak solutions are unique and smooth. A main step in the analysis of this problem is to show that the given weak solution is a strong one in the sense of J. Serrin, i.e., $$u \in L^{s}\big(0,T;L^{q}(\Omega )\big)$$ where s > 2, q > 3 and $$\frac{2} {s} + \frac{3} {q} = 1$$. In this review we report on recent results on this problem, considering first of all optimal initial values u(0) to yield a local in time strong solution, then criteria to prove regularity locally on subintervals of [0, T). Special emphasis is put on results for smooth bounded and also general unbounded domains. Most criteria are based on conditions of Besov space type.
Reinhard Farwig
### On Global Well/Ill-Posedness of the Euler-Poisson System
Abstract
We discuss the problem of well-posedness of the Euler-Poisson system arising, for example, in the theory of semi-conductors, models of plasma and gaseous stars in astrophysics. We introduce the concept of dissipative weak solution satisfying, in addition to the standard system of integral identities replacing the original system of partial differential equations, the balance of total energy, together with the associated relative entropy inequality. We show that strong solutions are unique in the class of dissipative solutions (weak-strong uniqueness). Finally, we use the method of convex integration to show that the Euler-Poisson system may admit even infinitely many weak dissipative solutions emanating from the same initial data.
Eduard Feireisl
### On the Motion of a Liquid-Filled Rigid Body Subject to a Time-Periodic Torque
Abstract
In this paper we investigate the existence of time-periodic motions of a system constituted by a rigid body with an interior cavity completely filled with a viscous liquid, and subject to a time-periodic external torque acting on the rigid body. We then show that the system of equations governing the motion of the coupled system liquid-filled rigid body, has at least one corresponding time-periodic weak solution. Furthermore if the size of the torque is below a certain constant, the weak solution is in fact strong.
Giovanni P. Galdi, Giusy Mazzone, Mahdi Mohebbi
### Seeking a Proof of Xie’s Inequality: On the Conjecture That $$\mu _{m} \rightarrow \infty$$
Abstract
I pursue an argument of Wenzheng Xie, as furthered in several of my papers, to prove a particular point-wise bound for solutions of the three-dimensional steady Stokes problem. If proven, it will provide the basis for an existence and regularity theory for the non-stationary Navier-Stokes equations, free of assumptions about the regularity of the boundary of the flow region. It will be valid for flow in an arbitrary open set.
In his doctoral thesis, Xie proved an analogous bound for solutions of the Poisson problem for the Laplacian, considering it as a model problem. His proof carries over to the Stokes problem except at one point where the maximum principle is invoked. Subsequently, I’ve proposed a variant of Xie’s argument that circumvents the maximum principle, but requires instead a proof that a certain sequence of functions introduced in Xie’s argument tends to become singular. I’ve expressed this as a further conjecture, which is studied here for both the Stokes problem and for the Poisson problem, the latter being considered as a model problem.
John G. Heywood
### Bounded Analyticity of the Stokes Semigroup on Spaces of Bounded Functions
Abstract
Let $$\Omega \subset \mathbb{R}^{n}$$, n ≥ 3, be an exterior domain with smooth boundary. It is shown that the Stokes semigroup on $$L_{\sigma }^{\infty }(\Omega )$$ is a bounded analytic semigroup on this space.
Matthias Hieber, Paolo Maremonti
### On the Weak Solution of the Fluid-Structure Interaction Problem for Shear-Dependent Fluids
Abstract
In this paper the coupled fluid-structure interaction problem for incompressible non-Newtonian shear-dependent fluid flow in two-dimensional time-dependent domain is studied. One part of the domain boundary consists of an elastic wall. Its temporal evolution is governed by the generalized string equation with action of the fluid forces by means of the Neumann type boundary condition. The aim of this work is to present the limiting process for the auxiliary $$(\kappa,\varepsilon,k)$$-problem. The weak solution of this auxiliary problem has been studied in our recent work (Hundertmark-Zaušková, Lukáčová-Medvid’ová, Nečasová, On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid, J. Math. Soc. Japan (in press)).
Anna Hundertmark, Mária Lukáčová-Medviďová, Šárka Nečasová
### Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations
Abstract
We consider the stability problem of time periodic solutions for the rotating Navier-Stokes equations. For the non-rotating case, it is known that time periodic solutions to the original Navier-Stokes equations are asymptotically stable under the smallness assumptions both on the time periodic solutions and on the initial disturbances. We shall treat the high-rotating cases, and prove the asymptotic stability of large time periodic solutions for large initial perturbations.
Tsukasa Iwabuchi, Alex Mahalov, Ryo Takada
### Weighted L p − L q Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations
Abstract
We consider the Navier-Stokes equations in half-space and in L p space with Muckenhoupt weight and show the $$L^{p} - L^{q}$$ estimates of Stokes semigroup with $$\langle x'\rangle ^{s_{1}}\langle x_{n}\rangle ^{s_{n}}$$ type weight. Finally as the application of the weighted $$L^{p} - L^{q}$$ estimates, we shall obtain the weighted asymptotic behavior of the solution to the Navier-Stokes equations.
Takayuki Kobayashi, Takayuki Kubo
### On Vorticity Formulation for Viscous Incompressible Flows in R + 3
Abstract
In this paper we study the vorticity equations for viscous incompressible flows in the half space under the no-slip boundary condition on the velocity field. In particular, the boundary condition for the vorticity field is presented explicitly, and the solution formula for the linearized problem is obtained.
Humiya Kosaka, Yasunori Maekawa
### A Weak Solution to the Navier–Stokes System with Navier’s Boundary Condition in a Time-Varying Domain
Abstract
We assume that $$\Omega ^{t}$$ (for t ∈ [0, T]) is a time-varying domain in $$\mathbb{R}^{3}$$. Particularly, $$\Omega ^{t}$$ can be a region around colliding bodies. Under certain conditions on $$\Omega ^{t}$$ and the way it varies, we prove the weak solvability of the Navier–Stokes system with Navier’s slip boundary condition in $$Q_{(0,T)}:=\{ (\mathbf{x},t);\ 0 < t < T,\ \mathbf{x} \in \Omega ^{t}\}$$.
Jiří Neustupa, Patrick Penel
### Effects of Fluid-Boundary Interaction on the Stability of Boundary Layers in Plasma Physics
Abstract
The present article addresses the asymptotic stability of stationary solutions to a system of the Euler-Poisson equations with an interaction between fluids and boundaries. The system describes motions of positive ions in a boundary layer called a sheath in a plasma flow, formed under the Bohm criterion, which requires the outflow velocity to exceed the ion acoustic velocity. In this model, charged particles accumulate as the plasma arrive at the boundary, which, at the same time affects fluid flows by changing the electric field over the entire domain through the change in the boundary condition. We show that the boundary layer is asymptotically stable under this fluid-boundary interactive setting.
Masashi Ohnawa
### On Incompressible Two-Phase Flows with Phase Transitions and Variable Surface Tension
Abstract
Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics (Prüss et al., Evol Equ Control Theory 1:171–194, 2012; Prüss and Shimizu, J Evol Equ 12:917–941, 2012; Prüss et al., Commun Part Differ Equ 39:1236–1283, 2014; see also Prüss et al., Interfaces Free Bound 15:405–428, 2013) is extended to the case of temperature-dependent surface tension. We prove well-posedness in an L p -setting, study the stability of the equilibria of the problem, and show that a solution which does not develop singularities exists globally, and if its limit set contains a stable equilibrium it converges to this equilibrium in the natural state manifold for the problem as time goes to infinity.
Jan Prüss, Senjo Shimizu, Gieri Simonett, Mathias Wilke
### On the Nash-Moser Iteration Technique
Abstract
The aim of this work is to provide a brief presentation of the Nash-Moser iteration technique for the resolution of nonlinear equations, where the linearized equations admit estimates with a loss of regularity with respect to the given data.
Paolo Secchi
### Rate of Convergence to the Stationary Solution of the Navier-Stokes Exterior Problem
Abstract
This paper is concerned with the nonstationary Navier-Stokes equation in two-dimensional exterior domains with stationary external forces, and provides the rate of convergence of solutions to the stationary solution under the smallness condition of the stationary solution.
Masao Yamazaki
Weitere Informationen
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2021-06-13 21:56:51
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https://cs.stackexchange.com/questions/12268/normal-form-lambda-calculus-expression
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# Normal form Lambda calculus expression
I need a little help with a lambda calculus reduction to normal form: $$(\lambda xxxx.xx)(\lambda x.xx)(\lambda x.x)y((\lambda x.x)x)$$ It should be solved like this: $$xx(\lambda x.x)y((\lambda x.x)x)$$ and then: $$xx(\lambda x.x)y(x)$$
This is the result of any of the lambda calculators that you can find online.
My question is: why can't I go on with reductions and make also $(\lambda x.x)y$ so the resulting expression would be $xxy(x)$?
Can you give me a complete answer, with theory of lambda calculus rules/proofs?
I really want to understand this exercise, any help would be appreciated.
• I think your first term is broken. There are too many x's before the first dot. (Also, migrating to Computer Science.) – Dave Clarke May 25 '13 at 11:46
As pointed out in the comments, the first term seems broken - too many $x$es.
The key is that function application is not associative (both in the lambda calculus and outside it). In particular, $a(bc)$ is different from $(ab)c$. In the first term, we apply $b$ to $c$ and then $a$ to the result. In the second term, we apply $a$ to $b$ and then apply the result on $c$.
In your case $xx(\lambda x.x)yx$ is parenthesised as $(((xx)(\lambda x.x))y)x$, because function application associates to the left. This means that there is no redex there, it can't be reduced further.
Your mistake was in that you added parentheses like $xx((\lambda x.x)y)x$, which is a completely different term.
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2020-01-23 00:55:49
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https://rin.io/elliptic-curve-fgl/
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# Elliptic Curve Formal Group Laws: Philosophy and Derivation
Eine deutsche Übersetzung des folgenden Abschnitts befindet sich hier.
#### Philosophical Motivation
In the study of groups with topological structure, we commonly replace the global object (the group) with a local object (the infinitesimal group). We play the following game.
2. Define a method of adding two points to get a third point of this space (which is associative, unital, commutative, and has inverses).
3. Derive an infinitesimal group.
Examples:
• Lie group (group internal to the category of smooth manifolds) (\to) Lie algebra (group internal to the category of infinitesimal spaces).
• elliptic curve formal group (\to) elliptic curve formal group law.
2. An elliptic curve is a group scheme (over (\text{Spec }R)) whose underlying object is 1-dimensional, proper, and smooth. In less abstract terms, it comes with an addition law and a marked point for free.
3. Formally complete the elliptic curve along the origin In less abstract terms, take the Taylor series expansion of the addition law.
The phrase “formal completion of E along 0″ looks like the Taylor series expansion of an elliptic curve about the origin. In some sense, ‘completion at a point’ does give you the Taylor series of a map in the algebraic-geometric setting, but it’s more general than this. That is, a Taylor series is usually of the form (f(x+y) = f(x) + yP_1(x) + y^2P_2(X) + …), where (P_i(x) = \frac{f^{(i)}(x)}{i!}).
For more on this, Aaron Mazel-Gee wrote a great paper on Dieudonne modules.
We can view formal completions as key to our search for an algebraic version of a Lie Algebra. In differentiable Lie theory, the Baker-Campbell-Hausdorff theorem describes the group-law in a small neighborhood of the identity. However, this uses the exponential, which fails to make sense, even as a formal power series, in characteristic (p).
This justifies our quest: describe the group law in a small neighborhood of the identity of the curve without using the exponential map. First, we must go on an excursion to understand completion.
#### You Complete Me
Recall the method of obtaining (\mathbb{Z}_p), the p-adic completion of the integers. \begin{align} & \mathbb{Z}/p \hookleftarrow \mathbb{Z}/{p^2} \hookleftarrow \mathbb{Z}/p^3 … \ \mathbb{Z}_p & = \text{lim } \mathbb{Z}/p^n \end{align}
Let (R) be a ring. We have a polynomial ring, (R[t]). How do we make a ring of formal power series from this? Well, note that (R[t]/t = R), so we get: \begin{align} & R \hookleftarrow R[t]/t^2 \hookleftarrow R[t]/t^3 \hookleftarrow … \ R[[t]] & = \text{lim } R[t]/t^n \end{align}
Similarly, \begin{align} & \text{Spec }A \hookrightarrow \text{Spec }A[t]/{t^2} \hookrightarrow \text{Spec }A[t]/t^3 \hookrightarrow … \ \text{Spf }A[[t]] & = \text{colim }\text{Spec }A[t]/t^n \end{align}
Completion is the process of picking a ring (R) together with a maximal ideal (m) and forming the limit of (R/m^n).
As an example, we consider the group scheme (E) (for example, an elliptic curve) over (\text{Spec }A).
(\text{Spec }A[t]/t^2) is the infinitesimal neighborhood of the first derivative/first infinitesimal neighborhood of (\text{Spec }A). This is like truncating the Taylor series after the information given by the first derivative, e.g. Lie algebra. Similarly, (\text{Spec }A[t]/t^3) tells us about 2nd derivative, and we need a larger infinitesimal neighborhood for the second derivative. In the case of a formal group law, we want to write down all of the infinitesimals, so we take the colimit of (\text{Spec }A[t]/t^n) and get a formal scheme.
Zariski locally on (S), the formal completion (\hat{E}) of (E) along the zero section is of the form:
$$\hat{E} \simeq \text{Spf }(A[[t]])$$ where (\text{Spf }A[[t]] := \text{colim }\text{Spec }A[t]/t^n)
For example, Zariski-locally over (Spec(A)), we can put an elliptic curve in Weierstraß normal form (y^2 + a_1 xy = x^3 + a_2 x^2 + a_4 x + a_6) (I think outside of characteristic 2 and 3, we may take (a_1 = 0)).
In this form, the variable (z = x/y) is a uniformizer at the identity ((y) has a pole of order 3 at the identity, (x) has one of order 2, so (x/y) has zero of order 1). It’s reasonable to expect (Spf(A[[z]])) to be the formal completion.
Note that we are choosing an isomorphism (G \simeq \text{Spf }R[[t]]) here, that is, choosing where to send (t) in (G) (sidenote: if (G) is associated to a cohomology theory, our choice of where to send (t) corresponds to a choice of complex orientation for the cohomology theory).
It is worth noting the difference between (\varinjlim \text{Spec }A[t]/t^n) and (\text{Spec}\varinjlim A[t]/t^n). $$\varinjlim \text{Spec }A[t]/t^n =: \text{Spf }A[[t]]$$ $$\text{Spec} \varinjlim A[t]/t^n =: \text{Spec }A[[t]]$$ Formal schemes live in a category of limits of schemes (affine formal schemes live in a category of rings with the (I)-adic topology for some ideal (I)). So Spec((A[[t]])), considered as a formal scheme, would just be the trivial limit of Spec of the non-topologized ring.
Think about it: with Zariski topology, Spec((k[[t]])) is dense in Spec((k[t])), while Spec((k[t]/(t^n))) is not, for any (n > 0).
#### Our elliptic curve is a projective beast: reviewing the necessary coordinate changes.
Projective polynomials are defined by the following property: (P(\lambda x, \lambda y, \lambda z) = \lambda^k P(x,y,z))
We can make any polynomial into a polynomial with this property by homogenizing (e.g. (y^2z = x^3 + axz^2 + bz^3)).
We ask for the completion of the elliptic curve at the identity wrt the group structure. That is, at the “point at infinity” if we write it in Weierstraß form. “Point at infinity” is the intuition, but “homogenize and look at the projective variety” is how its formalized. (Affine things are slightly awkward, and we can always homogenize equations by adding in another variable, so there’s a canonical way to compactify. Sadly, that’s often implicit in the literature.)
1. Input elliptic curve in homogeneous coordinates ((y^2z = …))
2. Coordinate transform (1) s.t. our elliptic curve contains the origin. ((f(t) = t…))
3. We want an equation for (S) in terms of (T), so we find the fixed point (T = \phi(T)) of (2) by repeatedly substituting (t…) for (f(t)). This gives us a power series of in terms of (T).
Let’s talk about step 2: we can’t talk about the point at infinity in our staring chart of the elliptic curve since it doesn’t include it , that is, ((0,0)) doesn’t even generally lie on (y^2 = x^3+ax+b) so we must coordinate change to an affine coordinate CONTAINING that point.
There’s three maps from projective coordinates back to affine coordinates. All are defined on a certain open subset of (\mathbb{P}^2) (namely the one where a certain coordinate doesn’t vanish), and the corresponding map gives a coordinate chart for that open subset).
For an elliptic curve in Weierstraß form, the (z \neq 0) chart doesn’t contain the identity of the elliptic curve, but the (y \neq 0) has the identity at ((0,0)). We’re basically changing coordinates from the classical affine equation ((y^2=..)), which lives on the (z \neq 0 thing), to the other one living on the (y \neq 0) thing.
Think about it as follows: the elliptic curve lives in (\mathbb{P}^2), but we can describe its intersection with each of the coordinate charts. That’ll of course be different equations. The (z \neq 0) and (x \neq 0) are not suitable to talk about the neighbourhood of the identity, because they simply don’t CONTAIN the identity.
#### Derivation (for simplified Weierstrass):
The explicit derivation of elliptic curve formal group law from an elliptic curve is performed with a series of coordinate changes:
By plugging the expression for (f(T)) into itself repeatedly, (f(T)) stabilizes to a power series with (T) as the only variable.
It is sometimes tiresome (and sometimes meditative) to go through the coordinate changes and explicit solving for (f(T)) in terms of (T) on paper. sage (available free online) automates this process:
sage: E = EllipticCurve([2,3]).formal_group(); E}
Formal Group associated to the Elliptic Curve defined by y^2 = x^3 + 2*x + 3 over Rational Field
sage: F = E.differential(15); F
1 + 4*t^4 + 9*t^6 + 24*t^8 + 120*t^{10} + 295*t^{12} + 1260*t^{14} + O(t^{15})
#### An afternote on Cartier’s curves
I’ll wrap this up by mentioning Cartier’s curves. Cartier’s method relies very heavily on the fact that a formal group law is the formal spectrum of a power series ring. The previous method relied heavily on the fact that a formal group law (G) is the inductive limit of the finite subgroup schemes (ker(p^n)), where (p^n) is the (n)th Frobenius morphism: (G \to G), (x \mapsto x^{p^n}). This relies on all modules being ind-finite, which Lubin mentions to be hopeless in the case of Dieudonne modules.
Let (B) be any commutative (A)-algebra which is separated and complete over the topology defined by (I^n) where (I) are ideals of (B) (i.e., let (B) be a formal (A)-scheme).
For example, take (B = A[[t]]), the formal power series ring in one variable. The ideal (I = tA[[t]]), the set of (n)-tuples of elements (type: power series) in (I) may be equipped with a composition law (\textbf{F}(a, b) = a*b) (this composition will be finite, as we are working with nilpotent elements). Cartier calls such maps (\text{Spf }A[[t]] \xrightarrow{F} \text{Spf }A[[t]]) “curves in \textbf{F}.”
This name choice makes sense. Recall that we can define a polynomial over (\mathbb{C}) as (\mathbb{C}[t] \to \mathbb{C}[t]), similarly, we can define a curve over over (\text{Spec }A) as (\text{Spf }A[[t]] \to \text{Spf }A[[t]]).
Thank you to Akhil Mathew (for explaining the definition of formal schemes), Jesse Silliman (for answering my various questions on completion and formal schemes), and Achim Krause (for walking me through the derivation of the group law).
Written on May 1, 2015
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2022-08-14 22:24:56
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https://www.r-bloggers.com/2011/04/example-8-33-merging-data-sets-one-to-many/
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Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
It’s often necessary to combine data from two data sets for further analysis. Such merging can be one-to-one, many-to-one, and many-to-many. The most common form is the one-to-one match, which we cover in section 1.5.7. Today we look at a one-to-many merge.
Since the Major League baseball season started last Thursday, we’ll use baseball as an example. Sean Lahman has compiled a large set of baseball data. In fact, it’s large enough that it’s only hosted in zipped form. The zipped comma-delimited files, with data through the 2010 season, can be downloaded here.
One file you get is the batting.csv file. This contains yearly batting data for all players. However, if you want to identify players by name, you have to use the playerid variable to link to the master.csv data set, which has names and other information. We’ll add the names to each row of the batting data set. Then we can pull up players’ batting data directly by name instead of with the playerid
SAS
We’ll start by reading the data from the csv files using proc import (section 1.1.4).
proc import datafile="c:\ken\baseball\master.csv"
out=bbmaster dbms=dlm;
delimiter=',';
getnames=yes;
run;
proc import datafile="c:\ken\baseball\batting.csv"
out=bbbatting dbms=dlm;
delimiter=',';
getnames=yes;
run;
Then we sort on playerid in both data sets and use the merge and by statements to link them (section 1.5.7). SAS replicates each row of the master data set for every row of the batting data set with the matching by values.
proc sort data=bbmaster; by playerid; run;
proc sort data=bbbatting; by playerid; run;
data bbboth; merge bbmaster bbbatting;
by playerid;
run;
Then we can use the data! Here, we plot the annual (regular season) RBIs of Derek Jeter and David Ortiz. Note the use of the v= option to the symbol statement (section 5.2.2) to display the players’ names at the plot locations, and the offset option in the axis definition to make extra space for those names to plot.
symbol1 i=none font=swissb v="JETER" h=2 c=red;
symbol2 i=none font=swissb v="ORTIZ" h=2 c=blue;
axis1 offset = (1.5cm,1.5cm);
axis2 offset = (.5cm,);
proc gplot data=bbboth;
where (namelast="Jeter" and namefirst="Derek") or
(namelast="Ortiz" and namefirst="David");
plot rbi * yearid = namelast / haxis=axis1 vaxis=axis2 nolegend;
run;
The result is shown above.
R
We start here by reading the data sets. Then we use the merge() function to generate the desired dataset. As with SAS, the default behavior of the merging facility does what we need in this case.
master = read.csv("bball/Master.csv")
mergebb = merge(batting,master)
To make the plot, we first make a new data set with just the information about Jeter and Ortiz. This isn’t really necessary, but it does make typing slightly less awkward in later steps. Then we make an empty plot. In order to make room for the names (which are much bigger than usual plot symbols) we have to set the x and y limits manually (section 5.3.7).
jo = mergebb[
(mergebb$nameLast == "Jeter" & mergebb$nameFirst == "Derek") |
(mergebb$nameLast == "Ortiz" & mergebb$nameFirst == "David"),]
plot(jo$RBI~jo$yearID, type = "n",xlim = c(1993, 2012),
ylim = c(-10,160), xlab = "Year", ylab = "RBI")
Then we can add the text values, using the text() function (section 5.2.11). We do this by separately pulling rows from the new jo dataset. In the reduced data set, we can specify rows using last names only.
text(jo$yearID[jo$nameLast == "Jeter"], jo$RBI[jo$nameLast == "Jeter"],
"JETER", col="red")
text(jo$yearID[jo$nameLast == "Ortiz"], jo$RBI[jo$nameLast == "Ortiz"],
"ORTIZ", col = "blue")
The result is seen below. David Ortiz has driven in more runs than Derek Jeter since about 2002 (Go Sox!).
Note that if space requirements prevent making a single massive dataset with many replicated rows, you can generate a lookup vector using the match() function, and use this to make the short data set. This version won’t have the names in it, though.
matchlist = match(batting$playerID, master$playerID)
lastname.batting = master$nameLast[matchlist] firstname.batting = master$nameFirst[matchlist]
jo2 = batting[
(lastname.batting == "Jeter" & firstname.batting == "Derek") |
(lastname.batting == "Ortiz" & firstname.batting == "David"),]
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2021-04-22 23:21:46
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https://ftp.aimsciences.org/article/doi/10.3934/cpaa.2013.12.2361
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Article Contents
Article Contents
# Nontrivial periodic solutions for asymptotically linear hamiltonian systems at resonance
• In this paper, we consider the existence of nontrivial $1$-periodic solutions of the following Hamiltonian systems \begin{eqnarray} -J\dot{z}=H'(t,z), z\in R^{2N}, \end{eqnarray} where $J$ is the standard symplectic matrix of $2N\times 2N$, $H\in C^2 ( [0,1] \times R^{2N}, R)$ is $1$-periodic in its first variable and $H'(t,z)$ denotes the gradient of $H$ with respect to the variable $z$. Furthermore, $H'(t,z)$ is asymptotically linear both at origin and at infinity. Based on the precise computations of the critical groups, Maslov-type index theory and Galerkin approximation procedure, we obtain some existence results for nontrivial $1$-periodic solutions under new classes of conditions. It turns out that our main results improve sharply some known results in the literature.
Mathematics Subject Classification: Primary: 34B15, 34C25, 37J45.
Citation:
• [1] H. Amann and E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Sup. Pisa Cl. Sci. Ser. IV, 7 (1980), 539-603. [2] H. Amann and E. Zehnder, Periodic solutions of asymptotically linear Hamiltonian systems, Manuscripta Math., 32 (1980), 149-189.doi: 10.1007/BF01298187. [3] P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some problems with strong resonance at infinity, Nonlinear Anal. TMA, 7 (1983), 241-273.doi: 10.1016/0362-546X(83)90115-3. [4] T. Bartsch and S. J. Li, Critical point theory for asymptotically quadratic functionals with applications to problems at resonance, Nonlinear Anal. TMA, 28 (1997), 419-441.doi: 10.1016/0362-546X(95)00167-T. [5] G. Cerami, An existence criterion for the critical points on unbounded manifolds, Istit. Lombardo Accad. Sci. Lett. Rend. A, 112 (1978), 332-336 (in Italian). [6] K. C. Chang, Solutions of asymptotically linear operator equations via Morse theory, Comm. Pure. Appl. Math., 34 (1981), 693-712.doi: 10.1002/cpa.3160340503. [7] K. C. Chang, "Infinite Dimensional Morse Theory and Multiple Solutions Problems," Birkhäuser, Boston, 1993.doi: 10.1007/978-1-4612-0385-8. [8] K. C. Chang, J. Q. Liu and M. J. Liu, Nontrivial periodic solutions for strong resonance Hamiltonian systems, Ann. Inst. H. Poincaré Anal. Nonlinéaire, 14 (1997), 103-117.doi: 10.1016/S0294-1449(97)80150-3. [9] C. C. Conley and E. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math., 37 (1984), 207-253.doi: 10.1002/cpa.3160370204. [10] G. Fei and Q. Qiu, Periodic solutions of asymptotically linear Hamiltonian systems, Chinese Ann. Math. Ser. B, 18 (1997), 359-372.doi: 10.1006/jdeq.1995.1124. [11] G. Fei, Maslov-type index and periodic solution of asymptotically linear Hamiltonian systems which are resonant at infinity, J. Differential Equations, 121 (1995), 121-133.doi: 10.1006/jdeq.1995.1124. [12] D. Gromoll and W. Meyer, On differentiable functions with isolated critical point, Topology, 8 (1969), 361-369.doi: 10.1016/0040-9383(69)90022-6. [13] Y. X. Guo, "Morse Theory for Strongly Indefinite Functional and Its Applications," Doctoral thesis, Institute of Mathematics, Peking University, Beijing, 1999.doi: 10.1142/9789812704283_0013. [14] Y. X. Guo, Nontrivial periodic solutions for asymptotically linear Hamiltonian systems with resonance, J. Differential Equations, 175 (2001), 71-87.doi: 10.1006/jdeq.2000.3966. [15] N. Hirano and T. Nishimura, Multiplicity results for semilinear elliptic problems at resonance and with jumping non-linearities, J. Math. Anal. Appl., 180 (1993), 566-586.doi: 10.1006/jmaa.1993.1417. [16] S. Li and J. Q. Liu, Morse theory and asymptotically linear Hamiltonian systems, J. Differential Equations, 78 (1989), 53-73.doi: 0022-0396(89)90075-2. [17] S. Li and J. Q. Liu, Computations of critical groups at degenerate critical point and applications to nonlinear differential equations with resonance, Houston J. Math., 25 (1999), 563-582. [18] S. Li and W. Zou, The computations of the critical groups with an application to elliptic resonant problems at a higher eigenvalue, J. Math. Anal. Appl., 235 (1999), 237-259.doi: 10.1006/jmaa.1999.6396. [19] Y. Long and E. Zehnder, Morse theory for forced oscillations of asymptotically linear Hamiltonian systems, in "Stochastic Processes, Physics and Geometry" (S. Albeverio, et al. Eds.), Proceedings of Conference in Asconal/Locarno, Switzerland, World Scientific, Singapore, 1990, pp. 528-563. [20] Y. Long, Maslov-type index, degenerate critical points and asymptotically linear Hamiltonian systems, Sci. China Ser. A, 33 (1990), 1409-1419. [21] S. Ma, Infinitely many periodic solutions for asymptotically linear Hamiltonian systems, Rocky Mountain J. Math., to appear. [22] S. Ma, Computations of critical groups and periodic solutions for asymptotically linear Hamiltonian systems, J. Differential Equations, 248 (2010), 2435-2457.doi: 10.1016/j.jde.2009.11.013. [23] S. Ma, Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups, Nonlinear Anal. TMA, 73 (2010), 3856-3872.doi: 10.1016/j.na.2010.08.013. [24] J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems," Appl. Math. Sci., 74, Springer-Verlag, New York, 1989.doi: 10.1007/978-1-4757-2061-7. [25] P. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differential Equations," in CBMS Reg. Conf. Ser. in Math., Vol.65, American Mathematical Society, Providence, RI, 1986. [26] C.-L. Tang and X.-P. Wu, Periodic solutions for second order systems with not uniformly coercive potential, J. Math. Anal. Appl., 259 (2001), 386-397.doi: 10.1006/jmaa.2000.7401. [27] C.-L. Tang and X.-P. Wu, Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems, J. Math. Anal. Appl., 275 (2002), 870-882.doi: 10.1016/S0022-247X(02)00442-0. [28] J. Su, Nontrivial periodic solutions for the asymptotically linear Hamiltonian systems with resonance at infinity, J. Differential Equations, 145 (1998), 252-273.doi: 10.1006/jdeq.1997.3360. [29] A. Szulkin, Cohomology and Morse theory for strongly indefinite functionals, Math. Z., 209 (1992), 375-418.doi: 10.1007/BF02570842. [30] A. Szulkin and W. Zou, Infinite dimensional cohomology groups and periodic solutions of asymptotically linear Hamiltonian systems, J. Differential Equations, 174 (2001), 369-391.doi: 10.1006/jdeq.2000.3942. [31] J. R. Ward, Applications of critical point theory to weakly nonlinear boundary value problems at resonance, Houston J. Math., 10 (1984), 291-305. [32] W. Zou, Solutions for resonant elliptic systems with nonodd or odd nonlinearities, J. Math. Anal. Appl., 223 (1998), 397-417.doi: 10.1006/jmaa.1998.5938. [33] W. Zou, S. Li and J. Q. Liu, Nontrivial solutions for resonant cooperative elliptic systems via computations of critical groups, Nonlinear Anal. TMA, 38 (1999), 229-247.doi: 10.1016/S0362-546X(98)00191-6. [34] W. Zou, Multiple solutions for second-order Hamiltonian systems via computation of the critical groups, Nonlinear Anal. TMA, 44 (2001), 975-989.doi: 10.1016/S0362-546X(99)00324-7. [35] W. Zou, Computations of the critical groups and the nontrivial solutions for resonant type asymptotically linear Hamiltonian systems, Nonlinear Anal. TMA, 49 (2002), 481-499.doi: 10.1016/S0362-546X(01)00115-8.
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2023-03-28 11:32:21
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http://www.gradesaver.com/textbooks/math/geometry/elementary-geometry-for-college-students-5th-edition/chapter-1-section-1-6-relationships-perpendicular-lines-exercises-page-52/20b
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## Elementary Geometry for College Students (5th Edition)
U denotes a $union$ of two or more sets.
A $U$, where $a$ and $b$ are sets (a collection of items), is every item included in set $a$ or set $b$ with no repetition. You can call this the "$union$" of $a$ and $b$. Generally, U denotes union.
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2018-02-23 01:05:51
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https://math.stackexchange.com/questions/2917173/conformal-killing-equation
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# Conformal Killing Equation
I saw this come up in a lecture on conformal field theory, and was a bit skeptical of the claim. So, given some conformal Killing field,
$$\mathcal{L}_{\xi}~g = \lambda g$$ it was said the following is true $$\mathcal{L}_{\nabla^2\xi}g=g\nabla^2\lambda$$ Where $\nabla^2=\nabla^a\nabla_a$ (a contraction of covariant derivatives). I have tried writing things out but can't get anywhere. I end up with a bunch of Riemann tensor terms that don't cancel. So, first off is this even true, and if so how can I show it?
• Have you tried using the metric property of the Levi-Civita connection $\nabla g=0$ to add the missing contributions you need to form the "total covariant derivatives"? I mean something like $(\nabla_a\xi^b)g_{dc}\rightarrow \nabla_a(\xi^bg_{dc})$. – green.onion Sep 14 '18 at 21:02
• yea of course... – ClassicStyle Sep 14 '18 at 22:17
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2019-09-17 02:41:11
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https://socratic.org/questions/how-do-you-test-the-series-sigma-1-n-from-n-is-0-oo-for-convergence#364238
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# How do you test the series Sigma 1/(n!) from n is [0,oo) for convergence?
Jan 14, 2017
Use the ratio test to show the series' convergence.
#### Explanation:
We will use the ratio test. The ratio test says that the for the series $\sum {a}_{n}$, we can make a determination about its convergence by taking $L = {\lim}_{a \rightarrow \infty} \left\mid {a}_{n + 1} / {a}_{n} \right\mid$. Examine the value of $L$:
• If $L > 1$, then $\sum {a}_{n}$ is divergent.
• If $L = 1$, then the test is inconclusive.
• If $L < 1$, then $\sum {a}_{n}$ is (absolutely) convergent.
So for the series sum_(n=0)^oo1/(n!) we let a_n=1/(n!). Then we see that
L=lim_(nrarroo)abs((1/((n+1)!))/(1/(n!)))=lim_(nrarroo)abs((n!)/((n+1)!))
This takes recalling a little bit about factorial. The definition of factorial states that (n+1)! =(n+1)(n!), similar to how 7! = 7*6!. Thus:
L=lim_(nrarroo)abs((n!)/((n+1)(n!)))=lim_(nrarroo)abs(1/(n+1))=0
Since $L = 0$ and therefore $L < 1$, we see that suma_n=sum_(n=0)^oo1/(n!) is convergent through the ratio test.
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2021-12-05 08:26:06
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https://aviation.stackexchange.com/questions/47251/what-is-the-physical-meaning-of-circulation-found-in-kutta-condition
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# What is the physical meaning of circulation found in Kutta condition?
The Kutta–Joukowski theorem is applicable for 2D lift calculation as soon as the Kutta condition is verified. When this is the case, there is a circulation $\small \Gamma$ around the airfoil. My question is related to this circulation:
• What is the physical meaning of the circulation $\small \Gamma$, often represented like this (example 1, example 2, example 3):
(Own work)
I'm interested in a simple explanation of the circulation (is air moving around the airfoil? for dummies) and how does this circulation relate to a view of the airflow in a wind tunnel, where there is no apparent air flowing clockwise around the airfoil:
The rest of this post is a presentation of the circulation theory which motivates my question, and as I understand it, but is not part of the question.
The Kutta condition is linked to stagnation points, the points where air tubes separate to flow on a given side of the airfoil, and where they join again behind the airfoil. The Kutta condition stipulates the latter point coincides with the airfoil trailing edge:
Wikipedia: A body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge.
(Own work)
According to theory, when the airfoil moves through air, the circulation moves the rear stagnation point to the trailing edge, and then maintains it at this position. When at this position, the circulation is finite and can be used to compute lift with Kutta–Joukowski theorem:
Wikipedia: The theorem relates the lift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid and the circulation around the airfoil. [...] The lift per unit span $L^{\prime}$ of the airfoil is given by:
$$L^{\prime} = −\rho_{\infty} V_{\infty} \Gamma$$
where $\small \rho_{\infty}$ and $\small V_{\infty}$ are the fluid density and the fluid velocity far upstream of the airfoil, and and $\small \Gamma$ is the circulation defined as the line integral
$$\Gamma = \oint _{C}V \cdot d \mathbf {s}$$
around a closed contour $C$ enclosing the airfoil and followed in the positive (anti-clockwise) direction.
• That video shows an airfoil shedding vortices, but that has little to do with the main question, that may be formulated as follows: Does a speck of dust caught in the midst of that 'circulation', really revolves round the wing...? or is the Kutta-Joukowski circulation just a useful mathematical construction...? – xxavier Jan 6 '18 at 12:40
Circulation of a fluid around an object by itself will produce no lift. The classic example of this is the spinning cylinder with no other airflow. Viscosity will cause the fluid near a cylinder rotating clockwise to circulate in a clockwise direction around the cylinder. If a left to right horizontal flow is introduced there will be a vector sum of the two flows. This results in the stagnation points near 8 o'clock and 4 o'clock (as opposed to the cylinder with no rotation in the left to right flow having the stagnation points at 9 and 3 o'clock.) The net result of this is the Magnus effect where lift is generated in the 12 o'clock direction.
In your first diagram (typical inviscid flow) there is no circulation. The shape of the airfoil in viscid flow causes the trailing stagnation point to move to the trailing edge (second image -- the Kutta condition). This has the same effect on the airflow as the spinning of the cylinder, in that it creates a clockwise circulation about the airfoil.
The line integral describes, for an arbitrary closed contour around the object, the dot product of the fluid flow velocity vector with the vector path moving around the contour. The simplest contour to analyze is created by following flow streamlines above and below the airfoil and connecting them before and after the airfoil with lines perpendicular to the streamlines.
Since the dot product of perpendicular vectors is 0, the integral along perpendicular portions of the contour are 0. The dot product of parallel vectors is just the multiplication of the scalar values, and since the direction of the contour is reversed between the upper and lower streamline the effect is adding one and subtracting the other. Due to differences in lengths and the different flow speeds (Bernoulli...) along the contour, the integral is non-zero. This number represents the net effective circulation about the airfoil (total flow minus the horizontal flow.)
The interesting thing is that if you extend the contour behind the airfoil far enough to enclose the wake of the airfoil from the beginning of movement, the circulation will be zero as the circulation of total wake is the vector opposite of the circulation about the airfoil.
There is no molecule in the air which actually revolves around the airfoil in the way you would normally think of it. Circulation is a mathematical concept used to explain the motion of air from a frame of reference bound to the wing. It is useful in understanding relative motion above and below the wing.
A similar situation might be a person walking toward the back of a train. The person can walk at 2mph and the train runs at 80mph, so is the person going forward or backward? The answer depends on your frame of reference: backward if you are on the train, forward if you standing by the tracks. Don't even ask about the direction from space.)
The simplest way to think of it is that airfow above the wing is moving faster than that below the wing, which gives the wing its lift. The cause is immaterial. For illustration assume a mach .8 aircraft has mach .88 airflow above its wing and mach .72 below. All molecules move to the trailing edge. If you want to compare these two flows, it is useful to subtract out the aircraft forward speed of .8 leaving mach +0.08 above the wing and -0.08 below, which defines the circulation. The negative speed (forward) below the wing only exists mathematically.
• Interesting analogy with the train, but I am still not clear on this circulation concept. Because from the relative position of an observer on the wing, the air molecules are still moving from the leading edge to the trailing edge. Can you help me better understand what this means? – Michael Hall Jul 29 '19 at 21:17
• @MichaelHall The simplest way to think of it is that airfow above the wing is moving faster than that below the wing, which gives the wing its lift. The cause is immaterial. For illustration assume a mach .8 aircraft has mach .88 airflow above its wing and mach .72 below. All molecules move to the trailing edge as you suppose. If you want to compare these two flows, it is useful to subtract out the aircraft forward speed of .8 leaving mach +0.08 above the wing and -0.08 below, which defines the circulation. The negative speed (forward) below the wing only exists mathematically. – Pilothead Jul 30 '19 at 19:59
• Got it, thanks! – Michael Hall Jul 30 '19 at 22:43
• Just because there's net circulation doesn't mean the fluid is rotating around the airfoil. That's not the definition is circulation. – JZYL Jul 31 '19 at 0:26
I very much like @Gerry's answer. It illustrates the principle of lift through potential theory very well.
I would like to add that circulation doesn't mean that fluid particles are rotating around the airfoil. In fact, even a simple rotating cylinder in an inviscid/irrotational flow would have well-defined streamlines flowing from upstream to downstream.
Rather, the integral definition of circulation in the OP is defined on a closed contour around the velocity vector field, not on a trajectory of any fluid particle. Intuitively, then, circulation illustrates how much a uniform flow has turned.
From Wolfram
• My understanding so far: circulation is a mathematical circulation of a field of vectors around a contour (nothing physical). We can use a holomorphic transform of this to obtain this. Moving the rear stagnation point to the trailing point starts the downwash and creates a transient opposite actual / physical vortex behind, which then disappears (more). But that's no so clear, that's why no answer is yet selected. – mins Jul 31 '19 at 9:12
• @mins Do you have a reference on who said these two are holomorphic? The first one is a non-lifting cylinder. As explained by Gerry, the circulation around the cylinder is zero. The second one has a non-zero circulation if you enclose the airfoil with any closed curve. The stagnation points are not the cause for circulation. If you explain what is not clear, maybe we can adjust our answers. – JZYL Jul 31 '19 at 15:09
• I've found several mentions of conformal mapping (e.g. at Nasa), which according this (end of second page) is a holomorphic function. – mins Jul 31 '19 at 21:56
• @mins Yes, you can transform the circulation of an airfoil to that of a rotating cylinder. But the first image in your previous comment was a non-rotating cylinder. So there is no mapping between the two. Kutta condition dictates where the stagnation point should be on the airfoil, but itself does not give rise to lift. Circulation does. – JZYL Jul 31 '19 at 22:28
• Ok, I got this image from a page (unfortunately in French), where the cylinder wasn't rotating, but a holomorphic transform was yet mentioned. – mins Aug 1 '19 at 6:32
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2020-01-17 16:58:53
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http://math.stackexchange.com/tags/symmetric-groups/new
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# Tag Info
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$(abc)$ maps $a$ to $b$, $b$ to $c$, and $c$ to $a$. Now, all we need to do is map $c$ to $a$ (so $b \mapsto c \mapsto a$), $a$ to $d$ ($c \mapsto a \mapsto d$), and $d$ to $c$ — i.e., $(cad)$. Thus, $(ab)(cd) = (cad)(abc)$.
1
Try $(ab)(cd) = (ab)(bc)(bc)(cd)= (abc)(bcd)$.
1
$\;\gamma^{-1}\;$ will be the permutation mapping each cycle of $\;\alpha\;$ to a corresponding cycle of $\;\beta\;$ of the same type, thus for example: $$\gamma^{-1}:=\begin{cases}1\to2\\2\to3\\5\to4\\.......\\4\to1\\6\to5\\.......\\3\to6\end{cases}\implies\gamma=(123654)$$ and we can now check that ...
2
Let $\gamma$ be the function that takes a number in the cycle of $\beta$ to the number in $\alpha$ in the corresponding position. That is, send $2 \rightarrow 1$, and $3 \rightarrow 2$, and $4 \rightarrow 5$ et cetera. Intuitively you can think of this as as you temporarily relabelling the numbers in $\beta$ (applying $\gamma$), applying the permutation ...
1
One solution is to rewrite $\gamma\alpha\gamma^{-1}=\beta$ as $\gamma\alpha=\beta\gamma$. Then $\gamma\alpha(1)=\beta\gamma(1)$, and from $\alpha(1)=2$ we get $\gamma(2)=\beta\gamma(1)$. Similarly, $\gamma(5)=\beta\gamma(2)$ and $\gamma(1)=\beta\gamma(5)$. Combining these, we get $\gamma(2)=\beta\gamma(1)=\beta\beta\beta\gamma(2)$, so $\gamma(2)$ has ...
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Note that $S_6$ is the symmetric group of $6$ symbols which consists of $6!$ element. We can use the theorem that two permutations are conjugate iff they have the same cycle type. As you have already simplified the permutations into the product of disjoint cycles, it is easy to see that the two permutations have the same cycle type. Fortunately, using the ...
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Let's go over how these representations are defined: We have a certain partition of the set $\{1,2,\ldots,n\}$; this partition is into an ordered collection of unordered sets. Such a partition might look like $[\{1,3\}, \{2,4\}]$; note this is exactly the same partition as $[\{3,1\}, \{2,4\}]$, but not the same as $[\{2,4\}, \{1,3\}]$. The problem with ...
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There are indeed $\frac156!=144$ different $5$-cycles in $S_6$ but note that a single $5$-Sylow accounts for 4 of them. Indeed $c$, $c^2$, $c^3$, $c^4$ are the 4 different non-trivial elements in $\langle c\rangle$. Thus the total number of $5$-Sylows is $\frac14144=36$.
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I know this post is old, but there's another elegant way to prove this - a subgroup of order 6 has index 2. We prove the following statement: Any subgroup of index 2 of a finite group must contain all elements of odd order. Let $G$ be finite and $H\subseteq G$ a subgroup of index 2. Any subgroup of index 2 is normal, so $G/H$ is a group and we write $\bar ... 0 Let$r\in[1\>..\>n-1]$be the length of the cycle containing the number$n$. Begin the listing of this cycle with$n$. There are$(n-1)(n-2)\cdots(n-r+1)$ways to choose the remaining entries of this cycle. Now there will be$n-r\geq1$numbers left over, one of them the largest. Begin the listing of the second cycle with this largest left-over number, ... 0 From the possible answers, it appears that the question intended to ask how many permutations have exactly two cycles in their cycle decomposition, including the$1$-cycles. If the smaller cycle has$k$elements, the greater has$n-k$, and$j$particular elements can form$(j-1)!$different$j$-cycles. Thus the desired count is $$... 0 Here is another proof, that actually proves a bit more: Let G,H be two non-abelian groups of order 6. Then G \cong H. First off, we seek to show each group has an element of order 3, and an element of order 2. Since both are non-abelian, we don't have any elements in either of order 6, for such an element would then generate the entire group, ... 0 There are four things you need when showing an isomorphism: \bullet Define a function \phi: A\rightarrow B. \bullet Prove that \phi is injective. \bullet Prove that \phi is surjective. \bullet Show that the homomorphism property \phi(xy)=\phi(x)\phi(y) holds. Generators do map to generators through isomorphism, but that is result of ... 0 D_3 can be embedded in S_3 by sending r to (123) and s to (23) and then extend homomorphically. You can see this intuitively by noticing that any element of D_3 is completely determined by its action on the three points of the triangle, and every element of D_3 then induces a bijection from this set of points to itself, label the points 1, ... 0 With a group this small you can almost get away with writing down an isomorphism explicitly as a table and verify by inspection that it is a homomorphism, and is injective and surjective. The only trouble is that there is 36 different products to check for the homomorphism condition f(ab)=f(a)f(b), and that's at the upper limit of where one would like to ... 0 A standard way to prove that these two sets are isomorphic is to prove that they satisfy the same defining relations. For this particular example, one can show without too much difficulty (i.e. just write out the full multiplication table) show that any group of order 6 such that there exist elements a and b where: order of a is 3, order of b is 2, ... 0 For H \subseteq G, if V is an irreducible representation of H and W is an irreducible representation of G, then Frobenius reciprocity says that$$ \mathrm{mult}_W(\mathrm{Ind}_H^G V) = \mathrm{mult}_V(\mathrm{Res}^G_HW). $$So we only need to determine the multiplicity of \mathrm{sgn}_{\mathfrak{S}_2} in the restrictions of the irreducible ... 0 Your mistake happened when you declared o(a)=9. Thats not true. It should read "|a| divides 9" ( sorry if you don't mind, I would like to use |a| notion instead of o(a) for order of a\in S_n ) This means |a|\in \{1,3,9\}. Let |a|=1. That means a=\varepsilon and hence (123)=a^3=\varepsilon^3=\varepsilon which is contradiction. Let ... 1 Let G=S_4,\ H=S_3 where H is regarded as pemutations of \{1,2,3\} and so is a subset (and a subgroup) of G regarded as permutations of \{1,2,3,4\}. Then none of (14),(24),(34) are in H, so we can form the three possibly distinct right cosets H(14),\ H(24),\ H(34) and none of these are H. If we can show any two of these are in fact ... 1 \sigma\cdot(2,3)=\sigma(2),\sigma(3)) holds for all \sigma\in S_3. So for example if \sigma=(1\,2\,3), then \sigma(2)=3 and \sigma(3)=1, so \sigma\cdot(2,3)=(3,1). 3 You have f:H \to H/K defined by f(h)=hK is a homomorphism (the natural projection). Since H/K is abelian, the image of f is abelian and thus H' \subset ker(f). But ker(f)=K (because f(h)=hK=K iff h \in K). Now consider a 3-cycle (a_1a_2a_3). Since n \geq 5, there are some numbers a_4 and a_5 disjoint from a_1,a_2,a_3. Note that if ... 1 We have \sigma(1) = 2 and \sigma(2) = 3, so the first factor (x_1-x_2) becomes (x_{\sigma(1)}-x_{\sigma(2)}) = (x_2 - x_3). Similarly for the rest. Does that clear things up? 6 The kernel of a surjective homomorphism from S_5 to S_4 would have order |S_5|/|S_4|=5. This is impossible because: S_5 has 1+4!=25 elements of order 1 or 5; the image of each of those 25 elements must have order 1 or 5 in S_4; but S_4 has no elements of order 5, so those 25 elements must all belong to the kernel of the ... 0 Let H be normal subgroup of S_5 such that S_5/H is isomorphic to S_4. Then H=<\sigma> for some 5 cycle \sigma. Note that \tau(a_1\ a_2\ a_3\ ....\ a_k)\tau^{-1} = (\tau(a_1)\ \tau(a_2) ... \ \tau(a_k)). It is very useful find \tau \in S_5 s.t \tau H \tau^{-1} is not H 6 The possible candidates for such an H are the subgroups of S_5 that are cyclic of order 5. All elements of S_5 of order 5 are given by 5-cycles. However, the subgroup generated by a 5-cycle is not normal, so no H can exist, as desired. 1 If \;n_p\; denotes the number of Syloy \;p\,- subgroups, then we know that$$n_p=[S_p:N_G(P)]=\frac{p!}{|N_G(P)|}$$and we know that \;n_p=(p-2)!\; 2 Here’s what Ian Stewart has to say on p. 268 of his book Galois Theory*: The transitive subgroups [of S_n], up to conjugacy, have been classified for low values of n by Conway, Hulpke, and MacKay (1998). … There is only one such subgroup when n=2, two when n=3, and five when n=4,5. The magnitude of the task becomes apparent when n=6: in this ... 0 Take \sigma\in S_n, we need to have \sigma^3(j)=j for all j\geq n. Take 4. We need to have \sigma^3(4)=4. Suppose \sigma(4)=4 then we are done. Suppose not, then we see that (4~l~m) belongs to decomposition of \sigma. Continuing this, way, neglecting elements which are mapped to itself, we are forced to have ... 1 Found it! http://sheaves.github.io/Subgroup-Lattice/ This shows how to build the lattice in Sage, and at the very end of the third post there is a complete generator. (You can use Sage freely on websites like sagemath.org, or installing it on your computer.) 0 The "standard" proofs of the simplicity of the finite classical groups like {\rm PSL}(n,q) make heavy use of permutation representations and the general theory of permutation groups. The final step in the proofs uses Iwasawa’s Theorem, which is criterion for a primitive permutation group to be simple. Of course the definition of these groups is in terms ... 1 Every permutation of X that leaves Y invariant as a set is really composed of two distinct, independent and non-overlapping permutations: one is a permutation of Y, and the other is a permutation of X \setminus Y. Indeed, if a permutation of X maps all the elements of Y back into Y, then the restriction of the original permutation (on X) to ... 5 Hint, as requested: the order of an element \sigma in \mathfrak{S}_n is the least common multiple of the cycle lengths of \sigma. 2 With q the total number of elements on the cycle that contains 1,2,\ldots,k we get the formula$$\sum_{q=k}^n \frac{q!}{q} {n-k\choose q-k} (n-q)!$$which says that there are$(q-1)!$cycles on the$q$elements, we must choose the remaining$q-k$elements for the cycle from the elements other than the first$k$and combine this with any ... 3 It sounds like you're describing the quotient space$\mathbb{R}^n/S_n$. Some people call this the$n^{th}$"symmetric power" (of$\mathbb{R}$), although be a little careful with that terminology because it can be used to refer to two other related but different constructions. This quotient is not a manifold, but can be thought of as an orbifold. For ... 1 It's important that on the first page the paper states that, without loss of generality, all of their irreducible representations are unitary, so that$\rho(g)^\dagger=\rho(g)^{-1}$for all$g\in G$. By the way, the beginning of section$3$is in error. The sum$\sum_{h\in H}\rho(h)$is not a projection, because it is not normalized correctly. Instead, ... 1$\sum_{1\le i,j\le d_\rho} |\hat{f}(\rho)_{i,j}|^2 = ||\hat{f}(\rho)||^2$is just the definition of the Frobenius norm of the matrix$\hat{f}(\rho)$. 2 Suppose$\sigma: H\to\mathrm{GL}(W)$is a complex irreducible representation of$H$. Call the trace$\chi$. Then character theory says that$\sum_{h\in H}\chi(h)$equals$|H|$if$\sigma$is trivial and$0$otherwise. Additionally, the sum$\sum_{h\in H}\sigma(h)$is an interwtining operator, and Schur's lemma says the intertwining operators of a complex ... 0 What your first observation amounts to is that$H$is (isomorphic to) a subgroup of$S_3 \times S_2$, where the first factor acts on$\{1,2,3\}$and the second factor acts on$\{4,5\}$. This only has$12$elements, which is a drastic reduction from the$120$elements of$S_5$we would have to test by "brute force". Moreover, it can be seen that any element ... 1 What you call "exponentiation" means conjugacy:$\phi$is a homomorphism$G\rightarrow Aut(V)$for some vector space$V$; an (invertible) matrix is an automorphism of$V$(once you choose a basis), and$\phi^A$is the representation$x\mapsto A\phi(x)A^{-1}$(or replace$A$with$A^{-1}\$ depending on the author's conventions). In other words, it's just the ...
0
What you want to read is Serre's book on Linear Representation of Finite Groups. Section 8.2 of chapter 8 covers the case of a semi-direct product by an abelian group. For the more general case, you want to use the theory of induced characters in a more subtle way. This is not as trivial as it sounds though ; make sure you have the mathematical background to ...
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2016-05-29 11:56:47
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https://socratic.org/questions/how-do-you-find-the-quotient-of-4n-2-3n-6-div-n-2-using-long-division
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# How do you find the quotient of (4n^2-3n+6)div(n-2) using long division?
Quotient $\left(4 n - 5\right)$; Remainder $- \frac{4}{n - 2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a} 4 n \textcolor{w h i t e}{a a a} - 5$
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2020-11-28 23:43:43
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http://www.reference.com/browse/chymistry
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Related Searches
Definitions
# Chemistry
[kem-uh-stree]
Chemistry (from Egyptian kēme (chem), meaning "earth") is the science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions. Historically, modern chemistry evolved out of alchemy following the chemical revolution (1773). Chemistry is a physical science related to studies of various atoms, molecules, crystals and other aggregates of matter whether in isolation or combination, which incorporates the concepts of energy and entropy in relation to the spontaneity of chemical processes.
Disciplines within chemistry are traditionally grouped by the type of matter being studied or the kind of study. These include inorganic chemistry, the study of inorganic matter; organic chemistry, the study of organic matter; biochemistry, the study of substances found in biological organisms; physical chemistry, the energy related studies of chemical systems at macro, molecular and submolecular scales; analytical chemistry, the analysis of material samples to gain an understanding of their chemical composition and structure. Many more specialized disciplines have emerged in recent years, e.g. neurochemistry the chemical study of the nervous system (see subdisciplines).
## Overview
Chemistry is the scientific study of interaction of chemical substances that are constituted of atoms or the subatomic particles: protons, electrons and neutrons. Atoms combine to produce molecules or crystals. Chemistry is often called "the central science" because it connects the other natural sciences, such as astronomy, physics, material science, biology, and geology.
The genesis of chemistry can be traced to certain practices, known as alchemy, which had been practiced for several millennia in various parts of the world, particularly the Middle East.
The structure of objects we commonly use and the properties of the matter we commonly interact with, are a consequence of the properties of chemical substances and their interactions. For example, steel is harder than iron because its atoms are bound together in a more rigid crystalline lattice; wood burns or undergoes rapid oxidation because it can react spontaneously with oxygen in a chemical reaction above a certain temperature; sugar and salt dissolve in water because their molecular/ionic properties are such that dissolution is preferred under the ambient conditions.
The transformations that are studied in chemistry are a result of interaction either between different chemical substances or between matter and energy. Traditional chemistry involves study of interactions between substances in a chemistry laboratory using various forms of laboratory glassware. A chemical reaction is a transformation of some substances into one or more other substances. It can be symbolically depicted through a chemical equation. The number of atoms on the left and the right in the equation for a chemical transformation is most often equal. The nature of chemical reactions a substance may undergo and the energy changes that may accompany it are constrained by certain basic rules, known as chemical laws.
Energy and entropy considerations are invariably important in almost all chemical studies. Chemical substances are classified in terms of their structure, phase as well as their chemical compositions. They can be analysed using the tools of chemical analysis, e.g. spectroscopy and chromatography.
Chemistry is an integral part of the science curriculum both at the high school as well as the early college level. At these levels, it is often called 'general chemistry' which is an introduction to a wide variety of fundamental concepts that enable the student to acquire tools and skills useful at the advanced levels, whereby chemistry is invariably studied in any of its various sub-disciplines. Scientists, engaged in chemical research are known as chemists. Most chemists specialize in one or more sub-disciplines.
## History
The genesis of chemistry can be traced to the widely observed phenomenon of burning that led to metallurgy- the art and science of processing ores to get metals (e.g. metallurgy in ancient India). The greed for gold led to the discovery of the process for its purification, even though, the underlying principles were not well understood -- it was thought to be a transformation rather than purification. Many scholars in those days thought it reasonable to believe that there exist means for transforming cheaper (base) metals into gold. This gave way to alchemy, and the search for the Philosopher's Stone, which was believed to bring about such a transformation by mere touch.
Some consider medieval Muslims to be the earliest chemists, who introduced precise observation and controlled experimentation into the field, and discovered numerous chemical substances. The most influential Muslim chemists were Geber (d. 815), al-Kindi (d. 873), al-Razi (d. 925), and al-Biruni (d. 1048). The works of Geber became more widely known in Europe through Latin translations by a pseudo-Geber in 14th century Spain, who also wrote some of his own books under the pen name "Geber". The contribution of Indian alchemists and metallurgists in the development of chemistry was also quite significant.
The emergence of chemistry in Europe was primarily due to the recurrent incidence of the plague and blights there during the so called Dark Ages. This gave rise to a need for medicines. It was thought that there exists a universal medicine called the Elixir of Life that can cure all diseases, but like the Philosopher's Stone, it was never found.
For some practitioners, alchemy was an intellectual pursuit, over time, they got better at it. Paracelsus (1493-1541), for example, rejected the 4-elemental theory and with only a vague understanding of his chemicals and medicines, formed a hybrid of alchemy and science in what was to be called iatrochemistry. Similarly, the influences of philosophers such as Sir Francis Bacon (1561-1626) and René Descartes (1596-1650), who demanded more rigor in mathematics and in removing bias from scientific observations, led to a scientific revolution. In chemistry, this began with Robert Boyle (1627-1691), who came up with an equations known as the Boyle's Law about the characteristics of gaseous state. Chemistry indeed came of age when Antoine Lavoisier (1743-1794), developed the theory of Conservation of mass in 1783; and the development of the Atomic Theory by John Dalton around 1800. The Law of Conservation of Mass resulted in the reformulation of chemistry based on this law and the oxygen theory of combustion, which was largely based on the work of Lavoisier. Lavoisier's fundamental contributions to chemistry were a result of a conscious effort to fit all experiments into the framework of a single theory. He established the consistent use of the chemical balance, used oxygen to overthrow the phlogiston theory, and developed a new system of chemical nomenclature and made contribution to the modern metric system. Lavoisier also worked to translate the archaic and technical language of chemistry into something that could be easily understood by the largely uneducated masses, leading to an increased public interest in chemistry. All these advances in chemistry led to what is usually called the chemical revolution. The contributions of Lavoisier led to what is now called modern chemistry - the chemistry that is studied in educational institutions all over the world. It is because of these and other contributions that Antoine Lavoisier is often celebrated as the "Father of Modern Chemistry". The later discovery of Friedrich Wöhler that many natural substances, organic compounds, can indeed be synthesized in a chemistry laboratory also helped the modern chemistry to mature from its infancy.
The discoveries of the chemical elements has a long history from the days of alchemy and culminating in the creation of the periodic table of the chemical elements by Dmitri Mendeleev (1834-1907) and later discoveries of some synthetic elements.
## Etymology
The word chemistry comes from the earlier study of alchemy, which is a pseudoscientific practice which encompasses elements of chemistry, metallurgy, philosophy, astrology, astronomy, mysticism and medicine. Alchemy is commonly thought of as the quest to turn lead or another common starting material into gold. As to the origin of the word "alchemy" the question is a debatable one; it certainly can be traced back to the Greeks, and some, following E. Wallis Budge, have also asserted Egyptian origins. Alchemy, generally, derives from the old French alkemie from the Arabic كيمياء al-kīmiyā' - "the art of transformation". The Arabs borrowed the word "kimia" from the Greeks when they conquered Alexandria in the year 642 AD. A tentative outline is as follows:
1. Egyptian alchemy [3,000 BCE – 400 BCE], formulate early "element" theories such as the Ogdoad.
2. Greek alchemy [332 BCE – 642 CE], the Greek king Alexander the Great conquers Egypt and founds Alexandria, having the world's largest library, where scholars and wise men gather to study.
3. Arabian alchemy [642 CE – 1200], the Arabs take over Alexandria; Jabir is the main chemist
4. European alchemy [1300 – present], Pseudo-Geber builds on Arabic chemistry
5. Chemistry [1661], Boyle writes his classic chemistry text The Sceptical Chymist
6. Chemistry [1787], Lavoisier writes his classic Elements of Chemistry
7. Chemistry [1803], Dalton publishes his Atomic Theory
Thus, an alchemist was called a 'chemist' in popular speech, and later the suffix "-ry" was added to this to describe the art of the chemist as "chemistry".
## Definitions
In retrospect, the definition of chemistry seems to invariably change per decade, as new discoveries and theories add to the functionality of the science. Shown below are some of the standard definitions used by various noted chemists:
• Alchemy (330) – the study of the composition of waters, movement, growth, embodying, disembodying, drawing the spirits from bodies and bonding the spirits within bodies (Zosimos).
• Chymistry (1661) – the subject of the material principles of mixt bodies (Boyle).
• Chymistry (1663) – a scientific art, by which one learns to dissolve bodies, and draw from them the different substances on their composition, and how to unite them again, and exalt them to an higher perfection (Glaser).
• Chemistry (1730) – the art of resolving mixt, compound, or aggregate bodies into their principles; and of composing such bodies from those principles (Stahl).
• Chemistry (1837) – the science concerned with the laws and effects of molecular forces (Dumas).
• Chemistry (1947) – the science of substances: their structure, their properties, and the reactions that change them into other substances (Pauling).
• Chemistry (1998) – the study of matter and the changes it undergoes (Chang).
## Basic concepts
Several concepts are essential for the study of chemistry, some of them are:
### Atom
An atom is the basic unit of an element. It is a collection of matter consisting of a positively charged core (the atomic nucleus) which contains protons and neutrons, and which maintains a number of electrons to balance the positive charge in the nucleus. The atom is also the smallest entity that can be envisaged to retain some of the chemical properties of the element, such as electronegativity, ionization potential, preferred oxidation state(s), coordination number, and preferred types of bonds to form (e.g., metallic, ionic, covalent).
### Element
The concept of chemical element is related to that of chemical substance. A chemical element is characterized by a particular number of protons in the nuclei of its atoms. This number is known as the atomic number of the element. For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon, and all atoms with 92 protons in their nuclei are atoms of the element uranium. However, several isotopes of an element, that differ from one another in the number of neutrons present in the nucleus, may exist.
The most convenient presentation of the chemical elements is in the periodic table of the chemical elements, which groups elements by atomic number. Due to its ingenious arrangement, groups, or columns, and periods, or rows, of elements in the table either share several chemical properties, or follow a certain trend in characteristics such as atomic radius, electronegativity, etc. Lists of the elements by name, by symbol, and by atomic number are also available.
### Compound
A compound is a substance with a particular ratio of atoms of particular chemical elements which determines its composition, and a particular organization which determines chemical properties. For example, water is a compound containing hydrogen and oxygen in the ratio of two to one, with the oxygen between the hydrogens, and an angle of 104.5° between them. Compounds are formed and interconverted by chemical reactions.
### Substance
A chemical substance is a kind of matter with a definite composition and set of properties. Strictly speaking, a mixture of compounds, elements or compounds and elements is not a chemical substance, but it may be called a chemical. Most of the substances we encounter in our daily life are some kind of mixture, e.g. air, alloys, biomass etc.
Nomenclature of substances is a critical part of the language of chemistry. Generally it refers to a system for naming chemical compounds. Earlier in the history of chemistry substances were given name by their discoverer, which often led to some confusion and difficulty. However, today the IUPAC system of chemical nomenclature allows chemists to specify by name specific compounds amongst the infinite variety of possible chemicals. The standard nomenclature of chemical substances is set by the International Union of Pure and Applied Chemistry (IUPAC). There are well-defined systems in place for naming chemical species. Organic compounds are named according to the organic nomenclature system. Inorganic compounds are named according to the inorganic nomenclature system. In addition the Chemical Abstracts Service has devised a method to index chemical substance. In this scheme each chemical substance is identifiable by a numeric number known as CAS registry number.
### Molecule
A molecule is the smallest indivisible portion, beside an atom, of a pure chemical substance that has its unique set of chemical properties, that is, its potential to undergo a certain set of chemical reactions with other substances. Molecules can exist as electrically neutral units unlike ions. Molecules are typically a set of atoms bound together by covalent bonds, such that the structure is electrically neutral and all valence electrons are paired with other electrons either in bonds or in lone pairs.
One of the main characteristic of a molecule is its geometry often called its structure. While the structure of diatomic, triatomic or tetra atomic molecules may be trivial, (linear, angular pyramidal etc.) the structure of polyatomic molecules, that are constituted of more than six atoms (of several elements) can be crucial for its chemical nature.
### Mole
A mole is the amount of a substance that contains as many elementary entities (atoms, molecules or ions) as there are atoms in 0.012 kilogram (or 12 grams) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state. This number is known as the Avogadro constant, and is determined empirically. The currently accepted value is 6.02214179(30) mol-1 (2007 CODATA). It is much like the term "a dozen" in that it is an absolute number (having no units) and can describe any type of elementary object, although the mole's use is usually limited to measurement of subatomic, atomic, and molecular structures.
The number of moles of a substance in one liter of a solution is known as its molarity. Molarity is the common unit used to express the concentration of a solution in physical chemistry.
### Ions and salts
An ion is a charged species, an atom or a molecule, that has lost or gained one or more electrons. Positively charged cations (e.g. sodium cation Na+) and negatively charged anions (e.g. chloride Cl) can form a crystalline lattice of neutral salts (e.g. sodium chloride NaCl). Examples of polyatomic ions that do not split up during acid-base reactions are hydroxide (OH) and phosphate (PO43−).
Ions in the gaseous phase is often known as plasma.
### Acidity and basicity
A substance can often be classified as an acid or a base. This is often done on the basis of a particular kind of reaction, namely the exchange of protons between chemical compounds. However, an extension to this mode of classification was brewed up by the American chemist, Gilbert Newton Lewis; in this mode of classification the reaction is not limited to those occurring in an aqueous solution, thus is no longer limited to solutions in water. According to concept as per Lewis, the crucial things being exchanged are charges. There are several other ways in which a substance may be classified as an acid or a base, as is evident in the history of this concept
### Phase
In addition to the specific chemical properties that distinguish different chemical classifications chemicals can exist in several phases. For the most part, the chemical classifications are independent of these bulk phase classifications; however, some more exotic phases are incompatible with certain chemical properties. A phase is a set of states of a chemical system that have similar bulk structural properties, over a range of conditions, such as pressure or temperature. Physical properties, such as density and refractive index tend to fall within values characteristic of the phase. The phase of matter is defined by the phase transition, which is when energy put into or taken out of the system goes into rearranging the structure of the system, instead of changing the bulk conditions.
Sometimes the distinction between phases can be continuous instead of having a discrete boundary, in this case the matter is considered to be in a supercritical state. When three states meet based on the conditions, it is known as a triple point and since this is invariant, it is a convenient way to define a set of conditions.
The most familiar examples of phases are solids, liquids, and gases. Many substances exhibit multiple solid phases. For example, there are three phases of solid iron (alpha, gamma, and delta) that vary based on temperature and pressure. A principal difference between solid phases is the crystal structure, or arrangement, of the atoms. Less familiar phases include plasmas, Bose-Einstein condensates and fermionic condensates and the paramagnetic and ferromagnetic phases of magnetic materials. While most familiar phases deal with three-dimensional systems, it is also possible to define analogs in two-dimensional systems, which has received attention for its relevance to systems in biology.
### Chemical bond
A chemical bond is a concept for understanding how atoms stick together in molecules. It may be visualized as the multipole balance between the positive charges in the nuclei and the negative charges oscillating about them. More than simple attraction and repulsion, the energies and distributions characterize the availability of an electron to bond to another atom. These potentials create the interactions which holds together atoms in molecules or crystals. In many simple compounds, Valence Bond Theory, the Valence Shell Electron Pair Repulsion model (VSEPR), and the concept of oxidation number can be used to predict molecular structure and composition. Similarly, theories from classical physics can be used to predict many ionic structures. With more complicated compounds, such as metal complexes, valence bond theory fails and alternative approaches, primarily based on principles of quantum chemistry such as the molecular orbital theory, are necessary. See diagram on electronic orbitals.
### Chemical reaction
Chemical reaction is a concept related to the transformation of a chemical substance through its interaction with another, or as a result of its interaction with some form of energy. A chemical reaction may occur naturally or carried out in a laboratory by chemists in specially designed vessels which are often laboratory glassware. It can result in the formation or dissociation of molecules, that is, molecules breaking apart to form two or more smaller molecules, or rearrangement of atoms within or across molecules. Chemical reactions usually involve the making or breaking of chemical bonds. Oxidation, reduction, dissociation, acid-base neutralization and molecular rearrangement are some of the commonly used kinds of chemical reactions.
A chemical reaction can be symbolically depicted through a chemical equation. While in a non-nuclear chemical reaction the number and kind of atoms on both sides of the equation are equal, for a nuclear reaction this holds true only for the nuclear particles viz. protons and neutrons.
The sequence of steps in which the reorganization of chemical bonds may be taking place in the course of a chemical reaction is called its mechanism. A chemical reaction can be envisioned to take place in a number of steps, each of which may have a different speed. Many reaction intermediates with variable stability can thus be envisaged during the course of a reaction. Reaction mechanisms are proposed to explain the kinetics and the relative product mix of a reaction. Many physical chemists specialize in exploring and proposing the mechanisms of various chemical reactions. Several empirical rules, like the Woodward-Hoffmann rules often come handy while proposing a mechanism for a chemical reaction.
A stricter definition is that "a chemical reaction is a process that results in the interconversion of chemical species". Under this definition, a chemical reaction may be an elementary reaction or a stepwise reaction. An additional caveat is made, in that this definition includes cases where the interconversion of conformers is experimentally observable. Such detectable chemical reactions normally involve sets of molecular entities as indicated by this definition, but it is often conceptually convenient to use the term also for changes involving single molecular entities (i.e. 'microscopic chemical events').
### Energy
Energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is invariably accompanied by an increase or decrease of energy of the substances involved. Some energy is transferred between the surroundings and the reactants of the reaction in the form of heat or light, thus the products of a reaction may have more or less energy than the reactants. A reaction is said to be exothermic if the final state is lower on the energy scale than the initial state; in case of endothermic reactions the situation is otherwise.
Chemical reactions are invariably not possible unless the reactants surmount an energy barrier known as the activation energy. The speed of a chemical reaction (at given temperature T) is related to the activation energy E, by the Boltzmann's population factor $e^\left\{-E/kT\right\}$ - that is the probability of molecule to have energy greater than or equal to E at the given temperature T. This exponential dependence of a reaction rate on temperature is known as the Arrhenius equation. The activation energy necessary for a chemical reaction can be in the form of heat, light, electricity or mechanical force in the form of ultrasound.
A related concept free energy, which incorporates entropy considerations too, is a very useful means for predicting the feasibility of a reaction and determining the state of equilibrium of a chemical reaction, in chemical thermodynamics. A reaction is feasible only if the total change in the Gibbs free energy is negative, $Delta G le 0 ,$; if it is equal to zero the chemical reaction is said to be at equilibrium.
There are only a limited possible states of energy for electrons, atoms and molecules. These are determined by the rules of quantum mechanics, which require quantization of energy of a bound system. The atoms/molecules in an higher energy state are said to be excited. The molecules/atoms of substance in an excited energy state are often much more reactive, that is amenable to chemical reactions.
The phase of a substance is invariably determined by its energy and those of its surroundings. When the intermolecular forces of a substance are such that energy of the surroundings is not sufficient to overcome them, it occurs in a more ordered phase like liquid or solid as is the case with water (H2O), a liquid at room temperature because its molecules are bound by hydrogen bonds. Whereas hydrogen sulfide (H2S) is a gas at room temperature and standard pressure, as its molecules are bound by weaker dipole-dipole interactions.
The transfer of energy from one chemical substance to other depend on the size of energy quanta emitted from one substance. However, heat energy is easily transferred from almost any substance to another mainly because the vibrational and rotational energy levels in a substance are very closely placed. Because, the electronic energy levels are not so closely spaced, ultraviolet electromagnetic radiation is not transferred with equal felicity, as is also the case with electrical energy.
The existence of characteristic energy levels for different chemical substances is useful for their identification by the analysis of spectral lines of different kinds of spectra often used in chemical spectroscopy e.g. IR, microwave, NMR, ESR etc. This is used to identify the composition of remote objects - like stars and far galaxies - by analyzing their radiation (see spectroscopy).
The term chemical energy is often used to indicate the potential of a chemical substance to undergo a transformation through a chemical reaction or transform other chemical substances.
### Chemical laws
Chemical reactions are governed by certain laws, which have become fundamental concepts in chemistry. Some of them are:
## Subdisciplines
Chemistry is typically divided into several major sub-disciplines. There are also several main cross-disciplinary and more specialized fields of chemistry.
## Chemical industry
The chemical industry represents an important economic activity. The global top 50 chemical producers in 2004 had sales of 587 billion US dollars with a profit margin of 8.1% and research and development spending of 2.1% of total chemical sales.
## References
• Atkins, P.W. Galileo's Finger (Oxford University Press) ISBN 0198609418
• Atkins, P.W. Atkins' Molecules (Cambridge University Press) ISBN 0521823978
• Stwertka, A. A Guide to the Elements (Oxford University Press) ISBN 0195150279
• Chang, Raymond. Chemistry 6th ed. Boston: James M. Smith, 1998. ISBN 0-07-115221-0.
• Atkins, P.W., Overton, T., Rourke, J., Weller, M. and Armstrong, F. Shriver and Atkins inorganic chemistry (4th edition) 2006 (Oxford University Press) ISBN 0-19-926463-5
• Clayden, J., Greeves, N., Warren, S., Wothers, P. Organic Chemistry 2000 (Oxford University Press) ISBN 0-19-850346-6
• Voet and Voet Biochemistry (Wiley) ISBN 0-471-58651-X
• Atkins, P.W. Physical Chemistry (Oxford University Press) ISBN 0-19-879285-9
• Atkins, P.W. et al. Molecular Quantum Mechanics (Oxford University Press)
• McWeeny, R. Coulson's Valence (Oxford Science Publications) ISBN 0-19-855144-4
• Pauling, L. The Nature of the chemical bond (Cornell University Press) ISBN 0-8014-0333-2
• Pauling, L., and Wilson, E. B. Introduction to Quantum Mechanics with Applications to Chemistry (Dover Publications) ISBN 0-486-64871-0
• Stephenson, G. Mathematical Methods for Science Students (Longman)ISBN 0-582-44416-0
• Smart and Moore Solid State Chemistry: An Introduction (Chapman and Hall) ISBN 0-412-40040-5
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2014-11-26 09:22:13
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https://www.physicsforums.com/threads/energy-stored-in-space-time-or-space.956967/
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# Energy stored in space-time or space?
• I
## Main Question or Discussion Point
I was talking to a graduate physics student about the issue of energy conservation in an expanding universe. I paraphrased the argument against energy conservation as follows -
Suppose we have a photon in outer space that is very far from earth. The universe is expanding (by this I meant that in some regions very far from earth, space is expanding). Let's assume that the photon does not make make contact with anything made out of matter. Well, since space is expanding around it, the wavelength of the photon must increase, and if the wavelength increases, then the energy of the photon decreases. So it seems that energy is destroyed in this process. I asked him where the energy goes, and his response was that the energy is stored in space (or space-time). I am quite skeptical of this response, because as far as I'm concerned, energy only makes sense as a property of matter. The only exception I can think of is gravitational potential energy.
My questions are -
1. Is the idea of energy being stored in space (or space-time) in the way in which he proposed possibly true? Is it plausible? Why, or why not?
Related Special and General Relativity News on Phys.org
This post by Sean Carroll is a good exposition of the viewpoint the student you talked to appears to be taking:
http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
I personally prefer this:
"'there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields.'"
Because I keep hearing about how Lagrangian mechanics can be used to derive relativity, and I've seen the Euler-Lagrange equation, and I've seen the Hamiltonian, how you can get the latter from the former, and they seem to be fairly dependent upon energy.
So, I'd personally prefer Sean Caroll's explanation that "does not actually increase anyone’s understanding," because to me, it definitely does. Or at least it feels more natural. Why can't gravitational fields have negative energy? Minkowski wrote that time can be thought of as imaginary space, and space as imaginary time (well, specifically what he said was: "Thus the essence of this postulate may be clothed mathematically in a very pregnant manner in the mystic formula 3⋅105 km = √(-1) secs.").
If we can have that, why can't gravitational fields have negative energy?
Orodruin
Staff Emeritus
Homework Helper
Gold Member
Because I keep hearing about how Lagrangian mechanics can be used to derive relativity, and I've seen the Euler-Lagrange equation
Then you also know that energy is not necessarily a conserved quantity in Lagrangian mechanics.
Then you also know that energy is not necessarily a conserved quantity in Lagrangian mechanics.
Yeah but ∂L/∂t = 0 looks better. ;)
I am a bit out of my league here. In fact the furthest I ever gotten in looking at Lagrangian mechanics WAS the conservation laws, but I do have one conceptual problem here: I’ve seen (and worked through) the proof using Lagrangian mechanics that shows that time symmetry of the laws of physics implies energy conservation.
How would this not apply to general relativity? Don’t we assume that the laws of physics do not change just because spacetime changes?
Dale
Mentor
How would this not apply to general relativity? Don’t we assume that the laws of physics do not change just because spacetime changes?
It does apply to general relativity. The thing is that the “law of physics” referred to is the Lagrangian, and certain space times have a Lagrangian which is not symmetric under time translations.
PeterDonis
Mentor
2019 Award
Don’t we assume that the laws of physics do not change just because spacetime changes?
The law of physics in this case is the Einstein Field Equation. It's the same everywhere in spacetime. But the stress-energy tensor and the Einstein tensor are not. The EFE doesn't say those tensors are constants; it just says that, however they vary in spacetime, they both vary the same way, so they are equal at every event.
So my last series of questions on this, if you don't mind: is it a completely arbitrary choice about whether you assume (1) negative energy in the gravitational field, which cancels energy being gained or (2) energy is just not conserved.
Is that like with synchronization conventions? You just make the choice? If so, is one more convenient than the other?
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https://hal-hprints.archives-ouvertes.fr/UNIV-PARIS8-OA/hal-03251327v2
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A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process - Archive ouverte HAL Access content directly
Journal Articles Bernoulli Year : 2023
## A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process
Bastien Mallein
Quan Shi
#### Abstract
A continuous-time particle system on the real line verifying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We obtain a necessary and sufficient condition for the convergence of the derivative martingale of such a process to a non-trivial limit in terms of $(\sigma^2,a,\Lambda)$. This extends previously known results on branching Brownian motions and branching random walks. To obtain this result, we rely on the spinal decomposition and establish a novel zero-one law on the perpetual integrals of centred L\'evy processes conditioned to stay positive.
#### Domains
Mathematics [math] Probability [math.PR]
### Dates and versions
hal-03251327 , version 1 (26-01-2022)
hal-03251327 , version 2 (17-11-2022)
### Identifiers
• HAL Id : hal-03251327 , version 2
• ARXIV :
• DOI :
### Cite
Bastien Mallein, Quan Shi. A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process. Bernoulli, 2023, 29 (1), pp.597-624. ⟨10.3150/22-BEJ1470⟩. ⟨hal-03251327v2⟩
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2023-03-27 20:02:38
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https://courses.lumenlearning.com/precalctwo/chapter/series-and-their-notations/
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## Using Summation Notation
To find the total amount of money in the college fund and the sum of the amounts deposited, we need to add the amounts deposited each month and the amounts earned monthly. The sum of the terms of a sequence is called a series. Consider, for example, the following series.
$3+7+11+15+19+..$.
The $n\text{th }$ partial sum of a series is the sum of a finite number of consecutive terms beginning with the first term. The notation $\text{ }{S}_{n}\text{ }$ represents the partial sum.
$\begin{array}{l}{S}_{1}=3\\ {S}_{2}=3+7=10\\ {S}_{3}=3+7+11=21\\ {S}_{4}=3+7+11+15=36\end{array}$
Summation notation is used to represent series. Summation notation is often known as sigma notation because it uses the Greek capital letter sigma, $\sigma$, to represent the sum. Summation notation includes an explicit formula and specifies the first and last terms in the series. An explicit formula for each term of the series is given to the right of the sigma. A variable called the index of summation is written below the sigma. The index of summation is set equal to the lower limit of summation, which is the number used to generate the first term in the series. The number above the sigma, called the upper limit of summation, is the number used to generate the last term in a series.
If we interpret the given notation, we see that it asks us to find the sum of the terms in the series ${a}_{k}=2k$ for $k=1$ through $k=5$. We can begin by substituting the terms for $k$ and listing out the terms of this series.
$\begin{array}{l}\begin{array}{l}\\ {a}_{1}=2\left(1\right)=2\end{array}\hfill \\ {a}_{2}=2\left(2\right)=4\hfill \\ {a}_{3}=2\left(3\right)=6\hfill \\ {a}_{4}=2\left(4\right)=8\hfill \\ {a}_{5}=2\left(5\right)=10\hfill \end{array}$
We can find the sum of the series by adding the terms:
$\sum _{k=1}^{5}2k=2+4+6+8+10=30$
### A General Note: Summation Notation
The sum of the first $n$ terms of a series can be expressed in summation notation as follows:
$\sum _{k=1}^{n}{a}_{k}$
This notation tells us to find the sum of ${a}_{k}$ from $k=1$ to $k=n$.
$k$ is called the index of summation, 1 is the lower limit of summation, and $n$ is the upper limit of summation.
### Does the lower limit of summation have to be 1?
No. The lower limit of summation can be any number, but 1 is frequently used. We will look at examples with lower limits of summation other than 1.
### How To: Given summation notation for a series, evaluate the value.
1. Identify the lower limit of summation.
2. Identify the upper limit of summation.
3. Substitute each value of $k$ from the lower limit to the upper limit into the formula.
4. Add to find the sum.
### Example 1: Using Summation Notation
Evaluate $\sum _{k=3}^{7}{k}^{2}$.
### Solution
According to the notation, the lower limit of summation is 3 and the upper limit is 7. So we need to find the sum of ${k}^{2}$ from $k=3$ to $k=7$. We find the terms of the series by substituting $k=3\text{,}4\text{,}5\text{,}6$, and $7$ into the function ${k}^{2}$. We add the terms to find the sum.
$\begin{array}{ll}\sum _{k=3}^{7}{k}^{2}\hfill & ={3}^{2}+{4}^{2}+{5}^{2}+{6}^{2}+{7}^{2}\hfill \\ \hfill & =9+16+25+36+49\hfill \\ \hfill & =135\hfill \end{array}$
### Try It 1
Evaluate $\sum _{k=2}^{5}\left(3k - 1\right)$.
Solution
## Using the Formula for Arithmetic Series
Just as we studied special types of sequences, we will look at special types of series. Recall that an arithmetic sequence is a sequence in which the difference between any two consecutive terms is the common difference, $d$. The sum of the terms of an arithmetic sequence is called an arithmetic series. We can write the sum of the first $n$ terms of an arithmetic series as:
${S}_{n}={a}_{1}+\left({a}_{1}+d\right)+\left({a}_{1}+2d\right)+…+\left({a}_{n}-d\right)+{a}_{n}$.
We can also reverse the order of the terms and write the sum as
${S}_{n}={a}_{n}+\left({a}_{n}-d\right)+\left({a}_{n}-2d\right)+…+\left({a}_{1}+d\right)+{a}_{1}$.
If we add these two expressions for the sum of the first $n$ terms of an arithmetic series, we can derive a formula for the sum of the first $n$ terms of any arithmetic series.
$\frac{\begin{array}{l}{S}_{n}={a}_{1}+\left({a}_{1}+d\right)+\left({a}_{1}+2d\right)+…+\left({a}_{n}-d\right)+{a}_{n}\hfill \\ +{S}_{n}={a}_{n}+\left({a}_{n}-d\right)+\left({a}_{n}-2d\right)+…+\left({a}_{1}+d\right)+{a}_{1}\hfill \end{array}}{2{S}_{n}=\left({a}_{1}+{a}_{n}\right)+\left({a}_{1}+{a}_{n}\right)+…+\left({a}_{1}+{a}_{n}\right)}$
Because there are $n$ terms in the series, we can simplify this sum to
$2{S}_{n}=n\left({a}_{1}+{a}_{n}\right)$.
We divide by 2 to find the formula for the sum of the first $n$ terms of an arithmetic series.
${S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}$
### A General Note: Formula for the Sum of the First n Terms of an Arithmetic Series
An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of the first $n$ terms of an arithmetic sequence is
${S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}$
### How To: Given terms of an arithmetic series, find the sum of the first $n$ terms.
1. Identify ${a}_{1}$ and ${a}_{n}$.
2. Determine $n$.
3. Substitute values for ${a}_{1}\text{, }{a}_{n}$, and $n$ into the formula ${S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}$.
4. Simplify to find ${S}_{n}$.
### Example 2: Finding the First n Terms of an Arithmetic Series
Find the sum of each arithmetic series.
1. $\text{5 + 8 + 11 + 14 + 17 + 20 + 23 + 26 + 29 + 32}$
2. $\text{20 + 15 + 10 +\ldots + -50}$
3. $\sum _{k=1}^{12}3k - 8$
### Solution
1. We are given ${a}_{1}=5$ and ${a}_{n}=32$.Count the number of terms in the sequence to find $n=10$.Substitute values for ${a}_{1},{a}_{n}\text{\hspace{0.17em},}$ and $n$ into the formula and simplify.
$\begin{array}{l}\begin{array}{l}\hfill \\ {S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}\hfill \end{array}\hfill \\ {S}_{10}=\frac{10\left(5+32\right)}{2}=185\hfill \end{array}$
2. We are given ${a}_{1}=20$ and ${a}_{n}=-50$.Use the formula for the general term of an arithmetic sequence to find $n$.
$\begin{array}{l}{a}_{n}={a}_{1}+\left(n - 1\right)d\hfill \\ -50=20+\left(n - 1\right)\left(-5\right)\hfill \\ -70=\left(n - 1\right)\left(-5\right)\hfill \\ 14=n - 1\hfill \\ 15=n\hfill \end{array}$
Substitute values for ${a}_{1},{a}_{n}\text{,}n$ into the formula and simplify.
$\begin{array}{l}\begin{array}{l}\\ {S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}\end{array}\hfill \\ {S}_{15}=\frac{15\left(20 - 50\right)}{2}=-225\hfill \end{array}$
3. To find ${a}_{1}$, substitute $k=1$ into the given explicit formula.
$\begin{array}{l}{a}_{k}=3k - 8\hfill \\ \text{ }{a}_{1}=3\left(1\right)-8=-5\hfill \end{array}$
We are given that $n=12$. To find ${a}_{12}$, substitute $k=12$ into the given explicit formula.
$\begin{array}{l}\text{ }{a}_{k}=3k - 8\hfill \\ {a}_{12}=3\left(12\right)-8=28\hfill \end{array}$
Substitute values for ${a}_{1},{a}_{n}$, and $n$ into the formula and simplify.
$\begin{array}{l}\text{ }{S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}\hfill \\ {S}_{12}=\frac{12\left(-5+28\right)}{2}=138\hfill \end{array}$
Use the formula to find the sum of each arithmetic series.
### Try It 2
$\text{1}\text{.4 + 1}\text{.6 + 1}\text{.8 + 2}\text{.0 + 2}\text{.2 + 2}\text{.4 + 2}\text{.6 + 2}\text{.8 + 3}\text{.0 + 3}\text{.2 + 3}\text{.4}$
Solution
### Try It 3
$\text{13 + 21 + 29 + }\dots \text{+ 69}$
Solution
### Try It 4
$\sum _{k=1}^{10}5 - 6k$
Solution
### Example 3: Solving Application Problems with Arithmetic Series
On the Sunday after a minor surgery, a woman is able to walk a half-mile. Each Sunday, she walks an additional quarter-mile. After 8 weeks, what will be the total number of miles she has walked?
### Solution
This problem can be modeled by an arithmetic series with ${a}_{1}=\frac{1}{2}$ and $d=\frac{1}{4}$. We are looking for the total number of miles walked after 8 weeks, so we know that $n=8$, and we are looking for ${S}_{8}$. To find ${a}_{8}$, we can use the explicit formula for an arithmetic sequence.
$\begin{array}{l}\begin{array}{l}\\ {a}_{n}={a}_{1}+d\left(n - 1\right)\end{array}\hfill \\ {a}_{8}=\frac{1}{2}+\frac{1}{4}\left(8 - 1\right)=\frac{9}{4}\hfill \end{array}$
We can now use the formula for arithmetic series.
$\begin{array}{l} {S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}\hfill \\ \text{ }{S}_{8}=\frac{8\left(\frac{1}{2}+\frac{9}{4}\right)}{2}=11\hfill \end{array}$
She will have walked a total of 11 miles.
### Try It 5
A man earns $100 in the first week of June. Each week, he earns$12.50 more than the previous week. After 12 weeks, how much has he earned?
Solution
## Using the Formula for Geometric Series
Just as the sum of the terms of an arithmetic sequence is called an arithmetic series, the sum of the terms in a geometric sequence is called a geometric series. Recall that a geometric sequence is a sequence in which the ratio of any two consecutive terms is the common ratio, $r$. We can write the sum of the first $n$ terms of a geometric series as
${S}_{n}={a}_{1}+r{a}_{1}+{r}^{2}{a}_{1}+…+{r}^{n - 1}{a}_{1}$.
Just as with arithmetic series, we can do some algebraic manipulation to derive a formula for the sum of the first $n$ terms of a geometric series. We will begin by multiplying both sides of the equation by $r$.
$r{S}_{n}=r{a}_{1}+{r}^{2}{a}_{1}+{r}^{3}{a}_{1}+…+{r}^{n}{a}_{1}$
Next, we subtract this equation from the original equation.
$\begin{array}{l}\\ \frac{\begin{array}{l}\text{ }{S}_{n}={a}_{1}+r{a}_{1}+{r}^{2}{a}_{1}+…+{r}^{n - 1}{a}_{1}\hfill \\ -r{S}_{n}=-\left(r{a}_{1}+{r}^{2}{a}_{1}+{r}^{3}{a}_{1}+…+{r}^{n}{a}_{1}\right)\hfill \end{array}}{\left(1-r\right){S}_{n}={a}_{1}-{r}^{n}{a}_{1}}\end{array}$
Notice that when we subtract, all but the first term of the top equation and the last term of the bottom equation cancel out. To obtain a formula for ${S}_{n}$, divide both sides by $\left(1-r\right)$.
${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}\text{ r}\ne \text{1}$
### A General Note: Formula for the Sum of the First n Terms of a Geometric Series
A geometric series is the sum of the terms in a geometric sequence. The formula for the sum of the first $n$ terms of a geometric sequence is represented as
${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}\text{ r}\ne \text{1}$
### How To: Given a geometric series, find the sum of the first n terms.
1. Identify ${a}_{1},r,\text{and}n$.
2. Substitute values for ${a}_{1},r$, and $n$ into the formula ${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}$.
3. Simplify to find ${S}_{n}$.
### Example 4: Finding the First n Terms of a Geometric Series
Use the formula to find the indicated partial sum of each geometric series.
1. ${S}_{11}$ for the series $\text{ 8 + -4 + 2 + }\dots$
2. $\underset{6}{\overset{k=1}{{\sum }^{\text{ }}}}3\cdot {2}^{k}$
### Solution
1. ${a}_{1}=8$, and we are given that $n=11$.We can find $r$ by dividing the second term of the series by the first.
$r=\frac{-4}{8}=-\frac{1}{2}$
Substitute values for ${a}_{1}, r, \text{and} n$ into the formula and simplify.
$\begin{array}{l}{S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}\hfill \\ {S}_{11}=\frac{8\left(1-{\left(-\frac{1}{2}\right)}^{11}\right)}{1-\left(-\frac{1}{2}\right)}\approx 5.336\hfill \end{array}$
2. Find ${a}_{1}$ by substituting $k=1$ into the given explicit formula.
${a}_{1}=3\cdot {2}^{1}=6$
We can see from the given explicit formula that $r=2$. The upper limit of summation is 6, so $n=6$.
Substitute values for ${a}_{1},r$, and $n$ into the formula, and simplify.
$\begin{array}{l}{S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}\hfill \\ {S}_{6}=\frac{6\left(1-{2}^{6}\right)}{1 - 2}=378\hfill \end{array}$
Use the formula to find the indicated partial sum of each geometric series.
### Try It 6
${S}_{20}$ for the series $\text{ 1,000 + 500 + 250 + }\dots$
Solution
### Try It 7
$\sum _{k=1}^{8}{3}^{k}$
Solution
At a new job, an employee’s starting salary is $32,100. She receives a 2% annual raise. How much will she have earned by the end of 8 years? Solution ## Using the Formula for the Sum of an Infinite Geometric Series Thus far, we have looked only at finite series. Sometimes, however, we are interested in the sum of the terms of an infinite sequence rather than the sum of only the first $n$ terms. An infinite series is the sum of the terms of an infinite sequence. An example of an infinite series is $2+4+6+8+..$. This series can also be written in summation notation as $\sum _{k=1}^{\infty }2k$, where the upper limit of summation is infinity. Because the terms are not tending to zero, the sum of the series increases without bound as we add more terms. Therefore, the sum of this infinite series is not defined. When the sum is not a real number, we say the series diverges. ## Determining Whether the Sum of an Infinite Geometric Series is Defined If the terms of an infinite geometric series approach 0, the sum of an infinite geometric series can be defined. The terms in this series approach 0: $1+0.2+0.04+0.008+0.0016+..$. The common ratio $r\text{ = 0}\text{.2}$. As $n$ gets very large, the values of ${r}^{n}$ get very small and approach 0. Each successive term affects the sum less than the preceding term. As each succeeding term gets closer to 0, the sum of the terms approaches a finite value. The terms of any infinite geometric series with $-1<r<1$ approach 0; the sum of a geometric series is defined when $-1<r<1$. ### A General Note: Determining Whether the Sum of an Infinite Geometric Series is Defined The sum of an infinite series is defined if the series is geometric and $-1<r<1$. ### How To: Given the first several terms of an infinite series, determine if the sum of the series exists. 1. Find the ratio of the second term to the first term. 2. Find the ratio of the third term to the second term. 3. Continue this process to ensure the ratio of a term to the preceding term is constant throughout. If so, the series is geometric. 4. If a common ratio, $r$, was found in step 3, check to see if $-1<r<1$ . If so, the sum is defined. If not, the sum is not defined. ### Example 6: Determining Whether the Sum of an Infinite Series is Defined Determine whether the sum of each infinite series is defined. 1. $\text{12 + 8 + 4 + }\dots$ 2. $\frac{3}{4}+\frac{1}{2}+\frac{1}{3}+..$. 3. $\sum _{k=1}^{\infty }27\cdot {\left(\frac{1}{3}\right)}^{k}$ 4. $\sum _{k=1}^{\infty }5k$ ### Solution 1. The ratio of the second term to the first is $\frac{\text{2}}{\text{3}}$, which is not the same as the ratio of the third term to the second, $\frac{1}{2}$. The series is not geometric. 2. The ratio of the second term to the first is the same as the ratio of the third term to the second. The series is geometric with a common ratio of $\frac{2}{3}\text{.}$ The sum of the infinite series is defined. 3. The given formula is exponential with a base of $\frac{1}{3}$; the series is geometric with a common ratio of $\frac{1}{3}\text{.}$ The sum of the infinite series is defined. 4. The given formula is not exponential; the series is not geometric because the terms are increasing, and so cannot yield a finite sum. Determine whether the sum of the infinite series is defined. ### Try It 9 $\frac{1}{3}+\frac{1}{2}+\frac{3}{4}+\frac{9}{8}+..$. Solution ### Try It 10 $24+\left(-12\right)+6+\left(-3\right)+..$. Solution ### Try It 11 $\sum _{k=1}^{\infty }15\cdot {\left(-0.3\right)}^{k}$ Solution ## Finding Sums of Infinite Series When the sum of an infinite geometric series exists, we can calculate the sum. The formula for the sum of an infinite series is related to the formula for the sum of the first $n$ terms of a geometric series. ${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}$ We will examine an infinite series with $r=\frac{1}{2}$. What happens to ${r}^{n}$ as $n$ increases? $\begin{array}{l}{\left(\frac{1}{2}\right)}^{2}=\frac{1}{4}\\ {\left(\frac{1}{2}\right)}^{3}=\frac{1}{8}\\ {\left(\frac{1}{2}\right)}^{4}=\frac{1}{16}\end{array}$ The value of ${r}^{n}$ decreases rapidly. What happens for greater values of $n?$ $\begin{array}{l}{\left(\frac{1}{2}\right)}^{10}=\frac{1}{1\text{,}024}\hfill \\ {\left(\frac{1}{2}\right)}^{20}=\frac{1}{1\text{,}048\text{,}576}\hfill \\ {\left(\frac{1}{2}\right)}^{30}=\frac{1}{1\text{,}073\text{,}741\text{,}824}\hfill \end{array}$ As $n$ gets very large, ${r}^{n}$ gets very small. We say that, as $n$ increases without bound, ${r}^{n}$ approaches 0. As ${r}^{n}$ approaches 0, $1-{r}^{n}$ approaches 1. When this happens, the numerator approaches ${a}_{1}$. This give us a formula for the sum of an infinite geometric series. ### A General Note: Formula for the Sum of an Infinite Geometric Series The formula for the sum of an infinite geometric series with $-1<r<1$ is $S=\frac{{a}_{1}}{1-r}$ ### How To: Given an infinite geometric series, find its sum. 1. Identify ${a}_{1}$ and $r$. 2. Confirm that $-1<r<1$. 3. Substitute values for ${a}_{1}$ and $r$ into the formula, $S=\frac{{a}_{1}}{1-r}$. 4. Simplify to find $S$. ### Example 7: Finding the Sum of an Infinite Geometric Series Find the sum, if it exists, for the following: 1. $10+9+8+7+\dots$ 2. $248.6+99.44+39.776+\text{ }\dots$ 3. $\sum _{k=1}^{\infty }4\text{,}374\cdot {\left(-\frac{1}{3}\right)}^{k - 1}$ 4. $\sum _{k=1}^{\infty }\frac{1}{9}\cdot {\left(\frac{4}{3}\right)}^{k}$ ### Solution 1. There is not a constant ratio; the series is not geometric. 2. There is a constant ratio; the series is geometric. ${a}_{1}=248.6$ and $r=\frac{99.44}{248.6}=0.4$, so the sum exists. Substitute ${a}_{1}=248.6$ and $r=0.4$ into the formula and simplify to find the sum: $\begin{array}{l}S=\frac{{a}_{1}}{1-r}\hfill \\ S=\frac{248.6}{1 - 0.4}=414.\overline{3}\hfill \end{array}$ 3. The formula is exponential, so the series is geometric with $r=-\frac{1}{3}$. Find ${a}_{1}$ by substituting $k=1$ into the given explicit formula: ${a}_{1}=4\text{,}374\cdot {\left(-\frac{1}{3}\right)}^{1 - 1}=4\text{,}374$ Substitute ${a}_{1}=4\text{,}374$ and $r=-\frac{1}{3}$ into the formula, and simplify to find the sum: $\begin{array}{l}S=\frac{{a}_{1}}{1-r}\hfill \\ S=\frac{4\text{,}374}{1-\left(-\frac{1}{3}\right)}=3\text{,}280.5\hfill \end{array}$ 4. The formula is exponential, so the series is geometric, but $r>1$. The sum does not exist. ### Example 8: Finding an Equivalent Fraction for a Repeating Decimal Find an equivalent fraction for the repeating decimal $0.\overline{3}$ ### Solution We notice the repeating decimal $0.\overline{3}=0.333..$. so we can rewrite the repeating decimal as a sum of terms. $0.\overline{3}=0.3+0.03+0.003+..$. Looking for a pattern, we rewrite the sum, noticing that we see the first term multiplied to 0.1 in the second term, and the second term multiplied to 0.1 in the third term. Notice the pattern; we multiply each consecutive term by a common ratio of 0.1 starting with the first term of 0.3. So, substituting into our formula for an infinite geometric sum, we have ${S}_{n}=\frac{{a}_{1}}{1-r}=\frac{0.3}{1 - 0.1}=\frac{0.3}{0.9}=\frac{1}{3}$. Find the sum, if it exists. ### Try It 12 $2+\frac{2}{3}+\frac{2}{9}+..$. Solution ### Try It 13 $\sum _{k=1}^{\infty }0.76k+1$ Solution ### Try It 14 $\sum _{k=1}^{\infty }{\left(-\frac{3}{8}\right)}^{k}$ Solution ## Solving Annuity Problems At the beginning of the section, we looked at a problem in which a couple invested a set amount of money each month into a college fund for six years. An annuity is an investment in which the purchaser makes a sequence of periodic, equal payments. To find the amount of an annuity, we need to find the sum of all the payments and the interest earned. In the example, the couple invests$50 each month. This is the value of the initial deposit. The account paid 6% annual interest, compounded monthly. To find the interest rate per payment period, we need to divide the 6% annual percentage interest (APR) rate by 12. So the monthly interest rate is 0.5%. We can multiply the amount in the account each month by 100.5% to find the value of the account after interest has been added.
We can find the value of the annuity right after the last deposit by using a geometric series with ${a}_{1}=50$ and $r=100.5%=1.005$. After the first deposit, the value of the annuity will be $50. Let us see if we can determine the amount in the college fund and the interest earned. We can find the value of the annuity after $n$ deposits using the formula for the sum of the first $n$ terms of a geometric series. In 6 years, there are 72 months, so $n=72$. We can substitute ${a}_{1}=50, r=1.005, \text{and} n=72$ into the formula, and simplify to find the value of the annuity after 6 years. ${S}_{72}=\frac{50\left(1-{1.005}^{72}\right)}{1 - 1.005}\approx 4\text{,}320.44$ After the last deposit, the couple will have a total of$4,320.44 in the account. Notice, the couple made 72 payments of $50 each for a total of $72\left(50\right) = 3,600$. This means that because of the annuity, the couple earned$720.44 interest in their college fund.
### How To: Given an initial deposit and an interest rate, find the value of an annuity.
1. Determine ${a}_{1}$, the value of the initial deposit.
2. Determine $n$, the number of deposits.
3. Determine $r$.
1. Divide the annual interest rate by the number of times per year that interest is compounded.
2. Add 1 to this amount to find $r$.
4. Substitute values for ${a}_{1}\text{,}r,\text{and}n$
into the formula for the sum of the first $n$ terms of a geometric series, ${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}$.
5. Simplify to find ${S}_{n}$, the value of the annuity after $n$ deposits.
A deposit of $100 is placed into a college fund at the beginning of every month for 10 years. The fund earns 9% annual interest, compounded monthly, and paid at the end of the month. How much is in the account right after the last deposit? ### Solution The value of the initial deposit is$100, so ${a}_{1}=100$. A total of 120 monthly deposits are made in the 10 years, so $n=120$. To find $r$, divide the annual interest rate by 12 to find the monthly interest rate and add 1 to represent the new monthly deposit.
$r=1+\frac{0.09}{12}=1.0075$
Substitute ${a}_{1}=100\text{,}r=1.0075\text{,}\text{and}n=120$ into the formula for the sum of the first $n$ terms of a geometric series, and simplify to find the value of the annuity.
${S}_{120}=\frac{100\left(1-{1.0075}^{120}\right)}{1 - 1.0075}\approx 19\text{,}351.43$
Solution
sum of the first $n$ terms of an arithmetic series ${S}_{n}=\frac{n\left({a}_{1}+{a}_{n}\right)}{2}$ sum of the first $n$ terms of a geometric series ${S}_{n}=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r}\cdot r\ne 1$ sum of an infinite geometric series with $-1 ## Key Concepts • The sum of the terms in a sequence is called a series. • A common notation for series is called summation notation, which uses the Greek letter sigma to represent the sum. • The sum of the terms in an arithmetic sequence is called an arithmetic series. • The sum of the first [latex]n$ terms of an arithmetic series can be found using a formula.
• The sum of the terms in a geometric sequence is called a geometric series.
• The sum of the first $n$ terms of a geometric series can be found using a formula.
• The sum of an infinite series exists if the series is geometric with $-1<r<1$.
• If the sum of an infinite series exists, it can be found using a formula.
• An annuity is an account into which the investor makes a series of regularly scheduled payments. The value of an annuity can be found using geometric series.
## Glossary
annuity
an investment in which the purchaser makes a sequence of periodic, equal payments
arithmetic series
the sum of the terms in an arithmetic sequence
diverge
a series is said to diverge if the sum is not a real number
geometric series
the sum of the terms in a geometric sequence
index of summation
in summation notation, the variable used in the explicit formula for the terms of a series and written below the sigma with the lower limit of summation
infinite series
the sum of the terms in an infinite sequence
lower limit of summation
the number used in the explicit formula to find the first term in a series
nth partial sum
the sum of the first $n$ terms of a sequence
series
the sum of the terms in a sequence
summation notation
a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series
upper limit of summation
the number used in the explicit formula to find the last term in a series
## Section Exercises
1. What is an $n\text{th}$ partial sum?
2. What is the difference between an arithmetic sequence and an arithmetic series?
3. What is a geometric series?
4. How is finding the sum of an infinite geometric series different from finding the $n\text{th}$ partial sum?
5. What is an annuity?
For the following exercises, express each description of a sum using summation notation.
6. The sum of terms ${m}^{2}+3m$ from $m=1$ to $m=5$
7. The sum from of $n=0$ to $n=4$ of $5n$
8. The sum of $6k - 5$ from $k=-2$ to $k=1$
9. The sum that results from adding the number 4 five times
For the following exercises, express each arithmetic sum using summation notation.
10. $5+10+15+20+25+30+35+40+45+50$
11. $10+18+26+\dots +162$
12. $\frac{1}{2}+1+\frac{3}{2}+2+\dots +4$
For the following exercises, use the formula for the sum of the first $n$ terms of each arithmetic sequence.
13. $\frac{3}{2}+2+\frac{5}{2}+3+\frac{7}{2}$
14. $19+25+31+\dots +73$
15. $3.2+3.4+3.6+\dots +5.6$
For the following exercises, express each geometric sum using summation notation.
16. $1+3+9+27+81+243+729+2187$
17. $8+4+2+\dots +0.125$
18. $-\frac{1}{6}+\frac{1}{12}-\frac{1}{24}+\dots +\frac{1}{768}$
For the following exercises, use the formula for the sum of the first $n$ terms of each geometric sequence, and then state the indicated sum.
19. $9+3+1+\frac{1}{3}+\frac{1}{9}$
20. $\sum _{n=1}^{9}5\cdot {2}^{n - 1}$
21. $\sum _{a=1}^{11}64\cdot {0.2}^{a - 1}$
For the following exercises, determine whether the infinite series has a sum. If so, write the formula for the sum. If not, state the reason.
22. $12+18+24+30+..$.
23. $2+1.6+1.28+1.024+..$.
24. $\sum _{m=1}^{\infty }{4}^{m - 1}$
25. $\underset{\infty }{\overset{k=1}{{\sum }^{\text{ }}}}-{\left(-\frac{1}{2}\right)}^{k - 1}$
For the following exercises, use the following scenario. Javier makes monthly deposits into a savings account. He opened the account with an initial deposit of $50. Each month thereafter he increased the previous deposit amount by$20.
26. Graph the arithmetic sequence showing one year of Javier’s deposits.
27. Graph the arithmetic series showing the monthly sums of one year of Javier’s deposits.
For the following exercises, use the geometric series ${\sum _{k=1}^{\infty }\left(\frac{1}{2}\right)}^{k}$.
28. Graph the first 7 partial sums of the series.
29. What number does ${S}_{n}$ seem to be approaching in the graph? Find the sum to explain why this makes sense.
For the following exercises, find the indicated sum.
30. $\sum _{a=1}^{14}a$
31. $\sum _{n=1}^{6}n\left(n - 2\right)$
32. $\sum _{k=1}^{17}{k}^{2}$
33. $\sum _{k=1}^{7}{2}^{k}$
For the following exercises, use the formula for the sum of the first $n$ terms of an arithmetic series to find the sum.
34. $-1.7+-0.4+0.9+2.2+3.5+4.8$
35. $6+\frac{15}{2}+9+\frac{21}{2}+12+\frac{27}{2}+15$
36. $-1+3+7+…+31$
37. $\sum _{k=1}^{11}\left(\frac{k}{2}-\frac{1}{2}\right)$
For the following exercises, use the formula for the sum of the first $n$ terms of a geometric series to find the partial sum.
38. ${S}_{6}$ for the series $-2 - 10 - 50 - 250..$.
39. ${S}_{7}$ for the series $0.4 - 2+10 - 50..$.
40. $\sum _{k=1}^{9}{2}^{k - 1}$
41. $\sum _{n=1}^{10}-2\cdot {\left(\frac{1}{2}\right)}^{n - 1}$
For the following exercises, find the sum of the infinite geometric series.
42. $4+2+1+\frac{1}{2}..$.
43. $-1-\frac{1}{4}-\frac{1}{16}-\frac{1}{64}..$.
44. $\underset{\infty }{\overset{k=1}{{\sum }^{\text{ }}}}3\cdot {\left(\frac{1}{4}\right)}^{k - 1}$
45. $\sum _{n=1}^{\infty }4.6\cdot {0.5}^{n - 1}$
For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate.
46. Deposit amount: $50; total deposits: $60$; interest rate: $5%$, compounded monthly 47. Deposit amount:$150; total deposits: $24$; interest rate: $3%$, compounded monthly
48. Deposit amount: $450; total deposits: $60$; interest rate: $4.5%$, compounded quarterly 49. Deposit amount:$100; total deposits: $120$; interest rate: $10%$, compounded semi-annually
50. The sum of terms $50-{k}^{2}$ from $k=x$ through $7$ is $115$. What is x?
51. Write an explicit formula for ${a}_{k}$ such that $\sum _{k=0}^{6}{a}_{k}=189$. Assume this is an arithmetic series.
52. Find the smallest value of n such that $\sum _{k=1}^{n}\left(3k - 5\right)>100$.
53. How many terms must be added before the series $-1 - 3-5 - 7….\text{ }$ has a sum less than $-75?$
54. Write $0.\overline{65}$ as an infinite geometric series using summation notation. Then use the formula for finding the sum of an infinite geometric series to convert $0.\overline{65}$ to a fraction.
55. The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?
56. To get the best loan rates available, the Riches want to save enough money to place 20% down on a $160,000 home. They plan to make monthly deposits of$125 in an investment account that offers 8.5% annual interest compounded semi-annually. Will the Riches have enough for a 20% down payment after five years of saving? How much money will they have saved?
57. Karl has two years to save $10,000$ to buy a used car when he graduates. To the nearest dollar, what would his monthly deposits need to be if he invests in an account offering a 4.2% annual interest rate that compounds monthly?
58. Keisha devised a week-long study plan to prepare for finals. On the first day, she plans to study for $1$ hour, and each successive day she will increase her study time by $30$ minutes. How many hours will Keisha have studied after one week?
59. A boulder rolled down a mountain, traveling 6 feet in the first second. Each successive second, its distance increased by 8 feet. How far did the boulder travel after 10 seconds?
60. A scientist places 50 cells in a petri dish. Every hour, the population increases by 1.5%. What will the cell count be after 1 day?
61. A pendulum travels a distance of 3 feet on its first swing. On each successive swing, it travels $\frac{3}{4}$ the distance of the previous swing. What is the total distance traveled by the pendulum when it stops swinging?
62. Rachael deposits \$1,500 into a retirement fund each year. The fund earns 8.2% annual interest, compounded monthly. If she opened her account when she was 19 years old, how much will she have by the time she is 55? How much of that amount will be interest earned?
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2020-09-29 18:37:37
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https://www.vn.freelancer.com/projects/LaTeX/Convert-formula-latex-code-14384314/
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# Convert formula to latex code -- 2
I will send Japanese textbook data.
Please only give me a formula as a latex code.
Kỹ năng: LaTeX
Về Bên Thuê:
( 3 nhận xét ) tottori, Japan
Mã Dự Án: #14384314
## 35 freelancer đang chào giá trung bình $23 cho công việc này hzeljko Hi, My name is Zeljko and I am have more than 25 years of experience in LaTeX, DTP and printing, and I think that you are going to find me qualified for this job if you take a minute or two and look at my portfolio, Thêm$30 USD trong 1 ngày
(23 Đánh Giá)
5.7
VolKa
Hi. I am very good in Latex and sure will be able to do this. Regards.................................
$30 USD trong 1 ngày (41 Đánh Giá) 5.5$50 USD trong 2 ngày
(3 Đánh Giá)
5.2
$30 USD trong 1 ngày (42 Đánh Giá) 4.9 jurko57 Dear Hiring Manager, I am very experienced in LaTeX as well as in conversion of hand-written notes to LaTeX. Would be glad to help You Thanks. Bogdan Yavorskyy Relevant Skills and Experience LaTeX, Mathematics Propos Thêm$30 USD trong 1 ngày
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3.8
cugamelover
I have a PhD degree in computational physics. I'm an author of dozens of research papers with a lot of complicated math equations, tables, and graphs, which I wrote in LaTeX. I've also done quite a few projects on this Thêm
$25 USD trong 1 ngày (8 Đánh Giá) 3.6 Createbooks2011 Hi, your project is interesting for me I'm freelancer since 2011 and please see my feedback history. So it's nice and easy for me to start with your job. I assure 100% word checked and fine execution job. For any Thêm$23 USD trong 3 ngày
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3.9
elmokhi
A proposal has not yet been provided
$25 USD trong 3 ngày (1 Đánh Giá) 3.1 paolagarosi Hello, my name is Paola Garosi, I'm expert about Latex. Your task can be easily complete in few hours. I then will give you the .tex document with the all 40 required formula. Here you can see an example of a docume Thêm$23 USD trong 1 ngày
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2.2
SergeyMatyushkov
Hello, I have a wide experience in Latex: I used it in my routine work in university (lectures, presentations, teaching plans). Also I was leading an extracurricular Latex course for my student. I hold a PhD in Electr Thêm
$30 USD trong 1 ngày (2 Đánh Giá) 1.6 hemantmayatra Published 6 IEEE papers, Google Scholar Profile Link : [url removed, login to view] - Completed two Math Books (Discrete Math, Partial Differential) with more than 400 pages and com Thêm$25 USD trong 1 ngày
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zainpacc
Expertise in latex and can provide you your complete task in decided time frame with quality work
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$25 USD trong 10 ngày (0 Đánh Giá) 0.0 Aunas hi there i can provide latex code for 40 formulas in$20 in one day. Relevant Skills and Experience I have experience of working in latex math content. You can ask for my sample works and project I have done previous Thêm
$25 USD trong 1 ngày (0 Đánh Giá) 1.1 anymath13 A proposal has not yet been provided$10 USD trong 1 ngày
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$25 USD trong 1 ngày (0 Đánh Giá) 1.7 princu2277 I am good at writing the Articles in LaTeX especially and i have a enough knowledge in research as i have published papers in various conferences across the world Relevant Skills and Experience LAtex: I am good at wri Thêm$25 USD trong 1 ngày
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2018-01-16 20:08:08
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http://www.quantatrisk.com/tag/erm/
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Quantitative Analysis, Risk Management, Modelling, Algo Trading, and Big Data Analysis
## Performance-related Risk Measures
Enterprise Risks Management (ERM) can be described as a discipline by which an organization in any industry assesses, controls, exploits, finances, and monitors risks from all sources for the purpose of increasing the organization’s short- and long-term value to its stakeholders. It is a conceptual framework and when adopted by a company it provides with a set of tools to, inter alia, describe and quantify a risk profile. In general, most of the measures common in the practice of ERM can be broken in two categories: (a) solvency-related measures, and (b) performance-related measures. From a quantitative view point the latter refers to the volatility of the organization’s performance on a going-concern basis.
Performance-related risk measures provide us with a good opportunity to quickly review the fundamental definitions of the tools which concentrate on the mid-refion of the probability distribution, i.e. the region near the mean, and relevant for determination of the volatility around expected results:
Volatility (standard deviation), Variance, Mean
$$Vol(x) = \sqrt{Var(x)} = \left[\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N}\right]^{0.5}$$
Shortfall Risk
$$SFR = \frac{1}{N} \sum_{i=1}^{N} 1_{[x_i\lt T]} \times 100\%$$
where $T$ is the target value for the financial variable $x$. Shortfall Risk measure reflects the improvement over $Vol(x)$ measure by taking into account the fact that most of people are risk averse, i.e. they are more concerned with unfavorable deviations rather than favorable ones. Therefore, $SFR$ can be understood as the probability that the financial variable $x_i$ falls below a specified target level of $T$ (if true, $1_{[x_i\lt T]}$ above takes the value of 1).
Value at Risk (VaR)
In VaR-type measures, the equation is reversed: the shortfall risk is specified first, and the corresponding value at risk ($T$) is solved for.
Downside Volatility (or Downside Standard Deviation)
$$DVol(x) = \left[\frac{\sum_{i=1}^{N}(min[0,(x_i-T)]^2}{N}\right]^{0.5}$$
where again $T$ is the target value for the financial variable $x$. Downside volatility focuses not only on the probability of an unfavorable deviation in a financial vairable (as SFR) but also the extent to which it is favorable. It is usually interpreted as the extend to which the financial variable could deviate below a specified target level.
Below Target Risk
$$BTR = \frac{\sum_{i=1}^{N}(min[0,(x_i-T)]}{N}$$
takes its origin from the definition of the downside volatility but the argument is not squared, and there is no square root taken of the sum.
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2016-12-08 00:03:39
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https://www.gradesaver.com/textbooks/math/algebra/elementary-linear-algebra-7th-edition/chapter-1-systems-of-linear-equations-1-1-introduction-to-systems-of-linear-equations-1-1-exercises-page-10/50
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# Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 10: 50
The system is inconsistent.
#### Work Step by Step
5$x_{1}$ - 3$x_{2}$ + 2$x_{3}$ = 3 4$x_{1}$ + 2$x_{2}$ - $x_{3}$ = 7 $x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3 $R_{1}$↔$R_{3}$ $x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3 4$x_{1}$ + 2$x_{2}$ - $x_{3}$ = 7 5$x_{1}$ - 3$x_{2}$ + 2$x_{3}$ = 3 -2$R_{1}$+$R_{2}$→$R_{2}$ -5$R_{1}$+$R_{3}$→$R_{3}$ $x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3 26$x_{2}$ - 9$x_{3}$ = 1 52$x_{2}$ - 18$x_{3}$ = -12 -2$R_{2}$+$R_{3}$→$R_{3}$ $x_{1}$ - 11$x_{2}$ + 4$x_{3}$ = 3 26$x_{2}$ - 9$x_{3}$ = 1 0 = -14 0 $\ne$ -14, so the system has no solution.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2019-06-27 05:59:36
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https://stats.stackexchange.com/questions/398038/probability-involves-bivariate-gaussian
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# probability involves bivariate gaussian
I'm working on a spatial project. I need to calculate the probability of a point being the closest to another. Say I'm given four points $$y$$, $$x_1$$,$$x_2$$ and $$x_3$$ in 2D plane, and let $$Y'=y+Z$$, where $$Z$$ is a bivariate normal with known mean and covariance. I want to know the probability that $$x_1$$ out of the three $$x$$'s is closest to $$Y'$$. How should I proceed? Thank you very much!
• Are you familiar with Thiessen polygons (aka Voronoi tessellations, polygons of influence, and Dirichlet cells)? That construction reduces your question to an integration of the density over a (possibly infinite) polygonal region, which ordinarily is done numerically. – whuber Mar 17 at 20:51
• Thanks. Yup I know of Thiessen polygons. That's an excellent suggestion!! But this operation needs to be repeated a lot of times, I'll have to look into the computation time. I am still trying to work out an analytic solution. – dynamic89 Mar 17 at 23:38
• Perhaps there are some special features of your problem. Are there any constraints at all on the possibly configurations of the $x_i$ and $y$? Note that you can choose coordinates in which $y$ is the origin and $Z$ is bivariate standard Normal, thereby offering a little simplification. – whuber Mar 17 at 23:50
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2019-07-18 09:13:39
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https://djdongjin.github.io/2018-12-21/Note-11-of-Deep-Learning-Practical-Methodology
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# Note 11 of Deep Learning: Practical Methodology
Practical design process:
1. Determine goals: what error metric to use and corresponding target value, both of which should be driven by the problem that the application is intended to solve.
2. Establish a working end-to-end pipeline and the estimation of the appropriate performance metrics as soon as possible.
3. Instrument the system well to determine bottlenecks, diagnose which parts are performing worse than expected and whether it is due to overfitting, underfitting or a defect in the data or implementation.
4. Based on specific findings from instruments, repeatedly make incremental changes, including gathering new data, tuning hyperparameters, changing algorithms.
## Performance Metrics
Need to decide both an expected target value, according to previous benchmark results or error rate that is necessary for a system to be safe, and which metrics to use such as accuracy, precision, recall, etc.
Precision is the fraction of detections reported by the model that were correct; Recall is the fraction of true events that were detected. When using them, it’s common to plot a PR curve with precision on the y-axis and recall on the x-axis.
We can also convert precision $p$ and recall $r$ into an $F-score$ given by
Another metric is Coverage which is the fraction of examples for which the machine learning system is able to produce a response. It is useful when the system is allowed to refuse to make a decision and deliver to human to make a decision.
Many metrics are available but what is more important is to determine which performance metric to improve ahead of time and then concentrate on that.
## Default Baseline Models
The goal is to establish a reasonable end-to-end system as soon as possible, which can be used as a baseline.
A reasonable choice of optimization method is SGD with momentum with a decaying learning rate. Popular decay schemes include 1) decaying linearly until reaching a fixed minimum learning rate; 2) decaying exponentially; 3) decreasing learning rate by a factor of 2-10 each time validation error plateaus. Another reasonable alternative is Adam.
Batch normalization may have a dramatic effect on optimization performance, especially for convolutional networks and networks with sigmoidal nonlinearities such as sigmod or tanh. Batch normalization should be introduced if optimization is likely problematic.
Some mild forms of regularization should be included from the start unless the training set contains tens of millions of examples. Early stopping should be used universally. Dropout is a regularizer compatible with many models.
## Determine whether to Gather More Data
After implementing the baseline, it’s often better to gather more data than to improve learning algorithm or try out different algorithms.
If current performance on the training set is poor, there is not reason to gather more data since the learning algorithm even doesn’t utilize the training set available so far (, which means underfitting). So try improve the size of the model by adding more layers or hidden units in each layer, or by tuning hyperparameters such as learning rate.
If large or fine-tuned models still do not work well, the problem may appear to be the quality of the training data, such as too noisy or no useful features. So turn to collect cleaner data or richer set of features.
If performance on training set is acceptable, then measure the performance on test set. If performance on test set is still acceptable, there is nothing left to be done (or you can try improve the learning algorithm). If performance on test set is poor (, which means overfitting), then gathering more data is one of the most effective solutions. An alternative of gathering more data, or say, reducing overfitting, is to reduce the size of the model or improve regularization by tuning hyperparameters such as weight decay coefficients or by adding regularization strategies such as dropout, L2 regularization.
When deciding to gather more data, it’s also necessary to decide how much data to gather. It’s useful to plot curves showing the relationship between training set size (may on a logarithmic scale) and generalization error.
## Selecting Hyperparameters
Learning rate may be the most important hyperparameter, so if you have no enough time, tune learning rate first.
## Debugging Strategies
1. Visualize the model in action: when training a object detection model, view some images with predicted result superimposed on it; when training a generative model of speech, listen to some of produced speech samples, etc. Directly observing the machine learning model performing its tasks can help you estimate if the quantitative performance result it achieves seem reasonable.
2. Visualize the worst mistakes: by viewing the training set examples that are the hardest to model correctly, one can often discover problems with the way the data has been preprocessed or labeled.
3. Reasoning about software using train and test error: if training error is low but test error is high, the software implementation should work properly, and the model overfits (or there is an error when saving the model and then reloading for evaluation).
4. Compare back-propagated derivatives to numerical derivatives.
5. Monitor histograms of activations and gradient.
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2020-03-28 09:28:15
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https://brilliant.org/problems/count-count/
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# Count Count!!!
If $$\frac{1}{21}$$ equals the repeating decimal $$0.0476190476190...$$, what is the $$51^{st}$$digit after the decimal point of the repeating decimal?
×
Problem Loading...
Note Loading...
Set Loading...
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2018-10-16 22:02:30
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https://physicslens.com/category/demonstrations/
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## Measuring speed of sound in air using Audacity
A physics demonstration on how to measure the speed of sound in air using Audacity, an open source audio recording software. There are Windows and Mac versions of this free software, and even a portable version that can run off a flash drive without needing to be installed on a computer (for school systems with stricter measures regarding installing of software).
The sound is reflected along a long hollow tube that somehow, existed in our school's laboratory. The two sound signals were picked up using a clip-on microphone attached to the open end of the tube and plugged into the laptop. I used my son's castanet which gives a crisp sound and hence, a simple waveform that will not have the echo overlapping with the generated sound. The timing at which the sound signals were first detected were read and subtracted to obtain the time taken for the wave to travel up and down the 237 cm tube.
The value of the speed of sound calculated is 356 m/s, which is a bit on the high side due to the temperature of 35°C and relative humidity of between 60-95% when the reading was carried out.
If you are interested, you can check out how the software can be used to determine the frequency of a tuning fork.
We are about to get students to conduct experiments to explore how tension, length and thickness of a guitar string affects its pitch (frequency). I might post some results here when there's time.
## Magnetic Force on a Current-Carrying Conductor
Using a neodymium magnet, some paper clips and a battery, you can demonstrate the magnetic force acting on a current-carrying wire while recalling Fleming's left-hand rule. Using the same frame constructed in the previous video, you just need to add a wire with a few bends in between to create a U-shape in the middle as shown in the picture below. A small piece of insulating tape (you can use any adhesive tape) is added to one end of the wire to show the original dangling position of the U-shape before current flows through it. Be sure to leave some space at the end with the insulating tape for you to switch on and off the current by pushing that end in and out.
## Building a Simple DC Motor
Using material that is easily available, you can build a simple homopolar D.C. motor (one that uses a single magnetic pole. I made the video above to help you do so.
The material used are as follows:
1. insulated copper wire
2. paper clips
3. neodymium magnet
4. 1.5V AA battery
5. plastic or wooden block (I used a 4x2 Lego block)
6. scissors
7. permanent marker
The steps involved are:
1. Attaching the magnet on the side of the battery using a long piece of adhesive tape and sticking both of them onto the Lego block. The polarity of the magnet does not matter.
2. Next, we need to shape one end of each paper clip so as to make it longer and to make a small loop at the top. The paper clips are then fixed on the ends of the battery using adhesive tape.
3. Coiling wire can be done with the help of a round cylindrical object such as a marker. Roughly 10-15 coils will do.
4. The ends of the wire can used to bundle the coils together. Make sure they are tied up tightly.
5. Since we are using an insulated wire (otherwise the current will just go straight from one paper clip to another without passing through the coils), we need to scrape of the insulation at the ends using either sandpaper or the edge of a pair of scissors.
6. Using a permanent marker, we can colour one side each end in order to insulate that side. This will prevent current from flowing through the loops for half of every cycle. It has the same effect as that of a commutator.
7. Finally, we will mount the coils onto the two paper clips and allow the motor to spin.
Do take note that the motor should not be left connected to the battery for too long as it will drain the battery very quickly and generate a lot of heat in the process.
How this can be used for the O-level/A-level syllabus
Teachers can use this as a demonstration that shows the motor effect of a current in a wire placed in a magnetic field, as well as to apply Fleming's left-hand rule.
One can also make an second coil without insulating half the surface of the points of contact with the paper clips to show the importance of the commutator in a DC motor. The coil will simply oscillate to and fro due to the change in direction of the magnetic force on the lower half of the loop every half a turn.
## Magnetic Shielding
I made this rather simple video this morning showing a physics demonstration on the effect of magnetic shielding. A paper clip is shown to be attracted to a magnet. A series of objects are placed in between, such as a plastic ruler, a steel ruler, a steel bookend, and some coins of different alloys.
It is interesting to note the types of material that provide magnetic shielding and those that do not. There is even a distinction between the types of steel, which is an alloy containing iron. Ferritic steel is magnetic while austenitic steel is not.
The theory behind magnetic shielding is that the flat magnetic material will direct the field lines of the magnet along its plane instead of allowing them to pass through, thus depriving the paper clip of a strong enough magnet field to keep it flying.
## Newton's 2nd Law Experiment using Motion Sensor
For my students: To download the file and video for analysis using Tracker, right-click the file here...
To verify the equation F = ma, where F is the resultant force on an object, m is the mass of the object and a is the acceleration, this is one of the ways to do so:
Equipment:
1. Motion Sensor
2. Datalogger
3. Cart with variable mass
4. End Stop
5. Pulley with clamp
6. Hanger Mass Set
For a system of a cart of mass M on a horizontal track that is connected to a hanging mass m with a string over a pulley, the net force F on the entire system (cart and hanging mass) is the weight of hanging mass. F = mg (no friction assumed).
According to Newton’s Second Law, mg = (M+ m)a. We will try to prove experimentally that this is true in the video below.
## Elevator Physics
In a recent IP3 class on Newton's 2nd Law, the students were presented the "Elevator Problem" based on the THINK Cycle approach - a version of inquiry-based learning that was started in Temasek Junior College, Singapore.
The "Elevator Problem" is a physics phenomenon observed in an everyday experience that students can relate to quite easily. It is presented to our IP3 (K9 students) right after the introduction of Newton's 2nd Law, with the students having a good understanding of the forces of weight and normal contact as well as what makes a resultant force.
TRIGGER
The THINK Cycle kicks off with a Trigger: a problem or phenomenon for which students have to solve or explain. In the "Elevator Problem", the Trigger is the observation that as I stand on a bathroom scale in a lift going from one floor to another, the reading on the scale changes in such a way:
1. When the lift starts moving, the reading on the scale increases momentarily.
2. For most of the journey, the reading is constant.
3. When the lift is stopping, the reading on the scale decreases momentarily
The video below (taken by myself) shows what happens:
The students are supposed to work in groups to explain this observation and hence, to deduce whether the elevator is on its way up or down.
HARNESS
In the Harness stage of the THINK Cycle, students would work in groups to answer some guiding questions to help them arrive at a conclusion:
1. What are the forces acting on the boy?
2. Which of these forces are constant and which can change?
3. How does the motion of the lift affect the changing force?
4. What force is the weighing scale showing?
I find that providing students with a small portable whiteboard or a few pieces of rough paper is necessary for them to represent their ideas in diagram form, especially when the objectives of this activity is best achieved with the help of free-body diagrams.
INVESTIGATE
After coming up with a hypothesis based on their discussions, they will then seek to verify their hypothesis. Task number 2, which is for students to determine whether the elevator is going up or down, can be tested by hanging a 500 g mass on a force meter attached to a datalogger. We use the Addestation aMixer in our school, which is a handy portable datalogger with a plug-and-play range of user-friendly sensors. It gives us a graph that looks like that shown below when the mass is being pulled upwards, thus confirming that the movement of the elevator is also upward.
The initial increase in tension acting on the mass is similar to that of the normal contact force on the man standing on the bathroom scale on the elevator. This is because both systems are accelerating upward.
The graph looks rather haphazard as the pulling is done manually and over a small height. By the time one pulls the mass up, he will have to decelerate already, which explains the dip in tension that follows right after the peak. Hence, we are unable to observe a stage where the tension is equal to weight, as we did for the scale in the elevator.
Nevertheless, students should be able to appreciate that a rise followed by a drop is observed for a mass being pulled upward.
NETWORK
For the sake of checking what the students have learnt collaboratively, each group is tasked to explain their observation and results on a A2-sized poster, with half the group staying at their own posters to answer questions while the other half going around to study the results from other groups. Their roles can be reversed after some time.
KNOW
In the final stage of our activity, the teacher will address the class and point out the common misconceptions that arose during the class discussions. For instance, many students are unaware that the upward force acting on the person standing on a weighing scale is the normal contact force and not the gravitational pull. This requires the teacher to introduce the terms "apparent weight" and "true weight" and making a distinction between the two.
Here are some interesting lecture demonstrations on adiabatic thermodynamic processes you can carry out. In an adiabatic process, there is no heat transfer between the system and other systems (including its environment.) According to the First Law of Thermodynamics ($\Delta U=Q+W$), where Q = 0, a compression of a gas which is associated with work being done on the gas will cause the internal energy and hence, the temperature of the gas to rise. On the other hand, when an expansion of a gas takes place, the gas will cool down.
##### 1. Adiabatic compression using a fire syringe
(available from Funlearners for \$30 in Singapore)
## Newton's Nightmare
This demonstration is called Newton's nightmare because it involves the slow dropping of a magnet that seems to be inconsitent with gravitational acceleration.
Using the "CFILE" structure, we can explain how the magnet moves much slower in a metal pipe than when it is undergoing free fall (as in the PVC pipe, which serves as a control).
Now, the metal that we use cannot be ferromagnetic, or the magnet will not even drop at all. It will simply be attracted to the pipe and stick to it.
However, if another metal such as copper or aluminum is used, as the magnet moves through the pipe, different sections of the pipe will experience either a change (either decreasing or increasing) in magnetic flux. Sections of the pipe that the magnet has just gone through suffers a decreasing flux while those that the magnet are approaching gains magnetic flux.
By Faraday's law, which states that an induced emf is proportional to the rate of change of magnetic flux linkage, emf and hence, current is induced within the pipes. These induced currents are called eddy currents.
By Lenz's law, the induced currents tend to flow in a way so as to oppose the change causing it. The current in the sections of the pipe that the magnet is leaving will trying to attract the magnet while those that the magnet is approaching will try to repel the magnet.
The effect is that the magnet experiences a retarding magnetic force that acts against gravitational force, hence decreasing its downward acceleration.
## Diamagnetism
I didn't want to spend money on buying a piece of pyrolytic graphite and large neodymium magnets so I made do with what I have to make the following video. While diamagnetism is not in the A-level physics syllabus, it's good for students to know that there are other classifications of magnetic materials.
What we study in our syllabus is ferromagnetism, which is exhibited by materials such as iron, cobalt and nickel. Some pencil leads are paramagnetic (weakly attracted to magnets) while others such as the one in the video are diamagnetic (repelled by magnets).
I bought my neodymium magnets from DX.com and the shipping to Singapore takes about 3 weeks, so you might want to factor that time in if you want to get some for your lessons. These magnets are great for other demonstrations such as homopolar motors and Newton's nightmare.
## Displacement, Velocity and Acceleration of Bouncing Ball using Datalogger
A video tutorial on the use of the Addestation datalogger with its motion sensor to measure the displacement of a bouncing ball and to observe the velocity and acceleration using its differentiation function.
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2018-04-21 07:28:00
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https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Nanking
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1911 Encyclopædia Britannica/Nanking
The T’aip’ing rebels, who carried the town by assault in 1853, swept away all the national monuments and most of the more conspicuous public buildings it contained, and destroyed the greater part of the magnificent wall which surrounded it. This wall is said by Chinese topographers to have been 96 li, or 32 m., in circumference. This computation has, however, been shown to be a gross exaggeration, and it is probable that 60 li, or 20 m., would be nearer the actual dimensions. The wall, of which only small portions remain, was about 70 ft. in height, measured 30 ft. in thickness at, the base, and was pierced by thirteen gates. Encircling the north, east, and south sides of the city proper was a second wall which enclosed about double the space of the inner enclosure. In the north-east corner of the town stood the imperial palace reared by Hung-wu, the imperial founder of the modern city. After suffering mutilation at the overthrow of the Ming dynasty, this magnificent building was burnt to the ground on the recapture of the city from the T’aip’ing rebels in 1864. But beyond comparison the most conspicuous public building at Nanking was the famous porcelain tower, which was designed by the emperor Yung-lo (1403-1428) to commemorate the virtues of his mother. Twelve centuries previously an Indian priest deposited on the spot where this monument afterwards stood a relic of Buddha, and raised over the sacred object a small pagoda of three stories in height. During the disturbed times which heralded the close of the Yuen dynasty (1368) this pagoda was utterly destroyed. It was doubtless out of respect to the relic which then perished that Yung-lo chose this site for the erection of his “token-of-gratitude” pagoda. The building was begun in 1413. But before it was finished Yung-lo had passed away, and it was reserved for his successor to see the final pinnacle fixed in its place, after nineteen years had been consumed in carrying out the designs of the imperial architect. In shape the pagoda was an octagon, and was about 260 ft. in height, or, as the Chinese say, with that extraordinary love for inaccurate accuracy which is peculiar to them, 32 chang (a chang equals about 120 in.) 9 ft. 4 in. and ${\displaystyle \scriptstyle {\frac {9}{10}}}$ of an inch. The outer walls were cased with bricks of the finest white porcelain, and each of the nine stories into which the building was divided was marked by overhanging eaves composed of green glazed tiles of the same material. The summit was crowned with a gilt ball fixed on the top of an iron rod, which in its turn was encircled by nine iron rings. Hung on chains which stretched from this apex to the eaves of the roof were five large pearls of good augury for the safety of the city. One was supposed to avert floods, another to prevent tires, a third to keep dust-storms at a distance, a fourth to allay tempests, and a fifth to guard the city against disturbances. From the eaves of the several stories there hung one hundred and fifty-two bells and countless lanterns. In bygone days Nanking was one of the chief literary centres of the empire, besides being famous for its manufacturing industries. Satin, crape, nankeen, cloth, paper, pottery, and artificial flowers were among its chief products.
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2019-11-15 03:37:56
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https://indico2.riken.jp/event/3082/timetable/?view=indico_weeks_view
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The 24th International Spin Symposium
from Monday, 18 October 2021 (09:00) to Friday, 22 October 2021 (18:00)
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2021-12-03 02:04:04
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http://mathoverflow.net/questions/22395/chow-groups-of-arithmetic-surfaces
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# Chow groups of arithmetic surfaces
Given an arithmetic surface $S$, I would like to know the following properties of its first and second Chow groups $CH^1(S), CH^2(S)$:
1. Are they finitely generated? If so, what is the rank?
2. What is the size of the torsion subgroup?
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The example you gave at the end doesn't seem to be homogeneous. Is that intentional? – S. Carnahan Apr 24 '10 at 0:24
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2015-11-30 13:43:45
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https://undergroundmathematics.org/thinking-about-geometry/distance-between-points
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Rich example
What is the distance between the points with coordinates $(1,2)$ and $(6,4)$?
Try to work this out for yourself. If you get stuck, there are video suggestions to help you along. If you’re feeling confident, then move to the later examples!
(These videos do not have any sound.)
What is the distance between the points with coordinates $(2, -5)$ and $(-1,1)$?
What is the distance between the points with coordinates $(x_1,y_1)$ and $(x_2,y_2)$?
For more practice with specific numerical examples of points, use Mathmo.
You might like to try What type of triangle? next.
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2021-10-28 11:56:12
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http://help.simetrix.co.uk/8.2/simetrix/simulator_reference/topics/digitalmixedsignaldevicereference_exclusiveorgate.htm
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# Exclusive OR Gate
In this topic:
## Netlist entry
Axxxx [ in_0 in_1 .. in_n ] out model_name
## Connection details
Name Description Flow Type Vector bounds in Input in d, vector $2 - \infty$ out Output out d n/a
## Model format
.MODEL model_name d_xor parameters
## Model parameters
Name Description Type Default Limits rise_delay Rise delay real 1nS $1\text{e}^{-12} - \infty$ fall_delay Fall delay real 1nS $1\text{e}^{-12} - \infty$ input_load Input load value (F) real 1pF none family Logic family string UNIV none in_family Input logic family string UNIV none out_family Output logic family string UNIV none out_res Digital output resistance real 100 $0 - \infty$ out_res_pos Digital output res. pos. slope real out_res $0 - \infty$ out_res_neg Digital output res. neg. slope real out_res $0 - \infty$ open_c Open collector output boolean FALSE none min_sink Minimum sink current real -0.001 none max_source Maximum source current real 0.001 none sink_current Input sink current real 0 none source_current Input source current real 0 none
## Device Operation
• If the OPEN_C parameter is FALSE, the output is at logic '1' if an odd number of inputs are at logic '1'. If any input is UNKNOWN the output will be UNKNOWN, otherwise the output will be at logic '0'.
• If the model parameter OPEN_C is true the device will be open collector. In this case the output logic state is always '0'. The state of the inputs instead determines the strength of the output. If an odd number of inputs are at logic '1' the output strength will be HI-IMPEDANCE allowing a pull-up resistor to force it to the logic '1' state. If any input is UNKNOWN the output strength will be UNDETERMINED. Otherwise the output strength will be STRONG.
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2018-12-14 02:00:39
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https://cs.stackexchange.com/questions/24343/is-dependency-analysis-required-in-order-to-type-a-program
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# Is dependency analysis required in order to type a program?
I have seen stated in various places that in order to allow an "increase in polymorphism," functional dependency analysis should be performed, and type inference should be used for every declaration group in topological order. It seems like a well-known fact... except that nobody provides any reference or example.
In fact I don't understand what is really meant by this statement. Does it mean that without doing dependency analysis I wouldn't be able to type some programs (i.e. some valid programs would fail type-checking) or only that I would type them with a type that is more specific than what really is?
I'm particularly interested in consequences in a Haskell-like language/type system. In particular during kind inference, is dependency analysis actually necessary to avoid rejecting valid programs? Can you provide an example that wouldn't be well-kinded if typed without performing dependency analysis?
Since kinds are monomorphic I struggle to understand why dependency analysis should matter in this particular case.
id = \x -> x
Now if we type foo first, we would unify the first argument of id with Int and thus conclude id had type Int -> Int. So therefore we must first type id and then generalize its signature to the polymorphic type forall a. a -> a, and then instantiate that at type Int when we apply it and attempt to unify the argument type with Int.
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2019-09-20 05:26:07
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http://zakjost.com/category/information-theory/
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Intro
In Part 1 of this series we set out learn why the Gaussian/Normal distribution is such a pervasive choice in modeling random variables. We claim that this distribution is the least biased choice possible when the only information we have is the average and variance of outcomes from a population. Our strategy was to establish a metric of uncertainty and then maximize this metric while simultaneously adhering to our known equation for variance from an average.
Intro
When dealing with probabilities or building mathematical models, the de-facto distribution is the normal/gaussian. The bell curve. But where does this come from? Why is it a better choice than any other distribution that centers on the average? It turns out that the Guassian distribution is the one that is the least biased choice if the only information you have are 1) the average and 2) the variance of a set of outcomes.
To get to this result, we will first establish a measure of our uncertainty. This will be useful because we will then (Part 2) choose a distribution to model our process that both maximizes this uncertainty function and simultaneously satisfies the constraints of our average/variance knowledge.
Criteria for a Measure of Uncertainty
How do you measure the amount of uncertainty in a probability distribution? We’ll start by establishing a few characteristics that would be required for a useful uncertainty function. From these we will derive the functional form that meets the criteria.
Suppose we have the possible outcomes of the process encoded by values represented by $(x_1, ... , x_n)$. For instance, if it were a 6-sided die, the values would be 1, 2, 3, 4, 5, and 6. One way to mathematically model the process of rolling the die would be to assign probabilities to each of the possible outcomes. In the case of a fair die, each probability is equal to 1/6. We assign a corresponding probability $(p_1, ... , p_n)$ for each outcome $(x_1, ... , x_n)$ and these probabilities represent our knowledge of the process. Let’s call our unknown uncertainty function “H”. We expect H to depend on our probabilities since we are trying to quantify our uncertainty in our knowledge and its our probabilities that represent that knowledge: $H=H(p_1, ..., p_n)$
So which criteria does H have to meet so that it is useful and in line with our intentions?
1. It must be a continuous function of the $p_i$. This means a small change in one of the probabilities can’t give a huge change in our knowledge state.
2. In the case that all outcomes are equally probable (as in the case of a fair 6-sided die), the uncertainty should increase as the number of possible outcomes increases. In other words, the uncertainty function monotonically increases with the number of equiprobable choices.
1. This just means that if you have more choices, you’re more uncertain than if you had fewer choices. Guessing the outcome of a coin-flip is easier than picking the lottery numbers.
3. No matter how you count the probabilities, you should arrive at the same value for the same state of knowledge.
1. For instance, let’s say that instead of having to guess the outcome of a fair six sided die roll directly, you first guess whether it’s in the set $\{1,2,3\}$ or $\{4,5,6\}$ and then guess the final number from the smaller list. The first choice has two equal outcomes, so your probability of success is 1/2. The second choice has three equal outcomes, so your probability of success is 1/3. Your total probability of success is the product of these two and is 1/6. Essentially this is another way of modeling the exact same process. The requirement above just means that no matter how we model a process and break it up into sub-decisions, we should get one consistent value for H, whatever it ends up being.
The Uncertainty Function
It turns out, the function that satisfies these criteria is $H(p_1,...,p_n)=-K\sum p_i \log p_i$ where $K$ is a positive constant that determines the units. If you’re interested in the derivation, see the Deriving the Uncertainty Function section below.
An Example
Let’s use a simple case where there are two outcomes with probabilities $p$ and $q = 1-p$. The uncertainty becomes
$H(p, 1-p)=-K[p\log p + (1-p)\log(1-p)]$
$= -K[p\log\frac{p}{1-p}+\log(1-p)]$
Plotting this function using $K=1$ and a logarithm of base-2, the following plot is generated with units of bits on the y-axis.
How does this fit our intuition? If we are certain in the outcome (i.e. $p=0$ or $p=1$) then our uncertainty function $H=0$. We have no uncertainty. If, on the other hand, $p=q=\frac{1}{2}$, then our function is maximized at $H=1$ bit. As we would expect, we are maximally uncertain when the two outcomes are equally probable.
Deriving the Uncertainty Function
Using the criteria stated above, let’s now derive our uncertainty function.
Uncertainty Function of Equally Probable Outcomes
Let’s assume we are dealing with equally probable events at first, like a fair die. We’ll simplify our notation so that instead of writing the uncertainty for $n$ equally probable events as $H(\frac{1}{n},\frac{1}{n},...,\frac{1}{n})$, we will just use $A(n)$.
According to requirement 3 above, we can deduce that to decompose a choice from $n = s^m$ equally likely possibilities, you can transform it to be $m$ choices from $s$ equally likely possibilities: $A(s^m) = mA(s)$. In other words, if you have $n = 9 = 3^2$ equally likely choices, you can decompose that into two subsequent choices, each from three possibilities. This decomposition is similar to what we did in the sub-point of requirement 3.
Now, for any specified number $t^n$, we can find an $m$ to satisfy the following equation: $s^m\leq t^n\leq s^{m+1}$. So if $t^n = 3^2 = 9$, we could choose $s^m = 2^3 = 8$ and then $s^{m+1} = 2^4 = 16$, which satisfies the inequality.
By taking the logarithms of each term, we get $m\log(s) \leq n\log(t) \leq (m+1)\log(s)$. Dividing by $n\log(s)$, we get $\frac{m}{n} \leq \frac{\log(t)}{\log(s)} \leq \frac{m}{n} + \frac{1}{n}$. Subtracting $\frac{m}{n}$ from each term we end up showing: $\frac{\log(t)}{\log(s)} - \frac{m}{n} \leq \frac{1}{n}$. And since $n$ can be arbitrarily large, $|\frac{\log(t)}{\log(s)} - \frac{m}{n}| < \epsilon$. So what?
Since requirement 2 says that our uncertainty function is monotonic that means the original inequality and subsequent forms of it apply: $A(s^m) \leq A(t^n) \leq A(s^{m+1})$. Using our decomposition rule just derived: $mA(s) \leq nA(t) \leq (m+1)A(s)$. Continuing with the same division/subtraction steps we just undertook we end up with the relation: $|\frac{A(t)}{A(s)} - \frac{m}{n}| < \epsilon$.
These inequalities essentially state the following: The ratios of $\frac{A(t)}{A(s)}$ and $\frac{\log(t)}{\log(s)}$ are both within a distance of $\epsilon$ from the quantity $\frac{m}{n}$. That means the furthest they can be from one another is $2\epsilon$. Or translating that to an inequality, $|\frac{A(t)}{A(s)}-\frac{\log(t)}{\log(s)}| < 2\epsilon$.
So what does this tell us? We have shown that the difference between a ratio of our unknown functions $\frac{A(t)}{A(s)}$ are arbitrarily close to a ratio of known functions $\frac{\log(t)}{\log(s)}$. This leads one to naturally conclude that the unknown functions are the known functions within some multiplicative constant. How else could they be arbitrarily close for any $s$ and $t$? Therefore:
$A(t) = K\log(t)$.
Uncertainty of General Probability Distributions
So that’s the function that quantifies the uncertainty of a process with $t$ equally probable outcomes. But what about processes that don’t have equally probable outcomes? Using requirement 3 we see that the way you decompose a process is that you take the uncertainty of the first choice and add the uncertainties of the additional choices that are weighted by their probability of occurrence. So in the case of our game in the example of requirement 3, the uncertainty of the process of choosing 1 of 6 equally probable sides is the same as the sum of the uncertainties of the two step process: 1) choosing one of the two subgroups $\{1,2,3\}$ or $\{4,5,6\}$ and 2) choosing among the three elements of each subgroup multiplied by the probabilities of getting that subgroup in the first place.
$A(6) = H(\frac{1}{2},\frac{1}{2})+\frac{1}{2}H(\frac{1}{3},\frac{1}{3}, \frac{1}{3})+\frac{1}{2}H(\frac{1}{3},\frac{1}{3}, \frac{1}{3})$
Now imagine a process where you have $n =\sum n_i$ outcomes where $n_i$ is the relative occurrence of the $i^{th}$ outcome. For instance, a 6 sided die where there are a single green, a single red, two blues and two yellows. The probabilities for each outcome are then straight-forward: $p_i = \frac{n_i}{\sum n_i}$. This also means that if you know you are on outcome $i$, this is like choosing from $n_i$ equally probable events since there are $n_i$ occurrences of $i$. To break down this process of $n =\sum n_i$ outcomes we have $A(\sum n_i) = H(p_1,...,p_n) + \sum p_i A(n_i)$. Let’s solve this for our unknown uncertainty function $H(p_1,...,p_n)$.
$H(p_1,...,p_n)=A(\sum n_i)-\sum p_i A(n_i)$
$= \sum p_i A(\sum n_i)- \sum p_i A(n_i) = \sum p_i [A(\sum n_i) - A(n_i)]$
$= K\sum p_i [\log(\sum n_i)-\log(n_i)]$
$= K\sum p_i \log\frac{\sum n_i}{n_i}$
$= K\sum p_i \log\frac{1}{p_i}$
$= -K\sum p_i \log p_i$
The only thing we did was recognize that a function weighted by its probabilities and summed is equal to the function itself (line 2) and substituted our equation of the $A(n)$ that we found above (line 3).
So, finally, we have solved our problem. The uncertainty associated with a process that’s characterized by the set of probabilities $\{p_i\}$ is given by the function
$H(p_1,...,p_n)=-K\sum p_i \log p_i$
where $K$ is a positive constant.
Conclusion
Our original goal was to find the least biased distribution to use to model a process when we only have knowledge of the average and variance of a sub-population. To do this we started by coming up with a metric for measuring our uncertainty when given a set of probabilities. In Part 2 of this treatment we will maximize this uncertainty function while using our knowledge of average/variance as constraints on the probabilities. In this way we work backwards from this uncertainty function and ultimately arrive at a functional form of our least-biased probability distribution.
References
This derivation and treatment follows almost exactly that found in Claud Shannon’s original work A Mathematical Theory of Communication. The image above was found on the wikipedia page on information entropy and can be found here.
The Entropy of First Names
I was recently working on a coding challenge for a job related to analysis of the first names of people born in the USA. The data set given was from the Social Security Administration and can be downloaded here. There is a text file for each state and for every name entry there is the associated gender, year, state, and count of people born that year with the stated name. For example, here are the first few lines of the Arkansas file:
AK,F,1910,Mary,14
AK,F,1910,Annie,12
AK,F,1910,Anna,10
While looking for inspiration for this challenge I found an interesting article that referenced the entropy of baby names. Entropy measures the amount of information contained in a choice from a distribution. I decided to explore the entropy concept further and the results are below.
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2017-10-21 06:48:51
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https://www.groundai.com/project/worldsheet-theory-of-light-cone-gauge-noncritical-strings-on-higher-genus-riemann-surfaces/
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1 Introduction
UTHEP-683
Worldsheet theory of light-cone gauge noncritical strings on higher genus Riemann surfaces
Nobuyuki Ishibashi***e-mail: ishibash@het.ph.tsukuba.ac.jp and Koichi Murakamie-mail: koichi@kushiro-ct.ac.jp
Graduate School of Pure and Applied Sciences, University of Tsukuba,
Tsukuba, Ibaraki 305-8571, Japan
National Institute of Technology, Kushiro College,
Otanoshike-Nishi 2-32-1, Kushiro, Hokkaido 084-0916, Japan
It is possible to formulate light-cone gauge string field theory in noncritical dimensions. Such a theory corresponds to conformal gauge worldsheet theory with nonstandard longitudinal part. We study the longitudinal part of the worldsheet theory on higher genus Riemann surfaces. The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory.
1 Introduction
Since light-cone gauge string field theory is a completely gauge fixed theory, there is no problem in formulating it in noncritical dimensions. It should be possible to find the worldsheet theory in the conformal gauge describing such a string theory, in which the spacetime Lorentz invariance shall be broken. In [Baba:2009ns, Baba:2009fi], we have constructed the longitudinal part of the worldsheet theory which we call the CFT. The CFT turns out to be a conformal field theory with the right central charge so that the whole worldsheet theory is BRST invariant. The light-cone gauge superstring field theory in noncritical dimensions can be used [Baba:2009kr, Baba:2009zm, Ishibashi:2010nq, Ishibashi:2011fy] to regularize the so-called contact term divergences [Greensite:1986gv, Greensite:1987hm, Greensite:1987sm, Green:1987qu, Wendt:1987zh], in the case of tree level amplitudes. The supersymmetric CFT plays crucial roles in studying such a regularization.
In this paper, we would like to study the CFT on higher genus Riemann surfaces. In a previous paper [Ishibashi:2013nma], we have dealt with the bosonic CFT on higher genus Riemann surfaces, but we have not investigated its properties in detail. In this paper, we will define and calculate the correlation functions of bosonic and supersymmetric CFT on higher genus Riemann surfaces and explore various properties of the theory. The results in this paper will be used in a forthcoming publication, in which we discuss the dimensional regularization of the multiloop amplitudes of light-cone gauge superstring field theory.
The organization of this paper is as follows. In section 2, the bosonic CFT is studied. We calculate the correlation functions based on the results in [Ishibashi:2013nma]. In section LABEL:sec:Supersymmetric--CFT, we deal with the supersymmetric CFT. In [Baba:2009fi], we have given a way to calculate the correlation functions of the supersymmetric CFT on a surface of genus 0, but it is a bit unwieldy. In this paper, we develop an alternative method to calculate them, apply it to higher genus case and explore various properties of the supersymmetric CFT. Section LABEL:sec:Discussions is devoted to discussions. In the appendices, we give details of definitions and calculations which are not included in the text.
2 Bosonic X± Cft
It is straightforward to calculate the amplitudes of light-cone gauge bosonic string field theory perturbatively by using the old-fashioned perturbation theory and Wick rotation. Each term in the expansion corresponds to a light-cone gauge Feynman diagram for strings. A typical diagram is depicted in Figure 1. A Wick rotated -loop -string diagram is conformally equivalent to an punctured genus Riemann surface . The amplitudes are given by an integral of correlation functions of vertex operators on over the moduli parameters.
As has been shown in [Baba:2009ns, Ishibashi:2013nma], the amplitudes in dimensions can be cast into the conformal gauge expression using the worldsheet theory with the field contents
X+,X−,Xi,b,c,¯b,¯c, (2.1)
in which the reparametrization ghosts and the longitudinal variables are added to the original light-cone variables . The worldsheet action for the longitudinal variables is given by
S[^gz¯z,X±]=−14π∫dz∧d¯zi(∂X+¯∂X−+∂X−¯∂X+)+d−2624Γ[^gz¯z,X+]. (2.2)
Here the metric on the worldsheet is taken to be and is the Liouville action
Γ[^gz¯z,X+]=−12π∫dz∧d¯zi(∂ϕ¯∂ϕ+^gz¯z^Rϕ), (2.3)
where the Liouville field is given by
ϕ≡ln(−4∂X+¯∂X+)−ln(2^gz¯z), (2.4)
and is the scalar curvature derived from the metric . The theory with the action (2.2) turns out to be a conformal field theory which we call the CFT.
In order for the action to be well-defined, should be a well-defined metric on the worldsheet at least at generic points. Hence we should always consider the theory in the presence of the vertex operator insertions
N∏r=1e−ip+rX−(Zr,¯Zr), (2.5)
with and . The amplitudes with such insertions correspond to light-cone diagrams with external lines at which have string length . With the insertion of these vertex operators, possesses a classical background
X+cl(z,¯z)=−i2(ρ(z)+¯ρ(¯z)), (2.6)
where is given by
ρ(z)=N∑r=1αr[lnE(z,Zr)−2πi∫zP0ω1ImΩIm∫ZrP0ω]. (2.7)
Here is the prime form, is the canonical basis of the holomorphic abelian differentials and is the period matrix of the surface.111For the mathematical background relevant for string perturbation theory, we refer the reader to [D'Hoker:1988ta]. The base point is arbitrary. For notational convenience, we introduce
g(z,w)≡lnE(z,w)−2πi∫zP0ω1ImΩIm∫wP0ω, (2.8)
so that (2.7) can be expressed as
ρ(z)=N∑r=1αrg(z,Zr). (2.9)
Notice that is a function of and not , but that of both of and .
coincides with the coordinate on the light-cone diagram defined as follows. A light-cone diagram consists of cylinders which correspond to propagators of closed strings. On each cylinder, one can introduce a complex coordinate whose real part coincides with the Wick rotated light-cone time and imaginary part parametrizes the closed string at each time. The ’s on the cylinders are smoothly connected except at the interaction points and we get a complex coordinate on . is not a good coordinate around the punctures and the interaction points on the light-cone diagram. The interaction points are characterized by the equation
∂ρ(zI)=0. (2.10)
Since
ds2=−4∂X+cl¯∂X+cldzd¯z=|∂ρ|2dzd¯z (2.11)
provides a well-defined metric on the worldsheet except for the points , , we can make well-defined.
2.1 Correlation functions on higher genus Riemann surfaces
As has been demonstrated in [Baba:2009ns], all the properties of the worldsheet theory of the longitudinal variables can be deduced from the correlation function of the form
⟨N∏r=1e−ip+rX−(Zr.¯Zr)M∏s=1e−ip−sX+(ws.¯ws)⟩X±^gz¯z (2.12) ≡(ZX[^gz¯z])−2∫[dX+dX−]^gz¯ze−S±[^gz¯z]N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws).
The correlation functions are normalized by being divided by the factor
(ZX[^gz¯z])2≡(8π2det′(−^gz¯z∂z∂¯z)∫dz∧d¯z√^g)−1, (2.13)
which coincides with the partition function of the worldsheet theory when As is explained in appendix LABEL:sec:Definition-of-the, taking the integration contours of appropriately, we can evaluate it and obtain
⟨N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z (2.14)
Therefore we need to calculate to get the correlation function.
Since the metric (2.11) is singular at as mentioned above, one gets a divergent result if one naively substitutes into in (2.3). One way to deal with the divergences may be to regularize them as was done in [Mandelstam:1985ww]. An alternative way is to integrate the variation formula
δ(−Γ)=∑IδTI∮CIdz2πi1∂ρTLiouville(z)+c.c.. (2.15)
Here labels the internal lines of the light-cone diagram and denotes the contour going around it as depicted in Figure 2. is defined as
TI=TI+iαIθI, (2.16)
where denotes the length of the -th internal line and , denote the string-length and the twist angle for the propagator. ’s and ’s should satisfy some linear constraints so that the variation corresponds to that of the shape of a light-cone diagram. denotes the energy-momentum tensor corresponding to the Liouville action (2.3) given as
TLiouville(z)=(∂ϕ(z))2−2(∂−∂ln^gz¯z)∂ϕ(z), (2.17)
where is now given as
ϕ=ln|∂ρ|2−ln(2^gz¯z). (2.18)
It is possible to calculate the right hand side of (2.15) and integrate it with respect to the variation to get . By doing so, we can fix the form of as a function of the parameter ’s. Imposing the factorization conditions in the limit where some of the ’s become infinity, it is possible to fix completely. By this method, we can calculate without encountering divergent constants.
Such a computation was performed in [Ishibashi:2013nma] and we can evaluate by using the results. The energy-momentum tensor (2.17) with in (2.18) can be rewritten as
TLiouville = (∂ln|∂ρ|2)2−2∂2ln|∂ρ|2−(∂ln^gz¯z)2+2∂2ln^gz¯z (2.19) = −2{ρ,z}−((∂ln^gz¯z)2−2∂2ln^gz¯z),
where
{ρ,z}=∂3ρ∂ρ−32(∂2ρ∂ρ)2 (2.20)
is the Schwarzian derivative. In [Ishibashi:2013nma], we have calculated which satisfies
(2.21)
where denotes the expectation value of the energy-momentum tensor of a free boson . On the other hand, the partition function satisfies
δlnZX[^gz¯z]=∑IδTI∮CIdz2πi1∂ρ(⟨TX(z)⟩+124((∂ln^gz¯z)2−2∂2ln^gz¯z))+c.c.. (2.22)
Comparing (2.21), (2.22) and (2.15), we get
e−Γ∝ZLC(ZX)−24, (2.23)
up to a possibly divergent multiplicative factor.
Taking to be the Arakelov metric , was calculated in [AlvarezGaume:1987vm, Verlinde:1986kw, Dugan:1987qe, Sonoda:1987ra, Wentworth:1991, Wentworth:2008] and its explicit form is
ZX[gAz¯z]24=ecge2δ(Σ)\leavevmode\nobreak , (2.24)
where is the Faltings’ invariant [Faltings:1984] defined by
e−14δ(Σ) = (detImΩ)32|θ[ζ](0|Ω)|2∏gi=1(2gA^zi¯^zi)∣∣detωj(^zi)∣∣2 (2.25) ×exp[−∑i
and is a numerical constant which depends on . Here and are arbitrary points on , and
ζ≡g∑i=1∫^ziP0ω−∫^wP0ω−Δ\leavevmode\nobreak . (2.26)
denotes the vector of Riemann constants for . The definitions of the Arakelov metric and the Arakelov Green’s function are given in appendix LABEL:sec:Arakelov-metric-and. Also taking to be the Arakelov metric, we obtain [Ishibashi:2013nma]
ZLC=1(32π2)4he2δ(Σ)e−W∏re−2Re¯Nrr00∏I∣∣∂2ρ(zI)∣∣−3, (2.27)
where
−W ≡ −2∑I
denotes one of the Neumann coefficients and is given by
¯Nrr00 ≡ limz→Zr[ρ(zI(r))−ρ(z)αr+ln(z−Zr)] (2.29) = ρ(zI(r))αr−∑s≠rαsαrlnE(Zr,Zs)+2πiαr∫ZrP0ω1ImΩN∑s=1αsIm∫ZsP0ω\leavevmode\nobreak ,
and denotes the coordinate of the interaction point at which the -th external line interacts. Therefore we get
e−Γ ∝ ZLCe−2δ(Σ) (2.30) = 1(32π2)4ge−W∏re−2Re¯Nrr00∏I∣∣∂2ρ(zI)∣∣−3,
and fix the right hand side of (2.14) to be
⟨N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z (2.31) = (2π)2δ(∑sp−s)δ(∑rp+r)∏se−p−sρ+¯ρ2(ws,¯ws) ×(1(32π2)4ge−W∏re−2Re¯Nrr00∏I∣∣∂2ρ(zI)∣∣−3)d−2624\leavevmode\nobreak .
Once we know the correlation function of the form (2.31), it is possible to calculate other correlation functions by differentiating it with respect to . For example,
⟨∂X+(w)N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z (2.32) =i∂w0∂p−0⟨N∏r=1e−ip+rX−(Zr,¯Zr)M+1∏s=0e−ip−sX+(ws,¯ws)⟩X±^gz¯z∣∣ ∣∣p−0=0,w0=w,
where we take . From (2.31), we get
⟨∂X+(w)N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z (2.33) =−i2∂ρ(w)⟨N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z.
It is easy to see that for any functional that can be expressed in terms of the derivatives of and the Fourier modes satisfying
F[X++c]=F[X+](c=const.), (2.34)
the following equation holds,
⟨F[X+]N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z (2.35)
This implies that the expectation value of is equal to .
The correlation functions involving can be evaluated in the same way. For example,
⟨∂X−(z)N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z (2.36) =i∂Z0∂p+0⟨N+1∏r=0e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z∣∣ ∣∣p+0=0,Z0=z,
with and we get from (2.31)
⟨∂X−(z)N∏r=1e−ip+rX−(Zr,¯Zr)M∏s=1e−ip−sX+(ws,¯ws)⟩X±^gz¯z (2.37) = [M∑s=1(−ip−s)∂zg(z,ws)+i∂Z0∂p+0(−d−2624Γ[^gz¯z,−i2(ρ′+¯ρ′)])∣∣∣p+0=0,Z0=z]
Here we have introduced
ρ′(z) ≡ N+1∑r=0αrg(z,Zr) (2.38) = ρ(z)+α0(g(z,Z0)−g(z,ZN+1)).
(2.37) can be rewritten as
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2020-10-25 14:04:12
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https://stats.stackexchange.com/questions/249677/asymptotically-normally-distributed
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# Asymptotically Normally Distributed
When we say an estimator is consistent, we mean "as the sample size increases, sampling distribution of the estimator converges to the true parameter value."
But when we say "an estimator is asymptotically normally distributed", what does it mean?
Are "central limit theorem" and "asymptotically normally distributed" synonymous?
But when we say "an estimator is asymptotically normally distributed", what does it mean?
Using similar language to your first sentence, when we say an estimator is asymptotically normally distributed, we mean something like as the sample size increases, the sampling distribution of a suitably standardized version of the estimator converges in distribution to some particular normal distribution.
Are "central limit theorem" and "asymptotically normally distributed" synonymous?
Not in general, I think. Some quantity may be asymptotically normal but not come about as a result of any of the versions of the CLT (at least not in any obvious way - it might perhaps be that all of them can ultimately relate to the CLT, but I suspect it's possible to construct cases that would not).
However, very many estimators can be cast as a kind of average of some random variable and in that case a CLT-type argument may be indeed possible.
In some other cases you can combine the CLT with some other result to produce an argument that some estimator should be asymptotically normal (so the CLT may be involved but doesn't stand alone as the basis for the asymptotic normality).
• I understand that Some quantity may be asymptotically normal but not come about as a result of any of the versions of the CLT (at least not in any obvious way). But if it is CLT, does not it asymptotically normally distributed? Dec 7 '16 at 3:45
• I'm sorry but I don't understand what your second sentence is asking. Dec 7 '16 at 13:01
• I haven't understood CLT may be involved by doesn't stand alone as the basis for the asymptotic normality. But CLT states that the sampling distribution of the sampling means approaches a normal distribution as the sample size gets larger, regardless of the shape of the population distribution. Then why CLT alone cannot assure an estimator is asymptotically normal? Dec 8 '16 at 0:17
• 1, Sorry, there's a typo there in what you quote. It should say "but" where I typed "by". That probably doesn't help. I will fix it. 2. The CLT gives a way to get asymptotic normality. But that doesn't imply there are no other ways for something to be asymptotically normal. By way of an example, consider $X_i \sim \text{Beta}(\alpha\cdot i,\alpha\cdot i)$. Let $Z_i=(X_i-\mu_i)/\sigma_i$ where $\mu_i$ and $\sigma_i$ are the mean and standard deviation of $X_I$. Then it turns out that $Z_i$ is asymptotically normal but we're not averaging anything... Dec 8 '16 at 1:54
• ... In this case (as with many others) it may turn out that with sufficient cleverness one may be able to find a connection to something where one could invoke a CLT type argument --- but that doesn't imply that there is always such an argument. [It would be interesting to know if that could always be done.] Dec 8 '16 at 2:03
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2021-10-16 17:51:11
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https://webot.org/info/en/?search=Actuarial_credentialing_and_exams
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# Actuarial credentialing and exams Information
https://en.wikipedia.org/wiki/Actuarial_credentialing_and_exams
The actuarial credentialing and exam process usually requires passing a rigorous series of professional examinations, most often taking several years in total, before one can become recognized as a credentialed actuary. In some countries, such as Denmark, most study takes place in a university setting. In others, such as the U.S., most study takes place during employment through a series of examinations. In the UK, and countries based on its process, there is a hybrid university-exam structure.
## Policies of various countries
### Australia
The education system in Australia is divided into three components: an exam-based curriculum; a professionalism course; and work experience. [1] The system is governed by the Institute of Actuaries of Australia. [2]
The exam-based curriculum is in three parts. Part I relies on exemptions from an accredited under-graduate degree from either Monash University, Macquarie University, University of New South Wales, University of Melbourne, Australian National University or Curtin University. [3] The courses cover subjects including finance, financial mathematics, economics, contingencies, demography, models, probability and statistics. Students may also gain exemptions by passing the exams of the Institute of Actuaries in London. [3] Part II is the Actuarial control cycle and is also offered by each of the universities above. [4] Part III consists of four half-year courses of which two are compulsory and the other two allow specialization. [5]
To become an Associate, one needs to complete Part I and Part II of the accreditation process, perform 3 years of recognized work experience, and complete a professionalism course. [1] To become a Fellow, candidates must complete Part I, II, III, and take a professionalism course. Work experience is not required, however, as the Institute deems that those who have successfully completed Part III have shown enough level of professionalism. [1]
The Canadian Institute of Actuaries (the CIA) recognizes fellows of both the Society of Actuaries and the Casualty Actuary Society, provided that they have specialized study in Canadian actuarial practice. For fellows of the SOA, this is fulfilled by taking the CIA's Practice Education Course (PEC). For fellows of the Casualty Actuarial Society, this is fulfilled by taking the nation-specific Exam 6-Canada, instead of Exam 6-United States. [6] Further, the CIA requires three years of actuarial practice within the previous decade, and 18 months of Canadian actuarial practice within the last three years, to become a fellow. [7]
### Denmark
In Denmark it normally takes five years of study at the University of Copenhagen to become an actuary with no professional experience requirement. There is a focus on statistics and probability theory, and a requirement for a master's thesis. [8] By Danish law, responsibility for the practice of any life insurance business must be taken by a formally acknowledged and approved actuary. Approval as a formally responsible actuary requires three to five years of professional experience.( Haastrup & Nielsen 2007)
### Germany
Current rules for the German Actuarial Society require an actuary to pass more than 13 exams. [9]
### India
The Actuarial Society of India (now converted into Institute of Actuaries of India) offers both associate-ship and fellowship classes of membership. However, prospective candidates must be admitted to the society as students before they achieve associate-ship or fellowship. The exam sequence is similar to the British model, with Core and Specialty technical and application exams. The exams are conducted twice a year during the months of May–June and October–November. [10] Starting from January 2012, the institute has started conducting entrance exam. Only those applicants who clear the entrance test can appear for the Core Technical papers.
### Norway
In Norway the education to become an actuary takes five years. The education usually consists of a bachelor's degree (three years) and a master's degree (two years). The bachelor's degree needs to contain a specific number of courses in mathematics and statistics. The master's degree usually consists of one year of courses and one year writing a master's degree about a topic related to the actuarial profession. The University of Bergen and The University of Oslo offer the education to become an actuary in Norway. [11] To become an international qualified actuary, a person with a Norwegian actuarial education must also take two courses in economics (macroeconomics and accounting) and a course in ethics. The ethics course, which lasts a day, is offered by the Norwegian Society of Actuaries. [12]
### South Africa
Actuaries in South Africa are served by the Actuarial Society of South Africa (ASSA). Until recently[ when?] the requirement to qualify as an actuary in South Africa was to pass the exams hosted by the UK bodies. Starting in 2010, a South African actuarial qualification hosted by ASSA has replaced this arrangement. Key changes include exam syllabuses based on South African-specific content. The UK actuarial professional bodies, however, still support qualification through the UK. Students may receive exemption from part of the examinations for qualification from approved universities. The South African qualification does have mutual recognition with many of the international actuarial bodies as well as approval of the syllabus from the International Actuarial Association.
One may obtain the Chartered Enterprise Risk Actuary (CERA) designation through the ASSA.
### Sweden
Actuarial training in Sweden takes place at Stockholm University. The five-year master's program (for those with no previous university-level knowledge in mathematics, or without a bachelor's degree in mathematics) covers the subjects mathematics, mathematical statistics, insurance mathematics, financial mathematics, insurance law and insurance economics. The program operates under the Division of Mathematical Statistics. [13]
### UK and Ireland
Qualification in the United Kingdom and Ireland consists of a combination of exams and courses provided by the Institute and Faculty of Actuaries. The exams may only be taken upon having officially joined the body, [14] unlike many other countries where exams may be taken earlier. Most trainee actuaries study while working for an actuarial employer using resources provided by ActEd (The Actuarial Education Company, a subsidiary of BPP Actuarial Education Ltd.), which is contracted to provide actuarial tuition for students on behalf of Institute and Faculty Education Ltd (IFE), a subsidiary of the Institute and Faculty of Actuaries. [15]
However, a candidate may offer proof of having previously covered topics (at a high enough standard, usually while at university) to be exempt from taking certain subjects. [16]
The exams themselves are split into four sections: [17] Core Principles (CP), Core Practices (CP), Specialists Principles (SP), and Specialist Advance (SA). For students who joined the Profession after June 2004, a further requirement that the student carry out a "Work-based skills" exercise has been brought into effect. This involves the student submitting a series of essays to the Profession detailing the work that he or she has performed. In addition to exams, essays and courses, it is required that the candidate have at least three years' experience of actuarial work under supervision of a recognized actuary to qualify as a Fellow of the Institute of Actuaries (FIA) or of the Faculty of Actuaries (FFA). [18]
Note that the UK Profession is currently introducing the Certified Actuarial Analyst (CAA) qualification to "provide those working in financial and actuarial roles at a technical level around the world with valuable skills and a well respected qualification". [19]
### United States
In the U.S., for life, health, and pension actuaries, exams are given by the Society of Actuaries, while for property-casualty actuaries the exams are administered by the Casualty Actuarial Society. The Society of Actuaries’ requirements for Associateship include passing five preliminary examinations, demonstrating educational experience in economics, corporate finance, and applied statistics—called validation by educational experience (VEE), completing an eight-module self-learning series, and taking a course on professionalism. [20] For Fellowship, three other modules, three or four exams depending on specialty track, and a special fellowship admission course is added. [21] The Casualty Actuarial Society requires the successful completion of seven examinations, two modules, and economics and corporate finance VEEs for Associateship and three additional exams for Fellowship. In addition to these requirements, casualty actuarial candidates must also complete professionalism education and be recommended for membership by existing members. [22]
To sign certain statements of actuarial opinion, however, American actuaries must be members of the American Academy of Actuaries. Academy membership requirements include membership in one of the recognized actuarial societies, at least three years of full-time equivalent experience in responsible actuarial work, and either residency in the United States for at least three years or a non-resident or new resident who meets certain requirements. [23] Continuing education is required after certification for all actuaries who sign statements of actuarial opinion. [24]
#### Preliminary exams
Dependent on which society a student chooses to pursue, there are anywhere from six to seven preliminary exams. Most of the exams are multiple choice and administered on computers at Prometric testing centers. Candidates are allowed to use a calculator from an approved list. [25] The exams are timed and last between three and four hours. Some tests provide instant feedback as to whether or not a candidate has passed that particular exam (see table below). All test scores (on a 0-10 scale with 6 or higher passing) are posted six to eight weeks after the test. However, due to the way the test is scaled, the scores can range from 0–10, but there are also situations where the highest grade for a test is a 9 even if every single question was answered correctly. This is because the interval is 10 percent of the score required to pass, [26] which means the following: [27]
Let P be the passing percentage.
Passing Scores:
• If you score between P and 1.1P, you get a 6;
• If you score between 1.1P and 1.2P, you get a 7;
• If you score between 1.2P and 1.3P, you get an 8;
• Between 1.3P and 1.4P, 9;
• Greater than 1.4P, 10;
Failing Scores:
• If you score between 0.9P and P, you get a 5;
• Between 0.8P and 0.9P, 4;
• Between 0.7P and 0.8P, 3;
• Between 0.6P and 0.7P, 2;
• Between 0.5P and 0.6P, 1;
• Less than 0.5P, 0.
If ${\displaystyle P>{\frac {100}{1.4}}\%\approx 71.4\%}$, then ${\displaystyle 1.4P>100\%}$, i.e. the requirement for the percentage of score to get grade 10 will be higher than ${\displaystyle 100\%}$. That is, grade 10 is unachievable. Hence, the highest grade achievable can be 9 for a test.
SOA administers exam LTAM (previously MLC), which covers life contingencies topics. Starting in May 2014, MLC includes both multiple choice and open-response questions. SOA made this change because, in their view, strict multiple-choice questions are not sufficient or adequate to test whether candidates are familiar and fluent in the material. The test is four hours long, allows calculators, and is administered via a paper-and-pencil format. Multiple-choice questions account for 40% of the exam, and open-response questions account for 60% of the exam. Candidates may freely move between the two sections. The two sections are graded separately. However, since the multiple-choice questions are easier, only candidates who have answered a certain percentage of the multiple-choice questions correctly have their written answers graded. For instance, a multiple-choice score of 24 points was needed to have written-answer questions graded for the April 2021 LTAM exam. [28]
SOA exam CAS exam Exam title Exam topics Format Tests per year Pass/fail estimate
P 1 Probability Law of total probability, Bayes' theorem, basic counting, common discrete and continuous distributions, univariate and multivariate distributions, order statistics, transformation of distributions, conditional expectation, variance and covariance, basic knowledge of insurance and risk management Computer 6 Yes
FM 2 Financial Mathematics Basic interest theory, annuities, bonds, loans, cash flows, portfolios, determinants of interest rates, interest rate swaps, spot rates, forward rates and immunization Computer 6 Yes
IFM 3F Investment and Financial Markets Interest rate models, derivatives, hedging, options, capital structure, debt and equity financing, rational valuation of derivative securities, and risk management techniques Computer 3 Yes
LTAM -- Long-Term Actuarial Mathematics Survival models, Markov chain models, life insurances and annuities, pension mathematics, and mortality improvement Paper and pencil 2 No
STAM -- Short-Term Actuarial Mathematics Severity models, frequency models, aggregate models, construction of empirical models, construction and selection of parametric models, estimating failure time and loss, determining the acceptability of a fitted model, credibility, simulation Computer 3 Yes
PA -- Predictive Analytics Exploratory Data Analysis, General Linear Model's (GLM), and Communication of Results using R Computer 2 No
SRM -- Statistics for Risk Modeling Basics of Statistical Learning, Linear Models, Time Series Models, Principal Components Analysis, Decision Trees, and Cluster Analysis Computer 3 No
-- MAS-I Statistics and probabilistic models Stochastic processes, survival models (including limited life contingencies concepts), statistics, general linear models (including ordinary least squares) and time series [29] Paper and pencil 2 No
-- MAS-II Modern Actuarial Statistics II Introduction to Credibility, Linear Mixed Models, Bayesian Analysis and Markov Chain Monte Carlo, and Statistical Learning Paper and pencil 2 No
## Notes
1. ^ a b c
2. ^
3. ^ a b
4. ^
5. ^
6. ^
7. ^ ( CIA 2004)
8. ^
9. ^ ( DAV 2011)
10. ^ ( ASI 2006)
11. ^
12. ^
13. ^
14. ^ "How to Register Student". www.actuaries.org.uk. Retrieved 2022-01-20.{{ cite web}}: CS1 maint: url-status ( link)
15. ^ "Exam preparation | the Actuarial Profession". Archived from the original on 2012-11-06. Retrieved 2013-12-31.
16. ^ "Frequently asked questions on exemptions | the Actuarial Profession". Archived from the original on 2013-03-05. Retrieved 2013-12-31.
17. ^ "Our Exams Explained". www.actuaries.org.uk. Retrieved 2022-01-20.{{ cite web}}: CS1 maint: url-status ( link)
18. ^
19. ^ "New qualification takes a step forward". www.actuaries.org.uk. Retrieved 2022-01-20.{{ cite web}}: CS1 maint: url-status ( link)
20. ^
21. ^
22. ^
23. ^ ( AAA 2010)
24. ^ ( AAA 2008)
25. ^ "Identification and Calculators | be an Actuary". Archived from the original on 2013-09-25. Retrieved 2016-06-18.
26. ^ "Grading - Reporting of Examination Results | SOA". www.soa.org. Retrieved 2021-12-01.
27. ^ "school_and_exam_questions - actuary". libreddit.spike.codes. Retrieved 2021-12-01.
28. ^ "APRIL 2021 EXAMINATION RESULTS" (PDF).{{ cite web}}: CS1 maint: url-status ( link)
29. ^ "Casualty Actuarial Society | Exam S Syllabus". Archived from the original on 2016-04-21. Retrieved 2016-06-18.
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2022-12-03 16:22:40
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https://calculator.academy/voice-over-rate-calculator/
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• C is the total cost of voice over ($) • T is the total time of voice over (min) ## How to Calculate Voice Over Rate? The following example problems outline how to calculate Voice Over Rate. Example Problem #1: 1. First, determine the total cost of voice over ($).
• The total cost of voice over ($) is given as: 300. 2. Next, determine the total time of voice over (min). • The total time of voice over (min) is provided as: 25. 3. Finally, calculate the Voice Over Rate using the equation above: VOR = C / T * 60 The values provided above are inserted into the equation below and computed. VOR = 300 / 25 * 60 = 720.00 ($/hr)
Example Problem #2:
For this problem, the variables required are provided below:
total cost of voice over (\$) = 600
total time of voice over (min) = 34
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2023-01-30 13:52:20
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http://pediaview.com/openpedia/Pseudorandom_binary_sequence
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# Pseudorandom binary sequence
A binary sequence (BS) is a sequence $a_0,\ldots, a_{N-1}$ of $N$ bits, i.e.
$a_j\in \{0,1\}$ for $j=0,1,...,N-1$.
A BS consists of $m=\sum a_j$ ones and $N-m$ zeros.
A BS is a pseudo-random binary sequence (PRBS) if its autocorrelation function:
$C(v)=\sum_{j=0}^{N-1} a_ja_{j+v}$
has only two values:
$C(v)= \begin{cases} m, \mbox{ if } v\equiv 0\;\; (\mbox{mod}N)\\ \\ mc, \mbox{ otherwise } \end{cases}$
where
$c=\frac{m-1}{N-1}$
is called the duty cycle of the PRBS, similar to the duty cycle of a continuous time signal.
A PRBS is 'pseudorandom', because, although it is in fact deterministic, it seems to be random in a sense that the value of an $a_j$ element is independent of the values of any of the other elements, similar to real random sequences.
A PRBS can be stretched to infinity by repeating it after $N$ elements, this in contrast to most random sequences, such as sequences generated by radioactive decay or by white noise, that are 'infinite' by nature. The PRBS is more general than the maximum length sequence, which is a special pseudo-random binary sequence of N bits generated as the output of a linear shift register. A maximum length sequence always has a 1/2 duty cycle and its number of elements $N = 2^k-1$. PRBS's are used in telecommunication, encryption, simulation, correlation technique and time-of-flight spectroscopy.
## Practical implementation
Pseudorandom binary sequences can be generated using linear feedback shift registers.[1]
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2013-05-18 11:43:23
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https://stats.stackexchange.com/questions/23779/most-interesting-statistical-paradoxes/23822
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Because I find them fascinating, I'd like to hear what folks in this community find as the most interesting statistical paradox and why.
It's not a paradox per se, but it is a puzzling comment, at least at first.
During World War II, Abraham Wald was a statistician for the U.S. government. He looked at the bombers that returned from missions and analyzed the pattern of the bullet "wounds" on the planes. He recommended that the Navy reinforce areas where the planes had no damage.
Why? We have selection effects at work. This sample suggests that damage inflicted in the observed areas could be withstood. Either planes were never hit in the untouched areas, an unlikely proposition, or strikes to those parts were lethal. We care about the planes that went down, not just those that returned. Those that fell likely suffered an attack in a place that was untouched on those that survived.
For copies of his original memoranda, see here. For a more modern application, see this Scientific American blog post.
Expanding upon a theme, according to this blog post, during World War I, the introduction of a tin helmet led to more head wounds than a standard cloth hat. Was the new helmet worse for soldiers? No; though injuries were higher, fatalities were lower.
• I recall having read this in a couple of places before, but I don't have a reference at hand. Is there one that you can add? – cardinal Feb 28 '12 at 17:18
• @cardinal, I found some memos for you. Looks like the research was actually for the U.S. – Charlie Feb 28 '12 at 17:45
• Somewhere, there's a scatterplot of a hypothetical airplane for this example, but I can't find it. – Fomite Jan 5 '13 at 7:55
• +1. This is an example of Survivorship Bias, perhaps the most detrimental of the biases. I expanded on it in an answer. – Cliff AB Feb 13 '16 at 17:19
Another example is the ecological fallacy.
Example
Suppose that we look for a relationship between voting and income by regressing the vote share for then-Senator Obama on the median income of a state (in thousands). We get an intercept of approximately 20 and a slope coefficient of 0.61.
Many would interpret this result as saying that higher income people are more likely to vote for Democrats; indeed, popular press books have made this argument.
But wait, I thought that rich people were more likely to be Republicans? They are.
What this regression is really telling us is that rich states are more likely to vote for a Democrat and poor states are more likely to vote for a Republican. Within a given state, rich people are more likely to vote Republican and poor people are more likely to vote Democrat. See the work of Andrew Gelman and his coauthors.
Without further assumptions, we cannot use group-level (aggregate) data to make inferences about individual-level behavior. This is the ecological fallacy. Group-level data can only tell us about group-level behavior.
To make the leap to individual-level inferences, we need the constancy assumption. Here, the voting choice of individuals most not vary systematically with the median income of a state; a person who earns \$X in a rich state must be just as likely to vote for a Democrat as someone who earns \$X in a poor state. But people in Connecticut, at all income levels, are more likely to vote for a Democrat than people in Mississippi at those same income levels. Hence, the consistency assumption is violated and we are led to the wrong conclusion (fooled by aggregation bias).
This topic was a frequent hobbyhorse of the late David Freedman; see this paper, for example. In that paper, Freedman provides a means for bounding individual-level probabilities using group data.
Elsewhere in this CW, @Michelle proposes Simpson's paradox as a good example, as it indeed is. Simpson's paradox and the ecological fallacy are closely related, yet distinct. The two examples differ in the natures of the data given and analysis used.
The standard formulation of Simpson's paradox is a two-way table. In our example here, suppose that we have individual data and we classify each individual as high or low income. We would get an income-by-vote 2x2 contingency table of the totals. We'd see that a higher share of high income people voted for the Democrat relative to the share of low income people. Were we to create a contingency table for each state, however, we'd see the opposite pattern.
In the ecological fallacy, we don't collapse income into a dichotomous (or perhaps multichotomous) variable. To get state-level, we get the mean (or median) state income and state vote share and run a regression and find that higher income states are more likely to vote for the Democrat. If we kept the individual-level data and ran the regression separately by state, we'd find the opposite effect.
In summary, the differences are:
• Mode of analysis: We could say, following our SAT prep skills, that Simpson's paradox is to contingency tables as the ecological fallacy is to correlation coefficients and regression.
• Degree of aggregation/nature of data: Whereas the Simpson's paradox example compares two numbers (Democrat vote share among high income individuals versus the same for low income individuals), ecological fallacy uses 50 data points (i.e., each state) to calculate a correlation coefficient. To get the full story from in the Simpson's paradox example, we'd just need the two numbers from each of the fifty states (100 numbers), while in the ecological fallacy case, we need the individual-level data (or else be given state-level correlations/regression slopes).
General observation
@NeilG comments that this just seems to be saying that you can't have any selection on unobservables/omitted variables bias issues in your regression. That's right! At least in the regression context, I think that nearly any "paradox" is just a special case of omitted variables bias.
Selection bias (see my other response on this CW) can be controlled for by including the variables that drive the selection. Of course, these variables are typically unobserved, driving the problem/paradox. Spurious regression (my other other response) can be overcome by adding a time trend. These cases say, essentially, that you have enough data, but need more predictors.
In the case of the ecological fallacy, it's true, you need more predictors (here, state-specific slopes and intercepts). But you need more observations, individual-, rather than group-level, observations as well to estimate these relationships.
(Incidentally, if you have extreme selection where the selection variable perfectly divides treatment and control, as in the WWII example that I give, you may need more data to estimate the regression as well; there, the downed planes.)
• How is it possible to formalize the consistency assumption? It sounds like assuming that there are no (causal) confounders missing from one's model. – Neil G Feb 29 '12 at 1:26
• Also, the example provided is also an example of Simpson's paradox because conditioning on the state reverses the correlation between income and party. When is the ecological fallacy different from Simpson's paradox? – Neil G Feb 29 '12 at 1:28
• I would also point out that making inferences about group-level associations or causation based on individual-level associations or causal relationships is also just a bad: the atomistic fallacy, well articulated here: [Diez-Roux, 1998] Diez-Roux, A. V. (1998). Bringing context back into epidemiology: variables and fallacies in multilevel analysis. American Journal of Public Health, 88(2):216–222. – Alexis Jul 21 '14 at 16:46
My contribution is Simpson's paradox because:
• the reasons for the paradox are not intuitive to many people, so
• it can be really hard to explain why the findings are the way they are to lay people in plain English.
tl;dr version of the paradox: the statistical significance of a result appears to differ depending on how the data are partitioned. The cause appears often to be due to a confounding variable.
Another good outline of the paradox is here.
There are no paradoxes in statistics, only puzzles waiting to be solved.
Nevertheless, my favourite is the two envelope "paradox". Suppose I put two envelopes in front of you and tell you that one contains twice as much money as the other (but not which is which). You reason as follows. Suppose the left envelope contains $x$, then with 50% probability the right envelope contains $2x$ and with 50% probability it contains $0.5x$, for an expected value of $1.25x$. But of course you can simply reverse the envelopes and conclude instead the left envelope contains $1.25$ times the value of the right envelope. What happened?
• brilliant paradox - interestingly if we go with the "second" interpretation on wikipedia and try to calculate $E[B|A=a]$, we find that in order to prevent preference for switching we require $E[B|A=a]=a=2ap+\frac{a}{2}(1-p)$ where $p=Pr(A<B|A=a)$. Solving for $p$ means we get $p=\frac{1}{3}$. Similarly we can calculate $E[A|B=b]=b=2bq+\frac{b}{2}(1-q)$ where $q=Pr(B<A|B=b)$ and get $q=\frac{1}{3}$ ....Bizzare! – probabilityislogic Mar 1 '12 at 13:05
• I have given presentations on this paradox in which the game is actually played with the audience, with real amounts of money (usually a check to the host institution). It gets their attention... – whuber Mar 1 '12 at 15:50
• Think I solved this one... The paradox is solved when we recognize the two envelope paradox incorrectly proposes 1) there are three possible quantities: 0.5x, x, and 2x, when there are only two quantities in the envelopes (say x and 2x), and 2) that we a priori know the left envelope contains x (in which case the right envelope would contain 2x with 100% certainty!). Given possible values of x and 2x randomly assigned to the two envelopes, the correct answer is an expected value of 1.5x whether I choose the left envelope or right envelope. – RobertF Oct 25 '12 at 13:55
• @RobertF The situation is more complicated. Suppose that it is known that the money is distributed in the two envelopes as follows. Toss a fair coin until it lands heads and count the number n of times the coin was tossed. Place 2^n dollars in one envelope and 2^(n+1) in the other. You can now perform very exact expectation computations and still retain the paradox. – Ittay Weiss Dec 24 '12 at 23:13
This is a recent invention; it was heavily discussed within a small set of philosophy journals over the last decade. There are staunch advocates for two very different answers (the "Halfers" and "Thirders"). It raises questions about the nature of belief, probability, and conditioning, and has caused people to invoke a quantum-mechanical "many worlds" interpretation (among other bizarre things).
Here is the statement from Wikipedia:
Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details. On Sunday she is put to sleep. A fair coin is then tossed to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday and Tuesday. But when she is put to sleep again on Monday, she is given a dose of an amnesia-inducing drug that ensures she cannot remember her previous awakening. In this case, the experiment ends after she is interviewed on Tuesday.
Any time Sleeping beauty is awakened and interviewed, she is asked, "What is your credence now for the proposition that the coin landed heads?"
The Thirder position is that S.B. should respond "1/3" (this is a simple Bayes' Theorem calculation) and the Halfer position is that she should say "1/2" (because that's the correct probability for a fair coin, obviously!). IMHO, the entire debate rests on a limited understanding of probability, but isn't that the whole point of exploring apparent paradoxes?
(Illustration from Project Gutenberg.)
### References
Arntzenius, Frank (2002). Reflections on Sleeping Beauty. Analysis 62.1 pp 53-62. Elga, Adam (2000). Self-locating belief and the Sleeping Beauty Problem. Analysis 60 pp 143-7.
Franceschi, Paul (2005). Sleeping Beauty and the Problem of World Reduction. Preprint.
Groisman, Berry (2007). The end of Sleeping Beauty’s nightmare.
Lewis, D (2001). Sleeping Beauty: reply to Elga. Analysis 61.3 pp 171-6.
Papineau, David and Victor Dura-Vila (2008). A thirder and an Everettian: a reply to Lewis’s ‘Quantum Sleeping Beauty’.
Pust, Joel (2008). Horgan on Sleeping Beauty. Synthese 160 pp 97-101.
Vineberg, Susan (undated, perhaps 2003). Beauty’s Cautionary Tale.
All can be found (or at least were found several years ago) on the Web.
• Do you think it's equally effective to formulate the solution in terms of "base units"? By that I mean, you have to consider whether the base unit is the person, or the interview. 1/2 of persons will have had a head, but 1/3 of interviews will. Then to choose our base unit, we can revisit the question and phrase as "What is the chance that this interview is associated with a 'heads' result?" – Jonathan Feb 29 '12 at 18:35
• SB does not know how many interviews there have been and the question is about her assessment of the probability, not the experimenters' assessment. From her point of view, the number of interviews cannot be determined. – whuber Feb 29 '12 at 18:52
• I think you should read the arguments in the literature first, Aaron. (I confess that I am a thirder, but I think the halfers will not find your reasoning convincing. At the very least, you need to show them why their argument is flawed.) – whuber Mar 8 '12 at 22:01
• Fair point, @whuber, I've now had a further look at the literature. I'm reading Ellis's Sleeping Beauty: reply to Elga. It's this sentence that worries me, at the start of section '4. My argument'. "Only new relevant evidence, centred or uncentred, produces a change in credence". I'll think further and maybe blog about it again. I had a long discussion with seven other PhD students about this! – Aaron McDaid Mar 10 '12 at 17:01
• Is Sleeping Beauty allowed to look at the calendar when awakened? If Monday, then she ought to reply P(X=head)=0.5. If Tuesday, then P(X=head)=0. – RobertF Oct 24 '12 at 15:33
The St.Petersburg paradox, which makes you think differently on the concept and meaning of Expected Value. The intuition (mainly for people with background in statistics) and the calculations are giving different results.
• Here is another that I like that seems so insufficiently known that it has no name attached to it, but has a similar flavor and an interesting statistical lesson: There exists a sequence of independent random variables $X_1,X_2,\ldots$ with mean zero and uniformly bounded variance such that $\sqrt{n} \bar X_n$ converges in distribution to a standard normal $\mathcal N(0,1)$ (just like the CLT). However, $\mathrm{Var}(\sqrt{n} \bar X_n) \to 17$ (or your favorite positive number). – cardinal Feb 28 '12 at 17:36
• @cardinal Any chance you could post some details of this as a separate answer? – Silverfish Jan 28 '15 at 11:12
• @Silver Let each $X_i$ have a Normal distribution with mean zero and variance $f(n)$. What would $f$ have to look like asymptotically for $\text{Var}(\sqrt{n}\bar X_n)$ to converge? – whuber Mar 23 '15 at 22:13
• @whuber Presumably I should read that as $X_i$ having variance $f(i)$; in which case (using independence of the $X_i$) we have $\mathrm{Var}(\sqrt{n}\bar X_n) = \frac{1}{n}\sum_{i=1}^n f(i)$ so we need the sequence $f(i)$ to be Cesàro summable if $\mathrm{Var}(\sqrt{n}\bar X_n)$ is to converge? – Silverfish Mar 24 '15 at 0:30
The Jeffreys-Lindley paradox, which shows that under some circumstances default frequentist and Bayesian methods of hypothesis testing can give completely contradictory answers. It really forces users to think about exactly what these forms of testing mean, and to consider whether that's what the really want. For a recent example see this discussion.
There's the famous two-girls fallacy:
In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
Most people intuitively say 1/2, but the answer is 1/3. The issue, fundamentally, is that uniformly choosing "one girl, from all girls with one sibling" at random is not the same as uniformly choosing "one family, from all families with two children and at least one girl."
This one is simple enough to mesh with intuition, once you understand it, but there are more complicated versions that are more difficult to comprehend:
In a family with two children, what are the chances, if one of the children is a boy born on Tuesday, that both children are boys? (Answer: 13/27)
In a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls? (Answer: very close to 1/2, assuming "Florida" is an extremely rare name)
• The answer is 1/3 not 2/3 surely? Only one out of GB, BG, GG – Martin Smith Feb 29 '12 at 13:29
• The "boy born on Tuesday" article is good. Its main point, which is made very clearly ("the problem is under-defined"), is that the answer depends on the probability model one adopts. Saying that "the" answer is 13/27 is misleading (at best). – whuber Feb 29 '12 at 16:01
• @Martin: hehe whoops :) – BlueRaja - Danny Pflughoeft Feb 29 '12 at 16:22
• The reason these problems are so confusing is that the question is worded so that its very difficult to ascertain what hypothesis space is. This in turn makes it confusing as to what the "equally likely" cases actually are (and hence what should be counted). – probabilityislogic Mar 1 '12 at 11:13
• I feel like being cheeky, and note that the way the question is worded really only indicates that children are exchangeable in terms of their order - knowing that the child is a girl doesn't tell us whether or not they were the first or second child. What this means is that $p(B_1G_2)=p(G_1B_2)$. But nothing else! So all we can really say is that the probability of another girl is that it is equal to $\frac{p(G_1G_2)}{2p(B_1G_2)+p(G_1G_2)}$. To get a numerical value requires us to assign probabilities, which cannot be done with the information given. – probabilityislogic Mar 1 '12 at 11:24
Sorry, but I can't help myself (I, too, love statistical paradoxes!).
Again, perhaps not a paradox per se and another example of omitted variables bias.
Spurious causation/regression
Any variable with a time trend is going to be correlated with another variable that also has a time trend. For example, my weight from birth to age 27 is going to be highly correlated with your weight from birth to age 27. Obviously, my weight isn't caused by your weight. If it was, I'd ask that you go to the gym more frequently, please.
Here's an omitted variables explanation. Let my weight be $x_t$ and your weight be $y_t$, where \begin{align*}x_t &= \alpha_0 + \alpha_1 t + \epsilon_t \text{ and} \\ y_t &= \beta_0 + \beta_1 t + \eta_t.\end{align*}
Then the regression $$\begin{equation*}y_t = \gamma_0 + \gamma_1 x_t + \nu_t\end{equation*}$$ has an omitted variable---the time trend---that is correlated with the included variable, $x_t$. Hence, the coefficient $\gamma_1$ will be biased (in this case, it will be positive, as our weights grow over time).
When you are performing time series analysis, you need to be sure that your variables are stationary or you'll get these spurious causation results.
One of my favorites is the Monty Hall problem. I remember learning about it in an elementary stats class, telling my dad, as both of us were in disbelief I simulated random numbers and we tried the problem. To our amazement it was true.
Basically the problem states that if you had three doors on a game show, behind which one is a prize and the other two nothing, if you chose a door and then were told of the remaining two doors one of the two was not a prize door and allowed to switch your choice if you so chose you should switch you current door to the remaining door.
From wikipdedia: "Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. It is named after its creator, Juan Parrondo, who discovered the paradox in 1996. A more explanatory description is:
There exist pairs of games, each with a higher probability of losing than winning, for which it is possible to construct a winning strategy by playing the games alternately.
Parrondo devised the paradox in connection with his analysis of the Brownian ratchet, a thought experiment about a machine that can purportedly extract energy from random heat motions popularized by physicist Richard Feynman. However, the paradox disappears when rigorously analyzed."
As alluring as the paradox might sound to the financial crowd, it does have requirements that are not readily available in financial time series. Even though a few of the component strategies can be losing, the offsetting strategies require unequal and stable probabilities of much greater or less than 50% in order for the ratcheting effect to kick in. It would be difficult to find financial strategies, whereby one has $P_B(W)=3/4+\epsilon$ and the other, $P_A(W)=1/10 + \epsilon$, over long periods.
There's also a more recent related paradox called the "allison mixture," that shows we can take two IID and non-correlated series, and randomly scramble them such that certain mixtures can create a resulting series with non-zero autocorrelation.
It's interesting that the Two Child Problem and the Monty Hall Problem so often get mentioned together in the context of paradox. Both illustrate an apparent paradox first illustrated in 1889, called Bertrand's Box Paradox, which can be generalized to represent either. I find it a most interesting "paradox" because the same very-educated, very-intelligent people answer those two problems in opposite ways with respect to this paradox. It also compares to a principle used in card games like bridge, known as the Principle of Restricted Choice, where it resolution is time-tested.
Say you have a randomly selected item that I'll call a "box." Every possible box has at least one of two symmetric properties, but some have both. I'll call the properties "gold" and "silver." The probability that a box is just gold is P; and since the properties are symmetric, P is also the probability that a box is just silver. That makes the probability that a box has just one property 2P, and the probability that it has both 1-2P.
If you are told a box is gold, but not whether it is silver, you might be tempted to say the chances it is just gold are P/(P+(1-2P))=P/(1-P). But then you would have to state the same probability for a one-color box if you were told it was silver. And if this probability is P/(1-P) whenever you are told just one color, it has to be P/(1-P) even if you aren't told a color. Yet we know it is 2P from the last paragraph.
This apparent paradox is resolved by noting that if a box has only one color, there is no ambiguity about what color you will be told. But if it has two, there is an implied choice. You have to know how that choice was made in order to answer the question, and that is the root of the apparent paradox. If you aren't told, you can only assume a color was chosen at random, making the answer P/(P+(1-2P)/2)=2P. If you insist P/(1-P) is the answer, you are implicitly assuming there was no possibility the other color could have been mentioned unless it was the only color.
In the Monty Hall Problem, the analogy for the colors is not very intuitive, but P=1/3. Answers based on the two unopened doors originally being equally likely to have the prize are assuming Monty Hall was required to open the door he did, even if he had a choice. That answer is P/(1-P)=1/2. The answer allowing him to choose at random is 2P=2/3 for the probability that switching will win.
In the Two Child Problem, the colors in my analogy compare quite nicely to genders. With four cases, P=1/4. To answer the question, we need to know how it was determined that there was a girl in the family. If it was possible to learn about a boy in the family by that method, then the answer is 2P=1/2, not P/(1-P)=1/3. It's a little more complicated if you consider the name Florida, or "born on Tuesday," but the results are the same. The answer is exactly 1/2 if there was a choice, and most statements of the problem imply such a choice. And the reason "changing" from 1/3 to 13/27, or from 1/3 to "nearly 1/2," seems paradoxical and unintuitive, is because the assumption of no choice is unintuitive.
In the Principle of Restricted Choice, say you are missing some set of equivalent cards - like the Jack, Queen, and King of the same suit. The chances start out even that any particular card belongs to a specific opponent. But after an opponent plays one, his chances of having any one of the others are decreased because he could have played that card if he had it.
• I don't follow your probabilities. If by "symmetric", you mean $P_G=P_S$ (which I think you mean), then shouldn't the probability of both be $P^2$, rather than $2P$? (This assumes independence, which I think you mean, although it would help to state that explicitly.) Furthermore, I think the probability of the box being neither should be $(1-P)^2$, rather than $1-2P$, shouldn't it? These can easily be seen if we consider the case where $P_G=P_S=.8$--then $P_{GS}=1.6$ & $P_{-G-S}=-.6$, unless by "symmetric" you mean that $P=.5$ & the properties are perfectly dependent. Sorry to nitpick. – gung - Reinstate Monica Mar 7 '12 at 14:57
• Sorry, maybe I didn't explain it well trying to be as brief as possible. My P was not the probability a box has the color gold, it was the probability it was only gold. The probability it has the color gold is 1-P. And while the two properties are symmertic, they do not have to be independent, so you can't just multiply probabilities. Also, no box is "neither." Bertrand used three box with two coins in each: gold+gold, gold+silver, and silver+silver. A box with any number of gold coins is "gold" in my generalization. – JeffJo Mar 7 '12 at 16:10
• +1, that helps. I now see the phrase "at least one of two" and the word "just", which I must have skimmed over. – gung - Reinstate Monica Mar 7 '12 at 17:25
I like the following: The host is using an unknown distribution on $[0,1]$ to choose, independently, two numbers $x,y\in [0,1]$. The only thing known to the player about the distribution is that $P(x=y)=0$. The player is then shown the number $x$ and is asked to guess whether $y>x$ or $y<x$. Clearly, if player always guesses $y>x$ then player will be correct with probability $0.5$. However, at least surprisingly if not paradoxically, player can improve on that strategy. I'm afraid I don't have a link to the problem (I heard it many years ago during a workshop).
• Dear Ittay, I believe Tom Cover is the original source of this problem. I think it is also listed in his Open Problems in Communication and Computation, but I don't have it handy to check. It's a nice problem. The restriction to $[0,1]$, or, even a random $y$ (or $x$, for that matter) is inessential. Cheers. – cardinal Mar 2 '13 at 19:50
This is Simpson's Paradox again but 'backwards' as well as forwards, comes from Judea Pearl's new book Causal Inference in Statistics: A primer[^1]
The classic Simpon's Paradox works as follows: consider trying to choose between two doctors. You automatically choose the one with the best outcomes. But suppose the one with the best outcomes chooses the easiest cases. The other's poorer record is a consequence of trickier work.
Now who do you choose? Better to look at the results stratified by difficulty and then decide.
There is another side to the coin (another paradox) which says that the stratified outcomes can also lead you to the wrong choice.
This time consider choosing to use a drug or not. The drug has a toxic side effect, but its therapeutic mechanism of action is through lowering blood pressure. Overall, the drug improves outcomes in the population, but when stratifying on post-treatment blood pressure the outcomes are worse in both the low and the high blood pressure groups. How can this be true? Because we have unintentionally stratified on the outcome, and within each outcome all that remains to observe is the toxic side effect.
To clarify, imagine the drug is designed to fix broken hearts, and it does this by lowering the blood pressure, and instead of stratifying on blood pressure we stratify on fixed hearts. When the drug works, the heart is fixed (and the blood pressure will be lower), but some of the patients will also get the toxic side effect. Because the drug works, the 'fixed heart' group will have more patients who have taken the drug, than there are patients taking the drug in the 'broken' heart group. More patients taking the drug means more patients getting side effects, and apparently (but falsely) better outcomes for patients who didn't take the drug.
The patients who get better without taking the drug are just lucky. The patients who took the drug and got better are a mixture of those who needed the drug to get better, and those who would have been lucky anyway. Examining only patients with 'fixed hearts' means excluding patients who would have been fixed had they taken the drug. Excluding such patients means excluding the harm from not taking the drug which in turn means we only see the harm from taking the drug.
Simpson's paradox arises when there is a cause for the outcome other than the treatment such as the fact that your doctor only does tricky cases. Controlling for the common cause (tricky versus easy cases) allows us to see the true effect. In the latter example, we have unintentionally stratified on an outcome not on a cause which means the true answer is in the aggregate not the stratified data.
[^1]: Pearl J. Causal Inference in Statistics. John Wiley & Sons; 2016
I find a simplified graphical illustration of the ecological fallacy (here the rich State/poor State voting paradox) helps me to understand on an intuitive level why we see a reversal of voting patterns when we aggregate State populations:
• This is a nice example, but I think this is Simpson's Paradox: en.wikipedia.org/wiki/Simpson%27s_paradox – Nick Oct 30 '12 at 18:12
• @Nick: this particular example is actually distinct from Simpson's Paradox, but it can be hard to know which fallacy/paradox applies in a particular situation because they look the same statistically. The difference is that SP is a "false effect" that appears only when analyzing subgroups. This trend shown is though to be a "true effect" that appears only when analyzing subgroups. In this case, it suggests that while income as a raw number doesn't affect voting patterns in aggregate, income as related to your neighbors (your state) does influence voting patterns. – Jonathan Jan 15 '13 at 20:56
• It's the ecological fallacy, discussed below. – Charlie Jun 5 '13 at 21:30
• @Charlie 'below' and 'above' are functions of whatever way a reader of the page is sorting (active/oldest/votes), and in any case the order under some of the sorting criteria can change over time (including the default). As such, it's probably better to mention the person that posted the discussion you refer to, or even link to it. – Glen_b Jun 20 '13 at 8:13
Suppose you obtained a data on births in royal family of some kingdom. In the family tree each birth was noted. What is peculiar about this family was that parents were trying to have a baby only as soon first boy was born and then did not have any more children.
So your data potentially looks similar to this:
G G B
B
G G B
G B
G G G G G G G G G B
etc.
Will the proportion of boys and girls in this sample reflect the general probability of giving a birth to a boy (say 0.5)? The answer and explanation can be found in this thread.
• This answer reads like a puzzle, not like a paradox. I can imagine why you wanted to post it like that, but I think for this answer to qualify as paradox and to fit this thread, you need to be more explicit. – amoeba Mar 23 '15 at 21:43
• This question (with boys and girls interchanged) was asked at stats.stackexchange.com/questions/93830, which received a large number of answers--not entirely in agreement! (I learned something by taking the problem seriously and thinking about it in increasingly realistic ways, exploring the assumptions needed to do that.) – whuber Mar 23 '15 at 21:52
• @whuber thanks for the link! I added it into the description. – Tim Mar 23 '15 at 21:56
One of my "favorites", meaning that it's what drives me crazy about the interpretation of many studies (and often by the authors themselves, not just the media) is that of Survivorship Bias.
One way to imagine it is suppose there's some effect that is very detrimental to the subjects, so much so that it has a very good chance of killing them. If subjects are exposed to this effect before the study, then by the time study begins, the exposed subjects that are still alive have a very high probability of having being unusually resilient. Literally natural selection at work. When this happens, the study will observe that exposed subjects are unusually healthy (since all the unhealthy ones already died or made sure to stop being exposed to the effect).This is often misinterpreted as implying that exposure is actually good for the subjects. This is a result of ignoring truncation (i.e. ignoring the subjects who died and did not make it to the study).
Similarly, subjects who stop being exposed to the effect during the study are often incredibly unhealthy: this is because they have realized that continued exposure will probably kill them. But the study merely observes that those who quit are very unhealthy!
@Charlie's answer about the WWII bombers can be thought of as an example of this, but there's plenty of modern examples too. A recent example are the studies reporting that drinking 8+ cups of coffee a day (!!) is linked to much higher heart health in subjects over 55 years of age. Plenty of people with PhD's interpreted this as "drinking coffee is good for your heart!", including the authors of the study. I read this as you have to have an incredibly healthy heart to be still drinking 8 cups of coffee a day after 55 years of age and not have a heart attack. Even if it doesn't kill you, the moment something looks worrisome about your health, everyone that loves you (plus your doctor) will immediately encourage you to stop drinking coffee. Further studies found that drinking so much coffee had no beneficial effects in younger groups, which I believe is more evidence that we are seeing a survivorship effect, rather than a positive causal effect. Yet there's plenty of PhD's running around saying "Science says drinking 8+ cups of coffee is good for seniors!"
• Im not so sure of your interpretation. In Norway drinking 8 cups of coffee a day isnt inusual at all, the mean value (including children and other nondrinkers) being around two cups a day. In Finland the mean is at around 2.5 cups a day. I used to drink mor ethan ten cups a day, butnot so anymore. – kjetil b halvorsen Jun 25 '17 at 20:25
I'm surprised no one has mentioned Newcombe's Paradox yet, although it is more heavily discussed in decision theory. It's definitely one of my favorites.
Let x, y, and z be uncorrelated vectors. Yet x/z and y/z will be correlated.
• Why is this a paradox ? it's seems intuitive. – lcrmorin Jun 5 '13 at 15:58
• I'd have been surprised if this weren't usually the case. – Glen_b Jun 20 '13 at 8:10
• It's unclear what $x/z$ and "correlated" are intended to mean. (Presumably "$x/z$" is componentwise division--assuming no components of $z$ are zero!) Is "correlated" to be interpreted in the sense of the correlation coefficient (essentially the standardized dot products) or are we to treat $X,Y,$ and $Z$ as random variables and consider their correlation coefficients in that sense? – whuber Mar 23 '15 at 21:57
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2020-09-28 16:07:12
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https://www.impetus.no/support/manual/?command=EOS_POLYNOMIAL
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#### EOS_POLYNOMIAL
###### SPH
*EOS_POLYNOMIAL
eosid, $A$, $B$, $C$
##### Parameter definition
VariableDescription
eosid Unique EOS identification number
$A$ Polynomial coefficient
$B$ Polynomial coefficient
$C$ Polynomial coefficient
##### Description
This is a polynomial equation-of-state that currently only works with $\gamma$SPH particles. Note that the linear bulk modulus, $K$, is determined from the elastic properties in the material command.
$p = K \mu + A \mu^2 + \frac{B + C \mu}{1 + \mu} e$
where $e$ is the specific internal energy per unit volume and $\mu$ is a measure of the volumetric compression.
$\displaystyle{\mu = \frac{\rho}{\rho_0} - 1}$
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2022-08-13 09:31:47
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https://www.techwhiff.com/issue/how-is-everyones-day-going--25535
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# How is everyones day going
###### Question:
how is everyones day going
### The fact that the earth is an ecosystem means which of the following? A- what happens in one part of the ecosystem will affect other parts B- as long as pollution doesn’t reach the ocean, the water supply is fine C-humans can’t really understand how to combat environmental issues D- population doesn’t affect global warming
The fact that the earth is an ecosystem means which of the following? A- what happens in one part of the ecosystem will affect other parts B- as long as pollution doesn’t reach the ocean, the water supply is fine C-humans can’t really understand how to combat environmental issues D- populati...
### "what does a negative net migration rate in a country tell us"
"what does a negative net migration rate in a country tell us"...
### For three months, Jude sticks to his plan of eating a vegetarian diet, a change recommended by his wrestling coach. Then one night Jude eats a big pile of barbecued ribs. This is an example of what type of behavior?
For three months, Jude sticks to his plan of eating a vegetarian diet, a change recommended by his wrestling coach. Then one night Jude eats a big pile of barbecued ribs. This is an example of what type of behavior?...
### In The Odyssey - Elpenor, the rituals that Odysseus performs on the island show that the ancient Greeks respected and honored -their cows. -the dead -the sea -their traditions.
In The Odyssey - Elpenor, the rituals that Odysseus performs on the island show that the ancient Greeks respected and honored -their cows. -the dead -the sea -their traditions....
### Según la gráfica cuadrática de la expresión y= x² + 1 ¿Cuales serían las coordenadas cuando x es igual a -2,-1 y 0?
Según la gráfica cuadrática de la expresión y= x² + 1 ¿Cuales serían las coordenadas cuando x es igual a -2,-1 y 0?...
### Laura sees a horse pulling a buggy. She wonders how it can accelerate if the action of the horse pulling the cart would causes an equal and opposite reaction of the cart pulling on the horse. Which explanation best answers her question
Laura sees a horse pulling a buggy. She wonders how it can accelerate if the action of the horse pulling the cart would causes an equal and opposite reaction of the cart pulling on the horse. Which explanation best answers her question...
### (-4, 6) and (3, -7) what’s the distance between them
(-4, 6) and (3, -7) what’s the distance between them...
### Use the following x-values (0, 1, 2, 3) to find ordered pairs for this equation: y = 2x - 3
Use the following x-values (0, 1, 2, 3) to find ordered pairs for this equation: y = 2x - 3...
### According to the American Probation and Parole Association PSI reports should contain which of the following components? a. Medical and mental status b. Summary and analysis c. Military service d. All of the above
According to the American Probation and Parole Association PSI reports should contain which of the following components? a. Medical and mental status b. Summary and analysis c. Military service d. All of the above...
### Witch is the equation of the line that passes through the point (-3,-11) and is parallel to the line with equation 2x-y=4?
witch is the equation of the line that passes through the point (-3,-11) and is parallel to the line with equation 2x-y=4?...
### Why was Stephan Austin going to Mexico City
Why was Stephan Austin going to Mexico City...
### Determine whether the lines below are parallel, perpendicular, or neither. * y=2x+9 x-2y=-6
Determine whether the lines below are parallel, perpendicular, or neither. * y=2x+9 x-2y=-6...
### ...VOLGA7O/2009 12 Which of the following is the best explanation of why a democratic system of government is similar to a team sport? Both are deeply concerned about the health and well- being of everyone involved Rising above the competition is the key to success in both Both depend heavily on participation Both can succeed without strong leadership
...VOLGA7O/2009 12 Which of the following is the best explanation of why a democratic system of government is similar to a team sport? Both are deeply concerned about the health and well- being of everyone involved Rising above the competition is the key to success in both Both depend heavily on par...
### In paragraph two, the tone is BEST described as A) calm and neutral. B) personal and playful. C) aloof and challenging. D) directly engaging and inspiring. E) angry and bombastic.
In paragraph two, the tone is BEST described as A) calm and neutral. B) personal and playful. C) aloof and challenging. D) directly engaging and inspiring. E) angry and bombastic....
### Determine the main purpose of each writing scenario: to inform, to persuade, or to entertain?
Determine the main purpose of each writing scenario: to inform, to persuade, or to entertain?...
### 13b: The sum of 3 consecutive even integers is -32. What are the 3 integers?
13b: The sum of 3 consecutive even integers is -32. What are the 3 integers?...
### Hasil dari 37²-√576:√144 adalah
hasil dari 37²-√576:√144 adalah...
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2022-08-13 21:49:53
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https://dev.goldbook.iupac.org/terms/view/L03646
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## Wikipedia - Flusso luminoso luminous flux
https://doi.org/10.1351/goldbook.L03646
Of a source of @L03647@ $$I$$ in an element of solid @A00346@ $$\text{d}\varOmega$$ is given by $$\text{d}\varPhi = I\ \text{d}\varOmega$$.
Sources:
Green Book, 2nd ed., p. 72 [Terms] [Book]
PAC, 1996, 68, 957. (Glossary of terms in quantities and units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)) on page 979 [Terms] [Paper]
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2021-06-19 10:01:15
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https://www.gradesaver.com/textbooks/math/algebra/linear-algebra-and-its-applications-5th-edition/chapter-1-linear-equations-in-linear-algebra-1-3-exercises-page-34/33
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Linear Algebra and Its Applications (5th Edition)
General strategy for both parts: compute both the left hand side (LHS) and the right hand (RHS) side of the equation in component form and show that they are equal. (a) LHS: First, from the definition of vector addition: $u + v$ = ($u_{1}$ + $v_1$, $u_2$ + $v_2$, ... , $u_n$ + $v_n$) Therefore, from the definition of vector addition again: $(u + v) + w$ = ($u_{1}$ + $v_1$, $u_2$ + $v_2$, ... , $u_n$ + $v_n$) + ($w_1$, $w_2$, ..., $w_n$) = ($u_{1}$ + $v_1$ + $w_1$, $u_2$ + $v_2$ + $w_2$, ... , $u_n$ + $v_n$ + $w_n$) .......... (1) RHS: First, from the definition of vector addition: $v + w$ = ($v_{1}$ + $w_1$, $v_2$ + $w_2$, ... , $v_n$ + $w_n$) Therefore, from the definition of vector addition again: $u + (v + w)$ = ($u_{1}, u_2, u_3$) + ($v_1 +w_1, v_2 + w_2, ... , v_n + w_n$) = ($u_{1}$ + $v_1$ + $w_1$, $u_2$ + $v_2$ + $w_2$, ... , $u_n$ + $v_n$ + $w_n$) .......... (2) Since equation (1) is the same as equation (2) the property is verified. (b) LHS: First, from definition of vector addition: $u + v$ = ($u_{1} + v_1, u_2 + v_2, ... , u_n + v_n$) Second, from definition of scalar multiplication: $c(u + v) = (c(u_{1} + v_1), c(u_2 + v_2), ... , c(u_n + v_n))$ Third, from the distributive property of real numbers i.e. if $x, y, z$ are all real numbers then $z(x + y) = zx + zy$ we find: $c(u + v) = (cu_{1} + cv_1, cu_2 + cv_2, ... , cu_n + cv_n)$ .......... (3) RHS: First, from definition of scalar multiplication: $c\times u = (cu_1, cu_2, ... cu_n)$ $c\times v = (cv_1, cv_2, ... cv_n)$ Therefore, from the definition of vector addition: $c\times u + c\times v$ $= (cu_1, cu_2, ... cu_n) + (cv_1, cv_2, ..., cv_n)$ $= (cu_1 + cv_1, cu_2 + cv_2, ... , cu_n + cv_n)$ .......... (4) Since equation (3) is the same as equation (4) the property is verified.
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2018-09-26 14:16:37
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http://mathoverflow.net/questions/98706/representing-a-real-number-as-the-value-of-a-countably-infinite-game
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# Representing a real number as the value of a countably infinite game
Is it true that for any real number $p$ between 0 and 1, there exist finite or infinite sequences $x_m$ and $y_n$ of positive real numbers, and a finite or infinite matrix of numbers $\varphi_{mn}$ each of which is either 0 or 1, such that
1) $\sum x_m=1$
2) $\sum y_n=1$
3) $\forall n\;\sum x_m\varphi_{mn}=p$
4) $\forall m\;\sum y_n\varphi_{mn}=p$
-
Generalization of my previous answer. Is this right? $p$ irrational...
For $0\lt p \lt 1/2$ let $x_1(p)=y_1(p)=p$, $\varphi_{1,1}(p) = 1$, $\varphi_{1,j}(p)=\varphi_{j,1}(p)=0$ for $j>1$, $x_n(p)=(1-p)x_{n-1}(p/(1-p))$ for $n>1$. And $\varphi_{n,m}(p) = \varphi_{n-1,m-1}(p/(1-p))$. For $1/2 \lt p \lt 1$ let $x_n(p)=x_n(1-p)$ and $\varphi_{n,m}(p) = 1-\varphi_{n,m}(1-p)$.
-
I ran a computational experiment and your solution seems to check out perfectly. Thanks!! How did you arrive at it? – Vladimir Slepnev Jun 4 '12 at 0:07
Well, first was the golden section proof. That works because of special properties of that number. Then when I tried to generalize, it turned out that it would work if the transformations p/(1-p) and 1-p return to the original value in a finite number of steps. But then why does it have to be the original value? Just proceed with whatever value it is... – Gerald Edgar Jun 4 '12 at 12:59
Thanks. I worked out the proofs, they're quite easy. I needed this result for a paper (about mostly unrelated topics, like computation theory). If the paper works out I will message you and put in an acknowledgement etc. I don't really know the right protocol for this though. – Vladimir Slepnev Jun 4 '12 at 13:50
I will show the following facts:
1. If $p\in\mathbb Q$, then your question has positive answer. (see Edit 2)
2. For general $p$ your question has positive answer up to $\varepsilon$, for all $\varepsilon$. (see Edit 2)
3. For general $p$ your question has positive exact answer if you allow the use of finitely additive probability measures. (see Proposition below). This is particularly motivated by the fact that, for countable games, people usually allow the use of finitely additive probability measures and not only countable additive ones.
Proposition. Let $p\in[0,1]$. There are finitely additive measures $\mu,\nu$ on the power set of $\mathbb Z$ and a countably infinite matrix $\phi_{mn}$ with entries either $0$ or $1$ such that
1. $\int_{\mathbb Z}d\mu(m)=1$
2. $\int_{\mathbb Z}d\nu(n)=1$
3. For all $m\in\mathbb Z$, $\int_{\mathbb Z}\phi_{mn}d\mu(n)=p$
4. For all $n\in\mathbb Z$,, $\int_{\mathbb Z}\phi_{mn}d\nu(m)=p$
Proof. Consider the following game. Choose $W\subseteq\mathbb Z$ having upper mean value[1] equal to $p$ and consider the following two-person game: two players choose simultaneously $m,n\in\mathbb Z$ and player 1 wins if $m+n\in\mathbb W$. Player 1's payoff function is exactly the countable infinite matrix $\phi_{mn}=\chi_W(m+n)$. Now consider the mixed extension of this game obtained by allowing the players to play all finitely additive strategies with Player 1's mixed extension payoff $$\int\int \chi(m+n)d\mu(m)d\nu(n)$$ where $\mu,\nu$ are finitely additive strategies. By Theorem 4.1 in [2] this game has a Nash equilibrium with value exactly $p$ and obtained with translation invariant probability measures $\mu,\nu$. These two measures verify your properties. The first two because they are probability measures; the third and the fourth because they are translation invariant.
[1] The upper mean value of $W$ is the supremum of $\int\chi_W(x)d\lambda(x)$, where $\lambda$ runs over the set of translation invariant finitely additive probability measure on $G$. This set of measures is weak* compact and then the supremum is attained.
[2] Capraro V., Scarsini M., Existence of equilibria in countable games: an algebraic approach, http://arxiv.org/pdf/1203.2301.pdf
Edit. I have realized that in the proof of the proposition it is not necessary to construct the game. Just take $W$ with with upper mean value $p$, construct $\phi_{mn}=\chi_W(m+n)$ and take $\mu=\nu$ be an invariant measure that gives measure $W$ to $p$. I leave that proof since the Original Question ask explicitly for a game theoretical interpretation of the result.
Edit 2. One can get an approximative solution in countable finitely additive measures as follows. Fix $\varepsilon >0$ and take $n$ big enough such that $\mathbb Z/(n\mathbb Z)$ contains set of normalized counting measure equal to $p$ up to $\varepsilon$. Apply the construction above to get the desired result. Notice that if $p\in\mathbb Q$, then this construction can be done with $\varepsilon=0$, giving an exact solution in countably additive measures.
-
Thanks! But actually I already knew the answer for rational p, which seems to trivially imply the approximate answer for all p. The "meat" of the question is whether we can get every irrational p (or indeed any irrational p) using countably additive measures. – Vladimir Slepnev Jun 3 '12 at 14:10
I have some doubt that it can be solved in c.a. measures. It seems to me that the game in consideration is: fix $A\subseteq\mathbb N\times\mathbb N$. Player 1 chooses $m\in\mathbb N$ and Player 2 chooses $n\in\mathbb N$. The first player wins 1 dollar if $(m,n)\in A$. Now, if $p\notin\mathbb Q$, the set $A$ must be quite strange: in particular, every horizontal and vertical section must contain infinitely many points and the complementary of these sections must have infinitely many points. This means (probably) that you cannot find Nash equilibria in c.a. strategies, since each player has a – Valerio Capraro Jun 3 '12 at 18:43
best reply concentrated further and further away. Does it sound reasonable? I'll try to make it formal. – Valerio Capraro Jun 3 '12 at 18:44
I think this argument can be made formal if one assume that $p\notin\mathbb Q$ and all $x_n,y_n\in\mathbb Q$. So maybe one should try to prove that if two sequences $x_n,y_n$ verify your properties, then there are rational sequences that still do it. It is possible that this is true, taking small perturbations. – Valerio Capraro Jun 3 '12 at 18:50
That would be cool, but intuitively I don't think the argument will work. The game might well have a unique Nash equilibrium in mixed strategies. After all, some finite games do. – Vladimir Slepnev Jun 3 '12 at 19:05
Golden Section The golden section works.
Write $u = (\sqrt{5}+1)/2$, I don't call it $\varphi$, since that symbol is already in the problem. So of course $u^m+u^{m+1}=u^{m+2}$.
Let $p=u^{-2} \approx 0.3819$. Define: $$x_1 = u^{-2}, x_2=u^{-3}, x_3=u^{-4},\dots,x_m=u^{-m-1},\dots$$ and $y_m=x_m$. Then compute $$\sum_{m=1}^\infty x_m = \sum_{j=2}^\infty u^{-j} = \frac{u^{-2}}{1-u^{-1}} = \frac{u^{-2}}{u^0-u^{-1}}= \frac{u^{-2}}{u^{-2}} = 1.$$ Define: \begin{align*} &\varphi_{1,1}=1, \qquad\varphi_{1,j}=\varphi_{j,1}=0, j>1. \cr &\varphi_{2,2} = 0,\qquad\varphi_{2,j}=\varphi_{j,2}=1, j>2. \cr &\varphi_{m,n} = \varphi_{m-2,n-2}, m,n>2. \end{align*} Now by induction on $n$ we will show $\sum_{m=1}^\infty x_m\varphi_{m,n} = u^{-2} = p$ for all $n$.
For $n=1$, compute $$\sum_{m=1}^\infty x_m \varphi_{m,1} = x_1\cdot 1 + \sum_{m=2}^\infty x_m \cdot 0 = u^{-2}.$$ For $n=2$, compute $$\sum_{m=1}^\infty x_m \varphi_{m,2} = x_1\cdot 0 + x_2\cdot 0 + \sum_{m=3}^\infty x_m\cdot 1 = \sum_{j=4}^\infty u^{-j} = u^{-2}.$$ For $n>2$ apply the inductive hypothesis: \begin{align*} \sum_{m=1}^\infty x_m\varphi_{m,n} &= x_1\cdot 0 + x_2\cdot 1 + \sum_{m=3}^\infty x_m \varphi_{m-2,n-2} = u^{-3}+u^{-2}\sum_{j=1}^\infty x_j \varphi_{j,n-2} \cr &=u^{-3}+u^{-2}u^{-2}=u^{-3}+u^{-4}=u^{-2}. \end{align*}
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2014-10-01 04:00:13
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http://asiimaging.com/docs/commands/afocus?rev=1555630377&do=diff
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commands:afocus
# Differences
This shows you the differences between two versions of the page.
commands:afocus [2016/09/07 22:04]asiadmin ↷ Links adapted because of a move operation commands:afocus [2019/04/18 23:32] (current) Both sides previous revision Previous revision 2018/02/07 22:11 jon 2016/09/07 22:04 asiadmin ↷ Links adapted because of a move operation2016/09/07 22:03 asiadmin ↷ Page moved from documentation:commands:afocus to commands:afocus2016/03/24 22:47 vik created Next revision Previous revision 2018/02/07 22:11 jon 2016/09/07 22:04 asiadmin ↷ Links adapted because of a move operation2016/09/07 22:03 asiadmin ↷ Page moved from documentation:commands:afocus to commands:afocus2016/03/24 22:47 vik created Line 1: Line 1: + ====== Command:AFOCUS (AF) ====== + --> MS2000 and RM2000 Syntax# + + ^Shortcut |AF| + ^Format |AFOCUS X= [% of speed] Y= [travel distance in mm] Z= [Hill Detect enable] F= [Hill Offset]| + ^Remembered |Using SS Z | + + <-- + + --> Tiger Syntax# + + ^Shortcut |AF| + ^Format |[Addr#] AFOCUS X= [% of speed] Y= [travel distance in mm] Z= [Hill Detect enable] F= [Hill Offset]| + ^Type |Card-Addressed| + ^Remembered |Using [Addr#]SS Z | + + <-- + + The ''AFOCUS'' command will invoke an auto-focus routine using the //speed// and //travel// range specified by the previously set **X** and **Y** parameter settings. This routine can also be activated by pressing **“@”** button on most controllers. Entering ''AF'' without arguments will initiate the auto-focus routine itself, whereas issuing an ''AF'' with arguments will only set the parameters. An auto-focus scan can be canceled with ''HALT'' command or by issuing the ''\'' shortcut. When an ''AF'' command is issued, the controller only replies after the operation is complete. It returns a '':A[###]'' if the operation was successful, or ''N-5'' if there was an error. + + **X= ** Speed. Range is 0 to 100 denoting the percentage of the focus drive’s maximum possible speed to travel during an auto-focus scan. This speed is also used by the [[commands:afcalib|AFCALIB (or AFC) command]]. + + **Y=** Total scan range in millimeters. The focus controller moves down one-half this travel distance, and then scans up the full travel distance. This range is also used by [[commands:afcalib|AFCALIB (or AFC) command]]. + + **Z=** Search type; either 0 or 1. A value of 0 enables //Normal// mode, while a 1 enables Hill Detect mode. (Z values 2 and 3 are reserved for future use.) + + **F=** Hill Offset. Range is 0 to 100 denoting a percentage of a hill. If the Search Type is Hill Detect, then this setting determines when the scan will end. Once a hill peak is detected, the scan will terminate when past the peak by the //Hill Offset// percentage value. + + == Response == + + :A or Error Reply.\\ + + + == Example == + + $AF + :A<CR><LF> +$ AF X=5 Y=0.1 Z=0 + :A + $AF X=10 Y=0.3 Z=1 F=10 + :A +$ AF X=200 Z=2 + :N-4 + (Error indicates arguments out of range) + \$ AF X? + :X=10 A + + AF \\ + Returns :A [quality#] after operation is complete, an :N-5 if the operation failed, or an :N-50 if the focus drive’s clutch is disengaged (if applicable). + + When all of the arguments are omitted, the A is transmitted after the focusing scan has completed. The number in brackets is the difference between //focus value// when in-focus compared to when out-of-focus. It indicates the quality of focus obtained. + + **Caution:** To protect the optical assembly and sample, ensure that the sample is at least 200 µm away from the optics and that the current position is zeroed, that is, the LCD display shows Z: 0.00000> 0.00000 before sending the AF command to the controller (where Z is the focus axis). + + + {{tag>commands autofocus ms2000}}
Address: 29391 W Enid Rd. Eugene, OR 97402, USA | Phone: +1 (541) 461-8181
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2020-02-18 00:55:10
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https://www.r-bloggers.com/2014/10/r-and-rstudio-incompatibility-with-yosemite-mac-os-x-10-10/
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Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
There is currently a bug (or feature?) in the current version of Yosemite (OS X 10.10) that messes with the passing of environmental variables to programs launched from Finder (as pointed out by Adam Maxwell). Notably, this means that PATH variables are not passed properly to R.app or RStudio.app. You may end up seeing errors such as the following:
Error in system("pdflatex", intern = TRUE) : error in running command sh: pdflatex: command not found Error in system("convert", intern = TRUE) : error in running command sh: convert: command not found
Until Apple releases a fix to this, the easy workaround is to launch the desired application from the command-line (terminal). For example to launch R, you can instead run
/Applications/R.app/Contents/MacOS/R
And for RStudio, you can run
/Applications/RStudio.app/Contents/MacOS/RStudio
Let’s hope Apple releases a fix soon. UPDATE from RStudio: ” We’ve fixed this on our end in the latest version of RStudio for OS X, available here: http://www.rstudio.com/products/rstudio/download/ Give it a try and let us know if it works for you. “
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2021-12-07 16:27:28
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https://tex.stackexchange.com/questions/334384/define-command-for-variable-and-use-of-capital-greek-letters/334392
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Define command for variable and use of capital Greek letters
as I read some time ago, it was recommended to define variable inside text within an environment, rather than using the mathmode $variable$ So I decided to introduce a new command in the preamble:
\newcommand{\variable}[1]{%
$\mathit{#1}$
}
This approach is working good for alphabetic variable as well as variables with indices etc. But when it comes to greek letter, I encountered that capital Greek letters lead to a black dot instead of the correct symbol.
\variable{\omega_{Ind}} or $\mathit{\omega_{Ind}}$ -> is working
\variable{\Omega_{Ind}} or $\mathit{\Omega_{Ind}}$ -> is not working
So my questions would be first, is this the overall right approach to introduce variable inside the text and second how can I resolve this issue?
• Just use $#1$. – Steven B. Segletes Oct 16 '16 at 19:48
• You were told wrong. That way of doing is incorrect. – egreg Oct 16 '16 at 20:48
I'm quite certain you misinterpreted what you read. Using \mathit should be reserved to multiletter identifiers, not single letter ones.
An example.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
Let $x$ and $y$ denote real variables. We define the function \emph{difference} by
$\mathit{diff}(x,y)=x-y$
just because we like fancy function names. We also define the
\emph{absolute difference} by
$\mathit{diff}_{\mathrm{abs}}=\lvert x-y\rvert.$
Note that typing \verb|$diff(x,y)$| would produce $diff(x,y)$
which is awful.
\end{document}
Note that the single letter variables are typed in in normal way. This applies to Greek letters as well, so you'll simply type $\Omega$ for the single variable in text, like in
The quantity $\Omega$ is defined by $\Omega=x+y$.
Textual subscripts should generally be upright, so
The quantity $\Omega_{\mathrm{Ind}}$ is defined by
$\Omega_{\mathrm{Ind}}=x+y$.
Of course you want to abstract the definition, in case you use several multiletter identifiers and want a uniform style. So you'll say something like
\documentclass{article}
\usepackage{amsmath}
\newcommand{\variable}[1]{\mathit{#1}}
\newcommand{\diff}{\variable{diff}} % a shorthand
\newcommand{\diffabs}{\variable{diff}_{\mathrm{abs}}} % a shorthand
\begin{document}
Let $x$ and $y$ denote real variables. We define the function \emph{difference} by
$\diff(x,y)=x-y$
just because we like fancy function names. We also define the
\emph{absolute difference} by
$\diffabs=\lvert x-y\rvert.$
\end{document}
in order to get the same output as before. First a generic wrapper is defined, then you can define shorthands for frequently used variable names in terms of the wrapper.
If your supervisor or a journal copy editor asks you to change the multiletter variables into Comic Sans Small Caps Boldface Reversed, you'll just change the definition of \variable.
Note
The silly text given as example is just so. I wanted to use diff in order to emphasize the reason why multiletter identifier (if chosen to be set in italics to begin with) should use \mathit. I'm in by no means promoting such usage without a proper “operator” syntax; as observed by Gustavo in his comment, one should distinguish between variables and functions. In particular this would be “more correct”:
%% two different abstractions
\newcommand{\function}[1]{\operatorname{\mathit{#1}}}
\newcommand{\variable}[1]{\mathit{#1}}
\newcommand{\diff}{\function{diff}}
\newcommand{\diffabs}{\diff_{\mathrm{abs}}}
On the other hand, such multiletter identifiers in italics used either as variable names or function names should never appear next to another letter or object of the same kind in order to avoid confusion. Thus the distinction between variable and function is somewhat blurry.
• I was wondering whether \diff and \diffabs shouldn’t rather be operators: after all, this is not quite the same situation as in, say, $\mathit{counter}\gets\mathit{counter}+1$; it’s more like \sin – GuM Oct 16 '16 at 22:50
• @GustavoMezzetti For function names it would be perhaps better, not for variable names. I didn't want to think too much to a meaningful example. – egreg Oct 16 '16 at 23:20
• @ egreg, thanks for the detailed explanation! I think we can close the topic with this and I will follow accourding to your suggestions. – Jäger Oct 18 '16 at 22:35
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2020-08-15 15:02:02
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https://marinerspoint.in/flemings-left-hand-rule/
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What is Fleming’s Left Hand Rule ?
Fleming’s Left Hand Rule is Rule for Finding the Direction Of Rotation of an Electric motor.
It show the relation between the direction of thrust on a conductor carrying a current in magnetic field.
Let us discuss in brief
There will be a force acting on the conductor whenever a current carrying conductor comes under a magnetic field. The direction of this force can be found using Fleming’s Left Hand Rule (also known as the Left hand rule of Fleming for motors )
Similarly if a conductor is forcefully brought under a magnetic field, that conductor will have an induced current. One can find the direction of this force using the Fleming’s Right Hand Rule.
What it states
Fleming’s left-hand rule states that if we stretch the thumb, the forefinger and the middle finger of our left hand such that they are mutually perpendicular to each other.
If the forefinger gives the direction of current and middle finger points in the direction of magnetic field then the thumb points towards the direction of the force or motion of the conductor.
How to use
Keeping the Thumb,Index Finger and Middle figure of the Left Hand at perpendicular to each other and the forefinger gives the direction of current and middle finger points in the direction of magnetic field then the thumb points towards the direction of the force or motion of the conductor.
Thumb :-Direction of Thrust or direction of motion of conductor.
Index :-Direction of field
Middle :-Direction of current
What is similarity between Fleming left hand rule and fleming Right hand rule
There is a relation between the magnetic field, the current and the force in both Fleming’s left and right hand rules.
This relation is directionally determined by Fleming’s Left Hand rule and Fleming’s Right Hand rule respectively.
What it determine
These rules do not determine the magnitude but instead show the direction of any of the three parameters (magnetic field, current, force) when the direction of the other two parameters is known.
This rule Applicable for
Fleming left hand rule is mainly applicable to electric motors
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2021-09-21 20:30:23
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